Abdel-Rahman, Tarek M. A Generalized Practical Method for Analytic Solution of the Constrained Inverse Kinematics Problem of Redundant Manipulators The International Journal of Robotics Research. Vol. 10, No. 4, August 1991, pp. 382-395 Inverse kinematics, Redundant Restraint This article addresses four important issues relating to practical solutions of the inverse kinematics problem of redundant manipulators. First, a generalized recursive method for systematic derivation of analytic expressions for all possible solutions of any redundant manipulator is presented. The method possesses the advantage of indentifying the linear dependence among joint axes and hence allows all singular configurations to be determined. Second, a joint constraint mapping approach for the integrated consideration of all joint constraints in the solution procedure of the inverse kinematics problem is presented. The result leads to practical real-time procedures. Mapping of the joint position and actuation constraints onto joint rate space is described. Third, simplification of end-effector velocity equations is shown to be possible for most practical manipulator sturctures by decomposing the end-effector velocity equations. To achieve this purpose, type-synthesis design guidelines are given for efficient decomposition or decoupling of the work space. Fourth, two general approaches are described for optimally resolving the kinematics redundancy. The first approach maximizes the end-effector speed in a prescribed direction, while the second approach minimizes a quadratic objective function defined by the user. Examples on work space decomposition and optimal solution of kinematic redundancy are given. In both cases, expressions for the general analytic solution are derived.
Abernethy, R.B., Benedict, R.P., Dowdell, R.B. ASME Measurement Uncertainty J. of Fluids Engineering, ASME, vol. 107, no. 2, 1985, pp. 161 Data & Modeling, Error Analysis The purpose of this paper is to introduce the new ASME measurement uncertainty methodology which is the basis for two new ASME/ANSI Standards and the ASME short course of the same name. Some background and history that led to the selection of this methodology are discussed as well as its application in current SAE, ISA, JANNAF, URC, IASF, NATO and ISO Standards documents and short courses. This ASME methodology is rapidly becoming the national and international standard.
Acton, F.S., Olds, E.G. Tolerances--Additive or Pythagorean? Industrial Quality Control, Nov. 1948, pp. 6-13. Statistical Methods Proposes RSS tolerance analysis method.
Agarwal, M.M. Optimal Synthesis of Tolerance and Clearance in Function Generating Mechanisms-A Parametric Programming Problem ASME Paper 81-DET-5, 1981. Manufacturing Tolerances in Mechanisms An improved method for optimal synthesis of tolerances and clearances is presented which encompasses recent advances in nonlinear mathematical programming methods for synthesis of mechanical error in function generating mechanisms. The methodology is based on a transformation of relationships between variance of random variables and variance of output function into a parametric constraint. This constraint is handled in the penalty function formulation of the Fiacco-McCorkmick type. Advances include formulation and solution for three different functions each for two permissible values of mechanical error. Alternative designs for selective assembly is an added attraction.
Ahang, Genbao, Porchet, Michel Some New Developments in Tolerance Design in CAD DE-Vol. 65-2, Advances in Design Automation-Volume 2, ASME 1993 This paper presents some recent developments in tolerance design in CAD. An Oriented Functional Relationship Graph (OFRG) is developed to identify all the relevant functional components which have an impact on the (evaluated) performance of a product. It is propopsed to use expert system technique to determine all the functional surfaces and necessary relational tolerance types on functional surfaces. Using an OFRG, it is easy to determine dimensional chains, error transmission chains, functional dimension trees and the functional dimensioning mode of a component. We propose to use a transformation matrix technique to determine the sensitivity of each tolerance. A new practical cost model, serving as the onterion for tolerance allocation, is presented. In contrast to empiric data (they are nearly uncollectible) based cost model, the cost model presented in this paper is a process data (they are collectable) based one. The discussion on optimal tolerance shows that shows that optimal functional tolerances can not be obtaained weithout considering the method in machining the workpieces. Hence, the concept of concurrent engineering must be introduced into tolerance design. Finally a mathematic model for tolerance design, called simultaneous toleranceing, in the ocntext of concurrent engineering is proposed.
Allen, George Tolerances and Assemblies in CAD/CAM Systems CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 229-240 The architectures of many of the leading mechanical CAD/CAM systems have undergone significant changes in the last few years, and these changes may provide new opportunitites for representing and using tolerance and assembly information.This paper is divided into two major sections. The first describes the techniques used to represent nominal models in contemporary CAD/CAM systems. We pay particular attention to features, associativity, and other aspects of model intelligence. The second action explores some ideas for incorporating tolerance information into nominal models, and for using this information in application algorithms.
Altschul, Roberto E., Scholz, Friedrich W. Statistical Tolerancing: A Case Study CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 199-206 This case study applies statistical tolerancing to the problem of attaching a cargo door to an airplane body through a series of ten hinges of two different types. The problem is treated only in the hinge axis dimension and at issue is whether the gaps and lugs of the hinges mate successfully when we allow for variation in lug widths and pitches and in the positioning of the hinge pair and then generalized to the whole sequence of fastened hinges, by viewing the two sequences as giant hinge halves. The hinge problem exhibits the feature that the usual linearization paradigm does not apply to the derived clearance criterion C, since it is not differentiable at the nominal dimensions. However, it is easy enough to simulate the distribution of C while properly modeling the various sources of variation.
Andersen, C.B., Chase,K.W.,Sorensen,C.D. Recent Developments in Tolerance Analysis Software for Mechanical Assemblies Part B: 2-D Tolerance Allocation Proc. of the ASQC Western Regional Conference-1989, pp. 98-105. This paper presents a recently developed method for estimating optimum tolerances for any number of parts in a mechanical assembly. The method uses a variation of Lagrange multipliers to efficiently assign part tolerances to achieve approximate minimum overall assembly cost. The method uses information about each individual part's production characteristics, including material costs, production costs and mean shifts. A general solution procedure is presented along with an example problem.
Anderson, Archie R. An Industrial User's Perspective of CAD Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME 1993 In order to make this report have more meaning, it is the result of interviews with individuals and groups in several large companies using CAD.Subjects that are inverstigated include: user friendliness, time proficiency, down stream use of math data, application of GD&T to components and assemblies, CAD system conformance to ANSI Yq4.5M-1982 and methods of tolerance analysis, manual, CAD based or PC based.
The groups and individuals interviewed represented producers of machines components and formed sheet metal components. Formed sheet metal components have unique tolerancing opportunities as the components are not rigid. Thre report on tolerance analysis will focus on the methods used for sheet metal components.
ASME Dimensioning and Tolerancing ASME, ANSI Y14.5M - 1982 GDT
ASME Preferred Limits and Fits for Cylindrical Parts ASME, USAS B4.1-1978 Cylindrical Fits, Standards The limits shown are in thousandths of an inch. The size ranges include
ASME CIME Staff Report CAD Follows New Scripts pp.62-67 November 1989 Mechanical Engineering CAD, Model Building Increasingly, engineers are using the programming tools in the latest generation of CAD systems to automate model building. But to use the tools effectively, engineers should understand how the programming affects the models' creation, modification, and integration with downstream applications.
Bakos, Frank, Hopp, Theodore, Parratt, Steffen, Robinson, Dean Questions and Discussions CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan, June 17-19,1993,ASME,pp. 131-136 This section provides a summary transcript of questions and discussions directed at the presentations in Sessions 1-3. The talks in these sessions were tightly scheduled, and only brief questions for clarification were admitted after each talk. Substantive questions were deferred to this session (#4), and were submitted in signed, written form. The session Moderators ordered the questions and managed the ensuing discussion.The Reporters produced this record from written notes and tape recordings; it has been edited lightly be Herb Voelcker, acting for the Proceedings Editor, Vijay Srinivasan. The questions, responses, and remarks attributed to individuals have not been checked by those individuals because of the compressed publication sechedule for the Proceedings. The Reporters and Editor aplogize for any misinterpretations.
Balling, Richard J., Free, Joseph C., Parkinson, Alan R. Consideration of Worst-Case Manufacturing Tolerances in Design Optimization. Journal of Mechanisms, Transmissions and Automation in Design pp 438-441, Vol. 108, December 1986. Optimization, Design Constraints The paper discusses the effect of manufacturing tolerances for the design variables on the solution to an optimization problem. Two formulations of the tolerance problem in an optimization context are presented. Linearization is employed to reduce the problems to quadratic and linear programming problems. The formulations and solutions fo the two tolerance are illustrated with an example application.
Ballu, Alex, Mathieu, Luc Univocal Expression of Functional and Geometrical Tolerances for Design, Manufacture and Inspection CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 31-52 Model for Tolerances, Tolerancing Language, Product Model, Life Cycle and Quality Issues With the systematic use of computers at all levels of product life cycle, especially at the levels of designing, manufacturing and inspecting, a coherent model of the product functional geometry is requrired.The analysis of various models on tolerancing expression, points out the lack of "company-wide" model. Some models integer the know-how of the standards, some develop new concepts, some are coherent but none takes into account all these aspects at once.
On the basis of a product geometrical model, a solution is proposed integrating the various points of view of the enterprise actors and the standards. This model is based on geometrical operations which are applied, not only to the ideal features, defined by the geometrical modelers, but also to the real features. The operations are themselves defined by the geometrical modelers, but also to the real features. The operations are themselves defined by constraints on the form and relative characteristics of the features.
With this common language, the differences between the various existing approach and their lacks can be pointed out. Moreover, with the model genericity, new concepts of specification to express a design, manufacture or inspection intent can be defined.
To illustrate the field of applications, an ordinary machanism which is easy to perceive is considered.
Ballu, Alex, Mathieu, Luc Analysis of Dimensional and Geometrical Specifications: Standards and Models Proceeding of 3rd CIRP Seminars on Computer Aided Toelrancing, Cachan, France, April 27-28, 1993,pp. 157-170 Dimensioning and Tolerancing, Standards, Geometrical Specifications, Tolerancing Model This article presents a model for the geometrical specification of parts. This model is based on the anlysis of current ISO standards dealing with tolerance. After demonstrating the two approaches for specification that support standard graphic language, specification by sizes and specification by tolerance zones, we present the objects for the geometric definition of a part; the operations used to manipulate these objects; and the expression of the functional condition that must be satisfied. The proposed model attempts to respond to imprecisons and insufficiencies of standard language.
Bandler, J.W. Optimization of Design Tolerances Using Nonlinear Programming. Journal of Optimization Theory and Applications: Vol. 14, No.1, 1974. pp.99-114. Vertex analysis, Optimization, Tolerance A possible mathematical formulation of the practical problem of computer-aided design of electrical circuits (for example) and systems and engineering designs in general, subject to tolerances on independent parameters, is proposed. An automated scheme is suggested, starting from arbitrary initial acceptable or unacceptabel designs and culminating in designs which, under reasonable restrictions, are acceptable in the worst-case sense. It is proved, in particular, that, if the region of points in the parameter space for which designs are both feasible and acceptable satisfies a certain condition (less restrictive than convexity), then no more than 2k points, the vertices of the tolerance region, need to be considered during optimization.
Barish, Thomas How to Design with Shims Product Engineering, Aug. 1957, pp. 164-166. Basic Assembly Analysis Relationship between shim thickness, clearance and tolerance requirements; recommended shim sizes; design of inspection fixtures to determine correct shim size at assembly.
Barton, Russell R., Tsui, Kwok-Leung Multivariate Yield Maximization Using CAD/CAE Models: Efficient Approximations Based On Mean and Variance DE-Vol. 31, Design Theory and Methodology ASME 1991
Baumgarten, J.R., Van Der Werff, K. A Probabilistic Study Relating to Tolerancing and Path Generation Error Mechanism and Machine Theory, Vol. 20, No. 1, p. 71-76, 1985. Statistical Methods, Linkages The effect of manufacturing tolerances on the performance of constrained kinematic chains is analyzed using probability theory. In particular, the method is applied to examples of path generating mechanisms to determine the mean and standard deviation of th evector position of a coupler point. The mean and standard deviation of errors in linkage methods is thus accumulated to produce the mean coupler curve and the deviated curves. Theory is compared with experimental results for a specific cople curve obtained from microadjustment of the links on a planar coupler path plotter. The probabilistic analysis utilzed a finite-element description of th kinematic chain and partial derivatives of the output variable with each length variable result from easy manipulation of the system coordinate transformation.
Beckwith, Walter, Parsons, Frederick G. Measurement Methods and the New Standard B89.3.2 Michigan, June 17-19 1993, CRTD-Vol.27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp.31-36 During the ASME/NSF workshop on mechanical tolerancing held in Orlando, Florida September 28 through October 2, 1988, it was suggested that work be initiated on developing a dimensional measurement standard. A common industrial dimensional measurement practice is to require that gaging uncertainties be small compared with workpiece tolerances. Thus, the component of risk associated with uncertianty is small. Two points are discussed. First, some aspects of gaging uncertainty have generally been ignored, and actual uncertainty is often greater than assumed. Second, manufacturing accuracy has improved faster than measurement accuracy, so measurement uncertainty is often a larger fraction of tolerance than in the past.A new standard under development to address these issues is discussed. A mandatory requirement of this standard, B89.3.2 Dimensional Measurement Methods, is that a plan must be prepared for each measurement. The plan is evaluated in terms of probability a feature measured as good is actually bad, and probability a feature measured as bad is actually good. This approach allows logical assessment of suitability of the plan. Formal requirements of the standard will be supplemented by extensive appendices designed to help in development and analysis of plans. To make the approach practical, most users will want to embed most of the theory in software. The B89.3.2 standard is being developed to assess compliance with specifications which comply with Y14.5 Dimensioning and Tolerancing. Both pass-fail and process control measurements are considered, as are hard gaging and point-data--set-gaging. Status and plans for completion of the standard are discussed.
Bender, A.Jr. Statistical Tolerancing as it Relates to Quality Control and the Designer (6 times 2.5 = 9) Society of Automotive Engineers, SAE Paper No. 680490, May 1968 Statistical Method, RSS Non-Normal Three methods of tolerancing are described. In widest use is the method of extremes which produces unnecessarily close limits on the components. For the same over-all limits on the assembly the probatility method allows wider limits on the components, but there are some unrealistic assumptions involved. A third method is described which results in tolerances falling between the other two. A case history is discussed comparing the three methods.
Bender, Arthur "Benderized" Tolerances. A Simple Practical Probability Method ofHandling Tolerances for Limit "Stack-ups" Engineering Dept. Paper, Delco-Remy, Nov. 1963 also: Graphic Science, Dec. 1962, pp 17ff
Bennett, G., and Gupta, L.C. Least-Cost Tolerances II The International Journal of Production Research (1969). Volume 8. No. 2.pp169-170 In this part of the paper, a method is given for allocating least-cost component tolerances to engineering designs who functional requirements lead to systems of simultaneous tolerance equations, having one or more component tolerances occurring in more than one tolerance equation. These least-cost tolerances are obtained by minimizing the total cost of achieving them, using the method of Lagrange's undetermined multipliers. Methods of solving the resulting non-linear equations in Lagrange's multipliers are given. A notation for the treatment of simultaneous tolerance equations is developed. The procedure is illustrated by examples.
Bennett, G., Gupta, L.C. Least-Cost Tolerances-1 The International Journal of Production Research (1969), Volume 8, No. 1.pp 65-ff This paper presents a method of assigning tolerances to components so that (a) assemblies composed of the components meet specified functional requirements and (b) the cost of manufacturing all the components to their respective tolerance is minimized. Methods of obtaining tolerance equations from functional equations are briefly reviewed; the "method of extremes" is explained in detail. A relationship between cost and tolerance is derived, based upon published data.
A method of assigning least-cost tolerances to a single tolerance equation is then developed.
Bennich, Per Chain of Standards: A New Concept in Tolerancing and Engineering Drawing GPS-Standards-Geometrical Product Specification Standards Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 269-278 Chains of standards is a new concept in tolerancing and engineering drawing standards. Chains of standards is a new way to link Geometrical Product Specification (GPS) standards together. Each chain of standards has six links - all six chain links shall be covered by standards (definitions) to form an unambiguous link between the drawing indication (design intent) and the result of assesment of a workpiece in e.g. SI-units. 49 chains of standards are defined in the area of General GPS chains of standards. It makes 6 x 49 = 294 matrix cells in the General CPS matrix. Only 48% of these cells are at the moment covered by ISO standards! In many cases the existing "covering" are outdated and insufficient. Only two of the 49 defined chains of standards are complete with standards covering all 6 links.Consequently it can be demonstrated that only extreme few ISO GPS drawing indications are unambiguous. Major general gaps exist. There are even contradictions between the existing ISO GPS standards produced by ISO/TC 3, TC10/SC5 and TC57. The situation is almost the same in most national GPS standards-systems. A need for a close coordination between the three ISO/TC's is demonstrated in order to solve the observed problems.
Beohar, S.B.L., Rao, A.C. Optimum Stochastic Synthesis of Four Bar Spatial Function Generators Transactions of the ASME, 80-DET-32, pp. 1-4. Manufacturing, Tolerances in Mechanisms, Optimization Optimization techniques are being used extensively for mechanism synthesis. In general the design parameters are taken deterministic in nature whereas they are probabilistic actually. In this paper optimum synthesis of a four bar spherical function generator has been done taking into account the stochastic nature of design parameters. Geometric programming has been used to minimize structural error.
Beutel, Dean E. The Practictioner's View of Measurement System Application CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,Dearborn, Michigan,June 17-19,1993,ASME,pp. 119-130 The measurement function is a process. It has variation caused by a variety of factors that detrimentally affect the reliability of the process. Historically the metrological engineer's basic function has been to design and/or apply measurement systems that have relatively small variation (or bias) when compared to blueprint tolerance. This paper will address important issues in ensuring that the measuring system is applicable from a global viewpoint.The five critical stages of development in proper gage application are summarized in the following list:
1. Pre-Design Review
2. Blue Print Review
3. Manufacturing System Analysis
4. Process Control System Analysis
5. Miscellaneous Procedural Issues
The involvement of the metrological engineer in the pre-design phase of product development will ensure that economical analysis is performed when assigning tolerancing to part features. Costs associated with excessively "tight" tolerancing can be astronomical (from both the gaging and the manufacturing process perspective). The metrological engineer will have much needed early input into decisions affecting cost, availability, reliability and capability of measuring systems applied during the production planning phase of the product development cycle.
Bhargava, Samir, Grant, B. Marion Taguchi Methods and Tolerance Assignment: The Wavelength Aspects of Surface Metrology Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 177-186 A study of crankshaft bearing failure was conducted using surface metrology techniques in conjunction with a Taguchi designed engine test. Preliminary results indicated that the failure mode was not a function of surface roughness as was initially expected. Software was developed on a DOS based PC to acquire unfiltered total profile data from a surface profiling stylus instrument. The software also implements phase-correct Gaussian filtering, according to ISO TC57 draft standards 1,2,3, in a band pass configuration to isolate waviness from both roughness and form. With these tools, the effects of all three components of the surface profile; roughness, waviness and straightness (form), could be isolated and evaluated separately. The Taguchi ANOVA results indicated that the failure mode was strongly correlated to waviness (Wt-evaluated using ISO band-pass Gaussian filtering), but weakly or not correlated to any aspect of roughness or straightness. The specification for the crank pin and main bearing surface profile was changed to include tolerances for Wt and Wc. The failure mode has not been observed since these changes were implemented. This work shows the wavelength spectral structure of the dimensional aspects generated by the honing process, and the dimensional wavelength spectral structure of the dimensional wavelenght dependence of the component performance. The indication is that for a form call-out to be effective (i.e. correlate to surface performance or be useful in controlling a manufacturing process), it must have associated with it an explicit or understood surface wavelength regime to which it applies.
Blanding, K. Confidence in Fits Mechanical Engineering, March 1978, pp. 29-31 Application Interference Fits, Probabilistic Design Why are fits not used without keys or other holding devices? The reason is confidence and lack of knowledge of the application. If the variation in friction, temperature, measuring error, and surface finish is known, then the shrink fit becomes completely suitable for transmitting torque alone without the aid of notch causing key, set screws, and other expensive devices.
Bohling, Dorothea M. and Lawrence A. O'Neill An Interactive Computer Approach to Tolerance Analysis IEEE Transactions on Computers, Vol. C-19, No. 1, Jan. 1970, pp. 10-16 Computer applications An interactive technique for statistical tolerance analysis has been developed for a computer with graphic display. The computer program called TAP provides for random perturbation of parameter values, repeated evaluation of system performance, and display of distribution histograms. The interactive capability of the program enables the designer to introduce modifications to the system so that the relative effects of these changes can be quickly evaluated with the graphic display. The program has been implemented on a computer facility consisting of a CDC 3300 digital computer, an ITT digital display scope, and an EAI 8800 analog computer.
Two applications are discussed to illustrate the adaptability of the technique to either linear or nonlinear problems. The digital simulation of an active circuit is used to show how the interaction with graphic display saves time in evaluating altenative designs. A hybrid dimulatin of an equalizer for a digital transmission system illustrates that complex time domain problems can be economically analyzed using TAP. In addition, it is shown how TAP is used to measure the reproducibility of an analog simulation.
Bourdet, Pierre, Ballot, Eric Geometrical Behavior for Computer Aided Tolerancing CIRP/JSPE/ASME Proceedings fo the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.143-154 Tridimensional tolerance chains, Model, Dimensioning The analysis of the difficulties encountered with traditional dimension chains in the description of the behaviour of a set of parts, with variation, has led us to develop a tridimensional model of variations. It is thus designed so as to treat the problem of transfer of dimensions.The definition of the model of the variation on surfaces of parts relies on a 2-type classification of defaults which allows to then connect them formally. With this model, the requirements of tolerancing have brought about a definition of two operators. The first determines the specification that may be found on a part by defining the intersection of the domains of deviation of surfaces in relation with their nominal model. The second one calculates the union of the set of motion of a part under the influence of the mating faces with contiguous parts.
The implementation of the model and of the two operators then allows for a definition of the varied possible configurations of the mechanism. For each of these configurations, the constraints of tolerancing that are exerted on the geometry of each part in a mechanism can be expressed mathematically.
Box, George and Soren Bisgaard Statistical Tools For Improving Designs Mechanical Engineering, January 1988, pp. 32-40. CAD Applications Statistically controlled experiments serve as a catalyst to design. These methods help engineers to build good quality into products, which should reduce the need to inspect bad quality out of them.
Boyer, David E. and John W. Nazemetz Introducing Statistical Selective Assembly--A Means of Producing High Precision Assemblies From Low Precision Components American Institute of Industrial Engineers, 1985 Annual Conference, pp. 562-570 Selective Assembly This study is concerned with developing an improved methodology for producing high precision assemblies from low precision components. This new methodology is called "statistical selective assembly". A computer simulation model was constructed to investigate the strengths and weaknesses of the developed assembly concept, and numberous runs were used to ascertain the viability of the concept. The results were encouraging. Statistical sleective assembly proved to be an effective technique for reducing assembly variability.
Boyer, Edward H. Certification in Tolerancing and Metrology Dearborn, Michigan, June 17-19, 1993, CRTD-Vol. 27,International Forum on Dimenional Tolerancing and Metrology,ASME, pp. 291-296 The use of the word "certification" raises the hair on the back of some peoples neck. Its use and misuse can bring numerous horror stories to mind. This discussion will review current needs in industry regarding effective use of tolerancing and how it impacts metrology. While this is necessarily a "new" topic, some technology advances have seriously undermined previous advances in real world aplications.Worldwide competition has obsoleted some previous methodology in order to maintain competitivemess. Many of these changes were long overdue, but some changes have created "holes" in the development cycle. The smooth continuity from product design to production, and subsequently to the end user, can be bery traumatic if it's not done correctly. The resultant program costs, litigation, and "assistance" from senior management could be phenomenal.
As a result of these changes, we have had to take a fresh look at "What is it that must be accomplished?" and "How do we prevent problems from happening?" for everything we do. Hi-Tech "toys" like CAD/CAM, computer simulation, robotics, software analysis, etc. are just money down the drain unless we know how to apply them to make the technology work for us, not against us.
Basic design practices with a strong understanding of applying geometric controls are MUST to initiate a viable design. Likewise, unless manufacturing can produce the intended design, it's just lines on paper (or a screen). The use of sophisticated metrology equipment in an ideal invironment will NOT provide correct data unless it is used correctly. Statistical Process Control doesn't mean a thing unless the right characteristics are identified and measured correctly. Identifying educational needs, expertise reuqirements and hands on applications experience are some of the methods being employed at Ford. Certification can play an important role in assisting us in this formidable task.
Boyer, M., Stewart, N.F. Modeling Spaces for Toleranced Objects The International Journal of Robotics Research, Vol. 10, No. 5, October 1991.pp570-582
Brandt, D.A. How Not to Use Statistical Dimensioning Machine Design, Feb. 22, 1973 pp. 111-113 Statistical Methods If tolerances are interpreted as physical limits, then practices of grading, sorting and biasing violates assumptions of RSS tolerance analysis.
Brayton, Robert K., Stephen W. Director, and Gary D. Hachtel Yield Maximization and Worst-Case Design with Arbitrary Statistical Distributions IEEE Transactions on Circuits and Systems, Vol. Cas-27, No. 9, September 1980,pp.756-762 Worst Case Design, Optimization, Statistics We describe a method by which a variety of statistical design problems can be solved by alinear program. We describe three key aspects of this approach. 1) The correspondence between the level contours of a given probability density function and particular norm, which we shall call a pdf-norm. 2) The expression of distance in this norm from a given set of hyperplanes in terms of the dual of the pdf-norm. 3) The use of a linear program to inscribe a maximal pdf-norm-body into a simplical approximation to the feasible region of a given statistical design problem. This work thus extends the applicability of a previously published algorithm, to the case of arbitrary pdf-norms and consequently to a wide variety of statistical design problems including the common mixed worst-case-yield maximization problem.
Briggs, C.W. Dimensional Tolerances for Steel Castings Steel Founders' Society of America, 606 Terminal Tower, Cleveland 13, OH Case Studies
Brooks, K.A. How to Set Up and Coordinate a Statstical Dimensioning Program Machine Design, Sept. 14, 1961, pp. 140-145 Statistical Methods Although the concept of statistical dimensioning was sugessted over thirty years ago, few assemblies actually required this approach in the early thirties. Times change. Today, the mass production of some types of critically dimensioned assemblies cannot be economically produced any other way. However, setting up a statistical dimensioning program is something more than the simple application of the laws of probability. It requires a closely co-ordinated program to make it function properly. Presented here is a guide to setting up such a program.
Brown, Curtis W. Feature-Based Tolerancing for Intelligent Inspection Process Definition CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19, 1993,pp. 249-258 This paper describes a feature-based tolerancing capability that complements a geometric solid model with an explicit representation of conventional and geometric tolerances. This capability is focused on supporting an intelligent inspection process definition system. The feature-based tolerancer model's benefits include advancing complete product definition initiatives (e.g., STEP - Standard for Exchange of Product model data), suppling computer-integrated manufacturing definition information, and assisting in the solution of measurement performance issues. A feature-based tolerance information model was developed based upon the notion of a feature's toleranceable aspects and describes an object-oriented scheme for representing and relating tolerance features, tolerances, and datum reference frames. For easy incorporation, the tolerance feature entities are interconncected with STEP solid model entities. This scheme will explicitly represent the tolerance specification for mechanical products, support advanced dimensional measurement applications, and assist in tolerance-related methods divergence issues.
Bryan, James B. The Deterministic Approach in Metrology and Manufacturing CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME,pp. 85-96 The basic idea is that automatic machine tools and measuring machines are perfectly repeatable just like the stars and the planets. They obey cause and effect relationships that are within our ability to understand and affordably control. There is nothing random or probabilistic about their behavior. Everything happens for a reason. The list of reasons is small enough to manage by common sense, good metrology, and a reasonable investment of resources.Some level of non-repeatability is observed in the performance of automatic machines. A determinist believes that all of this non-repeatability is caused by systematic sources and that there is no such thing as random behavior of an automatic machinel. We use the term "apparent non-repeatability" to emphasize this belief since each of the sources of apparent non-repeatability is itself repeatable if examined closely enough. The magnitude of apparent non-repeatability depends on the time, money, and skill of the user in creating the proper environment for the machine.
Statistical measures of apparent non-repeatability have limited usefulness since they cannot be used to predict future machine performance if the time, money, and skill of the user changes. On line monitoring and control of the variables, such as temperature, are a better alternative. Statistical measures can be counterproductive in somehow implying that non-repeatability is the fault of the machine rather than the user. A determinist believes that any automatic machine can be made to repeat to a value that is close to its resolution. The cost of doing so is not unreasonable when compared to the benefits.
Buckingham, E. Dimensions and Tolerances for Mass Production The Industrial Press Case Studies
Burr, I.W. Dimensioning and Tolerancing for Simplified and Economical Manufacturing ASME Paper 71-DE-4, 1971 Statistical Suppose that an important characteristic of an assembly is determined by the sum and/or difference of dimensions of the components--for example, total length of several parts or clearance between a shaft and a bearing. This paper provides simple process controls and acceptance sampling plans, which the design engineer can use, instead of the conventional specification limits for a part. These plans effectively control the distribution (average and variability) of the dimension. This can save great amounts of inspection, reworking, scrapping and can place the relations between engineering, production, and quality control on a more realistic basis.
Burr, I.W. Specifying the Desired Distribution Rather than Maximum and Minimum Limits Industrial Quality Control, vol 24, no 2, Aug. 1967, pp. 94-101 Statistical Methods See also Burr, 1971.
Burr, I.W., and R.E. James Specifying the Desired Distribution in Lieu of Tolerance Limits--A Systems Approach ASME Paper 74-DE-9, 1974 Statistics This paper urges placing the emphasis in tolerancing upon specifying controls upon the distributions of the various compoent part dimensions, so that the distribution of the assembly characteristic will meet requirements, that is, lie between specified limits.
Gives RSS methods - defines tolerance as an indication of standard deviation and not a physical limit.
Burr, Irving W. Some Theoretical and Practical Aspects of Tolerances for Mating Parts Industrial Quality Control, September 1958, pp. 18-22.
Burton, Michael F. Tolerancing: The Key to Parts Interchangeability and Manufacturing Cost The Engineering Society For Advancing Mobility Land Sea Air and Space Tolerance, Interchangeability, Manufacturing Cost In discrete parts mass production, interchangeability is critical. All the component parts you manufacture need to consistently assemble to some minimum level of lift, functionality and finish. Manufacturing has developed a costly infrastructure to achieve this interchangeability. The problem is, this infrastrucutre performs at significantly below 100 percent. And perhaps the bigger problem is that when the infrastrucutre fails, the consequences are expensive. The fact that we are spending so much to achieve so little is due to a factor in the equation that nobody has really recognized or addressed. This hidden factor is the implementation of tolerancing throughout design, manufacturing and inspection.A system, known as Valisys, automates tolerancing implementation, thus making it possible to insure part interchageability. The system performs design validation so that tolerance specifications properly reflect design intent. It then communicates this information to manufacturing for better process design, thus promoting more productive manuacturing. In inspection, Valisys automates inspection programming and analysis based on the original tolerance specifications.
Bury, K.V. The Reliability of Probabilistic Mechanical Design ASME Paper 76-WA/DE-7, 1976 Probabilistic Design
Cagan, Jonathan, Kurfess, Thomas R. Optimal Tolerance Allocation Over Multiple Manufacturing Alternatives DE-Vol. 44-2, Advances in Design Automation-Volume 2, ASME 1992,pp.165-170
Cao, Qiushu, Krishnaswami, Prakash Second Order Design Sensitivity Analysis of Kinematically-Driven Mechanical Systems DE-Vol. 44-2, Advances in Design Automation-Volume 2, ASME 1992, pp. 1-5
Carlisle, B.H. Bringing Tight Tolerances to Molded Plastics Machine Design, p. 82-86 Manufacturing Tolerances Thermoplastics are not generally thought of as precision materials. But where part and mold designs are suitably coordinated and processes strictly controlled, molded parts can be held to suprisingly tight tolerances.
Chandrupatla, T.R. Dimensional Accuracy in Turning Cylindrical Shafts ASME Paper No., 1982,pp.10-17. Turning is a basic production process in which a cylindrical surface of required dimensions is produced by removing material from a body which is nearly cylindrical initially. In removing the material, the cutting tool applies large cutting forces which cause the body to deform. The deformations in turn result in uneven material removal, resulting in inaccuracy of cylindricity. The problem is considered in a general setting and the analysis leads to prediction and control of cylindricity in the turning process.
Charbonneau, H.C. The Application of Statistics to Simple Fixed-Gage Design Transactions of the ASME, Vol. 77,Aug. 1955, pp. 949-956 Statistical Methods, Quality Control, Tolerance Using as an example a simple fixed-gage design, the author explains the application of statistics to quality control. The methods of selecting and designing gages are these tolerance theories may be applied and the results achieved are discussed at some length.
Chase, K. W., and W. H. Greenwood Design Issues in Mechanical Tolerance Analysis Manufacturing Review, ASME, vol 1, no 1, Mar. 1988, pp. 50-59 Tolerance analysis is a valuable tool for reducing manufacturing costs by improving producibility. Several useful methods fo selecting design tolerances are presented with examples. The common and more advanced tolerance analysis methods are also reviewed and evaluated. A simple new tolerance analysis model suitable for designers is described as an alternative to the advanced methods. It is much more flexible than the common engineering methods. It is much more flexible than the common engineering methods. For example, it can mix statistical and worst case components in the same assembly. Also, it includes a critical manufacturing variable that is often overlooked: "nominal shifts" or biased distributions.
Chase, K.W., Greenwood, W.H., Loosli, B.G., Hauglund, L.F. Least Cost Tolerance Allocation For Mechanical Assemblies With Automated Process Selection Failure Prevention and Reliability-1989, ASME Publ. DE-Vol. 16,pp.165-171
Chase, K.W., Greenwood, W.H., Loosli, B.G., Hauglund, L.F. Least Cost Tolerance Allocation for Mechanical Assemblies with Automated Process Selection Manufacture Review, vol. 3 no. 1 p.49 March 1990 The allocation of tolerances among the components of a mechanical assembly can significantly affect the resulting manufacturing costs. If cost versus tolerance data are available for each dimension, the least cost tolerance allocation may be determined by optimization techniques. However, when alternate manufacturing processes are available for some of the components, a discrete optimization problem results.
Chase, K.W., Sorensen, C.D., Andersen, C.B. Recent Developments in Tolerance Analysis Software for Mechanical Assemblies Part A: Two-Dimensional Modeling Proc. of the ASQC Western Regional Conference-1989, pp.73-80. Manufacturing variations can cause tolerance stacking or accumulation in mechanical assemblies, causing degradation of performance and increased production cost. A general procedure for performing a 2-D tolerance stack analysis of mechanical assemblies is presented. It is based on representing a mechanical assembly by a vector chain or loop, where each vector represents a propagate through the assembly model correctly. Form variations, such as roundness or parallelism, may also be added to estimate their effects. The accumulation of variance amy be estimated statistically or by worst case analysis. Complex assemblies may require solving several vector loops simultaneously for the dependent assembly parameters. A general solution procedure is demonstrated with an example problem.
Chen, J.S.-C., Wang, S., Zug, P. Optimal Tolerance Design of a Printer Actuator Journal of Mechanisms etc, ASME, Vol. 106, Dec, 1984, p. 510-517. Tolerance, Optimization In this paper we describe an extension of an existing optimization technique to the tolerance design of an actuator mechanism. We provide the designer with a method for selecting optimal nominal design values for the parameters of a generalized system which allows maximum tolerance excursions away from the nominal design values and yet still maintains performance standards. The method uses an interactive linear-programming based design optimization algorithm to select optimal nominal parameter values and their associated maximal tolerances. We illustrate the method with a simple two-dimensional example. Finally we show the results from the tolerance optimization of a printer actuator which demonstrates the applicability of the theory to a real design problem.
Chen, X., Lind, N.C. Fast Probability Integration By Three-Parameter Normal Tail Approximation. Structural Safety 1 (1983) 269-276Elsevier Science Publishers B.V., Amsterdam A new method of fast probability integration is presented, based on a three-parameter normal tail approximation to a non-normal distribution function. Values of the distribution function, the probability density function and its derivative are matched at the approximation point with the approximating function. The approximation point is the known "design point", used within the framework of second moment reliability theory. The proposed method is as fast as the available two-parameter algorithm, but is apparently more accurate.
Choi, B K, Yoo, W S, Lee C S Matrix Representation for NURB Curves and Surfaces Computer Aided Design, vol. 22 ,No.4,May 1990,pp.235-240 Computer-aided design, Curves, Surfaces, Matrix representation A systematic procedure that obtains matrix representation for non-uniform rational B-spline (NURB) curves and surfaces is presented. The coefficient matrix of a NURB curve of arbitrary degree can be obtained by transforming the B-spline curve into a sequence of curve segment defined on individual knot spans and then by symbolically evaluating Boehm's (multiple) knot insertion algorithm. Matrix representtaion for a NURB surface is given as a tensor product of NURB curves. A comparison is made with the computational efficiencies of the Cox-deBoor recursive function2,, Boehm's knot insertion algorithm and the proposed matrix representation. The matrix evaluations are found to be much faster than the recursive evaluations.
Choubey, M. Determining Tolerances in Geneva Mechanisms Machine Design, Oct. 9, 1980, pp. 219-20., Tech Briefs Case Studies, Mechanisms, Applications, General Geneva mechanisms convert rotary motion into a series of stop-start movements and are used as indexing devices in automatic lathes, turrets, rotary tables, and motion-picture projectors.
Choubey, M., Rao, A.C. Optimum Sensitivity Synthesis of a Cam System Incorporating Manufacturing Tolerances ASME Paper 80-DET-31, 1980 Manufacturing Tolerances in Mechanisms Sensitivity can be defined as the ratio of the change in output to a corresponding small change in input(1). Sensitivity is a desirable requirement in cam mechanisms used in instrumentation and controls. Sensitivity should be optimum so that the output element responds well, even for small changes in the output. The sensitivity is affected, firstly due to the manufacturing tolerances, and secondly, because of inertia and elasticity of the follower tran(2). An attempt is made to optimize the sensitivity taking both the effects, into account. An example problem is included to illustrate the appliction of method.
Chung, J.C.H., Schussel, M.D. Technical Evaluation of Variational and Parametric Design. Computers in Engineering, ASME,1990,pp. 289-298 Tolerance, Parametric Design The objective of this paper is to provide a better understanding of the fundamental differences between variational and parametric design, and the implication of these differences to their applicability to different design situations. This paper presents an overview of the theoretical foundations and practical capabilities of both approaches, using examples to illustrate the differences, strengths and limitations of each approach. It further discusses the potential extensions of each approach to tolerance analysis, mechanisms design and design optimization.
Chung, Jack C.H., Schussel, Martin D. Comparison of Variational and Parametric Design Research Report,Structural Dynamics Research Corporation Variational Design, Parametric Design, Tolerance Analysis, Mechanism Design and Optimization The intent of this paper is to provide a better understanding of the fundamental differences between variational design and parametric design and the implications of these differences to their applicability to different design situations. This paper presents an overview of the practical capabilities and theoretical foundations of both approaches, using examples to illustrate the differences, strengths and limitations of each approach. Then it discusses the potential extensions of each approach to tolerance analysis, mechanism design and design optimization. Finally, the paper discusses the type of situations in which each approach may prove most beneficial.
Clement, Andre, Riviere, Alain Tolerancing Versus Nominal Modeling in Next Generation CAD/CAM System Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 97-114 Dimensioning and Tolerancing, Assembly, Technologically and Topologically Related Surfaces (TTRS), Tolerancing Torsor This article deals with functional tolerance modeling for working parts and our endeavor to provide geometric mechanical parts modeling which integrates acceptable geometric defect limits for manufactured and inspected parts. The model we have used will enable us to perform design phase simulation calculations in order to check for and guarantee optimal functioning of a working part. It will aslo be of use in manufacturing and inspection. We will present a mathematical model, a physical model, a CAD/CAM model and a tolerancing method.
Clement, Andre, Riviere, Alain, Serre, Philippe A Declarative Information Model for Functional Requirements CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 1-20 Functional requirement, Mechanism specification, TTRS, EXPRESS, Tolerancing synthesis The tolerancing synthesis consists in proposing a part tolerancing diagram directly obtained from the mechanism good-working conditions. However, tools that can be used to describe the functional requirements are a few and often very specific. The objective of this paper is then to propose a mean to define, from a univocal and sufficiently adaptable point of view, all the functional requirement types a design engineer is brought to specify.A declarative information model based on TTRS2 will be explained using the EXPRESS language.
Three examples will be examined and described with the EXPRESS-I language:
- Parallelism condiiton between two gearwheels;
- Waterproof condition obtained by a sealing ring;
- Assemblability condition for an automatic machine assembly.
Clements, John Variation Simulation Analysis Solves Problems Before and During Production. Quality Progress pp. 76-77, December 1988. Monte Carlo, Tolerance, Simulation The following quotations, taken from Statistical Quality Control by Eugene L.Grant and Richard S. Leavenworth, are as relevant today as when they were first written in the early 1940's.
Cochin, Ira and Isakower, Robert Which component is the troublemaker? System-error analysis. Product Engineering, February 4, 1963, pp. 61-65. In the Utopia of design engineers all electronic, mechanical, hydraulic, and optical systems function perfectly.
Collings, Bruce Jay, Hembree, Barry G. Initializing Generalized Feedback Shift Register Pseudorandom Number Generators Journal of the Association for Computing Machinery, Vol. 33,No. 4,October 1986,pp.706-711 Random Number Generation, Non Tolerance Related The generalized feedback shift register pseudorandom number generators proposed by Lewis and Payne provide a very attractive method of random number generation. Unfortunately, the published initialization procedure can be extremely time consuming. This paper considers an alternative method of initialization based on a natural polynomial representation for the terms of a feedback shift register sequence that results in substantial improvements in the initialization process.
Conry, T.F. A Method of Optimal Tolerance Selection (Discussion of paper by Ostwald and Huang) J. of Engineering for Industry, ASME, Vol. 100, Aug. 1978, pp. 390-391. Optimization
Conway, H.G. The Use of Tolerance Systems Product Engineering-February 1956,pp.164-167 Tolerance, Tolerance Selection Tolerance systems and tables of limits and fits are intended to supply a standardized series of fits on drawings, thus restricting the number of limit gages which are required for production to these drawings. The new ABC System of Limits and Fits, agreed upon between representatives of America, Britain and Canada in 1953, and now under consideration as an American Standard, gives a wide varitey of tolerances and fits for all types of engineering products from fine precision components to rough manufacturing processes. There are also tolerances which may be used for specialized fabrication methods such as casting, molding, sintering, pressing, etc.
Corlew, Gordon T., and Fred Oakland Monte Carlo Simulation for Setting Dimensional Tolerances Machine Design, May 6, 1976, p. 91-95. Here's a way to size and tolerance critical parts in an assembly-and even to evaluate the operating characteristics of the finished product-without manufacturing a single part. Monte Carlo simulation uses statistical information to create "imaginary" assemblies that show how to establish the widest possible tolerances on individual components.
Couetard, Y. et Teissandier, D. A Tolerancing Modes Synthesis: Proportionned Assembly Clearnce Volume Proceedings of 3rd CIRP Seminars Computer Aided Tolerancing, Cachan,France,April 27-28,1993,pp. 75-84 Design, Manufacturing, Funcitonal dimension, Three dimensions, Tolerancing, Series of parts, Synthesis, Positionning, Mechanism In mechanics, in the Design-Manufacture field, the calculation of linear and angular dimensions caused by the addition of many parts is not resolved by functional dimensioning. Until now, it was possible to use several methods of calculation that did not consider angular and shape dispersions (dimension chain). They operated using aligned parts treated in the case of mass production. On the other hand, methods for tolerancing of a part in three dimensions already existed (each element of a mechanism). But these methods of calculations were unadapted for modelling parts in series (families of elements). The UPEL (Union Ponderee d'Espace de Liberte), a proportionned assembly clearance volume, is proposed in order to resolve this problem.
Cox, J.J., Anderson, D.C. Single Model Formulations that Link Engineering Analysis With Geometric Modeling Product Modeling for Computer-Aided Design and Manufacturing,pp. 249-265 Geometric Model, Finite Element Model This paper presents a method of constructing geometric and finite element models simultaneously. Through the use of penalty methods and mapped finite elements it is possible to correlate the construction fo a geometric model with that of an analysis model. Primitives have dual definitions in this method. First, the geometric description and second, the finite element formulations of a desired natural continuum field over the primitive's domain. Using weak form variational statements of appropriate continuum field equations it is possible to formulate a finite element approximation that is valid within the respective primitives. Using this method of forming finite elements approximations there exists a correlation between the solution of the finite element equations and the geometry over which they are formulated. They both are parameterized in the same parameters. Associating penalty methods with set theoretic operations these primitives can be combined geometrically and their associated finite element formulations can be tied together to create a global geometrical and analysis model. Continuity and compatibility of the solution between primitives are maintained through adding penalty terms to the finite element formulations.This paper presents the theory behind this method. It shows the method of formulating weak form variational statements in any set of parameters and then discusses the penalty terms as they relate to set operations which join the primitives. Finally, the paper presents the method of accumulating a global finite element model from the local primitives' formulations. Two examples are shown using a Poisson's equation in a heat transfer problem. These methods promise better understanding of the relationships between the shape of an object and the behavior of the continuum fields which operate within or around that object. The methods also promise better correlation and more efficient geometric and finite element modeling.
Cox, N.D. Tolerance Analysis by Computer Journal of Quality Technology, Vol. 11, No. 2, April 1979,pp. 80-87 Statistical Tolerancing, System Moments An improved error propagation technique was needed for the analysis of nuclear reactor safety systems. In response, a computer program for calculating the first four moments of a second-order function was prepared and validated. This program, call SOERP, can accomodate up to 30 statistically independent random variables. Thus, the moments for any function that can be expanded in a multivariable Taylor series up to the second order can be estimated. These moments can then be used to determine a probability density function describing the dependent variable. The above two steps represent a method for evaluating a complex system's performance fluctuations that arise from random variability in the behavior of system components. For example, tolerance limits on the performance of electrical circuits or on transit times in a repair facility may be evaluated more precisely. Another application is the evaluation of profitability calculations in which the input data are subject to uncertainty.
Cox, Niel D. How to Perform Statistical Tolerance Analysis ASQC, Basic References in Quality Control, Volume 11, 1986 This exposition deals with techniques of statistical tolerance anlaysis. The intent of the methodology is to allow the engineer to evaluate the effect of manufacturing tolerances and uncertainties in functional parameters on the performance or dimensions of a manufactured product. It provides information on the probability distribution of the output or dimension so that the analyst can make decisions on the quality of the product prior to actual manufacture. The technique provides a general tool which can be used in the anlaysis of systems of a general nature. Several potential applications are described, and the derivation of the mathematical foundation is shown. Numerical results are given for five examples.
Craig, Mark Managing Variation by Design Using Simulation Methods Failure Prevention and Reliability-1989, ASME Publ. DE-Vol 16. pp. 153-163. Monte Carlo In today's market, the product design engineering team has increased pressure to design a product for "manufacturing and assembly efficiency" as well as function. Statistical process control and design of experiments techniques have been widely implemented to identify, analyze, and control critical variation parameters in the maufacturing and assembly plant. These techniques, however, are used after the product is in production and do not provide the design engineering team with a method to predict variation during the design stage of a product, and thus prevent or control undesirable variation in production. In order for the design team to evaluate design and assembly proposals, before expensive tooling is committed, a simulation of the actual build process must be performed.
Craig, Mark Variation By Design Mechanical Engineering pp.52-54. November 1988. Monte Carlo The goal of variation simulation analysis is to arrive at a design that can tolerate the largest amount of deviation without lowering the quality of the product or impairing its funcioning. The benefits should include reduced manufacturing and assembly costs.
D'Errico, John R., Zaino, Nicholas A., Jr. Statistical Tolerancing Using a Modification of Taguchi's Method Technometrics, November 1988. Vol. 30, No. 4,pp.397-405 Designed Monte Carlo: Propagation of errors: Quadrature: Uncertainty analysis. The expanding use of experimental design techniques for statistical tolerancing is primarily due to their simplicity. They can be understood easily and implemented by engineers and scientists having only a limited knowledge of statistics and experimental design. The method is generally attributed to Taguchi (1978). In this article, we describe Taguchi's method and why it works, both intuitively and mathematically. Our results show that Taguchi's method, although giving good results for many applications, is not optimal. We propose alternative tolerancing procedures that are uniformly better than Taguchi's method with little sacrifice in simplicity. We illustrate the use of these methods, first with some simple examples and then with a partial-differential-equation model.
Dao-Thein, My, and M. Massoud On the Probabilistic Distributions of Stress and Strength in Design Problems Journal of Engineering for Industry, ASME, Aug. 1975, pp. 983-989 Stress and Strength Analysis Statistics This paper presents an approach to obtain the stress and strength density distributions in reliability design problems. The density and cumulative distributions of the stress and strength are obtained in the form of multiple integrals. Linear regression analysis is used to plot estimates of the cumulative distributions on probability paper. The distribution with the minimum error is chosen. A computer program to perform the calculations and to select the appropriate distribution is developed. An example is presented to illustrate the application of the method.
Dao-Thien, My An Approach for Optimum Tolerancing of the Design Components Proc. of the 8th Canadian Congress of Applied Mechanics, Moncton, June 7-12, 1981, pp. 333-334 Tolerance, Optimization The optimal selection of statistical tolerances of the machine parts in an assembly is of concern to every engineering designer. Designers are well aware that an optimizing of the dimensions of the machine parts by optimizing its tolerances will result in reduced manufacturing cost.
Today, with a high production cost and a limited capacity of the manufacturing process, the optimum selection of the tolerances does not only satisfy the design requiremnts but also the manufacturing conditions.
On the basis of the lowest cost, this paper presents to the designers, a new approach for the optimal selection of the basic dimensions and its tolerances of the machine parts, satisfying at the same time, the design and manufacturing.
Daschbach, J.M. and Henry Apgar Design Analysis Through Techniques of Parametric Cost Estimation Engineering Costs and Production Economics, 14 (1988) 87-93 This paper focuses on the parametric model as tool for design engineering analysis. The technique is made relevant to routine, every-day living and proceeds to the engineering design function with a case study of over 4000 instances where the parametric model provided estimates closer to actual costs than the traditional 'bottom-ups' means to cost estimation in an aerospace industrial application.
David, H.T., McCann, Michael J. Multiple Tolerancing Problems For Assembling Processes Statistical Laboratory Preprint Series Monte Carlo, Process Control, Sampling Inspection, Tolerances Assemblies fit together well when the dimensions and relative positions of their components satisfy certain relevant conditions. What is relevant depends on what sort of fit is demanded, and the degree of rigidity or freedom of motion of the components of an assembly relative to one another.Focusing on two simple configurations featuring a rigid plate of "pegs" and a rigid plate of "holes," we identify tightness of tolerancing of component dimensions and positions with standard deviations assumed associated with the processes producing these dimensions and positions, and study the impact of such tolerance standard deviations on the prospects (probablility) of fit.
We suggest the possiblity of addressing "upstream" design issues such as the relative importance of tight tolerancing of component position vs. tight tolerancing of component dimension within an assembly part, and the impact of a component's position within an assembly part on the role that the tolerancing of that component plays in determining the probability that the part to which it belongs will fit acceptably at the next stage of assembly.
The possiblity also mentioned of rating a part of an assembly "downstream" at the inspection stage in accordance with the probability of it fitting acceptably at the next stage of assembly.
DeDoncker, Dwight and Spencer, Al Assembly Tolerance Analysis with Simulation and Optimization Techniques. The Engineering Society For Advancing Mobility Land Sea Air and Space. Monte Carlo
DeFazio, T.L., Edsall, A,C., Gustavson, R.E., Hernandez, J.A., Hutchins, P.M., Leung, H.W., Luby, S.C., Metzinger, R.W., Nevins, J.L., Tung, K.K., Whitney, D.E. A Prototype of Feature-Based Design For Assembly Advances in Design Automation-1990, Vol.1,ASME Publication No. DE-Vol,23-1,pp.9-16 This paper describes a prototype software system that implements a form of feature-based design for assembly. It is not an automated design system but instead a decision and design aid for designers interested in Concurrent Design. Feature-based design captures design intent (assembly topology, product function, manufacturing, or field use) while creating part and product geometry. Design for assembly as used here extends existing ideas about critiquing part shapes and part count to include assembly process planning, assembly sequence generation, assembly fixturing assessments, and assembly process costs. This work was primarily interested in identifying the information important to DFA tasks, and how that information could be captured using feature-based design. It was not intended to extend the state of the art in feature-based geometry creation, but rather to explore the uses of the information that can be captured. The protoype system has been programmed in LISP on Sun workstations. Its research contributions comprise integration of feature-based design with several existing and new assembly analysis and synthesis algorithms: construction of feature properties to meet the needs of those algorithms: a carefully chosen division of labor between designer and computer: and illustration of feature-based models of products as the information source for assembly analysis and process design. Some of its functions have been implemented approximately or partially but they give the flavor of the benefits to be expected from a fully functional system.
Desrochers, Alain, Maranzana, Roland Constrained Dimensioning and Tolerancing Assistance for Mechanisms CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 21-30 Geometric dimensioning and tolerancing, Computer Aided Design (CAD), Technologically and Topologically Related Surfaces (TTRS), mechanism, assembly This paper presents a systematic approach for dimensioning and tolerancing mechanisms. The method is based on a model of Technologically and Topologically Reltated Surfaces (TTRS) and uses a binding graph representation of the mechanism. The complete dimensioning and tolerancing of each part is generated by recursively associating surfaces along kinematic loops on the graph. Technological requirements and user constrains are integrated in the system through specific choices of kinematic loops and partial references (Minimum Geometric Datum Element). The system developed insures that the geometric dimensioning and tolerancing be complete and non redundant while conforming to ANSI Y14.5M or ISO standards.
DeVos, L. Functional Dimensioning Design News, July 21, 1965, pp. 157-165. True Position Tolerancing
Dhande, S.G. and J. Chakraborty Analysis and Synthesis of Mechanical Error in Linkages-A Stochastic Approach Journal of Engineering for Industry, August 1973,pp. 672-676 Linkage Tolerances A stochastic model of the four-bar linkage considering tolerances and clearances is made. The mechanical error is analyzed for the three-sigma band of confidence level. The effectiveness of the dynamic programming procedure to optimally allocate tolerances and clearance to different members of the linkage for a specified maximum allowable mechanical error is shown.
Dhande, S.G., Chakraborty, J. Mechanical Error Analysis of Spatial Linkages Journal of Mech. Design, 1978, p. 732also ASME paper 77-WA/DE-8 Error Analysis, Spatial Linkage, Tolerance In this paper the effect on the output error of function-generating spatial linkages due to tolerances on the links and clearances at the hinges is analyzed. Tolerances on link lengths are assumed to be normally distributed. For the clearance error in spherical, prismatic, and revolute joints, uniform probability density function is assumed. However, the models developed and the analysis procedure proposed can be used for any other probability density functoin including the mean and variance values derived from experimental information. A synthesis procedure to allocate tolerance and clearance on different members of linkages to restrict the output error within specified units is developed. Results of analysis and synthesis are given for two example problems involving RRSS and RSSR mechanisms.
Ditlevsen, Ove Generalized Second Moment Reliability Index J.Struct.Mech., 7(4), 435-451 (1979) Advanced Statistics A crucial property of any measure of structural reliability should be comparativeness. With this point in mind this paper discusses some well-known versions of so-called reliability indices. Such reliability indices, defined by use of second moment information, have been used for the last decade, specifically within safety code committee work. This paper defines a generalized second moment reliability index that satisfies some few fundamental canonical rules and principles of simplicity. The reliability index is specifically defined to be used when no high quality information is available to the engineer other than the limit state surface and a second moment representation for the set of basic variables of the structrual problem. In a parallel paper the author demostrates the practical operability of this reliability index even for multimode failure systems.
Ditlevsen, Ove Narrow Reliability Bounds for Structural Systems J. Struct. Mech., 7(4), 453-472 (1979) Advanced Statistics For structural systems that may fail in any one of several possible modes, reliability analysis is greatly simplified by use of upper and lower bound techniques. General bounds based on all the single mode failure probabilities and all the pairwise mode intersection failure probabilities are established. For systems where the single mode limit state surfaces are hyperplanes in the space of basic variables, a simple geometrical interpretation of the correlation between mode safety margins combined with a well-known geometrical interpretation of the single mode reliability index makes the practical calculation of the system reliability bounds easy. This is particularly true when the set of basic variables is jointly normally distributed. Examples show very narrow bounds which, in the practically important domain of high reliability, are almost coincident.
Ditlevsen, Ove Principle of Normal Tail Approximation Journal of the Engineering Mechanics Division, ASCE, Dec. 1981, pp. 1191-1208 Reliability Methods, Index Calculating the probability content of the failure set in a multivariable structural reliability problem of limited state type presents some difficulties. Very often, however, practical problems have such properties that the failure probability may be assessed in a simple way and with sufficient accuracy solely by use of hyperplane approximations to the failure surface, as represented in a space in which the basic random variables appear as transformed into mutually independent, standardized, normal random variables. The approximation points are those origin projection points which are local minimum points for the distance from the origin to the failure surface points. It will be proved herein that these critical points may be determined by iterative use of the priciple of normal tail approximation. For hyperplane failure surfaces in the original space of basic variables, this method preserves the advantage of second moment reliability calculus.The method is illustrated with an example of its own value. It concerns the determination of the predictive distribution of a material strength quantity given no direct observations. Data are solely indirect, just as they typically result in nondestructive testing.
Doepker, P.E. Designing Brake Components Using Variation Simulation Modeling Failure Prevention and Reliability, 1989, ASME Publ. DE-Vol 16,pp. 131-138 Monte Carlo To assure the reliability of a designed structure, it is necessary to specify and control the final dimensions of the assembly and the range over which the critical dimensions will vary. These critical dimensions are dependent on the dimensions of the individual components that make up the assembled structure as well as the variation in these demensions. As part of the design process the dimensional tolerance is specified, thus providing a range of variation. This variation will significantly affect the final assembled dimensions and their variation.
Dong, Zuomin, Soom, Andres Automatic Optimal Tolerance Design for Related Dimension Chains Manufacturing Review,vol. 3,no. 4,December 1990,pp. 262-271 Tolerance, Optimization An optimal design approach to tolerance allocation is presented. To avoid design conflicts that may occur with current optimal tolerance design methods, the general formulation of optimal tolerance design for multiple and related dimension chains has been introduced. A method, which automatically generates the optimization objective function, incorporating manufacturing knowledge, has been developed. The method associates each design tolerance with an appropriate production cost-precision model, using an expert system. It has been implemented using the Davidson-Fletcher-Powell optimization technique and a dedicated inference program with the IGES interface to a CAD system. A design example is used to illustrate the approach.
Dopker, B., Murray, P., Choong, F.N. An Object Oriented Data Base and Application Management System for Integrated, Interdisciplinary Mechanical system Simulation Advances in Design Automation, ASME Publ. DE 19-3,pp. 81-87 Simulation, Data base, Stress and Strength, Monte Carlo, Mechanical System An object oriented data base and application management system for integrated, interdisciplinary mechanical system simulation is developed and implemented; with emphasis on flexible body dynamic simulation, stress history calculation, and fatigue life prediction. The system consists of (1) functional objects that perform a particular analysis task, (2) data objects that store data in the data base, (3) data and object management tools that manage the communication between the different parts of the system, and (4) network communication tools that communicate between different hardware platforms. Functional objects are developed and implemented for the different analysis needs of the system. Such objects (1) hide implementation details, (2) provide easy extendability, and (3) simplify use of the system. Data are organized in terms of objects, object hierarchies, and object attributes. This provides quasi data inheritance and information hiding, which allows for a data base schema that is both robust and extendable.
Dori, Dov, Miller, James R. Dynamic 3-D Visualization of Dimensions and Tolerances on Solid Models Using Ansi Standard Advances in Design Automation-1990,Vol.1,ASME Publication No. DE-Vol. 23-1,pp. 137-143 The use of current solid modelers as a comprehensive MCAE system is hampered by the lack of proper annotation capabilites, primarily dimensioning and tolerancing (D&T). An initial design done on a solid modeler must be transferred to some wireframe module for D&T annotation and analysis and for blueprint production. We propose a solid modeler which has D&T capabilities that will eventually enable a complete design cycle. Dimensions and size tolerances that follow the ANSI D&T standard are treated as objects in 3D that are attached to relevant object features. We discuss implementation issues and show how ANSI-based blueprints can be generated directly from the solid modeler.
Doydum, Cemal, Perreira, N. Duke Use of Monte Carlo Simulation to Select Dimensions, Tolerances, and Precision for Automated Assembly J. of Mfg Systems,V10,N3,pp. 209-221 Assembling, Design, Tolerances, Dimensions, Precision Design for assembly is a multifaceted problem that includes the determination of shape and size of mating parts and the selection of part production and assembly processes. An analytical method has been previously presented for selecting the dimensions and tolerances of mating parts and the precision of assembly equipment where the mating parts possess simple geometries such as lines and circles. This paper proposes a Monte Carlo modeling, simulation, and inferencing method to make the methodology applicable to the design of assemblies with irregular and complex cross sections. The method is implemented for the ellipse and convex polygon cross section to illustrate the analytical and geometrical ideas involved. The ellipse model determines the effect of out-of-roundness on the mating of what would ideally be circular parts. The assembly performance of polygon shaped geometries is studied employing two alternative methods; fixed side ratios, and proportional clearances. Using the presented method, the noncontact and/or chamberless insertion of precision mechanical components can be analyzed and designed for high performance processing. Other applications of the method include aligning beams in material combining processes such as laser sintering, and placing a cutting edge or beam against a material in machining processes such as stamping and electrical discharge machining.
Dresner, Thomas L., Barkan, Philip Optimal Tolerance Allocation For Tolerance Stack-ups DE-Vol. 65-2, Advances in Design Automation-Volume 2,ASME 1993 The allocation of individual tolerances that form critical stack-ups is an important task in mechanical design. It is desirable, but difficult in practice, to allocate tolerances to obtain all required stack-ups at minimum cost. A minimum cost allocation method is proposed here that works for both a single tolerance stack-up and for multiple tolerance stack-ups that share one or more individual tolerances. Tolerances can be optimally allocated for both worst case and a variety of 60 statistical cases. The method is applicable to one dimensional stack-ups and to multi-dimensional stack-ups with known sensitivity functions. It is a numerical Lagrange multiplier method that is more general than the Lagrange multiplier methods that have often been proposed. The basic method will almost always provide the lowest cost result when the manufacturing process to produce each toleranced dimension has been firmly established in advance. An exact method for efficiently extending the basic method to determine the lowest cost process for producing each dimension is also introduced.
Dufosse', Philipp Automatic Dimensioning and Tolerancing Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing,Cachan, France,April 27-28,1993,pp. 1-10 Toelrancing, Dimensioning, TTRS, Overconstraint A powerful CAD/CAM system must include a tool to help with tolerancing and functional dimensioning.This paper first presents the reasons for tolerancing in a mechanism, that is, overconstraints, and then covers TTRS's, a particularly useful concept in tolerance modeling.
A method is then outlined to identify overconstrained circuits in the mechanism. Finally, two dimensioning and tolerancing steps are mentioned, that is, TTRS creation along circuits, and evaluation of their tolerances.
Early, R. and Thompson, J. Variation Simulation Modeling-Variation Analysis Using Monte Carlo Simulation. Failure Prevention and Reliability-1989, ASME Pub. DE-Vol 16, pp. 139-144. Monte Carlo In order to design, manufacture, and assemble products most effectively, it is necessary to evaluate the effects of the variation that will naturally occur. The optimal method of analyzing this variation is through the use of simulation. Variation Simulation Modeling (VSM), used extensively within General Motors Corporation, is a simulation technique which can be used to study the effects of variation in mass production. Using VSM computer simulation production. Using VSM computer simulation it is possible to evaluate and optimize design tolerances, assembly tooling, and assembly sequencing early in the product development lifecycle. In this way, VSM can be used to generate a design which most effectively meets quality objectives while preventing build problems in production. This paper describes in detail VSM and its application within General Motors Corporation.
Early, Robert Statistical Tolerancing Applications at General Motors Corporation Society of Automotive Engineers, Inc., 1988 Monte Carlo In order to design, manufacture, and assemble products most effectively, it is necessary to evaluate the effects of the variation that will naturally occur. The optimal method of analyzing this variation is through the use of simulation. Variation Simulation Modeling (VSM) is a simulation technique which can be used to study the effects of variation., With VSM computer simulation, design tolerances, assembly tooling, and assembly sequencing can be evaluated and optimized during the design stage before commitment to tooling, thereby preventing problems later at the prototype stage and during production start-up. This paper describes VSM and what it can be used for, how VSM is applied, and illustrative examples of its application within General Motors.
Eaton, Fletcher Computer Modeling of a Three-Dimensional Assembly ASME Publication 75 DE-21. 3-D Statistical This paper describes a method for determining, in three dimensions, the effects of dimensions and tolerances on the critical parameters of a complex assembly. It was developed in collaboration with Dr. William T. Plummer as an aid to the design, inspection, and production of the SX-70 Camera. This camera possesses radically advanced optical and mechanical features whose performance could not readily be predicted or controlled without a three-dimensional method of analysis. The method is general and applies equally well to any assembly (appliance, automobile, airplane, etc.). It has proved useful in several ways. All mechanical assemblies are made up of parts which are attached to one another so as to provide one or more desired functions. Often, the individual parts are not precisely made and when joined to other parts, also not precise, tolerance accumulations may cause difficult assembly, mechanical interferences, misalignment, and other ills which must be corrected. However, correcting one problem may cause others and a method is needed which keeps all desired parameters under control while permitting attainable piece part tolerance. Such a method is sugested in this paper.
Edel, D. Henry, Auer, Thomas B. Determine the Least Cost Combination for Tolerance Accumulations in a Drive Shaft Seal Assembly General Motors Engineering Journal, Fourth Quarter, p. 37-38, 1964. First Quarter, p. 36-38, 1965 Optimization During the initial design of mechanisms, consideration of many functional and costs variables often is hindered by a lack of specific experimental data. Sample parts and associated measurements frequently do not exist at this stage, and statistical analysis procedures based on such measurements cannot be used. Relative cost estimates, however, usually are available to supplement projected functional design requirements. When the cost estimates are combined with tolerance functions in linear form, optimization of functional and cost aspects is possible using a linear programming method. The problem here is to arrange initial design information into linear forms with a view to solving the problem by a regular linear programming method.
Edensor, K. Geometric Analysis of Engineering Designs: Applications National Standards Laboratory Technical Paper No. 14,1961,Australia GD & T, Statistics, Engineering Design The dimensions contributing to a particular functioning dimension in the time switch were determined. Samples from production were measured and the variation in the functioning dimension was predicted using these measurements, together with simple statistical techniques. The advantages of such a method are noted, and finally the results are compared with the probable variation obtained when using drawing demensions only and techniques developed at the National Standards Laboratory.
Edensor, K. Geometric Analysis of Engineering Designs: Applications National Standards Laboratory Technical Paper,No.16,1961,Australia GD & T, Statistics, Engineering Design The permissible end-play is first of all determined using present drawing dimensions and tolerances. The probable variation is then calculated using techniques developed at the National Standards Laboratory. The result shows that the specification for end-play cannot be met with present dimensions and tolerances. An analysis is next conducted to determine the dimensions and tolerances required to meet the end-play specification. This shows that tolerances would have to be considerable reduced. Should this be undesirable, a method of selective assembly is suggested and finally the elements of a measuring fixture are shown which will enable assembly to the required specification to be carried out using selected washers and employing unskilled operators.
Eggert, R.J., Mayne, R.W. Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions Advances in Design Automation-1990,Vol.1,ASME Publication No. DE-Vol,23-1,pp. 129-136 Optimal design, Probability Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for th e optimization process, is described. This aproach incorporates the speed and robustness of analytical pprobability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.
Elgabry, A.K. A Framework For a Solid-Based Tolerance Analysis Computers in Engineering, V2, ASME 1986,pp. 79-84 The issue of representing and analyzing solid-based tolerances for design and manufacturing is addressed. An overview of geometric and dimensional tolerances defined by the ANSI-14.5M Standard is presented. Techniques for representing tolerances in Wireframe/Surface Geometric Modeling Systems and their impact on the ability to analyze tolerances are discussed. Different work on solid-based tolerances is evaluated. A new approach based on solid modeling and oriented toward design and manufacturing tolerance analysis is proposed. for any given Datum Reference Frame, a tolerance shell can be defined within which all the possible locations of surface points are contained. The tolerance shell can be sliced in any direction and the cross section, and related to the given datum, can be determined. Shells of assembled parts can be used for checking interferences and clearances and measuring them in any arbitrary direction. A road map for implementing the methodology is proposed.
Ellison, B.E. On Two-sided Tolerance Intervals for a Normal Distribution pp. 762-3#### Statistical Methods
ElMaraghy, Hoda A., ElMaraghy, Waguih H. A System for Modeling Geometric Tolerances for Mechanical Design Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing,Cachan,France,April 27-28,1993,pp. 11-24 Geometric Dimensioning and Tolerancing (GD&T), Tolerance Analysis and Synthesis, Computer Aided Design (CAD). A system for Tolerance Analysis, Simulation and Synthesis-TASS has been developed. It is capable of modelling, simulating and analyzing tolerance stack-ups and variations of functional requirements resulting from assembling mechanical parts with specified geometric and dimensional tolerances. The Monte-Carlo simulation is used in tolerance analysis, sensitivity analysis and tolerance sysnthesis and allocation. Both machined components as well as complex surfaces, such as formed sheet metal, may be analyzed.An interface with a Feature-Based Solid Modeler is now under development. In order to allow TASS to use the solid model generated by the Feature-Based Modeler (FBM), toleranced faces are extracted from the solid model and tolerance specifications are attached to those suraces as additional attributes. A tolerance specification language which enables the user to specify tolerance type, tolerance value and distribution (due to process capability), toleranced faces are extracted from the solid model and tolerance specifications are attached to those surfaces as additional attributes. A tolerance specification language which enables the user to specify tolerance type, tolerance value and distribution (due to process capability), material conditions and reference datums has been develoed. In this language, the same topological and geometric entities identification method used in the FBM is employed to enhance compatibility. Upon specifying parts relationship to one another by defining their functional datums, a complete assembly datum hierarchy is automatically generated and used for tolerance analysis.
Emannel, Richard Establishing Mechanical Tolerances with CAD/CAM Computer-Aided Engineering, July 1985, pp. 76-80. CAD Applications New software lets designers check interference and clearance of parts before machining and assembly, reducing manufacturing cost and increasing product quality.
Emery, J.K. Roundness Measurement, Part 1-Importance and Interrelationships. Mechanical Engineering,ASME, Part 1, Oct. 1969, pp. 26-29, True Position Tolerancing, GDT, Roundness Roundess is an independent geometric dimension distinguished from concentricity, cylindricity, runout, and diameter. Yet, until recently, it has been often erroneously attributed to surfaces when several constant-value diameters could be measured. Today, machines that rotate either the component or the gaging point on a precision spindle give a more accurate assessment of roundness. Here's how true roundess relates to other commonly specified measurements.
Etesami, F. On the Theory of Geometric Tolerancing ASME Computer in Engr., V2, 1987, pp. 327-334 The integration of tolerancing in solid modeling systems in an essential step toward full design and production automation. In this paper a review of two approaches are presented, one reflecting tolerances as constraints on compositions of solid description parameters and another which is based on solid model offsetting. The strengths and weaknesses of the proposed approaches are compared with the tolerancing capabilities of the practiced standards. Enhancements to proposed theories are suggested in order to obtain a more abstract theoretical basis for a robust tolerancing formalization.
Etesami, Faryar Tolerance Verification through Manufactured Part Modeling Journal of Manufacturing Systems, Vol. 7, No. 3, pp. 223-232 The geometry of manufactured parts is always slightly different from the theoretically perfect design description models. Certain inspection tests determine whether such variations are within acceptable range. There is, however, no theory for compiling the results of such tests and measurements in building a geometric model for the part. A manufactured part model can be used for tolerance verification, robot guidance in tight assembly tasks, and for quality and process control applications. In this paper a modeling scheme is proposed to integrate different forms of observations in constructing a part model. Inperfect features are modeled by constructor solids which have perfect forms. The boundaries of these solids tightly enclose the functional features and represent the extent of their geometric variations. The part model is then used to interpret the meaning of some practiced tolerance specification statements.
Evans, David H.,1 A Statistical Tolerancing Formulation Journal of Quality Technology, Vol. 2, No. 4, October 1970, pp. 226-231. Tolerance, Statistics, Tolerance Analysis In statistical tolerancing the tolerances on component parts of an assembly are specified as distributions. Allowances should be made for the fact that a distribution for a component may shift due to raw material variations, different suppliers, tool wear, and a myriad of other causes. We consider this problem for the simple case of a linear system with normal distributions which have known and fixed variances for the component tolerances; the component means are allowed to shift. We assume that the lots of incoming components are subjected to acceptance sampling by variables inspection and it is the purpose of this paper to relate the component tolerances and the sample sizes and levels of significance of the tests. An asymptotic expansion for the probability that an assembly will be out of specifications, which is derived elsewhere, and which rests on the pessimistic assumption that all possible component means for incoming lots are equally likely is explained and its use illustrated by example.
Evans, David H.,2 An Application of Numerical Integration Techniques to Statistical Tolerancing Technometrics, Vol. 9, No. 3, August 1967, pp 441-456 Integration Techniques In order to set statistical component tolerances their effect must be determined. Methods available to determine the probability distribution of the response of the system often suffer from defects, e.g., inadequate error analysis, necessity for sophisticated mathematical and statistical techniques. We develop a quadrature formula for obtaining the moments of the response by the application and adaptation of multi-dimensional numerical integration procedures. Our primary concern is the special, but most important case in which the component values come from normal distributions. Evaluations of the response are required for 1) all components at their mean values, 2) all except one at their mean values, and 3) all except two; the off-mean values are prescribed. 2n^2 + 1 evaluations are required for an n component system. A numerical example is given. Generally, if a high-low tolerance analysis is possible then quadrature can be used instead and to much greater advantage. Thus, good engineering is a preprequisite. No tolerancing method can make up for its lack.
Evans, David H.,3 An Application of Numerical Integration Techniques to Statistical Tolerancing, II-A Note on the Error Technometrics, Vol. 13, No. 2, May 1971, p. 315-324. Integration Techniques Previously quadrature approximations were developed to determine the moments of a distribution of the response of a multivariable function when each of the variables is a random variable from a normal distribution # measures of skewness and kurtosis, respectively. A parametric study of the function X = co(ao ± y1 ± y2 ± ... ± yn)m + bo where the yi all have the same standard deviation, #, is conducted both analytically and by quadrature. The mean and variance obtained by quadrature are essentially exact in the range of interest. It is shown that for a large range of # the above distribution is both a good approximation and a much better aproximation than either a normal approximation with the same mean and variance or a linear approximation. The example also shows that the # ß2 obtained by quadrature is a poor indicator of the precision of the quadrature approximation.
Evans, David H.,4 An Application of Numerical Integration Techniques to Statistical Tolerancing, III - General Distributions Technometrics, Vol. 14, No. 1, February 1972, p. 23-35 Statistical tolerancing, System moments Suppose one wants numerical estimates for the moments of the distribution of a response X which is a function of the statistically independent random variables yk, k=1,2,...,n, when the yk are from known distributions. The functional relationship between X and the yk is assumed to be known in the generalized sense that for the given values of the yk the response X may be obtained somehow, e.g., by experiment, by engineering calculations, by analog. The same problem considered in the first paper in this series (Evans, 1967) for the special case in which the yk were all from normal distributions; here the distributions for the yk are general. A quadrature formula is developed for approximating the moments of X within an error #O?5) where #?2 is a representative variance for the yk. It uses the values for X obtained for 2n^2 + 1 selected arguments, (y1, y2, ..., yn). Efficient quadrature formulas are given for the case in which multiple distributions of the yk are of interest. A numerical example is included which illustrates the possible use of the quadrature method for a wide variety of problems outside of the field of statistical tolerancing.
Evans, David H.,5 Statistical Tolerancing: The State of the Art, Part I. Background Journal of Quality Technology, Vol. 6, No. 4, October 1974, p. 188 - 195. The object of this paper is to review and illustrate the concept of statistical tolerancing and the methods which are applicable to assigning component tolerances. The approach is primarily theoretical, but the thoery is that which is useful in practice. Tolerancing and statistical tolerancing are discussed generally, but the in-depth discussion is confined to two facets: 1) the problem of ascertaining the distribution of the response of a mechanism for given component tolerance distributions and 2) the problem due to the shifting and drifting of component tolerance distributions.
Evans, David H.,6 Statistical Tolerancing: The State of the Art, Part II. Methods for Estimating Moments Journal of Quality Technology, Vol. 7, No. 1, January 1975, p 1-12. Part I of this paper was concerned with statistical tolerancing from the overall point of view. In particular it showed why and under what provisions one wants to find the distribution of the response of the mechanism being toleranced as a function of the tolerances of the components when they are random variables with known distributions. In Part II four general methods for estimating the moments of the response distribution are described: Section 1, linear propagation of error, otherwise known as stack tolerancing; Section 2, non-linear propagation of error; Section 3, the quadrature technique; and Section 4, the Monte Carlo approach. For each the realm of applicability and its advantages and disadvantages are examined. The use of each is illustrated by applying it to the same -section attenuator as the mechanism being toleranced.
Evans, David H.,7 Statistical Tolerancing: The State of the Art, Part III. Shifts and Drifts J. of Quality Technology, vol 7, no 2, April 1975, pp. 72-76 Meanshifts, Tolerance Review, Statistics In Part I tolerancing was discussed in general and statistical tolerancing in particular. Part II focues on general methods for determining the distribution of the response of a mechanism when the component tolerances are given distributions. Here in Part III cognizance is taken of the fact that the case of known distributions for the component tolerances is an idealization of what occurs in practice, i.e., the true tolerance distributions will shift and drift from the ideal ones. The several attacks known to the author which are aimed at being useful in practice are reviewed. While these methods provide insight, none is a panacea and this face to statistical tolerancing remains troublesome. A delineation of some open problems and some general remarks conclude the paper.
Fainguelernt, R. Weill and Bourdet, P. Computer Aided Tolerance and Dimensioning in Process Planning Annals of the CIRP Vol. 35/1/1986, pp.381-386 It is well known that the future computer integrated manufacturing systems will need fast and reliable production planning programs of different types. As a contribution to this requirement, this paper tries to demonstrate the feasibility of computerized tolerancing and dimensioning on a small micro-computer system. The algorithm which is developed takes into account all categories of tolerances relevant in manufacturing such as setting, positioning, machining tolerances and proposes a strategy to optimize tolerance ranges in relation with functional requirements and equipment capabilities. The application of the developed software to an industrial example shows the efficiency of the method and its simplicity.
Fenton, R.G., W.L. Cleghorn and Jing-fan Fu Allocation of Dimensional Tolerances for Multiple Loop Planar Mechanisms Journal of Mechanisms, Transmissions, and Automation in Design, December 1989, Vol. 111/465-470. Tolerance Allocation, Planar Mechanism A method is presented to determine tolerance bands for the dimensions of multiple loop planar mechanism such that output motions will be kept within specified allowable limits. The kinematic equations of mechanisms are generated by combining various link groups. A preliminary set of estimated tolerance bands is calculated using an analytical technique. An optimizationn and checking routine is then employed to determine the set of input parameters which satisfies the prescribed output motion requirements. Examples have been included to illustrate the method.
Fiessler, B., Neumann, H.J., Rackwitz, R. Quadratic Limit States in Structural Reliability Journal of the Engineerng Mechanics Division, Aug. 1979, pp. 661-677 Advanced Statistics, other
Fortin, Clement, Chatelain, Jean-Francois A Geometrical Tolerance Verification APproach for Compolex Cases Including Datum Shift Analysis CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on CAT, Japan, April 5-6, 1995, pp. 337-356 geometric tolerancing, datum shift, tridimensional alignment, measurement of points, solid modelling A soft-gaging approach using solid tolerance zones and three-dimensional alignment algorithms is proposed to verify various geometric and dimensional tolerances. The method is particularly well suited for the verification of position tolerances involving a possible datum shift which still requres traditional metrology techniques to be solved. The totally CAD based approach uses constrained and unconstrained alignment techniques in order to bring closer the measurement points relative to the toleranced features and the correspoiding tolerance zones. The process can either deal, with structured sparse CMM data or unsturctured dense data files generated by a manufactured part inspection process. Two typical examples are presented to illustrrate the developed methodology. The first refers to a datum shift problem, which is solved using a non-linear constrained optimization method, while the second considers the verification of various toleranced features of the IMS - TI part,m which was used in Testcase#6 of the Intelligent Manufacturing Systems initiative on rapid product development.
Fortini, E.T. Dimensioning for Interchangeable Manufacture Industrial Press Inc., 1967 General This book has been written to provide engineers, designers, draftsmen, and checkers with a reference work on a very important activity of mechanical design, and to make available to students a textbook with which they may systematically study a subject that is usually only superficially taught in technical schools or haphazardly learned on the job. It is also meant to assist those involved in the procurement or production of parts for mechanical products in gaining an understanding of how dimensional specifications are generated. This includes manufacturing engineers, production planners, tools and pattern makers, machinists, quality control personnel, and so forth.
Foster, Lowell W. Geo-metrics II Addison-Wesley, 1979 GD&T, Tolerance Workshop training manual. Geometric characteristic symbols, order of elements in a feature control symbol, modifiers, datum identification, special symbols, feature control symbol, datum target symbols.
Foster, Lowell W. "Geometric Dimensioning and Tolerancing" Society of Automotive Engineers, SAE Paper No. 680488, 1968. True Position Tolerancing, GDT Geometric dimensioning and tolerancing is both a "language" and "technique." Its objective is to facilitate design, production, and inspection and, simultaneaously, provide the most economic results. This paper describes the implementation and practice to accomplish these through illustrating methods, to state design requirements speciifically and clearly, and to provide for maximum producibility, uniformity of interpretation, etc. the need to reflect a common objective for design, production, and inspection via the stated drawing requirements is emphasized. Application and interpretation of geometric characteristics (emphasizing symbology), fundamentals, rules, etc. are presented. Basis for the content of this paper is ANSI Y14.5-1966 "Dimensioning snd Tolerancing for Engineering Drawings."
French, T.E., Vierck, C.J., Foster, R.J. Graphic Science and Design McGraw-Hill Book Co. Fourth Edition pp. 185-213, 637-652, Chapter 7 Drafting Practices Tolerancing and Dimensioning
Fu, Jingfan, W.L. Cleghorn and R.G. Fenton Synthesis of the Dimensional Tolerances of a Slider Crank Mechanism Transactions of the Canadian Society for Mechanical Engineering, Vol. 12, No. 1, 1988, pp. 9-14. Also 10th Applied Mechanism Conference, ASME Tolerance Synthesis, Optimization A method is presented to determine the tolerances in the link lengths and offset of a planar slider-crank mechanism which ensures that the output motions are kept within predetermined error bands. A preliminary set of estimates of allowable tolerance bands is calculated using an analytical technique developed from a Jacobian matrix equation. An optimization search is employed to determine the set of link lengths and offset which satisfy prescribed output motion requirements. A set of weighting factors, with its entries associated with the mechanism dimensions, is incorporated into the procedure to reduce the optimization to a one dimensional search. Examples have been included to illustrate this method.
Fuscaldo-Peelman, Jeff Optimizing Collet Chuck Designs Using Variation Simulation Analysis VSA Applied Computer Solutions Through the use of variation simulation analysis, the development of turning and grinding chucks can be greatly enhanced due to the ability to predict collet roundness for a proposed concept.
Gabriele, Gary A. A Perspective on Engineering Design Education: Where Do Tolerances Fit In? Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 279-290 The mechanical engineering curriculum at Rensselaer, along with many others, under went a significant evolution between 1950 and 1980 as the curriculum shifted from practice oriented course work to more theoretical, science based courses. As might be expected, much of this change is the result of the emergence of new technologies and engineering methods but also in response to perceived inadequaceis in our engineering graduates. The area of engineering design was one of the bigger casualties in this evolution and long with it basic design engineering skills such as dimensioning and tolerancing.This paper looks at this evolution and at the more recent changes in the mechanical engineering graduates to produce quality designs. We will also look at how the topics of dimensioning and tolerancing fit into these fundatmentals and how well they are addressed. We conclude that while the current curriculum is moving in the right direction in addressing engineering design, the specific topics of dimensioning and tolerancing are usually only superficially addressed.
Garcia, Christopher J. Automating GD&T Quality, June 1988, pp. 56-57. GD&T, Automation An excellent technique for manufacturing quality.
Garrett, R.E. and Allen S. Hall, Jr. Effect of Tolerance and Clearance in Linkage Design Journal of Engineering for Industry, ASME, February 1969, pp. 198-202. Linkage Tolerances In designing a linkage transform one motion into another motion, consideration is given to the design sensitivity by analyzing the difference between the function generated by an ideal model of the mechanism and a model which incorporates manufacturing tolerances and clearances. The effects of these tolerances and clearances are presented in the form of mobility bands for the linkages.
Gauntet, Dominique Vectorial Tolerancing Model Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing,Cachan,France,April 27-28,1993,pp. 25-50 Dimensioning and tolerancing, Assembly, offsets, Stacks, Dimensions transfer, Technologically and Topologically Related Surfaces (TTRS), Minimum Geometric Datum Element (MGDE), Tolerancing Torsor In this paper we present a model for dimensioning and tolerancing mechanism parts. This work is based upon the Technologically and Topologically Related Surfaces and Minimum Geometric Datum Element concepts. We introduce the torsor tolerancing concept. Dimension transfer can be done with this model, for a part.
For a mechanism, the model gives a warranty about assembly and minimal defined stacks. Minimal and maximal offsets between mechanism parts can also be evaluated.
Gavankar, P., Bedworth, D. Stacked Tolerance Analysis and Allocation Using Assembly Models Allocation of appropriate tolerances is critical to ensure that components fit right and function satisfactorily in an assembly involving stacked components. There are numerous techniques available today to model assemblies on a computer. What is lacking is a common platform to make use of these computer models in order to perform tolerance analysis and allocation. This paper describes a technique to automate tolerance analysis and allocation of an assembly involving components stacked one on another represented in the boundary form. An algorithm is developed to track dimension loops in the stacked assembly. Statistical tolerance analysis and allocation is then performed on these interrelating dimensions and tolerances encompassed by a dimension loop. Advantages and limitations of this technique are compared against the manual method to conduct tolerance analysis and allocation.
Gavanker, Prasad, Henderson, Mark R. Graph-Based Extraction of Protrusions and Depressions from Solid Models Graph-based Feature Extraction-CAD Journal Submission,Fri. Jul 28, 1989 Solid Model, CAD, CAM Manufactured parts can be mathematically defined as solid models. The part definition data in the form of a solid model typically describes the geometry and topology of a part modeled on a CAD system in low level primitive boundary elements (faces, edges and vertices). These elements can be used to drive atuomated engineering analyses, but are typically at a level which is too low to be of use by the analysis procedures. Redefining the part in terms of its pertinent high level features can improve the efficiency of automated analysis. Automated recognition of the particular features of the part is a first step toward achieving CAD/CAM integration.The most complete computer representation of a part is a solid model. Three distinct classes of representing a solid model are: decomposition models, constructive models, and boundary represenation (MANT88). Decomposition models represent a point set as a collection of simple objects from a fixed collection of primitive object types, combined with a single "gluing" operation. Constructive models represent solid model as a collection of point sets, commonly known as primitives. Cylinders, cubes, tetrahedrons are examples of such primitives. In a boundary model, the solid is defined in terms of its boundary elements such as faces, edges, and vertices. This paper deals with the boundary representation (Brep) of a solid model.
Giesecke, F.E., Mitchell, A., Spencer, H.C., Hill, I.L., Loving, R.O. Engineering Graphics, Second Edition Macmillan Publishing Co., Inc., Chapter 12 and appendix pp. 335-353, 822-829 General Drafting Practices Chapter 12: Tolerancing
Giordano, Max, Duret, Daniel Clearance Space and Deviation Space Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 179-196 Clearances, Trouncing for function, Three-dimensional Trouncing The clearance between two assembled parts is represented by a volume in the small displacement space. The set of allowable deviation between a theoretical surface associated to a real part surface, and its nominal position, is also represented by a volume in the small displacement space. The composition of deviations and clearances in an assembly is translated into topological operations on these volumes. It is, in fact, an extension to the three-dimensional case of the notion of chains of dimenions, which consists of the composition of clearances and deviations. The method is illustrated by three examples. The requirement for assembly is verified for parts whose dimensions and geometric tolerances are known.
Gladman, C.A. Manual for Geometric Analysis of Engineering Designs Australian Trade Publications,1966 Tolerance examples This manual is concerned with that stage in the development of and engineering product where the functional design has been proved, the performance specification established and the design is to be made ready for production. This is the "design for production" stage where the function of each component part of the assembly is analyzed for size, form and geometric relation, where design modifications are made, where tolerances are determined, and where the objective is to secure the best compromise between the requirements of function, production, inspection, installation, use and service.
Gladman, C.A. Techniques For Applying Probability to the Tolerancing of Machined Dimensions National Standards Laboratory Technical Paper No. 11, 1959 (Australia) Statistics, Tolerance Two general types of problems arising in the geometric analysis of engineering designs are discussed, one being concerned with chains of toleranced dimension and the other with toleranced products and quotients. The general method adopted involves calculating the probable maximum deviation for the dependent variable from the estimated standard deviations for the independent variables, assuming that the dependent frequency distribution is normal. A design factor is introduced which, when multiplied by the half-tolerance, enables an estimate to be made of the required standard deviation for a dimension. Values for the design factor are explored first in the case of machining a dimension with process variability less than the tolerance and with uniform tool wear across the field, and secondly in the case of machining a dimension with process variability greter than the tolerance.These two cases are used as a basis for recommending safe design factors for general use with the machined dimensions. The validity of the assumptions is discussed and three examples given to illustrate the application of the techniques.
Gladman, C.A. Applying Probability in Tolerance Technology Transactions Institute Engineering Austral. Mech. Engr. Vol. ME5, No. 2, 1980, p. 82-88. A general approach to the geometric analysis of engineering designs is developed and presented in a form practicable for the application of probaility using design factors related to frequency distributions for the production processes. Design factors are established for three general types of design tolerance problems covering feature tolerances, geometry tolerances and the play between two assembled features. Simplified formulae are developed for use where appropriate; and the case is discussed where variables are not independent. The techniques are illustrated by application to a particular engineering product.
Gossard, D.C., Zuffante, R.P. and Sakurai, H. Representing Dimensions, Tolerances, and Features in MCAE Systems Computer Graphics & Application, March 1988, pp. 51-59 We present a method for explicitly representing dimensions, tolerances, and geometric features in solid models. The method combines CSG and boundary representations in a graph structure called an object graph Dimensions are represented by a relative position operator. The method can automatically translate changes in dimensional values into corresponding changes in geometry and topology. The representation provides an important foundation or higher level application programs to automate the redesign of assemblies and to automate tolerance analysis and synthesis. We implemented a prototype interactive polyhedral modeler based on this representation.
Greenhow, J.N. and Butterworth, N.A. Tolerancing of Components for Assembly. Engineering Designer V.6, pp.26-29. March 1980 In this article, the authors develop tolerance relationships based upon rectangularly distributed populaitons and compare them with existing relationships, which are in the main based upon statistical techniques. This work shows that, even when unlikely component distributions are considered, the tolerances on assemblies given by the relationships developed are less than those obtained using conventional 'safe' tolerancing techniques.
Greenwood, W. H. and Chase, K. W. A New Tolerance Analysis Method for Designers and Manufacturers J. of Engineering for Industry, ASME, vol 109, May 1987, pp.112- 116
Greenwood, W. H. and Chase, K. W. Worst Case Tolerance Analysis with Nonlinear Problems J. of Engineering for Industry, ASME, vol 110, Aug. 1988, pp. 232-235
Griffith, Gary Tolerancing symbols Quality, June 1984, pp. 91-92 Tolerance Symbols Some industrial drawings use American National Standards Institute Y14.5M tolerancing methods. This tolerancing method uses symbols for geometric control instead of worded notes. Thes symbols are easily learned because they generally take the shape of the geometric characteristic under consideration.
Grossman, D.D. Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacturing and Assembly. Stanford Artificial Intelligence Laboratory Memo AIM-280 Computer Science Department Report No. STAN-CS-76-555, May 1976 Monte Carlo The assembly of discrete parts is strongly affected by imprecise components, imperfect fixtures and tools, and inexact measurements.
Guilford, James GEOS Tolerance Analysis: Examples July 2, 1992 This document describes several examples of tolerance analysis using GEOS. The examples chosen reflect several purposes: to illustrate how GEOS can be used in different situations, to show the range of capabilities of GEOS, and to list test cases than can be used to verify GEOS's operation.
Guilford, James, Sethi, Mani Tolerance Analysis of CATIA Models Using the GEOS Key User's Guide for GEOS Version 1.4.0., March 11, 1992 The GEOS tolerance analysis package is designed to be attached to a variety of solid modeling systems, which act as an interface to GEOS. This allows designers access to GEOS's capabilities while remaining in an environment with which they are familiar. One such system is CATIA.This report is a user's guide to CATIA interface to GEOS. It describes the concepts needed to effectively use GEOS, and then presents a tutorial example illustrating these ideas.
Guilford, James, Turner, Joshua Advanced Tolerance Analysis and Synthesis for Geometric Tolerances CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 187-198 With the increasing trend towards replacing engineering drawings with solid modeling systems, a means is needed for integrating tolerances within the solid modeling framework. Before this can be done, however, a clear understanding is needed of what a tolerance is and how it can be analyzed.This paper compares parametric and geometric tolerances. It then describes the theory behind the GEOS tolerance analysis system, which is designed explicitly to handle geometric tolerances.
The GEOS system integrates a tolerance analysis capability within a solid modeler. The solid modeler actually defines a complete variational model; the tolerances become constraints on the geometric variations. This allows GEOS to derive relationships between the variational model and the tolerances, and between the variational model and the design function being analyzed. Using linear programming techniques, the numerical relationship between the design function and the tolerances can be derived.
Tolerance analysis is the process of taking known tolerances and computing their effect on a particular design function. Tolerance synthesis is the process of taking some desired behavior of the design function along with suitable models relating tolerances to manufacturing cost and computing a set of tolerances which minimize the cost. Instead of working from fixed limits on the design function, the GEOS system considers variations of the design function from nominal as a cost associated with a "quality loss" function from Taguchi. The tolerance synthesis algorithm then attempts to minimize the total cost, which is the sum of the manufacturing cost and the cost due to the quality loss.
Gutmann, Fredrick T. Limits and Fits by The Numbers and Letters Mechanical Engineering, November 1987, pp. 68-72. Cylindrical Fits A standard system of dimensions and tolerances can ensure proper fits.
Hahn, G. J., and S. S. Shapiro Statistical Models in Engineering John Wiley & Sons 1967 Fundamental text on advanced statistical methods, describes use of Pearson & Johnson systems as well as random number algorithms by Monte Carlo simulation.
Hambleton, Fred Extracting Data from Mainframe CAD Systems December 1988,Mechanical Engineering,pp. 60-61 CAD, Data Structure Access software that runs on a PC has taken much of the pain out of a process that once could be compared to the pulling of teeth.
Hanka, W. Equations Predict Chance of Misfit in Assembly Product Engineering, May 26, 1958, pp. 61-63. Tolerance, Assembly, Reject, Estimation Tight tolerances aren't always necessary-sometimes you can gamble on wider ones that save money and will often work satisfactorily. But before gambling, know the odds. Uniform distributions.
Harry, Mikel J. and Reigle Stewart Six Sigma Mechanical Design Tolerancing Publication No. 6s-2-10/88, Motorola Corporation, 1988 Statistical Tolerancing, Tolerance Synthesis, Process Capability
Hasofer, A.M., Lind, N.C. Exact and Invariant Second-Moment Code Journal of the Engineering Mechanics Division, ASCE, Feb. 1974, pp. 111-121 Advanced Statistics, (Other)
Heath, H.H. Statistical Tolerancing of Engineering Components: Is it Worth It? Precision Engineering, 1979 p. 153-156. Tolerance, Statistics It is often claimed that if statistical methods were applied to engineering tolerances a worthwhile relaxation of accuracy would be possible. In this paper some typical cases are examined to show what advantages could result from the use of statistical tolerancing. A worthwhile gain can be obtained only in comparatively few situations.
Held, David O. Assembly Variation Analysis: Liberty's Process Driven Design Tool for Quality SAE Technical Paper Series, 880606International Congress and Exposition, Detroit, MI, Feb 29 - Mar 4, 1988 Monte Carlo Simulation The purpose of this paper is to describe the technical components that support the Assembly Variation Analysis group at the Liberty Development Center of Chrysler Motors. A short chronicle of these elements is presented, as well as a summary of the benefits afforded the user when these tools are properly utilized "up-front' in the advance engineering process.
This is followed by an example of a practical application of these tools to a major assembly process under development at Liberty. An analysis of the simluation results, and a brief outline of future developments is offered.
Also discussed is the development of a graphics program to enhance the simulation software presently used.
Henzold, Georg Comparison of Vectorial Tolerancing and Conventional Tolerancing Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 147-160 Coordinate measuring machines probe points of the workpiece surface. They store the coordinates of these points and evaluate the parameters of the workpiece geometry by calculation using appropriate computer programs.This method enables to achieve a new approach to assess the workpiece geometry called vectorial dimensioning and tolerancing which is dealt with in ISO TR 10- 360-1 (under preparation).
This new method is described. The differences between this method and the usual conventional method according to ISO 286, ISO 1947, ISO 5459, ISO 1101 etc. are shown. The advantages and disadvantages of each method are explained.
The vectorial method defines the components of size and geometry to be influenced in the manufacturing process in a clear and distinct way. It enables proper manufactruing control. The vectorial method separates form deviations from orientation deviations. Thereby it provides proper means to specify particular functional requirements, e.g. of kinematic linkages.
Hernla, Michael Calculation of Measuring Uncertainty with CMMs under Industrial Conditions Proceeding fo 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993, pp. 171-178 Measuring Uncertainty, Principle of Propogation of Measuring Uncertainty, Admissible Uncertainty, Golden Rule of Production Measuring Technics, Measurable Tolerances. Every mathematically described geometric feature can be evaluated by CMMs. The results are including measuring deviations, which can be described by measuring uncertainty. Its size depends on uncertainty of measured points or features as well as on the geometric relations between them.The deviations of parameters are usually limited by tolerances. To assure measuring accuracy, the measuring uncertainty is not allowed to exceed the admissible one, which is a fixed share of tolerance. The ratio between them is always the same for all results. The equations of propagation of uncertainty can also be used to calculate measurable tolerances.
In this way it is possible to establish tolerances for various geometric features on complete workpieces with the same geometric accuracy not only based on experience, but also on mathematical principles.
Hillier, Frederick S. and Lieberman, Gerald J. Introduction to Operations Research Holden-Day, Inc., 1986.
Hillyard, R.C. The Build Group of Solid Modelers. IEEE Computer Graphics of Appl., March 1982, pp. 43-52 Solid Model, B uild 2, Romulus Design Build 2, Design, and Romulus are solid modelers with evolutionary links. Consideration of their characteristics and histories yields some general insights into solid modeling.
Hillyard, R.C. and Braid, I.C. Characterizing Non-Ideal Shapes in Terms fo Dimensions and Tolerances. ACM Computer Graphics,V. 12, W3, 1978, pp. 234-238 A geometric model of a shape is extended so as to represent not only its nominal dimensions but also tolerance information and surface specifications. The data structure defining an object is visualised as a pin-jointed, infinitely elastic wire frame covered by elastic membranes. Constraints corresponding to the dimensions of technical drawings are applied to the structure, either by the designer or by an automatic dimensioning algorithm. The validity of the resultant scheme can be checked and then drawn using drawing office conventions. The data structure can handle dimensions fixing various types of curved surface; other types can easily be added by following the same rules. A method of changing the nominal shape of an object is demonstrated. These results provide a systematic and tolerancing, and should make the draughting process more amenable to computation.
Hillyard, R.C. and Braid, I.C. Analysis of dimensions and tolerances in computer-aided mechanical design. Computer-Aided Design-Volume 10 number, 3 May 1978, pp. 161-166 The paper sets forth a theory to explain how dimensions and views combine to specify the shape of a mechanical component. It provides a method to determine whether a component is under, over, or exactly defined by a given dimensioning scheme. Measures for assessing the quality of a scheme are proposed. A solution is offered to a problem of tolerancing: given a toleranced dimensioning scheme, find the resulting tolerances between undimensioned parts of a component.
Hocken, Robert J., Raja, (Jay)araman, Babu, Uppliappan Sampling Issues in Coordinate Metrology CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME,pp. 97-112 Coordinate measuring machines acquire data one point at a time on the surfaces of the parts being measured. These data must be analyzed in order to produce a substitute geometry to be compared to the design intent. Algorithms are used to analyze these data. The results obtained are strongly dependent upon measuring errors, the form error of the part, the sampling strategy, and the density of points sampled. In this paper we review these problems and discuss some of the progress addressing them during the past few years.
Hoeprich, Michael R. Geometric Variation Effects on Rolling Element Bearing Life. Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Toleranicng and Metrology, ASME, pp. 167-176 Variations from the nominal geometry in bearing components, combined with those of housings and spindles, provide a variety of interactions affecting the fatigue life of bearings. While tapered rolling element bearings do not appear to be complex devices, determining bearing fatigue lives can be very involved. The large number of components in a bearing and the wide variety of application conditions result in numerous possibilities of internal load distribution. To avoid unfavorable stresses, minute modifications to the basic conical shapes of tapered rolling element bearing componenets must be made to accommodate the elastic deflections occuring in bearings and machinery components during operation. These modifications to the rolling surfaces are designed for the expected ranges of load and other application conditions. The calculation of contact stresses between the rolling elements and races is the basic starting point for determining bearing fatigue life. Since bearing fatigue life is related to contact stresses raised to the 6.66 power, chanes in contact stressesfrom desiredlevels and distributions can have a significant effect on life. Geometric variations in bearings, housing, and spindles can alter loads on bearing rolling elements and change the distribution of contact stresses along the lengths of the rolling elements. The degree to which these geometric variations influence fatigue life is affected by the elasic deflections in bearings, housing, and spindles when the machinery is being operated. Some geometric variations become less important and others become more important as load increases. Since machinery generally operates at a variety of load levels, the determination of tolerances may require the evaluation of their net effect over the entire load cycle.
Hoffmann, Peter Analysis of tolerances and process inaccuracies in discrete part manufacturing. Computer-Aided Design, Volume 14 number 2 March 1982, pp. 83-ff. This paper discusses basic problems of tolerancing mechanical parts. The problem of part design analysis (determination of consistency, determinacy and stability) is reduced to the analysis of systemes of linear inequalities. It is shown that the calculation of resulting tolerances between components of parts can be easily solved by linear progamming. A method is provided for the construction of a system of inequalities which the working dimensions and inaccuracies of machining operations must satisfy if a given tolerance specification is to be met.
Hook, Richard Keynote Address, Interaction of Dimensioning, Tolerancing, and Metrology CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn, Michigan, June 17-19, 1993 This Forum is concerned with two activities that need to be better understood and integrated. They are specifying dimensions and tolerances for workpiece designs to capture and preserve design intent, and measuring actual workpieces to determine conformance with the specifications and design intent. The need for standards to govern dimensioning and tolerancing became apparent more than fifty years ago, but companion standards for measurement were not thought necessary until the 1980s, when coordinate measuring machines brought 'measurement divergence' to the force as a central problem. Work aimed at resolving measurement divergence and related matters accelerated after a 1988 Workshop brought the problems into public view, and new tolerancing and metrology standards are now emerging. This Forum will review the accomplishments to date, and consider what additional steps may be needed.
Hopp, Theodore H. Computational Metrology CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,pp. 207-218 Coordinate measuring systems (CMSs) assess length-based characteristics of mechanical parts by measuring points on the part surface and analyzing the point data. Data analysis software can contribute significantly to the total measurement error of a CMS. Factors affecting software performance include the choice of analysis method, the quality of the software, and characteristics of the specific measurement uncertainty of a CMS.This paper describes research at NIST on computational metrology. Metrological questions fall into two categories: (1) the proper choice of data analysis objective for a particular application and (2) the performance of the implementation. Our research goal is to develop the basis for a national standard in the U.S. for CMS software performance evaluation. We are implementing a Special Test service to be offered through the NIST Measurement Services Program. The service is based on a black-box model of software, in which the internal structure of the software and the choice of solution methods are assumed to be unknown. The model identifies a number of error sources for data analysis software. We are designing test methods for identifying the methods for identifying the various components of the model and how those components relate to measurement uncetainty in inspection applications.
Humienny, Zbigniew Language for Dimensional Analysis: The conception of a formal language for structure notiaon in selected, configurations of dimensional chains and system of this language's operational use Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 249-266 Dimensioning, computer aided tolerancing, dimensional, chains, redimensioning, dependent dimension. The basic principles of a formal language for notation and analysis of the structure in configurations of simple dimensional chains and configurations of flat dimensional chains with common datum feature linear dimensioning are presented. Dimensions given on engineering drawing are coded in the matrix notation. Algorithms which can detect redundant dimensions and generate equations of any dependent dimensions are briefly described. In the conclusions the potential of the methods introduced are discussed as well as proposals for the future directions of investigations.
Hummel, K.E., Wolf, M.L. Integrating Expert Systems With Solid Modeling Through Interprocess Communications and the Applications Interface Specification Computer in Engineering,ASME,Vol. one,1990,pp.355-360 Arguably the most elusive problems to automate in engineering are those that require a large degree of spatial reasoning. One of the most significant reasons for this has been the lack of appropriate software tools with which to perform research and development. The optimal software environment should integrate the symbolic reasoning capabilitiess of a solid modeling system. This paper describes such an environment, developed using interprocess communications and a standardized solid modeling interface language. This integration has resulted in a seamless coupling that provides an exprt system with dynamic access to the full power of a solid modeling system. The details of the interprocess communications protocol, the solid modeling interface language, and the data dependency tracking technique are discussed.
Hura, C.M., Caron, N.O., Kanik, J.A. and Hunt, W.A. SAE Technical Paper Series SAE Paper 881245
Hurt, James Tolerance Analysis with a Variational Geometry System This document outlines the theory used to design and develop the Tolerance and Sensitivity Analyis option for The Mechanical Advantage, a commercial Variation Geometry system. Its purpose is to describe what is computed in this option and to outline areas where further research is needed. No attempt is made to describe how anything is computed, but only what is computed and why.
Hurt, James A Taxonomy of CAD/CAE Systems Manufacturing Review, ASME, Vol.2, No-3, September 1989, pp. 170-178 This is a taxonomy of computer aided design (CAD) and engineering (CAE) systems thta are designed for use by mechanical, design and manufacturing engineers. This taxonomy looks at two characteristics of these systems: how the system handles geometric dimensionality; and how the system handles topology; and how each combination of these characteristics supports various types of engineering analysis. How a system handles geometric dimensionality considers the type of geometry that the system handles; where a system is in the range from two-dimensional to constructive solid geometry are stored (remembered by the system: where a system is in the range from fixed geometry to variational geometry. Geometry is where the objects are located, and topology is why they are located there.
Iannuzzi, Mark, Snadgren, Eric Tolerance Optimization Using Genetic Algorithms: Benchmarking with Manual Analysis CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.245-262 Genetic Optimization, Tolerance analysis, Simultaneous engineering A computational design methodology is presented which permits the optimal allocation of tolerances for mechanical assemblies. A nontraditional genetic optimization method is coupled to a Monte Carlo based tolerance analysis. The objective is to determine the maximum tolerance zone value fo reach nominal feature while simultaneously meeting all critical dimensional and functional constraints imposed upon the design. A discretization of possible tolerance zone values is performed and a global search is conducted using a genetic algorithm. The goal is to develop a comprehensive software tool which can support dimensional variation decisions from concept through design, manufacturing, assembly and inspection. Three industrial problems are considered and the best solution generated by a manual method for each problem is compared to the solution generated by the optimizer. The results demonstrate the current capability of the approach and provide direction for future development.
Inui, Masatomo, Miura, Masahiro Configuration Space Based Analysis of Position Uncertainties of Parts in An Assembly CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 155-172 Tolerance modeling, Tolerance analysis, Configuration space A configuration space based method for analyzing position uncertainties of two parts in an assembly is proposed if certain shape variations of individual parts are allowed by tolerances. Proposed method is applicable to 2 dimensional polygon models of machine parts, for example sections of polyhedron parts in an assembly. The analysis is achieved by calculating a variation bound of the configuration of the parts if nonnominal parts allowed by the tolerance satisfy the positioning condition in an assembly. Different from the prior approach, our method does not assume any specific deviation types of the nonnominal part. An algorithm for computing the variation bound is developed and the configuration uncertainty of some sliding joints in the positioning mechanism is analyzed. Computational experiments suggest that the visualized image of the bound is developed and the configuration uncertainty of some sliding joints in the positioning mechanism is analyzed. Computational experiments suggest that the visualized image of the bound of the configuration variation is helpful for understanding the positioning characteristic of the joint.
Inui, Masatomo, Otto, Harald, Kimura, Fumihiko Algebraic Interpretation of Geometric Tolerances for Evaluating Geometric Uncertainties in Solid Modeling 2nd ACM Solid Modeling, 1993-5 Geometric tolerances specify the allowable limit of manufacturing imperfectness from the ideal design geometry. An actual feature is acceptable if it can be contained within the spatial tolerance zone. An unambiguous representation of the possible variation of the allowed actual feature is required for the development of computer-aided tolerancing sytems. A general definition of the geometric tolerance is used as our basis, which includes the form, orientation, and position tolerances in the standards. Based on geometric characteristics of machined surfaces, and actual feature model is initiated as small position and orientation variations of boundary faces of the nominal solid. The spatial constraint imposed on the acceptable feature is interpreted as a containment condition of the actual feature model by its corresponding portion of the tolerance zone. This condition is systemically derived in terms of linear inequalties based on the polyhedral approximation of the tolerance zone boundary. This paper discussed theoretical aspects of the method. Implementation of the system and evaluation of its applicability for analyzing machine parts with complex tolerance specifications are considered as following steps in our future work.
Ioannou, Yiannakis A. and Eyada, Osama K. A Diagnostic Tolerance System Computers Ind. Engng Vol. 17, Nos 1-4, pp. 27-30, 1989. This paper describes a Diagnostic Tolerance System (DTS) designed to allow users to interactively select the appropriate class of fit and perform tolerance analysis for an assembly. The DTS is written in C programming language for a micro-computer and can be interfaced with CAD software, such as AutoCAD and CADkey. With the DTS, the productivity of designers is enhanced and design for manufacturability is easier to achieve.
Jablokow, Andrei G., Uicker, John J. Jr., Turcic, David A. Topological and Geometric Consistency in Boundary Representations of Solid Models Advances in Design Automation-1990,Vol. 1,ASME Publication No. DE-Vol. 23-1, Proceedings of ASME Design Automation Conference, Chicago, IL Sept. 16-19, 1990,pp. 59066 Solid model This paper describes a method of verifying the consistency between the topology and geometry of boundary representation (B-rep) of solid models. This verification is well suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow 1989). Information regarding boundary representations is typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.
Jamieson, Archibald Introduction to Quality Control Reston, Reston,VA. 1982 Process tolerance data Cost of process tolerance, Chap. 1
Jensen, C., Helsel, J. Engineering Drawing and Design McGraw-Hill Book Co., Second Edition, pp. 70-84, Chapter 5. True position tolerancing, GDT, Cylindrical fits, Machine tolerances Limits and Tolerances
Johnson, N.L., and J. O. Kitchen Biometrical Tables for Statisticians Cambridge University Press, 1976 Empirical Distributions
Johnson, R.H. How to Evaluate Assembly Tolerances Product Engineering, Jan. 1953, pp. 179-181. Basic Assembly Analysis General rules and examples of how to evaluate the effects of component tolerances on their overall assembly and thus assign more realistic limits. The cases discussed include those of components which are combined into assemblies by simple addition, multiplication and non-linear functions.
Kanai, Satoshi, Onozuka, Mamoru, Takahashi, Hidetomo Optimal Tolerance Synthesis by Genetic Algorithm under the Machining and Assembling Constraints CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.263-282 Tolerance synthesis, tolerance optimization, genetic algorithms, geometrical dimensioning & tolerancing, differential coordinate transformation, CAD, cost-tolerance model The designing of tolerance greatly affects the functions and manufacturing cost of mechanical assemblies. The purpose of this research is to develop a computer aided method of three dimensional tolerance synthesis. The assembly was represented by solid model, and dimensional and geometrical tolerances were formulated as a set of inequalitites constraining substitute features. Differential coordinate transformation and linear programming were used to analyze the dimensional features, tolerance ranges, machining and set-up costs. Tolerance synthesis was represented as the applied to solve the problem. The coding method and genetic operators were discussed. The algorithm was evaluated through the tolerance synthesis for the gear box.
Kanayama, Sunshine Taguchi Rules in some Japanese Standardizations of Tolerancing CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.229-244 Tolerancing, Taguchi loss function, Taguchi method, Taguchi quality engineering, Plastic part tolerance, calibration, measurement, Japanese Industrial Standard Three Japanese Industrial Standards and a Standard Draft are issued on tolerancing, incorporating Taguchi rules. Reference Table of the standard JIS K 7109-1986 tabulates thirty-nine operation tolerances for plastic parts in field as compared to the tolerance by the standard. Careful review proves that Taguchi quadratic loss function shall be modified to a higher-order one to meet with the actual cases, as well as proves that Taguchi tolerance is independent of the part population but guarantees the part quality not enough. The supplier's expense for care of the customer's objection, the dole, and the customer's duty depend on the population strongly. The population shall be more centered and more narrow compared to the tolerance. The Standard Draft is to extend this standard to any part value other than dimensions, yet no actual data available. The other two standards, JIS K 0971-1989 for microvolumeter and JIS Z 9090-1991 for measurement system, describe commonly known principles such as that of mean square errors sum or so, incorporating Taguchi rules only auxiliarily. Incorporation of the rules or the way in standards being promoted strongly, but the profound thought and the fine mathematics shall be reviewed more accurately and more precisely, and restated concisely and legibly.
Kane, Victor E. Process Capability Indices Journal of Quality Technology, Vo. 18, No 1, January 1986, pp. 41-52 SPC, Process capability The capability indices Cp, CUP, CPL, k and Cpk are presented and related to process parameters. These indices are shown to form a complementary system of measures of process performance, and can be used with bilateral and unilateral tolerances, with or without target values. A number of Japanese industries currently use the five indices and the US automotive industry has started using these measures in a number of areas. Various applications of the indices are discussed along with statistical sampling considerations.
Kase, Kiwamu An Evaluation of Geometrical Errors by Segmentation with Fitting Form Error Features. CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on CAT, Japan, April 5-6, 1995, pp. 357-365 Geometrical Error Evaluation, Segmentation and Fitting for Scattered Data, Bezier Template, Simulated Annealing Method Geometrical errors after manufacturing processes are conventionally evaluated by maximum width of tolerance zones which envelop actual features. Details of error shapes within such zones should however be investigated when the designer studies relation between errors and functionality of a product, or when he wants to compare and examine manufacturing methods in quest of high accuracy of machined surfaces.We propose a new method for the evaluation of form errors from a series of points data such as measuring points form product surfaces. This evaluation consists of two parts: 1. Form error features which consists of error models (Bezier Template) and error conditions 2. Segmentation by fitting of form error features are realized by the Simulated Annealing Method, a statistical optimization method which can search for the global minimum combinational solution. Using our method, the designer fitting Form Error Features as a substitute. This leads to functional tolerancing.
Kececioglu, D., Lamarre, G. Mechanical Reliability Confidence Limit Journal of Mechanical Design, 1978,pp. 607-612 Probabilistic Design, Reliability Charts are presented relating the lower one-sided limit on the reliability, R (L1), to the effective sample size, n (e) calculated from the sample size used to estimate the failure governing stress and strength distributions, or f(s) and f(S) respectively, and a factor K which is a function of the estimated means and standard deviations of f(s) and f(S). These graphs cover an n(e) range of 5 to 2000, confidence levels of 0.80, 0.90, 0.95, and 0.99, and lower one-sided limits on the reliability of 0.85 to 0.9(14)5. The equations used to develop these charts are derived and two examples of their applications are given.
Kennedy, Clifford W. and Andrews, Donald E. Inspection and Gaging M.F. Spotts in 3 books A training manual and reference work that discusses the place of inspection in industry; describes the types of automatic and manual gaging and measuring devices employed; shows the proper techniques of using inspection equipment; and outlines the various duties of inspection personnel.
Kim, S H, Lee, K An Assembly Modelling System for Dynamic and Kinematic Analysis Computer-Aided Design,v.21,N1,Jan/Feb 89, pp.2-12 Assembly Modelling, Dynamic Analysis, Kinematic Analysis An assembly modelling system, with which a designer can interactively create an assembly of components ready for dynamic analysis, has been developed. In this system, an assembly model is created from the mating conditions between the components in the assembly, and then most of the information required for the dynamic or kinematic analysis packags is derived. For this development, the following problems have been solved: creation of assembly data structure, structuring of assembly data, derivation of joint information, inference of each component's position, and creation of joint coordinate systems. Through this work, the designer can easily model an assembly by assigning mating conditions, and check the dynamic or kinematic performance with the automatic creation of inputs for the assembly analysis packages.
Kline, W.A., DeVor, R.E. and Shareef, I.A. The Prediction of Surface Accuracy in End Milling. ASME Paper In the end milling process, the cutting forces during machining produce deflection of the cutter and work piece which result in dimensional inaccuracies or surface error on the finished component. A previously developed mathematical model for the cutting force system in end milling is combined with models for cutter deflection and workpiece deflection so that the surface error profile may be predicted from the machining conditions and geometry and material properties of the cutter and workpiece. Machining experiments are performed on rigid and flexible workpieces of 7075 aluminum to verify the ability of the models to predict surface error. The model predicted surface error profiles are accurate both in magnitude and shape with the difference between measured and predicted surface errors raging from 5 to 15 percent. This approach for the prediction of surface errors provides a useful aid for the analysis of a variety of end milling process design and optimization problems.
Knauer, Karl and Hans-Jörg Pfleiderer Yield enhancement realised for analogue integrated filters by design techniques IEE Proc., Vol. 129, Pt. G, No. 4, August 1982, p. 122-126 Electronics fabrication The fabrication of analogue integrated circuits to yield depends on the tolerances and defect density in mask generation and device fabrication. Yield optimization, therefore, has to resolve two conflicting requirements. Whereas to reduce the influence of tolerances the device area has to be large, the larger the device area chosen, the higher will be the possible defect number. To determine the optimum device area with respect to yield in the fabrication of CCD transversal filters, the tolerances in mask generation and fabrication have first to be analyzed. Tolerances that are constant in a device can be eliminated by 'design cleverness'. The way in which the influence of statistical tolerances can be reduced by design centering will be demonstrated with reference to an implemented device. To determine the total yield it is further necessary to take into account the influence of defects. The optimum device area, considering yield, can then be determined as a function of both tolerance and defect density.
Koplewicz, Danielle Specification by tolerances zone-Current situation and evolutions Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 213-222 Product specification, toleranceing, geometrical tolerancing, tolerance zone. This paper gives an overview of the international standardization dealing with geometrical tolerancing of products. This tolerancing is based on feature specification through tolerance zone. The evolutions already agreed and to be studied in the (near) future, are presented: they are inteded to impove the definition, to avoid contradictions, and to fill the gaps.
Kuntze, Robert The Toleranced Design of the Model 520 Computer Hewlett-Packard Journal May 1984
Latta, Lester W. Least-Cost tolerancing Product Engineering September 16, 1963 How do you split the functional tolerances between mating surfaces? It depends on how they're to be made sometimes on the specific machine used.
Laurance, Neal A High Level View of Step- A Formal Specification of the Information Content of a Product Design. Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 37-48 This talk provides a brief introduction to STEP, an emerging International Standard covering all the requirements of an enterprise for information about a product from the time the product is first conceived until it is obsolescent. This standard is intended to replace IGES as a medium of interchange for geometrical data, and to include all the other types of data about a product in an industry. The standard is a blend of CAD/CAM models and advanced database concepts. In general, STEP draws its information models from appropriate technological domains and recasts them in a common information schema.While the early use of STEP will be for exchange between proprietary CAD systems, there is already evidence that next generation systems will have a native mode conceptually equivalent to the data base formulation prescribed by STEP. Examples of the use of STEP for relatively simple geometrical items are given. The current status and the work in progress of this standard is summarized.
STEP today handles only nominal geometry, i.e. ideal form. However, future versions of STEP will incorporate a tolerance model based on Y 14.5.1. That work is just now beginning, and the first results will not be available until next year. Standardization is similarly several years away.
Law, Averill M. How To Build Valid, Credible and Appropriately Detailed Simulation Models. Industrial Engineering, pp. 16-17, April 1990
Lee, Kunwoo and Andrews, Guy Inference of the positions of components in an assembly: part 2 Computer-aided design, Vol 17, no.1 Jan/Feb 1985, pp. 20-24 A method is dirived to compute the location and orientation of each component from the spatial relationships imposed on the component in an assembly. With this method, any assembly can be represented by the spatial relationship between its components instead of by the transformation matrices of each component.
Lee, Woo Jong, and Tony C. Woo Tolerancing: Its Distribution, Analysis, and Synthesis Technical Report No. 86-30, University of Michigan, Dept of Industrial and Operations Engineering, December 1986 Tolerance, Analysis, Synthesis Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach makes it possible to perform trade-off between performance and tolerance rather than worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance synthesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probabilistic optimization problem for tolerance synthesis is simplified into a deterministic nonlinear programming problem. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliability index, and cost. Examples from the implementation of the algorithm are given.
Lee, Woo-Jong and Tony C. Woo Optimum Selection of Discrete Tolerances Technical Report No. 87-34, University of Michigan, Dept of Industrial and Operations Engineering, Dec. 1987 Tolerance synthesis, Cost optimization, Branch and Bound Tolerance determination involves considerations from manufacturing, design, and assembly. Along with minimum cost and maximum functionality and interchangeability, the practice of tolerancing urges a process engineer to choose an appropriate manufacturing process as well. This situation is formalized by using a discret model. For an optimum selection of tolerances from given tolerances of various manufacturing processes, minimization of manufacturing cost is achieved under the constraints of tolerance stack-ups.
A random variable and its standard deviation are assigned to a dimension and its tolerance. This probabilistic approach enables trade-off between performance and tolerance but it also suggests stochastic optimization. With the aid of a notion called the reliability index [8], tolerance selection is formulated as an integer programming problem. A branch and bound algorithm for ensuring an optimum selection is developed by exploiting the special structure of the constraints. To make the enumeration tree small, monotonic relations among the reliability index, cost, and tolerances are examined. The algorithm is tested with examples.
Lee, Woo-Jong, Woo, T.C. Tolerances: Their Analysis and Synthesis Journal of Engineering for Industry. Vol. 112/113, May 1990 Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probalistic approach makes it possible to perform trade-off between performance and tolerance rather than the worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance sythesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probalistic optimization problem for tolerance sythesis is simplified into a deterministic nonlinear programming problen. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliablilty index, and cost. Examples from the implementation of the algorithm are given.
Lehtihet, E.A. and Dindelli, B.A. TOLCON: Microcomputer-Based Module for Simulation of Tolerances. Manuf. Ref. Vol.2, Num.3, Sept 1989. pp.179-188. One of the fundamental aspects of design and maufacture is the transformation of product functional requirements into tolerances or dimentional bounds on the individual components which make up the product. Tolerance problems in design and manufacturing often require the solution to linear or nonlinear combinations of stochastic variables. This paper describes progress towards the development of integrated computer modules for the solution of statistical tolerancing problems. A software package for the automatic generation fo Monte Carlo simulation for combinations of stachastic variables has been designed and implemented. The structure and capabilities of this package are described. Its usefulness in the analysis of tolerances is illustrated by a position tolerance application.
Lehtihet, E.A. and N.U. Gunasena Models for the Position and Size Tolerance of a Single Hole Manufacturing Metrology, ASME Publication No PED-Vol 29, 1988, pp. 49-63. Geometric form, Tolerance Hole True position tolerancing enables designers to convey a concise statement of design intent to both production and inspection. The position tolerance of a feature can be specified as a static quantity by using the Regardless of Feature Size (RFS) modifier or as a dynamic quantity by using the Maximum Material condition (MMC) modifier. However, the constraints imposed on production errors are not evident from the tolerance frame. This paper develops several models relating position and size tolerance of a feature to inherent production errors. Performance under different models is evaluated by computing the probability of an acceptable feature with respect to position and size requirements.
Lenz, R.G. Roundness Measurement, Part Three-Applying the Standard Mechanical Engineering, Dec. 1969, pp. 30-36. GDT, Inspection, Roundess The roundness standard currently being developed by a U.S.A. Standards Committee proposes methods for assessing the circular geometry of parts with a rotatable precision spindle measuring machine. This article describes how such a machine has been used to evaluate the geometry and improve the operation of automotive components.
Leveaux, Florence, Bourdet, Pierre, Lartique, Claire Geometrical validation of Dimensioning and tolerancing specifications Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 233-248 Dimensioning and Tolerancing, CAD models (Computer Aided Design). geometrical control, CMM (Coordinate Measuring Machine). A complete and sytaxically consistent data model of Dimensioning and Tolerancing specifications is elaborated following STEP project concepts (Standard for Exachange of Product Data.)With this conceptual data representation, a Dimensioning and Tolerancing specifications validation method is proposed. This method, illustrated thanks to a specification example, is based on the algorithmic simulation of a high level geometric control process.
This approach uses coordinate measuring principles and is independent form the inspection process and the dimensional measuring equipments. Variations on specified geometric features location and orientation are quantitatively estimated and are used to validate the Dimensioning and Tolerancing specifications a priori and during the design phase.
This validation method could be a contribution to automatic tolerancing for concurrent engineering.
Levy, S.J. Applied Geometric Tolerancing TAD Products Corp., 1974 True Position, GDT
Liggett, J.V. The Boundary Concept of Position Tolerance Society of Automotive Engineers, SAE Paper No. 680489 True Position, Tolerancing, GDT Current position tolerance standards treat noncircular shapes (square holes, slots, keyways) either as special applications, or in a different manner than round features are treated. The Boundary Concept enables position tolerance to be applied in a consistent manner to all feature shapes by defining position tolerance as the interaction of a surface (the feature) and a boundary. Good correlation with the functional gaging practices of the automotive and aircraft industries is achieved. Drastic changes in current standards have been avoided. The Boundary Concept is the result of a project of the SAE Drawing Standards Committee.
Light, Robert and David Gossard Modification of Geometric Models Through Variational Geometry Computer-Aided Design, Vol. 14, No. 4, July 1982, p. 209-214 Computer-Aided Design, Geometric Model, Variational Geometry Systems for computer-aided mechanical design use geometric models for drafting, analysis and programming of NC machines. Because design is iterative in nature, the topology, geometry or dimensioning of a geometric model must be modified many times during the design cycle. The effectiveness of future CAD systems will depend in large part upon the ease wiht which geometric models can be created and modified.
This paper represents the results of a research effort to develop flexible procedures for the definition and modification of geometric models. A central idea of this effort is that dimensions, such as appear on a mechanicla drawing, are a natural descriptor of geometry and provide the most appropriate means for altering a geometric model.
A procedure is described by which geometry is determined from a set of dimensions. The gemetry corresponding to an altered dimension is found through the simultaneous solution of the set of contraint equations. Presented in this paper are the basic approach to modifications of gemetric models, a procedure for significant reduction of the number of constraint equaions to be solved, and the effect of sparse matrix methods in reducing the time required to solve the equations.
Lin, Chin-Wen A Statistical Analysis Tool for Variation Simulation Modeling Computers & Industrial Engineering, Vol. 13, Nos. 1-4, pp. 386-391, 1987 Monte Carlo Simulation The analysis of an assembly process in the discrete part manufacturing industry usually involves a large number of dimensions. Each dimension tolerance influences the dimension variation of the final product, which is the so-called "quality". Furthermore, there are many random factors (noise) present during the assembly operations (tool wear, loose fixture, etc.). Few mathematical models can represent the assembly process. By applying a geometric standard and simulating the physical operations, the statistics of the final product dimensions can be predicted. With the simulation results, statistical anlysis is essential to identifying the critical factors (component dimensions). The traditional experimental designs, such as full factorial design, however, are not practical since the number of factors is too large. Taguchi method, which explores a special subset of factor combinations (called the orthogonal array) is able to examine a large number of factors (and interactions) in a much smaller number of experiments. With this unified tool, engineering understanding and judgement become more effective in product and process design.
Lin, V.C., Gossard, D.C., and Light, R.A. Variational Geometry in Computer -Aided Design Computer Graphics, vol. 15, Num. 3, Aug. 1981, pp. 171-177 Abstract: A system has been developed which utilizes variational geometry in the design and modification of mechanical parts. Three-dimensional constraints between characteristic points are used to define an object's geometry. Modification of geometry is accomplished by alteration of one or more constraints. A matrix method is used to determine the shape of the part by simultaneous solution of constraint equations. A method for increasing the speed and efficiency of the solution procedure is described. The method uses the relationships between the geometry and constraints to minimize the number of equations and variables to be solved.
Linares, Jean Marc, Marty, Claude Tolerancing by functional group Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 267-277 Tolerancing, small displacements, functional, spacial, clearance In the concept of analytical model conception of tolerancing an essential stage of the process is the model conception of functional groups, these are constituted by all surfaces which take part at the realization of functional conditions.The model, obtained from the connection graph and described by small displacements representing the difference of postition and orientation; permits to define the internal and external dimensioning and tolerancing.
This analytical process, very useful to approach the automatic tolerancing on CAD, CAM, proposes minimal and sufficient conditions. The surface errors, in a functional group, influence the assembly or the functional conditions and the choice of clearance between functional groups.
The assignment of specifications must stay compatible with the potentialities of production methods and control.
Little, R.E. Statistical Tolerance Limits for Censored Log-Normal Data Journal of Testing and Evaluation, Vol. 8, No. 2, March 1980, pp. 80-84 Reliability, Log-Normal Distribution A-basis and B-basis statistical tolerance limit computations are given for Type sII failure censored log-normal data. The statistical tolerance limits are established by using factors given by Nelson and Schmee in conjunction with the best linear unbiased estimates for hte normal distribution based on the coefficients tabulated by Sarhan and Greenberg. Thes tolerance limit computations complement analogous computations based on the Weibull distribution which have been illustrated in recent tutorial paper by Little.
Liu, S., Dong, Z. A Solid Boundary Based Tolerance Representation Model Advances in Design Automation - DE-Vol. 44-2, ASME 1992 An ambiguous representation of design geometry and its allowed variation is essential to design and manufacturing analysis tools using geometric modeling. In this paper, a new approach for modeling and representing mechanical tolerances, using information embedded in the solid model, is introduced. THe work focuses on mathematical mapping between the nominal and variant configurations of design geometry, using boundary face-based model variables. The method identifies the realtion between the errors of part geometry, represented by a solid model and measured using acoordinate measureing machine, and the tolerances, specified by dimensioning and tolerancing standards. The work is of benefit in understanding of the fundamental nature of geometric errors and tolerances; it guides the specification of dimensional and geometric tolerances; and, contributes to automated mechanical tolerancing in a solid modeling based system.
Loewen, E.G.. Microinch Accuracy...Really? American Machinist, Vol. 111, Number 12, June 5, 1967, pp. 135-141 Gaging A metrologist does not believe all that he hears and sees about claims that gages can actually measure to millionths. Here are his arguments supporting his views.
Lorenz, G. Dimensional Analysis of Production Processes National Standards Laboratory Technical Paper No.13, 1960 Australia Tolerance, Production Process Cost The aims of the dimensional analysis of production processes, together with the significances of the analysis in economical production, are described. The terms process variability, process capability, process tolerance, mean process displacement, and safety margin are defined, and their application illustrated by practical examples.
Lu, Stephen C-Y., Wilhelm, Robert G. Automating Tolerance Synthesis: A Framework and Tools Journal of Manufacturing Systems. Vol. 10, N4, pp. 279-296. This paper describes CASCADE-T - a new approach to tolerance synthesis that uses a complete representation of the conditional tolerance relations that exist between features of a part under design. Conditional tolerances are automatically determined from functional requirements and shape information. Tolerance primitives based on the virtual boundary requirements approach to tolerance representation are composed to form more complex tolerance relationships. Artificial intelligence techniques, including a constraint network, frame-based system, and dependency tracking are used to support flexible and detailed computation for tolerance analysis and synthesis.
Luby, S.C., Dixon, J.R., Simmons, M.K. Designing With Features: Creating and Using a Features Data Base for Evaluation of Manufacturability of Castings. Computers in Engineering Conference Proceedings. Vol. 1, pp. 285-292, 1986 ASME Feature Design, Casting, Manufacturability This paper describes a working research prototype features based design aid for aluminum castings. The program, called Casper, employs macro-features (such as boxes or L-brackets) together with co-features (such as holes, bosses. or ribs) for use by the designer in creating parts. An add-modify-delete menu allows the designer considerable scope and flexibility. As the design proceeds the program develops and updates a representation of the design in terms of the features used and also in terms of faces, edges, and points, which are readily derived from the feature. This representation is used to provide the designer with a visual display in an interactive graphics environment.Manufacturability evaluation, when requested by the designer, occurs in two steps. First, process limits (such as section thickness and overall dimensions) are checked. Then a directional solidification analysis is done and interpreted. Both steps identify the location ot the program's operation are shown and discussed.
Luzadder, P.E. Graphics for Engineers Prentice-Hall, Inc., Englewood Cliffs, N.J., 1957, pp. 424-435, Chapter 16. True Position Tolerancing, GDT Size Dimension, Limit Dimension, Basic Shaft System, Square Tolerances, True Position Dimensioning, Surface Quality
Luzadder, W.J. P.E. Fundamentals of Engineering Drawing Fourth Edition, Prentice-Hall, Inc. pp. 354-365, Ch. 15 General, Drafting Practices Chapter 15: Dimensioning
Lynch, A.F., Vanderploeg, M.J. A Symbolic Formulation for Linearization of Multibody Equations of Motion. Computer in Engineering,ASME,Vol. one,1990, pp. 201-207 Linearization, Kinematics, Loop constraint, Mathematics This paper presents as method for obtaining linearized state space representations of open or closed loop miltibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform synbolic linearizations. The resulting syumbolic, linear equations are in terms of the system parameters and the equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of alegraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.
Machining Tolerances Machining Tolerances Product Engineering, May 1957, p. 219 Machining Tolerances Design data sheet. Variations from basic dimensions for different machining operations based on automotive engineering standards. Tolerances may be applied generally to designs for quantity production, with changes as needed to suit individual requirements. Based on engineering standards used by a leading automotive manufacturer.
Maeda, Toshio, Yonekura, Daisuke, Tokuoka, Naochika Toleranced Feature Modeling by Constraint of Degree of Freedom for Assignment of Tolerance CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 121-130 Feature modeling, Degree of freedom, Vector tolerancing, Assignment The purpose of this study is the expression of tolerance information that indicates accuracy and the investigation of operation on CAD. We examined the tolerance zone ISO recommended and classified the relationship between tolerance and feature forth faithful expression following the current tolerancing. The tolerance zone is the set of allowable feature and the behavior of feature is represented by using matrices and constraint equations that limit the degree of freedom (DOF) of feature. And the relationship of features and tolerances were classified by the feature, datum, size and tolerance information as unit. Every behavior of toleranced feature is expressed by the combination of them. Furthermore, in addition to these DOF constraint model, we proposed the functional expression of each manufacturing lot of the current geometrical feature model. The manufacturing group of it consists of the material, manufacturing and functional shape to connect the manufacturing information. We also considered the assignment of tolerances that satisfies the target cost or performance using the manufacturing cost.
Magleby, Spencer P., Jackson, David B. A Standardized Application Interface for Geometric Modelers Product Modeling for Computer-Aided Design and Manufacturing, IFIP, 1991, pp. 227-243 Software interface, Geometric Model, AIS A standardized application interface for geometric modelers allows engineering, design, and manufacturing applications to be developed and implemented independently of a particular geometric modeling system. Issues surrounding the definition of such a specification are explored. Development of an Applicaitons Interface Specification (AIS) was begun by an industrial group and is now proposed as an international standard. A structured approach to designing application programs in the context of the AIS is presented using an assembly tolerance application as an example. The AIS concept can be extgended to diverse areas of a product model including features and dimensioning and tolerancing. Some outstanding issues remain before a large scale commercial implementation will be possible.
Mallik, Asok K. and Sanjay G. Dhande Analysis and Synthesis of Mechanical Error In Path-Generating Linkages Using A Stochastic Approach Mech. Mach. Theory, Vol. 22, No. 2, pp. 115-123, 1987. Linkage Tolerances A stochastic model of the four-bar, path-generating linkage has been made. Tolerances and clearances have been assumed to be random variables. The mechanical error in the path of a coupler point is analyzed for the three-sigma band of confidence level. For a specified path, the mechanical error depends on the selection of either the original or its cognate mechanism. A synthesis procedure to allocate tolerances and clearances on different members and joints of a linkage so as to restrict the output error in the path of the coupler point within specified limits is developed. The synthesis procedure helps the designer in finding out how much the tolerance or clearance on a particular variable is critical in terms of affecting the output error in the path of a coupler point. Results of an illustrative example are given in the paper.
Manocha, Dinesh Solving Polynomial Systems for Curve, Surface and Solid Modeling 2nd ACM Solid Modeling 1993-5 Current geometric and solid modeling systems use semi-algebraic sets for defining the boundaries of solied objects, curves and surfaces, geometric constraints with mating relationship ihn a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many of the geometric operations on the solid boundaries or interacting with geometric constraints is reduced to finding common solutions of the polynomial equations. Current algorithms in the literature based on symbolic, numeric and geometric methods suffer from robustness, accuracy and efficiency problems or are limited to class of problems only. In this paper we present algorithms based on multipolynomial resultants and matrix computations for solving polynomial systems arising in modeling applications. These algorithms are based on the linear algebra formulations of resultants of equations and in many cases there is an elegant relationship between the matrix structures and the geometric formulation. The resulting algorithm involves matrix computations and in the context of floating point computation their numerical accuracy is well understood. We also present techniques to make use of the structure of the resulting algorithm and highlight the performance of the algorithms on boundary computations.
Mansoor, E.M.. Application of Probability to Tolerances Used in Engineering Designs Proc. Instn. Mech. Engrs, Vol 178, Pt 1 No 1, 1963, pp. 29-51 Case Studies, Manufacturing Distributions, RSS, Non-Normal The paper examines the nature of variatons in the dimensions of components produced by manufacturing processes; this examination leads to the development of design formulas for the selection of tolerances based on probability theory. Studies in the dimensional variations of actual assemblies are given and these are compared with the limits predicted from the theory. Manufacturing errors are composed of bias from tolerance zone midpoint as well as process variance.
Marrelli, Richard S. Specifications with Geometric Tolerancing Machine Design, Aug. 22, 1985, pp. 119-122. Geometric Tolerance, Specification Controlling the geometry of part features in addition to their location permits wider manufacturing variations while increasing the number of acceptable parts.
Marrelli, Richard S. New Rules for Dimensioning and Tolerancing Drawings Machine Design, March 11, 1982, pp. 215-218. ANSI standards for engineering drawings are being changed for the first time since 1973. The new standards are an extensive departure from current practice, but in the long run are expected to cut costs by saving drafting time, improving clarity, and increasing commonality with European practice.
Marshall, C.W., Maringer, R.E. Dimensional Instability, an Introduction Pergamon Press, Inc., Chapter 1-5 Quality Assurance This book addresses the fact that little is available concerning general principles of dimensional stability that might provide direction in solving specific engineering problems. It deals primarily with general principles of how dimensional instability can occur and offers general suggestions on how it can be minimized.
Martino, P., Gabriele, G.A. A Review of Tolerance Design TEchniques for Computer Integrated Manufacturing. ASME Computers in Engineering, Vol. 2, 1987,pp. 343-350 Associated with the dimensions of every manufactured part are variations caused by the natural variation of the manufacturing process. Designers deal with this by specifying tolerances, which are allowable variations from the nominal dimensions. Tolerances can have a significant impact on the cost and quality of a product. The selection of tolerances is one of the most difficult aspects of mechanical design. They are often assigned by rules of thumb, experience, trial and error, or tedious and error prone calculations. This paper surveys techniques that have been proposed for the rational and efficient assignment of tolerances.Tolerance design techniques are divided into two categories: tolerance analysis and tolerance sythesis. The paper discusses five tolerance analysis techniques: Monte Carlo simulations, Taylor series method, the quadrature method, tolerance charts, and Bjorke's method. Four tolerance synthesis techniques are also discussed: Michael and Siddall's method, Parkinson's method, Sayed and Kheir's method, and Taguchi's method. The paper goes on to discuss the use of solid models and variational geometry in tolerance design. The paper concludes with some speculation on tolerance design functions in future CIM systems.
Martino, P.M., Gabriele, G. A. Estimating Jacobian and Constraint Matrices in Variational Geometry Systems Failure Prevention and Reliability, ASME Paper DE-Vol. 16, 1989, pp. 79-84. 3-D, Solid Models, Constructive Variational Geometry The use of variational geometry (or parametric programming as it is sometimes referred as) is becoming a growing trend in current computer aided design systems. Currently, its most important application has been in the quick redimensioning of CAD models and the tying of the geometric relationships in the model to engineering relationships used in design. Another important application that has not reached its full potential is in the area of tolerance design. A key operation in variational geometry systems is the estimation of a Jacobian matrix, or a closely related linear program constraint matrix. This paper explains what variational geometry is, how it can be used in redimensioning and tolerance design, and the role of Jacobian and constraint matrices in variational geometry. In this paper we address methods for quickly, and accurately, estimating the required Jacobian and constraint matrices in variational geometry systems.
Martino, P.M., Gabriele, G.A. Application of Variational Geometry to the Analysis of Mechanical Tolerances Failure Prevention and Reliability-1989,ASME Publications,De-Vol. 16,pp. 19-27 The proper selection of tolerances is an important part of mechanical design that can have a significant impact on the cost and quality of the final product. Yet, despite their importance, current techniques for tolerance design are rather primitive and often based on experience and trial and error. Better tolerance design methods have been proposed but are seldom used because of the difficulty in formulating the necessary design equations for practical problems.In this paper we propose a technique for the automatic formulation of the design equations, or design functions, which is based on the use of solid models and variational geometry. A prototype system has been developed which can model conventional and statistical tolerances, and a limited set of geometric tolerances. The prototype system is limited to the modeling of single parts, but can perform both a worst case analysis and a statistical analysis. Results on several simple parts with known characteristics are presented which demonstrate the accuracy of the system and the types of analysis it can perform. The paper concludes with a discussion of extensions to the prototype system to a broader range of geometry and the handling of assemblies.
Martinsen, Kristian Vectorial Tolerancing for All Types of Surfaces Advances in Design Automation, DE-Vol. 65-2, ASME 1993 Tolerance, Deviation, Vector, Co-ordinate systems This article is a systematization of Vectorial Tolerancing in order to show how it can be adapted to all kinds of surfaces on a workpiece. Vectorial Tolerancing provides a clear distinction between the different geometrical features size, form, location, and orientation for each surface. In Vectorial Tolerancing are location and orientation of a surface described with vectors in a Workpiece Co-ordinate System. The tolerance on the location and orientation vectors is described in the Tolerance Co-ordinante System. Only the fixed degrees of freedom are given tolerances on a surface.
Martinsen, Kristian Statistical Process Control Using Vectorial Tolerancing CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.195-210 Vectorial Tolerancing, Milling, Multivariate Statistical Process Control There will always be a certain amount of systematic and random errors in a manufacturing process. Quality loss is kept at minimum when the systematic error is minimal and the process is centered at nominal value. To achieve this, controlling the manufacturing process is vital. In Vectorial Tolerancing surface location and orientation is described with vectors in a Workpiece Co-ordinate System. Vectorial Tolerancing provides as opposed to conventional tolerances, a clear distinction between the size, form, location, and orientation deviations. The magnitude and direction of each feature is known. Deviations on these different features will have different causes and must be controlled separately. This paper shows how orientation and location of a surface can be controlled. Correction to the systematic process errors was done by mirroring the calculated mean values onto the nominal plane, and making a new NC-code for the milling machine with the mirrored planes as new nominal. Mutivariate Statistical Process Control charts were used to keep the process in control. The results showed that Statistical Process Control of surface location and orientation using Vectorial Tolerancing is possible.
Mauritzson, B.H. Cost Cutting with Statistical Tolerances Machine Design, Nov. 25, 1971, pp. 78-81 Statistical Methods Reiterates RSS method and possibility of larger component tolerances for same permissible assembly variation or tolerance.
Mauritzson, B.H. Cost Cutting with Statistical Tolerances Machine Design, Nov. 25, 1971,pp. 78-81 Mating parts may actually measure beyond max-min tolerances, but if they're within statistical limits, the odds are they'll still assemble. Savings resulting from such liberalized tolerances should spark an appraisal of statistical tolerancing. Here's a brief description, with practical numerical examples.
McCallister, Jeff Solid Modeling Investigation HP Property, 6 July 1987, Disc Memory Division
McKim, Paul E. Strategy for Managing Standards CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, Dearborn, Michigan, June 17-19, 1993 The voluntary standards system in the United States faces many issues that must be resolved. Many companies are looking to strategic use of standards as part of their business strategy to enhance competitiveness. This requires easy access to existing standards, and improved standards setting environment, and a commitment to develop and use technically correct standards.The United States voluntary standards development process has the potential to bring the right people together in a forum to develop strategies that will produce standards that meet specific needs.
ASME committees such as Y14, and B89 are developing standards that meet strategic needs. The committees have made progress in developing better, more technically correct standards in the field of dimensional tolerancing and metrology. The committees need to continue this spirit of cooperation as we move toward more internationalization of standards setting.
Meagley, Nelson G. Factors of Safety In Tolerance Specifications Product Engineering, March 1953, pp. 155-159 Tolerance, Safety, Quality Many gaps still exist in the practice of the principles for interchangeable manufacturing. One of these is an accurate evaluation for factors of safety necessary in the specification of tolerances as based on statistical quality control.
Michael, W., and Siddall, J.N. The Optimization Problem With Optimal Tolerance Assignment and Full Acceptance J. of Mechanical Design, ASME, Oct. 1981, Vol 103, pp. 855-860 Optimization, Tolerance Allocation The conventional optimization problem, where the nominal values of the design variables are of interest, is extended to include the optimal allocation of manufacturing tolerances. Thus the tolerances are also treated as design variables. The approach is illustrated by an example using a sequence of increasingly generalized formulation. Finally the solution is provided in general mathematical form. This paper limits the model to a production process with 100 percent acceptability. The method appears to offer a practical technique provided a satisfactory cost function can be defined.
Michael, W., and Siddall, J.N. The Optimal Tolerance Assignment with Less Than Full Acceptance Journal of Mechanical Design, ASME, vol 104, Oct. 1982, pp. 855-860. This paper proposes an approach that integrates the relationship between design and production engineers through the theory of nonlinear optimization. It attempts to cope with the problem of optimally allocating tolerances in a manufacturing process. The upper and lower limits of the random variables of an engineering system are allocated so as to minimize production cost, with allowance for the system scrap percentage. The approach is illustrated by an example, and the general mathematical theory is also provided. An important distinction between the design and the manufacturing scrap is introduced, and the cell technique is utilized to estimate efficiently the system scrap.
Michael, W., Siddall, J.N. The Optimization Problem with Optimal Tolerance Assignment and Full Acceptance ASME Paper, 80-DET-47 The conventional optimization problem , where the nominal values of the design variables are of interest, is extended to include the optimal allocation of manufacturing tolerances. Thus the tolerances are also treated as design variables. The approach is illustrated by an example using a sequence of increasingly geralized formulations. Finally the solution is provided in general mathematical form. This paper limits the model to a production process with 100% acceptability. The method appears to offer a practical technique provided a satisfactory cost function can be defined.
Michalec, Geroge W. The Value of Probabilistic Techniques in Design ASME, Design Technology Transfer, October 5-9, 1974 p.483. Use of probabilistic techniques in the design of components, products, or systems offers a powerful tool for handling inevitable variations of supposed fixed parameter values. Rather than considering manufacturing tolerances and other variables as unavoidable evils, in which the worse-case must be considered as setting the design constraints, probabilistic and statistical treatment of variations in their combining and propagation permits closing in on design parameters and system performance. The result is identification of critical design items, relaxed tolerances (where possible), performance assurance, better understanding of reliability, and ability to make trade-offs to achieve the most optimum design.This writing presents the philosophy of probabilistic techniques. For proper identification of all variates (or errors), a system of classification is described that categorizes them as man and machine caused, modeling deviations, or arising from external uncontrollable and unpredictable sources. The value of probabilistic designing is summarized in a list of benefits derived for the design engineer, systems engineer, manufacturing facility, and operations.
Michelena, Nestor F., Agogino, Alice M. Formal Solution of N-Type Taguchi Parameter Design Problems with Stochastic Noise Factors DE-Vol. 31, Design Theory and Methodology, pp. 13-20 The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The obtained design is robust, i.e., the least sensitive to variations on uncontrollable factors (noise). The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the charactersitic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven, despite the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of contraints allows a problem reduction strategy to be employed, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multi-parametric case must take into account the characteristics of the probability space on which the random parameters are defined.
Mischke, C.R. A Rationale for Mechanical Design to a Reliability Specification ASME Publ. Design Technology Transfer October 5-9, 1974. Probabalistic design Design to a reliability specification is desirable and possible. Reliability is a more meaningful (measurable) index to system performance than the traditional factor of safety. This paper considers the rationale associated with the problem of mechanical design to a reliability specification, beginning with the design criterion, random variable algebra, stimulus parameter, tolerance and manufacturing quantitative considerations, probabilistic materials behavior, significant strength, Marin's fatigue modification factors, finiteness of sample size, and the placing of a lower bound on the reliability associated with the design. The papers entitled "Implementing Mechanical Design to a Reliability Specification" (10) and "Organizing the Computer for Mechanical Design" (11) particularize the rationale presented here in a form useful to the practicing engineer.
Mischke, C.R. Stochastic Methods in Mechanical Design: Part 1: Property Data and Weibull Parameters Failure Prevention and Reliability, ASME Publ. DE-Vol 16 pp. 1-10. 1989. Probabalistic design This is the first paper in a series of four. Stochastic materials data are in short supply, yet a surprising amount is available to those who look, interpret published data, and reduce their own tests. This paper shows published histographic data that was converted to three-parameter Weibull distributional fits, together with relevant goodness-of-fil information.
Mischke, C.R. Stochastic Methods in Mechanical Design: Part 2: Fitting the Weibull Districution to the data Failure Prevention and Reliability, ASME Publ. DE-Vol 16 pp.11-15. 1989. Probabalistic design This second paper of a series of four addresses fitting Weibull distributions to data. Since data may be sparse, many investigators prefere employing transforms that rectify the data string, using a least-squares regression to seek the best fit. In this approach there is some bias introduced with the usual least-squares technique. A method is presented to reduce the bias. It involves recognition of the nature of the cariance at each order-statistic location and an associated compensation in the least-squares method. The three-parameter Weibull fit is optimized to produce the maximum correlation coefficient.
Mischke, C.R. Stochastic Methods in Mechanical Design: Part 3: A Methodology. Failure Prevention and Reliability, ASME Publ. DE-Vol 16 pp.17-20. 1989. Probabalistic design Some products are mass-produced in large quantities. In such circumstances extensive testing can be carried out, prototypes built, and tests made. When production is small, material testing may be limited to simple tension tests or perhaps none at all. How shall the designer proceed in order to achieve a reliability goal or assess a design to see if the goal is realized? This third paper of four in the series, "Stochastic Methods in Mehchanical Design," presents a stochastic methodology to assist the designer in these circumstances.
Mischke, C.R. Stochastic Methods in Mechanical Design: Part 4: Applications Failure Prevention and Reliability, ASME Publ. DE-Vol 16 pp.21-28. 1989. Probabalistic design The three preceding papers, Stochastic Methods in Mechanical Design: Property Data and Weibull Parameters, Fitting the Weibull Distribution to the Data, and A Methodology, present the groundwork for addressing stochastic problems in machinery design in conjunction with a reliability goal coupled with a scarcity of data. This paper illustrates procedures for estimating the reliability of machine elements when yielding, fracture, or distortion are the limiting or active constraints.
Mischke, Charles R. A Caution in the Matter of Confidence Bounds on Measurements ASME Publ. Design Technology Transfer October 5-9, 1974. The classical t-statistic used in placing confidence bounds on the mean of a sample drawn from a Gaussian universe does not include the dispersion resulting from resolution limitations on the method(s) of gathering the statistic al information. Confidence limits applied to statistics of data gatherered in the laboratory must reflect the limited resolution of the instrumentation, even if the data arise from as simple an event as reading a meter face or a linear vernier scale. A new recommended practice is proposed for confidence interval estimation which includes uncertainties due to resolution.
Mischke, Charles R. Implementing Mechanical Design to a reliability Specification ASME Publ. October 5-9, 1974. Design Technology Transfer. Probabalistic design The paper entitled "A Rationale for Mechanical Design Reliability Specification" (1) presented the basis for probabilistic mechanical design. This paper develops the methodology for use by the practicing engineer, including such steps as the determination of the constructive load, determination of endurance strength, determination of stimulus parameter, determination of required geometries, decision checking, and concludes with two examples. The presentation emphasizes methodology when distributions are substantially Gaussian.
Mischke, Charles R. Some Tetative Weibullian Descriptions of the Properties of Steels, Aluminums, and Titaniums Design Engineering Division , 71-Vibr-64, ASME paper, June 1971 Engineers confronted with the necessity of designing to a reliability specification requre statistical descriptions of material properties and computer assistance in the exercise of the design algoritym. This paper presents Weibull statistical parameters of ultimate and yield strength distributions of steels, aluminums, and titaniums based upon information published in the "Metals Handbook." It also presents a stimulus-response potential failure model particularized for circumstances wherein are used Weibull statistical descriptions of stimulus and response potential.
Monte, M. E., and Datseris, P. Optimum Tolerance Selection for Minimum Manufacturing Cost and Other Criteria ASME Paper No. 82-DET-35, 1982 Optimum Tolerancing, Linkages, Optimum tolerance selection for minimum manufacturing cost and other design criteria is studied. Three basic tolerancing problems are presented in this paper, including optimum tolerance selection for a function generating four-bar mechanism. Optimum tolerance selection for minimum manufacturing cost is a significant problem in mechanical design. Tolerance selection itself is important for proper function of a mehanisms: tolerances that are too large may result in poor performance or even failure. Yet, tolerances that are too small may unnecessarily elevate the manufacturing cost. This is called over tolerancing. Heuristic techniques as developed in (23,27) are extended and modified for the solution of the optimum tolerance selection problem. The problem is shown to be of discrete nature and therfore, heuristics, a discrete, combinatorial optimization technique was chosen for the optimization. It is shown that the method circumvents some of the problems that slope dependent techniques may encounter. It is believed that the software package developed, including a users' manual, will aid design engineers in optimum tolerance selection.
Monte, M.E., Datseris P. Optimum Tolerance Selection For Minimum Manufacturing Cost and Other Design Criteria American Society of Mechanical Engineers,82-DET-35 Optimum Tolerancing Optimum tolerance selection for minimum manufacturing cost and other design criteria is studied. Three basic tolerancing problems are presented in this paper, including optimum, tolerance selection for a function generating four-bar mechanism. Optimum tolerance selection for minimum manufacturing cost is a significant problem in mechanical design. Tolerance selection itself is important for proper function of a mechanisms: tolerances that are too large may result in poor performance or even failure. Yet, tolerances that are too small may unnecessarily elevate the manufacturing cost. This is called over tolerancing. Heuristic techniques as developed in (23,27) are extended and modified for the solution of the optimum tolerance selection problem. The problem is shown to be of discrete nature and therefore, heuristics, a discrete, combinatorial optimization technique was chosen for optimization. It is shown that the method circumvents some of the problems that slope dependent techniques may encounter. It is believed that the software package developed, including a users' manual, will aid design engineers in optimum tolerance selection.
Mullins, S.H., Anderson, D.C. A Positioning Algorithm for Mechanical Assemblies with Closed Kinematic Chains in Three Dimensions Purdue university A task common to assembly design systems is the determination of the position and orientation of a set of parts given the mating conditions between them. Two methods for doing this are to position the parts either simultaneously or sequentially. Simultaneous positioning requires the solution of a large set of nonlinear equations, a process which is computationally expensive and subject to convergence problems. Sequential positioning requires that the assembly not contain any closed kinematic chains necessary to the positioning of the parts, meaning that a part must be positioned with respect to parts whose position is completely known. Assemblies with closed kinematic chains that simultaneously determine the position of several parts cannot be positioned sequentially.We present a computerized method for determining part positions in assemblies that contain closed kinematic chains without solving for all the positions simultaneously. The method relies on a two stage solution process, an initial hierarchical positioning phase followed by a final simultaneous position solution. In the first stage, the parts are positioned one at time and the degrees of freedom removed from the part by the mating conditions used for the initial positioning are recorded. The part degrees of freedom not fixed by the initial mating conditions can be used to satisfy other mating conditions considered in the second stage of the solution process. All the parts in the assembly are given an initial position by the end of the initial positioning phase. The final simultaneous positioning phase takes the mating conditions not used in the initial phase and the free part degrees of freedom and solves for the final positions of the parts. Free degrees of freedom, such as occur in mechanisms, can be solved using the solution procedure.
Murphy, R.B. Non-parametric Tolerance Limits p. 581####
Nassef, Ashraf O., Elmaraghy, Hoda A. Allocation of Tolerance Types and Values using Genetic Algorithms Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 147-156 Geometric Tolerancing, Tolerance Synthesis, Genetic Algorithms Parts' features are controlled by specifying appropriate types of tolerances according to the GD&T standards such as ISO & ANSI. Every feature can be controlled by more than one type of tolerance. For example the orientation of a feature can be controlled by specifying perpendicularity to a datum or parallelism to another datum. The whole assembly can have several combinations of tolerance controls. The tolerance selection criteria are satisfying the design functional requirements (constraints on clearances, dimensions, etc.) and keeping the manufacturing cost to a minimum. The selection process is thus a combinatorial optimization problem. Genetic Algorithms (GAs) have been used to solve combinatorial optimization problems and their performance was found to be better than most conventional methods. This paper presents the use of GAs to select the necessary tolerance types. The algorithm developed is extended to include the determination of the best values for every selected tolerance control. The objective of this research is to extend the tolerance synthesis to the selection of tolerance controls and thus increase the robustness of the synthesis process.
Nassef, Ashraf O., ElMaraghy, Holda A. Probabilistic Analysis of Geometric Tolerances CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.211-228 This paper describes a procedure for the statistical analysis of geometric tolerances. The proposed procedure assumes that a manufactured surface lies between two ideal offset surfaces positioned at equal distance from the nominal surface. These surfaces do not represent a tolerance zone, but rather the volume which has the highest probability of containing a point on the generated surface. The generated surface is represented by a set of points, which are assumed to be random variables having a multinormal distribution. Using the generated points, the minimum deviation zone of each geometric deviation in each set is compared with the tolerances specified for the feature. Genetic algorithms are used to conduct these checks to ensure reaching the global optimum value of the minimum deviation zone of each geometric deviation in each set is compared with the tolerances specified for the feature. Genetic algorithms are used to conduct these checks to ensure reaching the global optimum value fo the minimum deviation zone. If the set of points is acceptable the Monte Carlo simulation is updated. To ensure that the probability of rejection of the feature due to the violation of the specified tolerances is calculated with a low variance of error, two methods of variance reduction techniques were used during the simulation. These are, Latin Hypercube Sampling and Antithetic Variates. An example for simulating a cylindrical feature is given at the end of paper and the results of the algorithms using the proposed variance reduction techniques is compared with those using simple Monte Carlo simulation.
Nelson, W. The Truncated Normal Distribution-With Applications to Component Sorting Industrial Quality Control, Nov. 1967, pp. 261-171. Statistical Methods, Non-Normal
Nelson, Wayne The Truncated Normal Distribution-With Applications to Componenet Sorting Industrial Quality Control, November 1967. pp. 261-271. Cited by M.F. Spott's 1983 book. The chief aim of quality control in maintaining statistical control on a manufacturing process is to keep production within specifications. For manufatured items that will be used as componenets in an assembly, specifications must be chosen in designing the assembly to insure that assemblies manufactured from the componenets will perform satisfactorily. Proper choice of component specifications is essential to successful mass production of assemblies that perform within specifications. Statisical methods for determining tolerances on components used in an aassembly are becoming recognized as a valid, useful approach to the design of an assembly. When applicable, a statistical analysis of component tolerances provides more realistic description of the effect of component destributions than does a worst case analysis, which makes the spread in performance of assemblies often look worse than it actually is. This is not meant to imply that a statistical analysis is better than a worst case analysis for all tolerance problems...
Neumann, Alvin g. The New ASME Y14.5M Standard on Dimensioning and Tolerancing Michigan, June 17-19, 1993, CRTD-Vol.27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp.7-18 The current American national standard for dimensioning and tolerancing is the ANSI Y 14.5M, 1982. This document has been under review for the past 11 years. During this period, twenty-three full subcommittee meetings and many working group meetings have been held in various cities around the country. As a result of these meetings a new draft standard has been prepared and will soon be available for public review.Many changes have taken place since the publication of the standard in 1982. There have been major advances in the computerization of product enineering, manufacturing and quality control. There has been an explosive growth in the quest for knowledge in the area of product definition, total quality management and world-class engineering. Around the globe, private organizations, government agencies and universities are studying dimensioning and tolerancing to better understand how to define, verify and manufacture product.
This presentation will explore some of the proposed changes in the new draft document,. We will examine the impact these proposed revisions will have on dimensioning and tolerancing in engineering, manufacturing and quality.
The rationale and logic for some of the revisions will be explained. This will include the coordination and connections with the other related draft standards including the new ASME Y14.5.1 on "Mathematical Definition of Dimensioning and Tolerancing Principles, the ASME Metrology". In our quest for global competitiveness, international papers were presented and decisions were made to more closely align in the international arena. The connection and inter-relationship with the international standards will be discussed.
Nielsen, L.M. Shop-Run Tolerances, Part 2 Product Engineering, June 1948, pp. 141-145. Machine Tolerances Shop-run tolerance data for parts produced on screw machines and general machine shop equipment. Eccentricity and angularity tolerances for parts threaded on screw machines.
Nielsen, L.M. Shop-Run Tolerances, Part 1 Product Engineering, May 1948, pp. 142-144. Manufacturing Tolerances Advantages of shop-run tolerance standards and how they are established. Definitions for shop terms that are often misinterpreted. Tolerance table for iron castings, blanked and pierced parts and parts bent on dies and bending machines.
Nigam, Swami D., Guilford, James D., Turner, Joshua U. Derivation of Generalized Datum Reference Frames for Geometric Tolerance Analysis DE-Vol. 65-2, Advances in Design Automation-Volume 2,ASME 1993 Datum reference frames define coordinate systems for use in determing part compliance with geometric tolerances. A datum reference frame is specified based on the perfect nominal geometry of the part feautres called out as datums. However, the actual computation of a coordinate system frame of reference from the datum callouts becomes quite challenging when the features depart from nominal location, orientation, size, and form. We present a general method for representing datum reference frames (both partial and complete), and for computing a coordinate system from a simulated varianced part and a datum reference frame specificaiton. The method makes use of builit-in construction procedure, and derived or "virtual" geometry, in conjunction with a powerful parts positioning module that simulates the placement fo the varianced part in a fixutre represented by the datum surfaces. The reliance on virtual geometry as an intermediate representation, permits the concise representation of not only the datum reference frame types defined in the standard, but also allows for any arbitrary datum reference frames constructed by the user.
Nikravesh P.E., Gim, G. Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops Advances in Design Automation-ASME DE-Vol.19-3,Proc. of ASME Design Automation Conf., Montreal, Canada,Sept. 17-21, 1989,pp. 27-33 Kinematics, Loop constraint This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is ued to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elemets are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are intially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity tranformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.
Nooss, W. A Numerical Way of Optimizing Chains of Tolerances ASME Paper No. 81-DET-92 June 1989 Numerical optimization is discussed as an aid to cutting costs by making concatenated tolerance ranges of technical parts or components as narrow as necessary and as wide as possible. In an outer optimization loop the computer varies upper and lower limits of the tolerances are varied with the aim of finding the worst case configuration in an inner loop. In practice this configuration will be a statistical one. As soon as none of these combinations violates any functional requirement, the objective function of the outer loop is given a negative sign. The absolute value of the objective function increases as the tolerance ranges increase. The computer searches for the minimum, i.e. for the widest ranges possible. An extremely simple test example is discussed, followed by a brief recapitulation of the optimization technique used.
Norton, Mary R. Development of STANDARDS for ARMY ORDNANCE FINISHES Cited by M.F. Spotts in 1983 book. As used in this paper, "ordnance finishes" are those surfaces produced during the final machining of metal components of ordnance material. For the benifit of the design, production, and inspection units of the Ordnance Department, the relative roughness and smoothness of such surfaces are identified by means of a series of symbos listed in "Drafting Room Regulations of the Ordnance department, U.S. Army," revised April 2, 1941. The following extract from these regulations defines the symbols:...
O'Leary, J.R. A Computer Simulation of a True position Feature Pattern Gage Transactions of the ASME, July 1983, Vol. 105, pp. 280-285Also: ASME Paper No. 81-DE-9 Monte Carlo, Simulation, Geometric Tolerance, Gauge Described in this paper is an approximate technique for the simulation of a mechanical feature pattern gage (a go/no-go gage). The procedure involves the unconstrained minimization of a judiciously constructed response function. The formulation of this function as well as the development of the associated algorithm are presented. Moreover, the technique is demonstrated on an assortment of sample problems.
Ostwald, P.F. Modeling Dimensions and Tolerances by Simulation ASME Paper No.71-DE-5, 1971 Statistical Methods, Monte Carlo The adoption of conventional anlaysis to specify dimensions and manufacturing tolerances is sometimes ill-suited for difficult designs. Shortcomings of the statistical dimensioning techniques are revealed and design using this method is not recommended except for highly controlled situations. This paper formalizes the statistical method of Monte Carlo to the selection of tolerances with true position dimensions as given parameters, and it shows how the technique can be applied once field data are available. Restrictions upon the general usefulness of the simulation method to a class of mechanical designs are provided. A planocentric gear transmission serves as an illustrative example.
Ostwald, P.F., and Huang, J. A Method for Optimal Tolerance Selection J. of Engineering for Industry, ASME, vol 99, Aug. 1977, p. 558-565. Also: ASME Paper No. 76-WA/DE-23. Optimization, Discrete Cost, Zero-one This paper introduces and formalizes a method for specifying independent functional tolerances in an optimal least-cost manner. Previous methods have been thwarted by formulation and computational difficulties presented by nontrivial designs. This method is versatile, submits to a diversity of mechanical problems, and relates the production process and cost to process tolerance in the optimization. This tolerance-specification scheme follows Balas' zero-one algorithm. Generality and efficiency of the method are discussed. Effects of tolerance relaxation on costs are given. Small and large design problems, constructed to satisfy the requirements of the algorithm, show the practical ramifications. The problem is treated with limit, sensitivity, and probability analysis. Widespread adoption of the method through out industry is encouraged.
Ostwald, Philip F. Modeling Dimensions and Tolerances by Simulation ASME Pub. Paper #71-DE-5 The adoption of conventional analysis to specify dimensions and manufacturing tolerances is sometimes illsuited for difficult desings. Shortcomings of the statistical dimensioning technique are revealed and design using this method is not recommended except for ghighly controlled situations. This paper formalizes the statistical method of Monte Carlo to the selection of tolerances with true position dimensions as given aparameters, and it shows how the technique can be applied once filed data are available. Restrictions upon the general usefulness of the simulation method to a class of mechanical designs are provided. A planocentric gear transmission serves as an illustrative example.
Otto, Kevin N., Antonsson, Erik K. Extensions to the Taguchi Method of Product Design DE-Vol. 31, Design Theory and Methodology,ASME 1991,pp. 21-30 The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi's method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (necessity), and designs which involve variables each of which has a range of values any of which might be used (possibility). Tuning paramaters, as a part of the design process, are also introduced into Taguchi's method. The method is also extended to solve design problems with constraint, invoking the methods of constrained optimization. Finally, the Taguchi method uses a factorial method to search the design space, with a confined defintion of an optimal solution. This is compared with other methods of searching the design space and their definition of an optimal solution.
Otto, W.L. Jr., Finnie, Iain Unit Manufacturing Processes CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME A critical factor in the manufacture of products with superior quality at competitive prices is an understanding of the manufacturing system by which the products are produced. The manufacturing system can be broken down into a series of unit processes that in part both physical shape and structure to the product. The unit processes are intimately linked to one another by the fact that the output of one process becomes the input for the next process. The quality of the final product is dependent not only upon the capability of each unit process, but also upon the unit processes working together. Continuous improvement of the manufacturing system involves creation of a physical understanding of each process by itself as well as the influence of each unit process upon subsequent unit processes.A current study by the Manufacturing Studies Board (MSB) of the National Research Council (NRC) is developing by the future process science research needs for unit processs. The information developed by the study is the basis for this presentation, which discusses the concept of a unit manufacturing process and presents a taxonomy of five unit process families that categorizes unit processes by their prime change mechanism: mass change, structure change, phase change, consolidation, and deformation. The research needs of each unit process family are reviewed in terms of several areas of research which are crucial to the improved understanding of unit processes. These areas, know as enabling technologies, offer challenges and opportunities for future advances in processing science. Specific emphasis is given to the connecting role of process precision and metrology among the enabling technologies.
Parkinson, D.B. The Application of Reliability Methods to Tolerancing ASME, Journal of Mechanical Design, July, 1982, Vol. 104. pp. 612-618 2-D Application Reliability Method, Tolerance, Statistics Techniques which have been developed to estimate failure probability in reliability analysis are here applied to problems associated with the tolerances of the dimensions of manufactured components. In particular, a procedure is described which permits, for the general nonlinear problem, the deduction of an estimate of the frequency with which a set of components will fail to assemble together to the design specification. The method may also be used at the design stage to adjust the relative size of tolerances on different dimensions and to permit the relaxation of tolerances to the maximum degree commensurate with a required level of assurance of correct assembly. The calculatons required are relatively simple and do not require the use of simulation techniques on a large digital compute. the application of the method described is illustrated by means of examples.
Parkinson, D.B. Equivalent Linear Limit States Civ. Engng. Syst., Vol. 1, December 1984, p 304-310 Reliability, Structural Safety, Index of Reliability, Limit States, Structural Systems, Modes of Failure The replacement of any limit state function by an equivalent linear function is discussed in detail and it is shown that there are several methods by which such an equivalence may be established. In the case of multiple failure mode problems the definition of fully equivalent linear functions requires the additional consideration of mode correlations. The manner in which this may be carried out is discussed and it is shown that, for most practical cases, a relatively simple analysis is likely to be sufficient to define the set of equivalent linear limit states. With the advantage that the established theory of such linear limit states may then be employed in the majority of reliability analyses.
Parkinson, D.B. Tolerancing of Component Dimensions in CAD Computer-aided Design, Vol. 16, No. 1, January 1984, pp. 25-32. The author's previous work on the application of probabilistic design methods to the particular case of the tolerancing of component dimensions is here extended to the most general case, where there exist many interdependent modes by which the components may fail to assemble to specification. Other aspects of the analysis (particularly that of assume distribution functions) are simplified, with due regard for manufacturing capabilities, with the intention of permitting the development of standard computing procedures (for design and analysis) to be employed in computer-aided design and manufacture.
Parkinson, D.B. Assessment and Optimization of Dimensional Tolerances Computer-Aided Design Volume 17 Number 4 May 1985. pp. 191-199. tolerances, optimize, probabilistic methods, CAD The author's previous work on the application of probabilistic design methods to the tolerancing of component dimensions in CAD is here extended to the development of a group of computer programs in Fortran which will enable the adjustment of tolerances to minimize the risk of rejection or malfunction, on assembly, or alternatively, given certain relative cost data, to optimize the tolerances (and/or dimensions where relevant), for minimum overall cost.
Parkinson, D.B. First-order reliability analysis employing translation systems Eng. Struct., Vol 1, October, 1978, p. 31-40. Empirical Distributions, Moments, Adv. Statistical Methods (other) A reliability analysis is described in which sample moments are used to transform the design parameters to a space in which they have a multivariate normal distribution. The technique can be rendered quite simple by the use of tabulated data. Th analysis then proceeds to generate failure risk estimates based on regions of estimated probability content or on statistical tolerance regions in the normal parameter space. A particularly useful Bayesian analysis based on the multivariate normal distribution is also described. Assumes normal distributions, and find probability of assembly non-conforming fraction by assuming normality. Useful for non-linear assembly functions.
Parkinson, D.B. Solution for Second Moment Reliability Index Journal of Engineering Mechanics Division, Oct. 1978, pp. 1267-1275 Reliability Index, Reliability Method, Statistics
Parkinson, D.B. Reliability Indices Employing Measures of Curvature Reliability Engineering 6 (1983) p. 153-179 A measure of average curvature of an n-variate failure surface is considered and shown to be of use in defining a comparable reliability index, as a combination of the curvature measure with a location parameter (Hasofer-Lind index). The form of this combination is derived by consideration of the probability content of offset hyperspheres in the space of the design variables. The resulting reliability index displays comparability (i.e. varies with the shape and location of the failure surface) whilst requiring much less computational effort than generalized indices based on the integration of density functions over the failure region or its complement. It also provides a means of defining an equivalent linear limit state surface.
Parkinson, D. B. Four-Moment Reliability Analysis for Static and Time-Dependent Problems Reliability Engineering I (1980) 29-42. Empirical Distributions, Moments, Adv Stat (other) A reliability analysis is described in which the sample moments of the design variables are used to define the first four moments of a function representing the condition of failure, or malfunction, in the space of the design variables. These moments are then employed in transforming the failure function to a space of a normal random variable so permitting an estimate of failure probability t be made. A four-moment Reliability indes is defined and some examples of the technique are provided. The extension of the technique to stationary stochastic processes, for time-dependent problem, is discussed, and some alternative transformation procedures are compared.
Parkinson, D.B. Quadratic Reliability Indices To be published in "Reliability Engineering" Limit state models based on multi-dimensional rotational paraboloids and hyperboloids are described and approximate closed form solutions obtained for the associated Failure Probaility and corresponding Reliability Index. The solutions presented depend only on the number of variables, minimum distance of the limit state surface from the origin and mean curvature at the design point, in a standard Normal space. These results extend the range of analytic solutions for Reliability Indices, from linear and spherical surfaces, to include these rotational quadratics, and so permit a wider choice of limit state models.
Parks, Jean M. Holistic Appraoch and Advanced Techniques & Tools for Tolerance Analysis & Synthesis CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.301-312 Tolerance Analysis, Tolerance Synthesis, Toleranicng. Variability Analysis, Reliability, Sensitivity Analysis, Contribution Analysis, Latitude, Design Methodology, Robust Design, Optimization, Taguchi Methods, Probabilitstic Design, Probability Distributions, Variability Propagation This paper presents a holistic Methodology on Design and the associated Toolset developed to enable its implementability; the approach is based on comprehensively addressing effects of Variability. In Design, Tolerancing for Fit and for Function is one of the most crucial and interlinked efforts during technology and product development. Tolerancing for Function, especially, has been little addressed, and at best rudimentarily, by the engineering community. This is because to do so appropriately and adequatley requires local and global approaches to enable decision making of nominals and tolerances form the piece part level to ultimately the system level. For this, one not only needs techniques and tools for properly conducting Contribution Analysis and Variabililty Analysis for any given set of input variabilities and relationship, but one must be able to quantitatively propagate the thousands of variabilities to a few resulting performance variabilities. Lacking these capabilites, as a user-friendly computaitonal toolset that is "complete," has been the fundamental level barrier to holistic Tolerancing. This has now been provided by our breakthrough Toolset. Quantification and decision making require yet more; the Methodology addresses those and putting relevant Design Practices in context. The Methodology has been implemented.
Patel, A. M. Computer-Aided Assignment of Manufacturing Tolerances Proc. of the 17th Design Automation Conference, ASME, Minneapolis, MN., June 1980, pp. 129-133 Tolerance, Tolerance Allocation
Pegna, Joseph, Guo, Chi Computational Metrology of the Circle and Applications to Precision Machinery CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on CAT, Japan, April 5-6, 1995, pp. 313-324 The work presented in this paper derives from the design of a position sensing interferometer, in which circular fringe patterns are automatically analyzed by a computer vision system. Central to this process is a circle fitting problem in the sense of least L-infinity norm, also known as Chebichev or MinMax fit. The problem at hand can be formulated as follows: Given a set of points in the plane, find the pair of concentric circles with minimum radial gap enclosing all the points.The solution to this problem is elegantly given by common computational geometry tools, indeed the center of such a circels is necessarily a vertex of the Nearest Point Voronoi Diagram (NVD), a vertex of the Farthest Point Voronoi Diagram (FVD), or an intersention of edges from both diagrams.
An algorithm for determining the Chebichev circular fit is presented and illustrated on the basis of that observation. Applications and potential extensions of this method to soft gauging and image metrology will also be discussed.
Peters, J. Tolerancing the Components of an Assembly for Minimum Cost Journal of Engineering for Industry, ASME, Aug., 1970, pp. 677-682. Statistical Methods, Cost, Allocation Based on the contributions of the work of A. Gladman and of R. Cave, a comprehensive study is made of the different possiblities of distributing the tolerances between the components of an assembly in order to achieve the minimum cost requirement, taking into account the process variability and th ecosts of the components. Sample tables and graphs value are presented.
Pheil, George D. Probability Applied To Assembly Fits Product Engineering, Nov. 25, 1957, pp. 88-89. Statistics, Tolerance Production runs of assemblies call for statistical analysis of part tolerances. But with shorter runs, mathematical probability provides a simpler method that's just as positive.
Placek, Chester Mechanical Tolerancing Workshop Quality,December 1989,pp. 16-17 Report identifies research opportunities in mechanical tolerancing, lists top research and education needs.
Porchet, Michel, Zhang, Genbao Incorporating Geometrical Tolerances and Processing Inaccuracy into Dimensionsing and Tolerancing DE-Vol. 44-2, Advances in Design Automation-volume 2,ASME 1992, pp. 151-156. The geometrical tolerances and the processing inaccuracy have a great influence on dimensioning and tolerancing. However, it is quite difficult to integrate them into dimensioning and tolerancing. This paper presents a way in which geometrical tolerances and process inaccuracy can be taken into consideration. The distance between two surfaces is defined clearly. The relationship between distnace tolerances, form errors and position errors is established. Different sources influencing a distance precision have been investigated. A model where geometrical tolerances and processing inaccuracy can be dealt with is proposed. This model closely approaches practice.
Portman, V.T., Shuster, V.G. Computerized Synthesis of a Theoretical Model of a Three-Plane Dimension Chain Soviet Engineering Research, Vol. 7, No. 8,pp. 57-60
Portman, Vladimir T. Higher order approximation in accuracy computations for complex mechanical systems. Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 197-212 machine kinematics, accuracy, higher order approximation Second and higher order approximations for machine accuracy calculations are necessary when the precision of the error estimation obtained on the basis of the first order approximations is poor or when first order approximations are not influencing the output accuracy of machines, in particular when estimating the machine tool set-up errors or when calculating the influence of machine setting displacements. In the case of machining operations, the second order approximation for the normal position error of the real surface relatively to the nominal one is shown to depend on the second fundamental form of the nominal surface. As a real world application, the setting of a grinding machine for a crowned comic surface grinding operation is calculated.
Portman, Vladimir T., Weill, Roland D. Modelling Spatial Dimensional Chains for CAD/CAM Applications CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 73-92 Tolerancing, Dimensional chain, Compensation, Accuracy evalaluation, Accuracy optimization. An analytical and compuational procedure for modeling spatial dimensional chains (DC) is based on the kinematic interpretation of the links* of the DC and their errors. The goal of the investigation is to assess the accuracy of the closing link of the DC. The three-stage procedure successively models the nominal DC, the actual DC with positional errors of the links, and the metrological estimations of the accuracy. The latter stage is undertaken using metrological models of accuracy, which brings the accuracy estimation into conformity with a nominal form of the boundaries of the DC's closing link and the relative positions of the boundaries. The theoretical results apply to important design problems, such as evaluating closing tolerances, choosing compensating links, and structural optimization of the DC according to accuracy criteria. As an example, calculation of the spatial DC between two perpendicular bores and in relation with the accuracy of the form-shaping system of a machine tool for machining these bores is considered.
Ragon, Dan and Al Spencer John Deere Assembly Variation of Crawler Track Chain/Shoe Assembly SAE Technical Paper No. 881243, 1988 Monte Carlo, Simulation, Tolerance, Crawler Track Chain/Shoe A computer simulation method of assembly parts of a mechanical assembly has been developed by Deere & Company to statistically analyze tolerance stack-up of comlex two-dimensional and three-dimensional assemblies. It is called Assembly Variation Simulation System (AVSS). AVSS offes a way to predict the impact of design tolerance and manufacturing variation on assembly quality of a John Deere Crawler Track Chain/Shoe Assembly. This method identified both the amount of variation relative to specifications and the percent contribution of the major contributors to the variation. In addition, AVSS has been used on a variety of other assembly applications. It is a proprietary system presently being marketed.
Ramberg, S., Dudewicz, E.J., Tadikamalla, P.R., Mykytka, E.F. A Probability Distribution and its Uses in Fitting Data Technometrics, Vol. 21, No.2, May 1979, Ref. from Shapiro & Gross-Chapter 7. Empirical Distributions, Moments A four-parameter probability distribution, which includes a wide variety of curve shapes, is presented. Because of the flexibility, generality, and simplicity of the distribution, it is useful in the representation of data when the underlying model is unknown. A table based on the first four moments, which simplifies parameter estimation, is given. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies and Monte Carlo sampling studies of the robustness of statistical procedures. This is the Lambda distribution and is described by Gross & Shapiro.
Ranyak, Paul S., Fridshal, Richard Features for Tolerancing a Solid Model Research Report Solid Model, Tolerance This paper is based upon two prototype development projects: the first project implemented a Dimension and Tolerance (D&T) modeler in conjunction with a solid modeler, and the second project added process planning feature definitions to the first configuration.Solid modeling is an unambiguous way to define the nominal part: however, more information is necessary to complete the variational model, a model which represents all allowable variations for the part. Dimensions and notes on drawings have veen the traditional way fo describing the variational model, but their meaning is usually subjective and difficult for a computer to interpret.
Three types of entities have been difined for the model: features, tolerances, and datum reference frames. Discussed in this paper are the identified feature and tolerance classes and how they may be used as the first level of a hierarchical feature model.
The feature classes for tolerancing focus on the primitive elements of the part. The rule used for defining these classes is that each tolerancable feature must have only one inherent tolerance value in each of the tolerancing categories. These primitive features are components of the more commonly used complex feature classes, such as slots or blind holes. The second development project illustrated this capability by extracting the specific tolerances for process planning features.
Rao, S.S., Gavane, S.S. Analysis and Synthesis of Mechanical Error in Cam-Follower Systems ASME Paper 80-DET-22, 1980, pp. 1-11. Tolerance Analysis & Synthesis: Can-follower, Kinematics, Dynamics A method of evaluating the mechanical error in the kinematic and dynamic response of cam-follower systems is presented based on probability principles. The error is analyzed for the three-sigma band of confidence level. A synthesis procedure, using nonlinear programming techniques, of distributing tolerances on geometrical and other system parameters is discuussed. The objective on the synthesis problems is to minimize a measure of the manufacturing cost for specified maximum allowable error in the kinematic or dynamic response of the cam-follower system. The application of anlaysis and synthesis procedures is demonstrated with reference to a disc cam with translating roller follower.
Requicha, Aristides A.G. Mathematical meaning and Computiational Representation of Tolerance Specifications CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,Dearborn, Michigan, June 17-19, 1993,pp. 61-68 The meaning of tolerance specifications must be defined mathematically, to avoid ambiguous interpretations and to provide a sound basis for assessing the correctness of measurement techniques and algorithms. This paper surveys critically the various approaches to tolerancing proposed to date. It classifies these approaches at several levels. Syntactically, it distinguishes between dimensional limits and geometric tolerance specifications; semantically, it considers shape and pose (location and orientation) parameterization versus tolerance zones; and it contrasts worst-case, deterministic approaches with their statistical (stochastic) counterparts.The principles of the offset zone theory of tolerancing, proposed over a decade ago, are presented, to show that there are general approaches, with firm mathematical foundations, which can capture the meaning of geometric tolerances.
To support automatic tolerance analysis and other important applications, tolerances must be associated with surfaces and other geometric entities within unambiguous computer representations for mechanical parts (i.e., solid models). Tolerances attached to graphic entities such as lines in a computer-generated drawing do not provide a suitable basis for supporting applications that go much beyond drafting. The paper closes by showing that relatively simple data structures can be used to computationally represent geometric tolerances. These structures can be associated with both of the two most common solid modeling schemes, boundary representation and constructive solid geometry (CSG).
Requicha, Aristides A.G. Representation of Geometric Features, Tolerances and Attributes in Solid Modelers Based on Constructive Solid Geometry IEEE Journal of Robotics and Automation, RA-2, No.3, pp.156-166, Sept. 1986
Requicha, Aristides A.G. Representation of Tolerances in Solid Modeling: Issues and Alternative Approaches Solid Modeling by Computers: from Theory to Applications, 1984, pp. 3-22. The lack of facilities for representing tolerances and related information is a major deficiency of contemporary solid modelers. This paper discusses the semantics of tolerancing for mechanical parts, with particular emphasis on the problems that arise when the features of physical objects cannot be assumed to have perfect form (e.g., when a machined hole is not perfectly cylindrical). Alternative theoretical approaches are proposed, and the representational implications of each approach are explored.
Requicha, Aristides A.G. Toward a Theory of Geometric Tolerancing The International Journal of Robotics Research, Vol.2, No.4, Winter 1983, pp. 45-60 3-D, Solid Modeling, Tolerance Theory Manual drafting is rapindly being replaced by modern, computerized systems for defining the geometry of mechanical parts and assemblies, and a new generation of powerful systems, called geometric (solid) modeling systems (GMSs), is entering industrial use. Solid models are beginning to play an important role in off-line robot programming, model driven vision, and other industrial robotic applications.A major deficiency of current GMSs is their lack of facilities for specifying tolerancing information, which is essential for design analysis, process planning, assembly planning for tightly toleranced components, and other aplications of solid modeling. This paper proposes a mathematical theory of tolerancing that fomalizes and generalizes current practices and is a suitable basis for incorporating tolerances into GMSs.
Tolerance specification in the proposed theory is a of geometric constraints on an object's surface features, which are two-dimensional subsets of the object's boundary. An object is in tolerance if its surface features lie within tolerance zones, whcih are regions of space constructed by offsetting (expanding or shrinking) the object's nominal boundaries.
Requicha, Aristides A.G, Voelcker, H.B. Solid Modeling: A Historical Summary and Contemporary Assessment March 1982,pp. 9-24 Solid Model, Review A new generation of industrial geometry systems is emerging based on teh technology of the 1970's. The generations of the eighties and nineties will require more research.
Rice, W.B. Setting Tolerances Scientifically Mechanical Engineering, ASME, Dec. 1944, pp. 801-803 Statistical Methods Proposes RSS tolerance analysis method.
Rivest, Louis, Fortin, Clement Tolerance Modeling for 3D Analysis Presenting a Kinematic Formulation Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing,Cachan,France,April 27-28,1993,pp. 51-74 Tolerancing, Tolerance modeling, Tolerance analysis, Tolerance transfer, Tolerancing standards This paper presents a kinematic approach for tolerance modeling which enables the solution of tridimensional tolerance transfer problems. The proposed kinematic approach allows the modeling of the complete set of data applicable to both geometrical and dimensional tolerances. This includes the topological link imposed by a tolerance between a toleranced feature and the datum features, the datum precedence, the effects of modifiers and of course the tolerance zone itself. The modeling of tolerance zones by a kinematic approach makes possible the analysis fo the complex interactions between a part features linked by various toelrances. The potential of this approach is showed by the description of a tridimensional tolerance transfer strategy based on the kinematic model.
Rivest, Louis, Fortin, Clement, Morel, Claude Tolerancing a solid Model With a Kinematic Formulation Department of Mechanical Engineering, Quebec, Canada. The three-dimensional analysis of tolerances is one of the critical functional requirements of solid modeling systems which is most lacking at the present time. The 3D tolerance analysis, when carried out by hand, is most difficult and sometimes impossible to realize when applied in 3D for complicated geometries. A kinematic formulation to the full 3D dimensional and geometrical tolerance modeling particularly applied to the manufacturing engineering aspects is proposed. The scheme represents all tolerances with a kinematic chain within a technotopological model, which is compatible with existing standards such as ANSI Y14.5M. The semantics of tolerances is respected as tolerances are automatically interpreted to yield tolerances zones while their meaning and syntax are validated. The concept has been implemented on the PADL-2 solid modeler but could be easily applied to other exact solid modelers. Toelrance induced topological links are added to the solid modeler representation and allow the user to visualize the exact dimension and shape of the resulting tolerance zone. The concept can be applied to manipulate multiple tolerances in order to solve 3D tolerance transfer problems.
Ross, Sheldon M. Introduction to Probability and Statistics for Engineers and Scientists John Wiley & Sons,Chapter 12,1987
Rossignac, Jaroslaw R. Constraints in Constructive Solid Geometry Proceedings of the 1986 Workshop on 3D Interactive Graphics, U. Of N. Carolina, Oct. 1986,pp. 93-129 Solid modelling, quadric surfaces, constraints, rigid motions, computer graphics, CSG, Solid Model The succes of solid modelling in industrial design depends on facilities for specifying and editing parameterized models of solids through user-friendly interaction with a graphical front-end. Systems based on a dual representation, which combines Constructive Solid Geometry (CSG) and Boundar representation (BRep), seem most suitable for modelling mechanical parts. Typically they accept a CSG-compatible input (Boolean combinations of solid primitives) and offer facilities for parameterizing and editing part-definitions. The user need not specify the topology of the boundary, but often has to solve three-dimensional trignometric problems to compute the parameters of rigid motions that specify the positions of primitive solids.
Roy, U., Mantooth, K., Pollard, M.D., Liu, C.R. Tolerance Representation Scheme in solid Model: Part II Advances in Design Automation-1989,Vol. 1,ASME Publ. DE-Vol. 19-1,ASME Design Automation Conf., Montreal, Sept. 1989 Tolerance representation in a CAD data stucture demands a user interactive environment which enables the user to input the tolerance information in both the unevaluated (CSG) and in the evaluated (B-Rep) databases (4). This requires an effective linking mechanism between the CSG and the B-Rep data models at each stage of the object development. This has been achieved through the development of a reference face list. Tolerance information has been attached with this face list as "constraint nodes," which are formed and updated after each "set operation." Several functions have also been develped to retrieve essential information from the data structure in order to answer various queries.
Roy, Uptal, Fang, Ying-che Tolerance Representation Scheme for 3-Dimensional Product in Object Oriented Programming Environment CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp. 93-120 The representation and analysis of geometric tolerance information is an integral part of the development of an "informationally complete" product model. Since the tolerance specification captures the design intent, an effective representation scheme must be adopted to facilitate this representation. The objective of this study is to develop a new representation scheme which is not only able to represent geometrical and technological information, but is also capable of inputting, retrieving and manipulating data very effectively. A new hybird CSG/B-rept scheme in an Object Oriented Programming (OOP) environment has been proposed in this paper. It also reports a successful implementation of a prototype of the proposed scheme in the Wisdom's Concept Modeller [1]. In this new representation scheme, each of part's tolerance, functional requirement, cost function, machining process,etc. is regarded as a class with its attributes. Several OOP's concepts, such as inheritance, tree referencing, dependency backtracking and demand driven processing has been fully exploited to make the representation scheme effective.
Sakurai, Hiroshi, Gossard, David C. Solid Model Input Through Orthographic Views Computer Graphics,Volume 17,Number 3,July 1983,pp. 243-252 Solid Model This paper describes the results of basic studies on procedures for creating solid models of component geometry from two-dimensional orthographic projections. An interactive graphic program was developed to allow the input of three orthographic views of a component geometry by digitizing from a drawing. The views may contain straight lines and circular arcs, solid or dashed. No restrictions are placed on the order or direction of lines and arcs in any view. Using an extension of the Wesley-Markowski procedure, the program constructs a three-dimensional solid model of the object. When the projections are ambiguous, multiple solid models are produced. The solid model may contain planar, cylindrical, conical, spherical and toroidal surfaces. Topological information of the solid model is sotred in a winged edge sturcture. Geometric information is stored as vertex coordinates and surface equations.
Salomons, O.W., Poerink, H.J. Jonge, Slooten, F. van, Houten, F.J.A.M., van, Kals, H.J.J. A Computer Aided Tolerancing Tool based on Kinematic Analogies CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Yokyo, Japan,April 5-6,1995,pp. 53-72 Tolerance representation, Tolerance specification, Tolerance analysis A computer aided tolerancing tool is presented that assists the designer in functional tolerance specification. The theorectical concepts for subsequent tolerance analysis are also provided. The computer aided tolerancing tool is part of a feature based object oriented (re)-design support system, called FROOM. FROOM's assembly modelling capabilities provide basic information for funciotnal tolerance specificaiton. Assembly constraints are satisfied by means of degrees of freedom (DOF) analysis. This method is based on the use of kinematic analogies. The rotations and translations (macro-DOF's) that components are allowed to have, are inferred using this technique. The tolerance representation in FROOM is based on the TTRS method, by Clement et al., which is also based on kinematic analosgies. In this method, the small displacements that are allowed in the tolerance zone can be described by a tolerance torsor are referred to as micro-DOF's. For tolerance analysis, the torsor approach offers a mathematcially correct description of tolerance zones, although a lot of equations are genterated. These are reduced by applying a kind of degrees of freedom analysis considering both the macro-DOF's and the micro DOF's (tolerances).
Sandquist, W.L., Enrick, N.L. Practical Ways to Apply Statistical Tolerancing Product Engineering, May 27, 1963. pp. 47-50. Statistical Methods, RSS Presents basic RSS method, several good (easy) examples of linear assemblies.
Sayed, Salah E.Y., and Naim A. Kheir An Efficient Technique for Minimum-Cost Tolerance Assignment Simulation, April 1985, p. 189-195. A computer-aided design technique to assign tolerances to system components is introduced. The essence of the method is to accurately represent the allowable margins of the system's perofrmance functions in the percent deviation parameter space (PDPS) and to determine the point in the PDPS corresponding to the most efficient tolerance assignment. The criteria used involve minimum cost-tolerance assignments.
The technique presented solves the tolerance assignment problem for a significant class of systms for which one hundred percent yield is sought and whose components are statistically independent. The most salient feature of this technique is the simple and straightforward manner in which the "curse of dimensionality" associated with tolerance assignment problems is overcome.
A computer program has been developed; it accepts a system's topology, nominal compnent values, a figure-of-merit for ysystem performance, and information relating a component cost to its tolerance. The outpout of the program includes the set of component tolerances that will produce the least expensive design with a hundred percent yeyeidld. As an example, a rather complex low pass filter has ben simulated to solve the tolerance assignment problem. Computation time is about seven seconds on the Univac-1100 computer.
Schade, George R. A Probabilistic Model Of Adjustment Of Four-Bar Mechanisms ASME paper 82-DET-43 Linkage Tolerances A probabilistic model is presented to predict the statistical properties of coupler-point position of a four-bar mechanism given that one or two component dimensions have been adjusted. Several adjustment strategies are presented. Models are verified by Monte Carlo techniques.
Schade, R. Probabilistic Models in Computer Automated Slider-Crank Function Generator Design ASME paper 80-DET-48 Design Automation, Statistics, Slider-crank Using deterministic algebraic techniques, it is possible to synthesize function generator mechanisms which can produce extremely small structural error. However, due to normal variations in dimensions inherent in the manufacture of the components of the mechanism, there may be an extremely low probability of assembling a mechanism which approaches the accuracy predicted by a deterministic representation of the mechanism. This paper presents a probabilistic model of the slider-crank function generator, and a method of optimization of this model. Mechanisms are optimized on the basis of both deterministic and probabilistic models, and the resulting optima are compared by computer simulated production. If the statistical properties of the production techniques are known, it is possible to significantly increase the production yield of acceptable mechanisms by using the probabilistic model for design optimization.
Schall, Ronald C., German, Dennis G. The Impact of Tolerancing on Gage Repeatability and Reproducibility Studies CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME,pp. 113-118 Tolerancing certainly has an immense impact on a Gage R&R study. This paper will explain what a gage R&R is, how and why it is performed. We will then illustrate the impact of tightening tolerances on performing and passing a gage R&R on the manufacturing floor.This paper will illustrate what type of gage repeatability is required as the tolerance tightens. We will also give estimates of the cost impact associated with tighter tolerancing. Keep in mind this cost impact is from a gaging viewpoint only, there will also be increased cost from the machine tool aspect.
The important factor is that the engineer be aware of these issues when designing and tolerancing a part.
Schneider, E.J. 2. Roundness Measurement, Part Two-The Proposed Standard Mechanical Engineering, Nov. 1969, pp. 36-40 True Position, Tolerancing, GDT, Roundness The demand for greater accuracy and the development of new more realistic means of measuring roundness has, with the past years, pointed up the need for an American Standard. That Standard is now "in the works" and here's a report on the progress made.
Schneider, Fabien, Vincent, Joil Remy The Assembly Function Applied to the Definition, Control and Manufacture of Mechanical Components Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 129-146 Dimensioning, Tolerancing, Mechanical, Technical Drawing, Manufacturing, Adjusting In this paper, we present several new elements for the geometric tridimensional definition of mechanical assembly components. We study the assembly condition and its effect on definition, control and manufacturing organization. Our analysis takes into account two essential facts: how the mechanism functions and how it is produced. We show why it is necessary to propose a model for the behaviour and manufacture of a mechanism in order to optimize its tolerancing.
Schwint, W. Analytical Geometry Leads to Accurate Gear Center Coordinates. Product Engineering, April 12, 1965, pp. 99-101 Case Studies, Gear Backlash, Applications, General Converting center distances to rectangular coordinates seems easy. Use trig, you'd say. But ever-so-slight errors in finding angles cause excessive backlash.
Serrano, D., Gossard, D. Constraint Management in Conceptual Design KBES in Engineering: Planning and Design,pp. 211-224 Design is constraint-oriented; much of the design process involves the recognition, formulation and satisfaction of constraints. Constraints are continually being added, deleted and modified throughout the development of a new product. The management of these constraints throughout the evolving design is a non-trivial task.Effective tools for constraint mangagement will be of great importance in knowledge-based for conceptual design. They will provide designer with assistance druing the early stages of design and will help close the gap between novice and experienced designer.
This paper presents methods for maintaining consistency in systems of constraints. Techniques are presented for the evalutation of constraint networks, the detection of over--and underconstrained systems of constraints, as well as identification and correction of redundant and conflicting constraints.
Serrano, D., Gossard, D.C. Combining Mathematical Models with Geometric Models in CAE Systems Computers in Engineering,ASME,Vol.1,1986,pp.277-284 Solid model, CAE Geometry in mathematics are generic to virtually all engineering decision making activities. Throughout the design process engineers make numerous simple "first order" calcuations in order to determine suitable values for geometric design parameters. A prototype system, called MATHPAK, has been developed. MATHPAK is an interactive software package which integrates mathematical models (consisting of sets of nonlinear algebraic equations, associated variables, units and status) with solid geometric models. The system allows the user to define variables of interest, create sets of equations in those variables and to link the resulting mathematical model to a solid geometric model via its dimensions. Subsequent changes in the mathematical model alter the geometric model and vice versa. This paper presents the solution to a key problem encountered in the development of the system: automating the solution of the equation sets. Graph traversal techniques were used to determine the solution sequence. This and other solutions to problems encountered will be presented. Extensions to other applications, limitations and directions for future work are also discussed.
Sethi, Mani, Guilford, James, Turner, Joshua Worst Case Tolerance Analysis of Daughter Card Assembly, Draft Jume 20, 1991 Designers are increasingly finding the need for an automated tolerance analysis package which follows the standards for tolerancing. Unfortunately, most of the commercial packages available make simplifying assumptions for the conventional plus-minus tolerances and do not support geometric tolerancing at all. GEOS is an automated tolerance analysis package which tries to overcome these shortcomings. It is based on variational modeling and feasibility space approaches. This report presents the results for the worst case tolerance analysis done ona real-life assembly using GEOS. For this no special models had to be created as GEOS can accept the 3-D CAD model directly. The models contained both conventional plus-minus tolerances as well as geometric tolerances. The GEOS front-end was used to define the assembly relations, design function, and analysis parameters.
Shah, Jami J., Miller, David W. A Structure for Supporting Geometric Tolerances in Product Definition Systems for CIM Manufacturing Review, ASME,Vol. 3, No.1, March, 1990 Geometric Tolerance, CAD, CIM, CAM The basic components of product definition data needed in CIM includes the following: a solid model to define the nominal geometry, a feature model to capture the semantics of the geometry, and variational attributes to specify tolerances and finish. This paper outlines such a part defintion system with particular emphasis being on the design and implementation of a data structure for information needed to support geometric tolerance frames, zone and material modifiers, and datum reference frames. Associations among tolerances, geometric entities, features, feature atttributes, and relationships are incorporated in this structure. The system is extendable to new tolerance classes without any changes to the code. The structure also permits incorporation of rules and validation procedures.
Shah, Jami J., Rogers, Mary T., Sreevalsan, Palat C., Hsiao, David W., Mathew, Abraham, Bhatnagar, Anant, Liou, Bongee B., Miller, David W. The A.S.U. Features Testbed: An Overview Computer in Engineering, ASME,Vol. one, 1990 The A.S.U. Features Testbed is a collection of modules for design, documentation, and evaluation of mechanical parts. The Testbed is organized into two shells, one for design and the other for mapping and applications. With the addition of feature libraries, design rules, and application knowledge bases, user-organizations can customize and application knowledge bases, user-organizations can customize the Testbed shells for their own needs. The Testbed allows one to integrate features, dimension & tolerances, geometry, topology, and design rules into a unified product description. The mapping shell facilitates the implementation of applications, such as manufacturability evaluation, GT coding, stress analysis, etc. Design, analysis, evaluation, and manufacturing planning can be performed concurrently. The Testbed is designed to conduct experiments related to feature concepts, definition methods, validation problems, design environment, life-cycle analysis, and so on. The Testbed represents about 10 person years of efforts and is still growing in a modular fashion. We have written about each constituent modeler of the Testbed in several prior papers; this paper gives an overview of the entire system.
Shah, Jami J., Zhang, Bing-Chun Attributed Graph Model For Geometric Tolerancing DE-Vol.44-2,Advances in Design Automation-Volume 2,ASME 1992,pp. 133-140 The development of a face-based attributed graph structure for modeling geometric tolerances is described here. The structure, designated as the DTF graph, provides an integrated view of the dimensioning scheme, dimensions, tolerances, features, and datums. In the current versionof the DTF model, all ANSI Y14.5M tolerance classes are supported, except profile tolerances. Edge related tolerances (straightness, circularity) are supported by derived face intersecitons. Other tolerances, and datum reference frames, are supported as face attributes or attributes of the DTF graph. The tolerance model is compatible with commonly used hybrid CSG-Brep solid modelers and has the property of uniqueness for any dimensioning scheme. Applications of the DTF Graph include: detection of over and under-constrained dimensions, automatic re-dimensioning if the designer changes the dimensioning scheme, and automatic discovery of dimension-tolerance stack-up loops.
Shalon, Dari, Gossard, David, Ulrich, Karl, Fitzpatrick, David Representing Geometric Viariations in Complex Structural Assemblies on CAD Systems DE-Vol. 44-2,Advances in Design Automation-Volume 2,ASME 1992,pp. 121-132 In previous airplane programs, Boeing identified interferences and misalignments between airplane parts as the two largest causes of engineering changes. Boeing is currently designing the 777 with a state-of-the-art solid modeling system. While the system is capable of detecting interferences and misalignments between ideally-sized and ideally-located solid modes, it cannot model the effects of variation in the size, shape an location of parts and tools. This paper presents an initial, novel framework for modeling these variations called Indexed Pre-Assembly with Variation (IPAV).The main points made in this paper are:
-Variations in both parts and tools should be modeled in exactly the same way.
-Mating features of parts and tools can be represented in the solid models with local index-point coordinate systems.
-Linking the mating index-point coordinate systems enables the positioning of the solid models in an assembly.
-The order in which the index-point coordinate systems are linked corresponds to the planned assembly sequence.
-The effects of size, shape and location variations on an assembly can be modeled by manipulating the index-point coordinate systems within the individual solid models.
Shapiro, S. S., and A. J. Gross Statistical Modelling Techniques Marcel Deker, Inc., 1981. Moments Five fundamental textbook on advanced statistical methods. Covers, Monte Carlo & Method of Moments. Explains Lambda empirical distribution for Method of Moments
Sheppard, S. Failure Prevention and Reliability-1989 ASME Publ.,DE-Vol. 16
Shunmugam, MS New Approach for Evaluating Form Errors of Engineering Surfaces Computer-aided Design,V.19 n 7,Sept. 1987,pp. 368-ff Manufactured features generally deviate in size, form and relations with respect to other features from the features desired by the designer. Designers specify certain limits for these deviations that depend on functional requirements. The specification of different form errors is dealt with by the Internaional Organization for Standardization (ISO). ISO also specifies that an ideal geometric feature must be established from the actual measurements such that the maximum deviation between it and the actual feature concerned is the least possible value. In practice, the least squares (LS) method is sometimes used for establishing the ideal feature, as this method is based on sound mathematical principles. Hoever, the least squares procedure does not yield a minimum value. Therefore some attempts have been made to arrive at a form error based on the minimum deviation (MD) principles. A stray peak or valley on the actual feautre introduces considerable variation in the results obtained by the minimum deviation method. This paper suggests a new approach based on the minimum average deviation (MAD). In this method, the ideal feature is established by using a search technique for different geometric features such as straight lines, circles, planes, cylinders and spheres. Using simple numerical examples, the values obtained by this approach are compared with the values obtained by the least squares and minimum deviation methods.
Siddall, J.N. Probabilistic Modeling in Design Transactions of the ASME, Vol. 108, September 1986, p. 330-335, Journal of Mech., Transm, and Automation in Design Probabilistic design, 4866 A general procedure is proposed for evolving the form of a density function that is consistent with the concept of subjective probability. The procedure directly applies new data information to the updating of the form of a density function without imposing on it any theoretical distribution that could restrict its shape, and permits the direct use of judgement arising from real world experience. It is based on the simple concept that sample size is a measure of confidence in the shape of a density function. Two possible algorithms are given, and the concept is extended for simple "true" or "false" events. The importance of probability in artificial intelligence is also discussed, and its essentially subjective nature is described. Procedures are briefly discussed.
Siddall, J.N., Diab, Y. The Use in Probabilistic Design of Probability Curves Generated by Maximizing the Shannon Entropy Function Constrained by Moments Journal of Engineering for Industry, ASME, vol 96, August 1975, pp. 843-852 A general algorithm is described for obtaining the maximum entropy distribution constrained by moments in functional form. It is based on Jaynes' principle. The distribution is porposed as a useful tool in probalistic design. The maximum entropy distribution is generated for a large number of analytical distributions, and compared with the original. The results appear to confirm that it can represnt well most populations when four or five moments are used. The maximum entropy distribution is also compared with the Johnson and Pearson empirical distributions. The results are favorable in the two examples given. The practical convenience of the method in probabilistic design is illustrated by an example in structures.
Singhal, Kishore and J.F. Pinel Statistical Design Centering and Tolerancing Using Parametric Sampling IEEE Transactions on Circuits and Systems, Vol. CAS-28, No. 7, July 1981 Centering, Optimization, Electronics A new statistical circuit design centering and tolerancing methodology based on network analysis, recent optimization methods, sampling theory, and statistical estimation and hypothesis testing is presented. The method permits such realistic manufacturing constraints as tuning, correlation, and end-of-life performance specifications. A data base containing the results of a few hundred network analyses is first constructed. As the nominal values and tolerances are changed by the optimizer, each new yield and its gradient are evaluated by a new method called Parametric sampling without resorting to additional network analyses. Thus the most costly phase of statistical design, statistical simulation, may be carried out only once, which leads to considerable computational efficiency. Equivalent or superior designs for intermediate size networks are obtained with less computational effort than previously published methods. For example, a worst-case design gave a filter cost of 44 units, a centered worst-case design reduced the cost to 18 units and statstical design using Parametric sampling reduced the cost to 5 units (800 analyses, 75 CPU seconds on an IBM 370/158).
Sitko, Anthony G. Applying Variation Simulation Analysis to 2-D Problems Applied Computer Solutions, Inc. Variation simulation analysis is a technology that has achieved broad popularity in the automobile, appliance, electrical machinery and other industries as a method of predicting and analyzing manufacturing variation due to tolerances of individual components and assembly operations. The technology is widely considered to be the only method to accurately analyze three dimensional variation problems.Recently, a substantial body of work has been developed which indicates that variation simulation analysis can provide major advantages over traditional methods even on two dimensional problems.
Variation simulation analysis uses the Monte Carlo method to accurately simulate the effects of each individual tolerance distribution and complex relationships between individual tolerances can be defined. This article will go on to provide several examples of the variation simulation analysis method as applied to two dimensional parts and compare the results to traditional methods to demonstrate the accuracy improvements which can be achieved.
Smathers, E.W., Ostwald, P.F. Optimization of Component Functional Dimensions and Tolerances ASME Paper No. 72-DE-18 Optimization, Cost Conventional methods of tolerance optimization are mostly descriptive. This paper extends the principles of optimization of dimensions and tolerances where the objective is to maintain an overall assembly tolerance and minimize cost. In this analysis a design having N discrete component tolerances is decomposed into N subprograms then follows Bellman's Principle of Optimality. The method optimizes the sum of specified tolerances with respect to cost while honoring the constraint of design. Equations suitable for a variety of designs are given. A practical problem illustrates the method.
Smith, C.O. Probability in Mechanical Design Design Technology Transfer,ASME,presented at The Design Engineering Technical Conference, New York City, N.Y.,October 5-8,1974 The engineering profession has become increasingly concerned with the adequacy of design calculations. This concern indicates a need for critical evaluation of designs based on arbitrary multipliers, such as safety factors or worst-case treatment. Mechanical deisgn has customarily been based on applied loading, geometry, and handbook property values to give a deterministic solution.This paper discusses the design of circular members in combined bending and torsion in probabilistic terms. The paper also presents the Soderberg, Goodman, Gerber and elliptical design-relationships, and the maximum shear stress and distortion energy failures in probabilistic form. Inherent in these equations are the facts that (1) design variables are generally characterized by spectra of values, rather than unique values, and (2) a small, but finite, probability of failure must be recognized in any design. Conversely, for a given reliability or acceptable probability of failure, the appropriate size can be determined.
Illustrations are provided. The influence of range (different standard deviations) is demonstrated. A comparison is made between safety factor and reliability.
Soderberg, Rikard CATI: A Computer Aided Tolerancing Interface DE-Vol. 44-2, Advances in Design Automation-Volume 2,ASME 1992,pp.157-164 This work presents an interface for tolerance analysis in a CAD system. A method for picking up necessary information from a 2D drawing is develped and implemented as an interface in a commercial CAD system. The interface commucates with an external calculation program which determines unknown tolerance limits using the normal distribution model. Results from the calculation program is in the end used by the interface to present measures with tolerances on the drawing.The advantage of using CATI in preliminary design is discussed, and a strategy for treating interrelated tolerance chains is presented.
Soderberg, Rikard
Tolerance Allocation Considering Customer and Manufacturer Objectives DE-Vol. 65-2, Advances in Design Automation-volume 2, ASME 1993 Involving customer values in the design process is necessary for improving the total quality of a product. This paper presents the basic ideas for a method that allows tolerances to be assigned to dimensions in a tolerance chain with regard to both custmer and manufacturer objectives. The method uses and extended "quality loss function" to consider customer objectives. The total life of a component is here focused, representing one important aspect of quality. A minimum manufacturing cost function for the tolerance of a critical dimension, dependent on a number of manufactured components, is determined. This function is used to consider manufacturers' objectives. Based on the customer's total loss function and the minimum manufacturing cost function, the optimal tolerance limits of a critical dimension are determined. These are the tolerances that simultaneoulsy satisfy the customer and the manufacturers as much as possible. The ideas behind the method are described using a roller bearing application as an example.
Sodhi, Rajneet, Turner, Joshua U. Representing Tolerance and Assembly Infromation in a Feature-Based Design Environment Proceedings of the ASME 1991 Design Automation Conference, Miami, Florida, September 22-25, pp. 101-108 This paper describes a strategy for representing tolerance information and assembly information in a feature-based design environment. The concept of designing with features is extended to incorporate the specification of tolerance information. This allows appropriate tolerancing strategies to be provided within the feature definitions themselves. Thus a closer connection is formed between features and the functional intent implicity in their use. The concept of designing with features is also extended to incorporate the specification of assembly information, through the use of assembly features which provide a high-level user interface for the creation and modeling of assemblies, and which handle the identification and creation mating relations between components. Several examples of component and assembly design using this extended feature-based approach are presented.
Sorensen, Carl D., Nielsen, Dale B., Chase, Kenneth W. Improved Methods for Tolerance Analysis of Mating Hole Patterns International Design Productivity Conf., Honolulu, HI,Feb. 6-8, 1991 Tolerance analysis, the process of determining the effects on an asembly of tolerances of individual part, is an important part of design for manufacturing at lowest cost and high quality. Current tolerance analysis methods work well for linear stacks of parts but have serious shortcomings when applied to mating hole patterns. ANSI specifications and worst-case methods are generally applied incorrectly; and simulation methods are computationally intensive and sensitive to correlations in random number generators. A tractable analytical solution to the mating hole problem would be a great improvement, allowing rational tolerance selection to balance competing objectives of reducing cost and increasing precision. This, in turn, provides important information that allows concurrent engineering, with design of manufacturing processes proceeding in parallel with design of parts.A common dificulty in analyzing mating hole patterns is a lack of understanding of the correct techniques to apply. The conceptually simple but computationally expenseive Monte Carlo nmethod is first described. Next a commonly applied but incorrect conventional statistical tolerancing method is presented. Finally, an analytically correct solution involving the use of infinite integrals is derived along with two methods for evaluating the analytical solution, convolution and direct integration.
This paper demonstrates the application of Monte Carlo simulation, conventional tolerance analysis, convolution methods, and direct integration to a simple two-hole pattern. The Monte Carlo method is shown to work correctly but at a significant penalty in computer time, especially as the number of defective parts is reduced. The conventional analysis is shown to predict up to 50% fewer defective parts than actually exist. The convolution method produces results that agree with the Monte Carlo method at a significant savings in time. Finally, the direct integration method is shown to be the fastest of the correct methods, with accuracy that may exceed that of the Monte Carlo method. This direct integration method is recommended for use in analyzing two-hole patterns.
Spalding, F.L. How and When to Specify Tolerances of Form Machine Design, May 15, 1958, pp. 104-11 Quality Assurance, GDT This article interprets and summarizes the recommendations of the new ASA standard, for specifying geometric requirements.
Speckhart, F.H. Calculation of Tolerance Based on a Minimum Cost Approach J. of Engineering for Industry, ASME, vol. 94, May 1972, pp. 447-453. Optimization, Lagrange Mult. This paper presents a workable analytical method for finding the optimum set of dimension tolerances for a mechanical device that will minimize manufacturing costs and meet the imposed restraint conditions. The constraint conditions represent physical requirements that critical parts must fit relative to each other with a given precision. Using the mathematical description of the restraints and information on the costs of manufacturing each dimension as a function of the tolerance, the method utilizes Lagrange multipliers to minimize exponential cost function subject to nonlinear restraint conditions. For all but the simplest problems the use of the method requires computer progrmaming. The method is presented in sufficient detail to allow the reader to develop a computer code. A Fortran computer program that will handle essentially any mechanism and calculate tolerances on a sure fit or statistical-fit basis has proven that the method will give useful results. Three example problems are given with cost equations, shaft & bearing, helical spring, and web cutter. Multiple constratints are used.
Spence, Robert, Soin, Randeep Singh Tolerance Design of Electronic Circuits Addison-Wesley Publishing Company,1988
Spotts, J.F. Quick Way to Compute Tapped-Hole Tolerances Machine Design,June 21, 1979,pp. 114-118 Dimensioning the precise positions of tapped holes usually is tedious and time-consuming with conventional drafting techniques. A quicker way to find the exact tolerances you need for a smooth fit is with these simple true-position dimensioning equations.
Spotts, M.F. Dimensioning of Assemblies Machine Design, Feb. 20, 1986, pp. 100-101. GD&T, Form, Feature and Locational Tolerances, Dimensioning, Tolerance
Spotts, M.F. Taking the "Play" Out of Bolt-Hole Tolerances Machine Design,June 5, 1979,pp. 88-91 Holes in bolted parts must be properly dimensioned for smooth, precise fits. But the task is tedious and time-consuming with conventional drafting standards. Hole tolerances may be determined quickly and easily with true-position dimensioning equations.
Spotts, M.F. Dimensioning and Gaging Machine Parts From Datums Machine Design, June 6, 1985,pp. 97-100 The proper use of datums on production drawings ensures that machine components are manufactured according to design specifications.
Spotts, M.F. Dimensioning Tapped Holes for Smooth Assembly Machine Design, Mar. 23, 1978, pp. 55-59. GD&T, Form, Feature and Locational Tolerances, Tolerance, Dimensioning, Hole Conventional drafting standards don't show how to dimension the positions of tapped holes to ensure that mating parts will fit together. Instead of adding extra-wide tolerances, use the simple equatios given here to specify the exact tolerances you need.
Spotts, M.F. Predicting Length of Assemblies With Monte Carlo Simulation Machine Design,Nov. 20, 1980,pp. 84-88 The length of an assembly falls between some maximum and minimum values, depending on how tolerances of individual parts stack up. The distribution of lengths for assemblies with many parts can be found easily with Monte Carlo Simulation-a mathematical approach that uses random numbers.
Spotts, M.F. A Faster Way To Set Statistical Tolerances Product Engineering, March 21, 1960, pp. 55-57. Basic Assembly Analysis
Spotts, M.F. The Combination of Uniform Probability Curves in Engineering The American Society of Mechanical Engineers,75-DET-1 Almost all machine parts are eventually combined with others to form assemblies and clearance fits and the designer is continually faced with the question of determining what the expected variations in the length of the resulting assembly will be. Engineers are familiar with the problem where variations in a dimension follow the normal or Gaussian law. While it is true that the errors in a dimension may be grouped around the mean of the dimension, it is also true that the frequencey of the errors rarely fades to zero at the ends of the tolerance zones. Yet this requirement must necessarily be met if the assumption of normal distribution of errors is to be valid. A more realistic approach is to accept the fact that errors may be distributed over the entire tolerance zone. A valid assumption, and one that is usually on the safe side, is to assume that the distribution of errors over the tolerance is uniform. This paper considers assemblies made from piece parts with such distributions for their errors and will also indicate the rate at which the assembly curve approaches the normal form as the number of parts in the assembly increases.
Spotts, M.F.,1959 An Application of Statistics to the Dimensioning of Machine Parts Journal of Engineering for Industry, ASME, vol. 81, Nov. 1959, pp. 317-322 Statistical Methods, RSS An outstanding industrial achievement during recent years has been the development of quality control and acceptance sampling methods for the purpose of maintaining the high standards of manufactured products. It is equally important to make use of statistics in the engineering office in connection with the dimensioning of machine parts. This paper will be concrned with the dimensioning of assemblies, and will demonstrate how it is possible to maintain tolerances for proper engineering functioning, and at the same time widen the tolerances so far as production is concerned.Puropses RSS method, compatible with quality control method for large production.
Spotts, M.F.,1972 Application of the Normal Curve to Dimensioning of Assemblies ASME Paper 72-DE-10 Statistical Methods The build-up of tolerances in the assembly of machine parts is of concern to every mechanical designer. Designers are well aware that a widening of the peice part tolerances will result in reduced manufacturing costs. Statistics will serve as a helpful guide showing how such widening can be done without exceeding the desired variation in the resulting assembly.
Spotts, M.F.,1973 Quality Control Analysis: Distribution of the Errors of an Assembly ASME Paper 73-DE-34, 1973 Statistical Methods The variations in the length of an assembly depend on the variations in length of the component parts. Under conditions of random assembly of mass-produced components the lengths of the latter, in general, are not known. However, if the distribution of the variations in the lengths of the assembly can be determined.
Spotts, M.F.,1973 Allocation of Tolerances to Minimize Cost of Assembly J. of Engineering for Industry, ASME, vol 95, Aug. 1973, p. 762-764. Optimization, Cost, Allocation, Lagrange Mult. When there are variations in the costs of producing the dimensions directly involved in an assembly, the paper shows how to allocate the tolerances to give the assembly of minimum cost. Cost equation is COST(I) = K(I)/TOL(I)**2. For linear constraint equations, and use of Lagrange multipliers, closed form solutions for optimal set of component tolerances is possible for Worst Limit and RSS methods.
Spotts, M.F.,1974 Dimensioning of Clearance Fits with Overlapping Tolerances Using Probability Theory ASME Paper 74-DE-8 Statistical Mehods, RSS (Non-Normal) When the variation in diameter for a hole and shaft are grouped around the centers of their tolerance zones, it is obvious that the tolerances can have an overlap with but nominal risk that assembly will be adversely affected. This paper applies probability theory to indcate probable proporton of interferences which depend on the manner in which the peice part errors are distributed. Curves are given to enable tolerances to be determined without the need of making calculations.
For shaft & bearing, un-conforming fraction for components distributed Uniformly and Normally are found.
Spotts, M. F.,1975 Probability Theory for Assemblies with Piece Part Errors Concentrated Near End of Tolerance Limit ASME Paper 75-DE-1, 1975
Spotts, M.F.,1975 Tolerancing Determines How Round Parts Take Shape Machine Design, Oct. 16, 1975., pp. 139-141 Tolerance, Round parts Whenever two round surfaces share the same centerline, concentricity becomes an important engineering specification. Here's how two tolerancing systems--runout and true positioning--can be used to specigy concentricity.
Spotts, M. F.,1975a 1.Simple Guide to TP Dimensioning Machine Design, Nov. 13, 1975, pp. 132-135 True-Position Tolerance, GDT True-position dimensioning is not a new concept, yet it continues to baffle many people. This series of articles uses a new approach to explain TP dimensioning--and helps clear up some of the misunderstanding about TP principles.
Spotts, M.F.,1975b 2. Simple Guide to TP Dimensioning Machine Design, Nov. 27, 1975, pp. 66-69 True Position, Tolerance, GDT, Gages True-position dimensioning is easy to understand if holes and similar mating features can be reduced to one of these four conditions. Each article in this series show how to dimension and tolerance parts for one of these conditions. Part 1 discussed clearances and assembly tolerances for the "loose bolts, datums at edges" condition. Here, Part 2 shows how a go/no-go gage is used to check this condition and introduces the second assembly condition, "loose bolts, datums at centerline."
Spotts, M. F.,1976c 3. Simple Guide to TP Dimensioning Machine Design, Jan. 8, 1976, pp. 86-90 True Position, Tolerance, GDT The four articles in this series show how true-position dimensioning and tolerancing is applied to each of these assembly conditions. Parts 1 and 2 discussed clearances, assembly tolerances, and fixed-gage inspection for th first two cases. Here, Part 3 continues with the assembly condition.
Spotts, M.F.,1976d 4.Simple Guide to TP Dimensioning Machine Design, Jan. 22, 1976, pp. 84-88 True Position Tolerance, GDT In four installments this series presents a new way to explain true-position dimensioning and tolerancing. Parts 1,2, and 3 showed how TP is applied to three possible assembly conditions. Here, Part 4 concludes with the final assembly condition.
Spotts, M.F.,1977 Running the Risk of Interference Fits Machine Design, July 21, 1977, pp. 106-111. Statistical Methods, RSS Statistical tolerances for closely fitting parts normally allow slight dimensional overlap. This cuts machining costs but also creates some risk of interference during random assembly. Here's how to evaluate that risk.
Spotts, M.F.,1978 How to Use Wider Tolerances Safely, in Dimensioning Stacked Assemblies Machine Design, April 20, 1978, pp. 60-63. Statistical Methods, RSS In any stacked assembly of parts, the maximum possible total length is the sum of the nominal dimensions and the plus tolerances of all parts; same is true for the minimum length. But the probability theory tells us that the actual variations in length of the assembly will very likely not reach these extremes. You can take advantage of this fact by widening the tolerances on some or all of the cmponents, thereby reducing production costs.
Spotts, M.F.,1978 Fast Dimensional Checks-with Statistics Machine Design, Oct. 12, 1978, pp. 170-174. Quality Assurance Here is a simple technique which shows-from measurement only a small sampling of parts-whether a full production run is meeting specified values for dimensional mean and variability. In addition, this statistical method quickly indicates whether a change in the manufacturing process has moved dimensional characteristics in the desired direction.
Spotts, M.F.,1983 Dimensioning and Tolerancing for Quantity Production Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1983 True Position Tolerancing, GDT The object of this book is to establish basic rules and procedures for good dimensioning practice. The book is not a drafting standard, but attempts to provide the background that will aid in the solution of dimensioning problems as they arise in day-to-day work. At present, such information is fragmentary and scattered through the literature. This book, therefore, attempts to present a unified treatment of the subject.
Spotts, M.F., and C. R. Mischke,1989 Mechanical Engineering Design Fifth Edition, Prentice-Hall, Inc., 1989 General pp. 145-182, (Chapter 4.).
Srikanth, S. A Unified Framework for Assembly Modeling Technical Report No: 90023
Srikanth, S., Turner, Joshua U. Toward a Unified Representation of Mechanical Assemblies Engineering with Computers 6,103-112 (1990) Current solid modeling systems are suitable for modelling individual mechanical parts but they do not capture the relationships and/or dependencies among the geometric features of parts in an assembly. Research in the area of "part and assembly modeling" focuses on capturing this missing information.This paper surveys feature-based modles for mechanical assemblies and methods for deriving the actual part positions from the part relationships. We have attempted to extract from the literature the essential requirements for a unified feature-based assembly model.
Three levels of representation are envisaged-representation of part positions in terms of their spatial coordinates, representation of geometric (feature) relations between individual part, and representation of the assembly hierarchy. The actual relative positions can be derived from the hierarchical assembly model. Possible areas of application are tolerance analysis and synthesis, automatic generation of assembly sequences, and kinematic analysis and synthesis.
Srinivasan, R.S., Wood, Kristin, L. Fractal-Based Geometric Tolerancing for Mechanical Design,pp. 107-115 DE-Vol. 42,Design Theory and Methodology,ASME 1992 The submacrogeometric variations of mechanical components have an important impact on product function and performance. These variations are in the tolerancing domain. The problem of combining tolerance specification in engineering design with tolerance control in manufacturing and quality assurance present a continuing challenge to researchers. This paper illustrates the feasibility of using fractal-based methods for the problem of tolerance assignment in engineering design (design for manufacturing). Error data are generated as a function of the fractal dimension using the fractional Brownian motion model and are superposed on an ideal profile of a slider bearing. The consequent changes in performance parameters are studied and the detrimental effect of larg variations perceived. This simple case study indicates the potential of the method to be extended for more complex problems.
Srinivasan, Vijay Role of Sweeps in Tolerancing Semantics CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Deartborn, Michigan, June 17-19,1993,pp. 69-78 Tolerancing semantics are defined as theoretical inspection procedures. These procedures invoke the existence of a tolerance zone which contains a geometric feature, or some geometric element extracted from it or some parameters estimated from it. Many of the tolerance zones can be defined using the offset operation. Others, however, require more general operations such as sweeps. This paper describes the role of sweeps in defining tolerance zones for size, circularity, and virtual boundaries. It also touches on the use of sweeps in manipulating tolerance zones for tolerance analysis.
Srinivasan, Vijay Recent Efforts in Mathematization of ASME/ANSI Y14.5M Standard Proceeding of 3rd CIRP Seminars on CAT, Cachan, France, April 1993, pp. 223-232 Tolerancing, standards, ANSI, ASME, mathematical definitions Y14.5.1 is a technical subcommittee that was formed in 1989 to recommend mathematical definitions of dimensioning and tolerancing principles found in the ASME/ANSI Y14.5M standard. This is the first official link between research and standards in this critical area. In this paper I will summarize some of the results of these efforts to date on size, datum, and location tolerancing.
Srinivasan, Vijay, O'Connor, Michael A. Towards an ISO Standard for Statistical Tolerancing CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.181-194 ISO, tolerancing, standards, statistics Although statistical tolerancing has been practiced in industry for a long time, standards have paid only limited attention to it. This is changing now because of economic reasons, and ISO is investigating how to standardize statistical tolerancing. In this paper we trace the history and document the current state of the knowedge in standardizing statistical tolerancing. Our objective is to disseminate this information as widely as possible so that the international community is aware of, and has an opportunity to influence, the thinking behind the future ISO standard.
Steel Founders Society Tolerances Steel Casting Design, Engineering Data File Sec. 3, Steel Founders' Society of America Manufacturing Tolerances In the section on design rules, some data on the tolerances for steel castings were given. The present section will discuss the subject in more detail. Additional information on ths subject will be found in the Steel Castings Handbook, 3rd Edition, published by Steel Founders' Society of America.
Subramaniam, Srikanth, Turner, Joshua, Sanderson, Arthur Establishing Part Positions in Assembly Modeling Product Modeling for Cumpter-Aided Design and Manufacturing,pp. 199-226 CAD, Assembly Modeling Current CAD systems model individual parts accurately, but do not capture the logical relations and dependencies among parts in a meaningful way. They represent part positions only as coordinate transforms. Various types of assembly analysis also require some information about the logical relationships between parts. This paper proposes a unifying assembly representation comprising three levels: (i) a CAD model of the assembly containing the parts and their positions in space, (ii) a relational model containing the parts and logical relations among boundary features, and (iii) a hierarchical CAD model that models the functional dependencies among part positions. This paper also presents an algorithm for deriving a hierarchical model from a relational model by establishing a sequence for the relative positioning of the parts. The sequential strategy avoids numerical problems that occur in sumltaneous strategies, and effectively reduces an O(N3) process to O(N). For each pair of parts being positioned, a relative positioning operator is identified. During a variational analysis, this RPO is used to propagate part variations.
Suri, Rajan, Diehl, Gregory W., Ho, Yu-Chi Optimization of Manufacturing System Simulations Using Perturbation Analysis and SENSE Proc. Winter S Perturbation Analysis (P/A) of discrete event systems is a recent technique which enables sensitivty analysis of decision parameters from a single simulation run. Thus, from a single simulation of a manufacturing design, one can estimate the effects of changing many different decisions such as adding more machines or fixtures, changing buffer sizes or changing lot sizes. The first part of this paper gives an overview of this new technique. The second part describes SENSE (SENSitivity Evaluator), a software package implementing the theories of P/A in easily usable form. Application of SENSE to GPSS/H simulations is described, with examples of its use for the design of flow lines at a major U.S., corporation. By using SENSE a simulation team is able to improve their designs in less time, and with less manpower and CPU-time, than previously required. The result is better designs and better turnaround time for simulation activities in general.
Sutherland, G.H., and Roth, B. Mechanism Design: Accounting for Manufacturing Tolerances and Costs in Function Generating Problems J. of Engineering for Industry, ASME, vol 97, Feb. 1975, pp. 283-286. Manufacturing Tolerances in Mechanism, Application Theory and design algorithms, which account for the manufacturing cost and statistical manufacturing tolerance effects as well as the structural error, are presented for the synthesis of funciton generating mechanisms. The algorighms are illustrated n a planar, four-bar synthesis problem. The theory and asociated algorighms may be applied to the synthesis of any planar or spatial funcion generating linkage.
Suzuki, Hiromasa, Kase, Kiwamu, Kimura, Fumihiko Physically Basee Modelling for Evaluating Shape Variations CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.173-180 Computer aided tolerancing, variational modelling, physically based modelling, contact state, rigid body motion It is important for designing mechanical products to analyze causal relationship between variations in part's shapes and their effects in product's functionality. Computer simulations are promising design tools for evaluating those effects. This paper features our attempt for applying physically based modelling methods to implement simulations, in particular, those for calculating contact states of an assembly of simple parts and its motion. These simulations adopt simplified physical models, since their real physical behaviors, but results of the simulations are considered helpful for designers to qualitatively grasp relationship between behaviors of an assembly and variations in part's shapes.
Sweet, Donald H. Simplified Calculations for the Cumulative Effects of Tolerances Machine Design,Jan 4,'62,pp. 104-109 A new concept-resultant size-is useful for finding maximum and minimum material thicknesses between features in a part and between these features and the surfaces of the part itself.
Symons, J.D. Shaft Geometry-A Major Factor in Oil Seal Performance Transactions of the ASME, Journal of Lubrication Technology, April 1968, pp. 365-375. Application, Shaft Seals, Roundess, Case Study Five seal variables, viz., flex section thickness, lip length, trim diameter, material, and lip force, and two shaft variables, shaft out-of-round (OOR) and number of lobes, were investigated by means of fractional-factorial experimentation to determine the effects of shaft OOR and number of loves on seal performance and to determine th einteractions between the five seal design factors and the two shaft variables. A 1/4 replicate, 2^7 fractional-factorial experiment was conducted with leakage as the dependent variable to determine these effects. For the levels of OORD, lobing and shaft speed, the tests indicated that shaft OOR and number of lobes in themselves had no effect. Also, at higher speeds, both OOR and lobing are extremely important. Analysisi of the interactions and further test work with lobed shafts indicate that due to the interactions between several seal design factors and shaft OORD, the setting of an acceptable shaft OOR tolerance is extremely difficult. However, a general recomendation of 200 mircoin. Maximum shaft OOR, with a minimum number of lobes is supported by the data and is still valid.
Takahashi, Kiwamu, Suzuki, Hiromasa, Kimura, Fumihiko Motion Analysis of Parts with Geometrical Errors Based on Dynamic Simulation Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cahcan, France, April 27-28, 1993,pp. 85-96 Motion Analysis, Geometrical Errors, Dynamic Simulation One of the major concern of designers in tolerancing procedure is the effect of geometrical errors on product's functionalities. We propose the following three steps of tolerancing procedures with computers: 1. Generate error models for nominal models, 2. Analyze the effect of geometrical errors, and 3. Determine tolerance specification and change the nominal shape models. In this paper we treat the second issue. Amongst various functionalities of mechanical products, we select motion of a part, which is functionally fundamental and sensitive to geometrical errors. We developed a dynamic simulation method by which we can calculate rigid body motion of a polyhedral object. A motion path is generated by integrating the motion equations, along which the contact state is dynamcially changed. By giving simplified geometrical errors to the object's shape, we can estimate the distortion of the motion path. This leads to evaluation of the robustness of product design shapes.
Takamasu, Kiyoshi, Fukuda, Iturou, Furutani, Ryousyu, Ozono, Shigeo Data Processing Method for Geometrical Forms with Form Deviations in Coordinate Metrology CIRP/JSPE/ASME Proceeding of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.301-312 Coordinate metrology, Coordinate measuring machine, Ceometrical form, Form deviation, Gaussian substitute feature, Actual derived feature In coordinate metrology, actual derived feaures (Gaussian substitute features) are normally calculated from measured data sets of CMM (Coordiante Measuring Machine). Then, the actual derived features are compared with the nominal features which are indicated on the drawings. The actual derived features are calculated using least squares method and expressed without form deviations. The novel data processing method for geometrical form with form deviations has been developed. In the method, every geometrical form can be processed with its form deviation which is calculated form the measured data set using Gaussian (least squares) method as a standard variations. Using the method, we can calculate the form deviations of 2-D geometrical features. This directly implies that these values and these calculations can be used for the evaluations of measurement uncertainties and a computational tolerancing.
Tanaka, Fumiki, Ikonomov, Pavel, Okamotoa, Hideaki, Kishinami, Takeshi Inspection Method for Geometrical TOlerances using Coordinate Measuring Machine CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing, Japan, April 5-6, 1995, pp. 325-336 Geometrical Tolerance, Computational Metrology, Coordinate Metrology The method of inspecting gometrical toelrances is important from the economical and qualitative viewpoints in Coordinate Measuring Machine (CMM) measurement. Much work has been done on the evaluation of the geometrical deviation of form for a single feature from a measured data set. But, on the other hand, the inspection of geometrical deviation for related features has not been well developed. In this papter, we first discuss the following topics: 1) Problems of CMM inspection based on ISO Geometrical Tolerance, 2) Formal representation of ISO geometrical tolerance using EXPRESS, and 3) Necessity of a virtual gauge as a criterion for deriving the geometrical deviation of the toleranced feature from a measured data set. For the mathematical representation of the virtual gauge, we introduce mathematical representations of geometrical elements and the relationship between datum and toleranced feature. We extend the small displacement screw method in order to find out the minimum geometrical deviation based on the virtual gauge. We also show that the prosed method is very effective by applying it to some examples.
Tarasov, L.P. Relation of Surface-Roughness Readings to Actual Surface Profile Transactions of ASME, April, 1945; p. 189-196 Surface Finish Studies of surface finish have shown the desirability of relating profilometer roughness readigs to actual peak-to-valley distances of the type that a micrometer measures. Approximate multiplying factors for converting profilometer reading into peak-to-valley roughness have been obtained from taper sections fo a variety of abrasive-finished steel surfaces with profilometer roughness in the range of 1 to 100 microinches rms. For cylindrical ground surfaces, the factor can be taken as about 4 1/2; for other types of fixed-abrasive finishes, as 6 or 7; and for loose-abrasive-lapped surfaces, as 10. These are mean values and individual factors may deviate by as much as one third of the mean value. the factors quoted give values for "predominant peak" roughness; they should be doubled to obtain "deepest maximum" roughness, this being a second way of describing the peak-to-valley roughness. No evidence was found of any increase in the factor for a given type of finish with a decrease in the profilometer roughness, even for the finest surfaces studied.
Tarello, W.R. How Much Clearance for Mating Holes? Use Tabled Tolerances Product Engineering,June 24, 1963 A practical, easy-to-follow system for fastened assemblies includes effect of screw size and tolerance on dimension between holes.
Taylor, Barry N., Kuyatt, Chris E. The New NIST Policy on Statements of Uncertainty* CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology,Dearborn,Michigan,June 17-19,1993,ASME,pp. 79-84 A measurement result is complete only when accompanied by a quantitive statement of its uncertainty. In October, 1992, then NIST director John W. Lyons announced a new NIST policy regarding statements of uncertainty associated with NIST measurement results. The new policy requires that NIST measurement results be accompanied by quantitative uncertainty statements and that a uniform approach to expressing measurement uncertainty be followed. Until the new policy was announced, there had never been a uniform approach at NIST to the expression of uncertainty. The new policy was effective immediately with a full implementation date of January 1, 1994.The policy is based on the approach to expressing uncertainty in measurement recommended by the International Committee for Weights and Measures (CIPM) in 1981. The original recommendation was recently elaborated on by a committee composed of experts nominated by the International Bureau of Weights and Measures (BIPM), the International Electrotechnical Commission (IEC), the International Organization for Standardization (ISO), or the International Organization of Legal Metrology (OIML). The CIPM recommendation is the only recommendation concerning the expression of uncertainty in measurement adopted by an intergovernmental organization.
To aid the NIST staff in putting the policy into practice, a document containing guidelines was prepared and published.
Taylor, Benjamin R. Dimensional Control Through the Tolerancing of the Solid Model Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 161-166 The use of conventional tolerancing methods such as the ANSI Y14.5 OR BS308 requires the use of detailed drawings, but does provide a very comprehensive means of defining the nominal geometry of the part and the allowable variations of position, size and form.If the part manufactured is being accomplished within a single system which encompasses the concept part configuartion and tolerancing, and also the anamufacturing process, it is possible to utilize other methods to provide the same function.
Renishaw has developed a process in whcih the solid model is developed within the Computer Aided Design system that has been toleranced utilizing a specially developed tolerancing scheme, whereas individual gauge points are located on the surface with an allowable variation specified.
As a result, no conventional detailed drawings are developed or produced and the process control method is then part of the specification of the part itself. This vastly reduces the design time and allows a comprehensive on machine process control method to be used.
Tech Briefs (cont.) Thermal Tolerance Control Machine Design
Tietjen, Gary L. and Mark E. Johnson Exact Statistical Tolerance Limits for Sample Variances Technometrics, Vol. 21, No. 1, Feb. 1979 Tolerance intervals, control charts, variances, standard deviations Exact statistical tolerance limits of the population of sample variances and standard deviations arising from a normal (--) distribution are derived. The use of tolerance limits on the variance or standard deviation is motivated by a number of applied problems which we describe. These tolerance limits are discussed in relation to the usual control chart limits.
Tonshoff,Dr.-Ing, E.h. H.K., Erhmann, Dipl.-Ing. M. Quality Features in CAD-and CAPP- Systems CIRP/JSPE/ASME Proceedings of the 4th CIRP Seminar on Computer Aided Tolerancing,The University of Tokyo,Tokyo,Japan,April 5-6,1995,pp.131-142 Feature Based Tolerancing, Tolerances in CAD-/CAPP-Systems The contributed paper describes an approach for the integration of tolerances in CAD- and CAPP-systems. The use of Quality Features eases the work of the users in design, process planning and NC-programming.Computer systems used in product development support the tasks of designers, process planners and NC-programmers. The systems aim at increasing the competitiveness of a company by reducing time and costs needed for product development and improving the product quality. In computer systems products or components are represented as internal workpiece models, which have a perfect shape. Tolerances for dimensions and geometry are used to state the limits of deviations, which are allowed in manufacturing. A workpiece produced with an accuracy within the limts of the stated tolerances will fulfil its function.
Similar to the feature approach in design and process planning accuracy information can be stored in Quality Features. According to the type of accuracy data the Quality Featurs can be divided in several groups: Dimensional tolerances, geometrical tolerances and surface treatments. Current European standards do no sufficiently regard tolerances with reference to three-dimensional models that are widely used in CAD- and CAPP-systems. Therefore standards developed for two-dimenisonal drawings have to be extended for their use in a volumetric model. A Quality Feature comprises information on toelrance type, toelrance value, toelranced feature, reference feature and attributes for the tolerance zone and plane. Quality Features support tolerance relationships within one feature or between different features. New techniques allow to apply tolerances to the resultant geometry, which may not exist in the feature templates.
Traband, Mark T., Joshi, Sanjay, Wysk, Richard A., Cavalier, Tom M. Evaluation of Straightness and Flatness Tolerances using the Minimum Zone Manufacturing Review,Vol 2,No. 3,September 1989 This paper presents an algorithm that can be used to determine if sample measurements from a coordinate measuring machine, or other two-or three-dimensional measuring device, meet the ANSIY14.5M requirements for straightness or flatness. The procedure utilizes the concept of a courer hull to give the minimum tolerance zone from a set of measure points. To date, approximation methods or iterative search techniques have been primarily utilized for determining the minimum zone, but these methods do not necessarily provide the absolute minimum zone. This paper presents a method that guarantees the minimum zone. Examples are presented which compare the miniumum zone method developed with the least-squares evaluation method.
Trucks, H.E. Designing for Economical Production Society of Manufacturing Engineer, Dearborn, MI, 2nd Ed, 1987 Moting hole patterns, machine tolerances, process tolerances
Tukey, John W. The Propagation of Errors, Fluctuations and Tolerances Supplementary Formulas. Technical Report No. 11 Tolerance, Tolerance Analysis, Statistics
Turner, J.U., Wozny, M.J., Hoh, D.D. Tolerance Analysis in a Solid Modeling Environment ASME Computers in Engineering,V2,1987,pp. 169-175 An ongoing project an Rensselaer Polytechnic Institute(RPI) has investigated the use of a solid modeling system as a basis for the engineering analysis of design tolerances on parts in assemblies. A software package has been developed that can perform a complete automated tolerance analysis of a complex assembly of parts, using a novel application of techniques from computer graphics and geometric modeling. The package uses part geometric information represented in a solid modeling data base to assess the effect of each possible part geometric variation on the design constraints of the assembly. The approach is computationally intensive, and the potential for an extensive use of both vector operations and parallel processing makes it a suitable candidate for exploitation of supercomputer capabilities.
Turner, Joshua Current Tolerancing Packages CRTD-Vol. 27,International Forum on Dimensional Tolerancing and Metrology,ASME,Dearborn,Michigan,June 17-19,1993,ASME,pp. 241-248 Commercially available software provides support for analysis of the effect of geometric and parametric tolerances on the functionally significant properties of parts and assemblies. Available technology still requires considerable input from the user in building the analysis models, and a thorough understanding of the assumptions and limitiations of the package. Support for the ANSI/ISO geoemtric tolerancing standards is limited. However, when used with care and knowledge, the available products can be of considerable value to design engineers in reducing product cost and improving product quality.This paper provides an overview of the basic capabilities for tolerance analysis of the technologies used in currently availbale software packages. Three major generic approaches are identified.
Turner, Joshua, Gangoiti, Alex Beascoechea Tolerance Analysis Approaches in Commercial Software Concurrent Engineering,March/april 1991,vol. 1,n2,pp. 11-23 Tolerance, Software By analyzing tolerances early in the product development process, not only can you create a robust design, but you can avoid expensive design and manufacturing process rework.
Turner, Joshua U. Research in Automated Tolerancing at RPI Improved tolerancing methods can result in lower manufacturing costs, higher product quality, shorter product development cycles, and greater designer productivity.We have developed new advanced methods for the solution of tolerancing problems can be solved without extensive interaction with the designer, since most of the required information is automatically derived from the designer's CAD model. Other features include: ability to solve three dimensional problems; ability to use either conventional or geometric tolerances; solution of problems on either a worst-case or a statistical basis; extensive facilities for assembly modeling which accurately characterize the part interactions.
Our strategy for technology transfer is aimed at the integration of these new methods with existing corporate CAD systems. We are working with developers of CAD systems to assure the ease of integration of our code. We are working with users of CAD systems to assure the applicability of our methods to the real tolerancing problems faced by industry.
Turner, Joshua U. Exploiting Solid Models for Tolerance Computations ASME,pp. 88-159 Tolerances, Solid Modeling, Variational Geometry In the computer-aided mechanical design, tolerances play an important role in determining product quality and cost. Handbook tolerancing methods are time-consuming, error-prone, and have limited applicability. However solid modeling technology can potentially be exploited for the automated solution of three-dimensional tolerancing problems. The focus of this paper is on the modeling techniques necessary to achieve this objective. A strategy referred to as constructive variational geometry (CVG) is advocated, which is based on constructive solid geometry ideas. The two principal components of CVG are a strategy for developing variational models for each individual part, and a strategy for combining the part variational models into a variational model for and assembly. The CVG techniques and their application to tolerance analysis are illustrated using the GEOTOL experimental solid modeling system.
Turner, Joshua U. Automated Tolerancing Using Solid Modeling Technology AUTOFACT,Proceedings,MS88-692,1988 The tolerancing of parts in assemblies is important to overall product quality and cost. The incorporation of automated tolerancing capabilities with existing CAD systems, is an important piece of the integration puzzle. This paper presents recent experience with the use of solid modeling technology to automate the tolerancing process. Methods have been developed that are automatic; can solve three-dimensional tolerancing problems; can be applied on a worst-case or statistical basis. Both geometric and dimensional tolerances can be used. Several example problems are solved.
Turner, Joshua U. Relative Positioning of Parts in Assemblies using Mathematical Programming Rensseaer Polytechnic Institute Assembly Modeling, Solid Modeling, Variational Geometry, Tolerancing In the variational modeling of part assemblies it is necessary to specify the position of each part not in absolute terms, but relative to the positions of other parts in the assembly. The position of each part is specified based on geometric relationships between various features and of the part and mating features of its neighboring parts. These feature relationships are treated as inequalities. Mathematical programming is used to find the optimal configuration of the parts. The approach is amenable to both sequential and simultaneous assembly strategies. Computation of the part positions is tractable and robust. In consequence, a variational assembly model can be constructed and evaluated at reasonable cost. The assembly model is compliant with part variations. The variational assembly model is particularly useful for solving problems in tolerancing. The mathematical programming formulation is currently being implemented in the Geos geometric modeling system being developed at RPI.
Turner, Joshua U. Geos Design Overview RPI, June 1, 1990 This document provides an overview of the major design concepts of the Geos system. (For an overview of the objectives of the Geos system, see the GEOS Overview document. For a user's perspective on the interative interface to the Geos system, see the Geos User Notes document.)
Turner, Joshua U. New Methods for Tolerance Analysis in Solid Modeling RPI, May 23-15, 1988 This paper presents the results of new research at IBM, into the use of solid modeling technology for the automated solution of tolerancing problems. This paper focuses on the tolerance analysis problem, and presents several methods for the automated solution of three-dimensional tolerance analysis problems, using solid modeling technology. A Monte Carlo method is presented for both worst-case and statistical tolerance analysis. Linear programming and sequential linear programming methods are presented for worst-case tolerance analysis. Example problems are solved using the experimental GEOTOL solid modeling system.
Turner, Joshua U. Geos Overview RPI, TR-89047 Improved tolerancing methods can result in lower manufacturing costs, higher product quality, shorter product development cycles, and greater designer productivity.Geos is a variational geometric modeling system developed at the Rensselaer Design Research Center, and based on the principles of constructive variational geometry (CVG). Geos has been used as a reasearch vehicle for developing new advanced methods for the solution of tolerancing problems.
One of the major features of the Geos approach is that new tolerancing problems can be solved without extensive interaction with the designer. Other features include: ability to solve three dimensional problems; ability to use either conventional or geometric tolerances; solution of problems on either a worst-case or a statistical basis; extensive facilities for assembly modeling, and accurate characterization of part interactions.
Geos is also a vehicle for technology transfer, and is aimed at the integration of these new methods with existing commercial CAD systems.
Turner, Joshua U., Srikanth, S. Constraint Representation and Reduction in Assembly Modeling and Analysis RPI, May 30, 1990 A number of researach papers have described various types of constraints for relating the positions of parts in assemblies. The relations may include simple planar contacts, as well as certain assembly tolerances. This paper presents a comprehensive representation for such constraints. The representation incorporates a wide variety of assembly constraints given in the literature. A systematic procedure for constraint reduction is also given: if two parts or subassemblies are related by multiple constraints, this procedure will determine a single aggregate constraint reduction methods to problems in assembly modeling and tolerancing are discussed.
Turner, Joshua U., Subramaniam Srikanth, Gupta Suvajit Constraint Representation and Reduction in Assembly Modeling and Analysis RPI, June 30, 1991 Various types of contraints may be used for relating the positions of parts in assemblies. The constraints may involve different types of contacts between the parts, as well as certain assembly dimensions. This paper presents a uniform representation for assembly constraints that applies to a wide variety of constraint relations given in the literature. A systematic procedure for constraint reduction is also given: if two parts or sub-assemblies are related by multiple constraints, the constraint reduction procedure computes a single net constraint having the same effect. Three broad applications of the constraint representation and constraint reduction methods to problems in assembly modeling and tolerancing are discussed.
Turner, Joshua U., Wozny, Michael J. The M-Space Theory of Tolerances Advances in Design Automation-1990,Vol. 1,ASME Publication No. DE-Vol. 23-1,Proceedings of ASME Design Automation Conference,Chicago,IL,Sept. 16-19,1990,pp. 217-226 A rigorous mathematical theory of tolerances is an important step toward the automated solution of tolerancing problems. This paper develops a mathematical theory of tolerances in which tolerance specifications are interpreted as constraints on a normed vector space model variations (M-space). This M-space provides concise representations for both dimensional and geometric tolerances, without deviating from the established tolerancing standards. This paper extends the authors' previous work to include examples of geometric orientation and form tolerances. We show that the M-space theory supports the development of effective algorithms for the solution of tolerancing problems. Through the use of solid modeling technology, it its possible to automate the solution of such problems.
Turner, Joshua U., Wozny, Michael J. A Mathematical Theory of Tolerances Geometric Modeling for CAD Applications,pp. 163-187 Existing standards give informal definitions of the various tolerances used in mechanical design. However to cumpute with tolerances, it is necessary to develop a rigorous mathematical interpretation. This paper develops a theory in which instances of in-tolerance parts are associated with points in a normed vector space over the real numbers. This permits the use of a distance metric to establish a correspondence between a tolerance specification and an "in-tolerance" region of the vector space. The exploration of examples drawn from both geoemtric and dimensional (plus-minus) tolerancing practice, leads to a number of computationally significant insights. The theory developed in this paper has been successfully used as the basis for the development of automated methods for tolerance analysis and tolerance synthesis, based on solid modeling technology.
Turner, Joshua U., Wozny, Michael J. A Framework for Tolerances Utilizing Solid Models Proceedings of Third Int'l Conf. on Cumputer-Aided Production Engineering, Ann Arbor, MI,June 1-2,1988,pp. 714-723 Tolerance, Solid model, Tolerance Analysis and Synthesis Taditional methods for tolerance analysis and synthesis are time-consuming, and have limited applicability. This paper presents a conceptual framework for tolerances, devloped at IBM, which supports the use of solid modeling technology for the automated solution of tolerancing problems. As illustration of the general applicability of this framework, we develop a linear programming method for worst-case tolerance analysis, and demonstrate the application of this method with a simple example, solved using the experimental GEOTOL solid modeling system.
Valaer, Paul, Hall, James The Problems With Geometric Dimensioning and Tolerancing Machine Design,August 23, 1990,pp. 129-133 ANSI Y14.5 was supposed to take the ambiguity out of mechanical drawings. But many experts feel that the standard has made drawings worse. Is it too late to fix?
Velsher, B. Tolerance Analysis in Electronic Packaging Electonic Packaging and Production Monte Carlo Simulation The importance of tolerance analysis is intensified by today's trend toward high-density products and quality manufacturing.
Veneziano, D., Grigoriu, M., Cornall, C.A, Vector-process Models for System Reliability Journal of the Engineering Mechanics Division ASCE, June 1977, pp. 441-461 Advanced Statistics, Other
Voelcker, Herbert B. A Current Perspective on Tolerancing and Metrology Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Toleranicng and Metrology, ASME, pp. 49-60 Tolerancing and metrology are primary tools for specifying, assessing, and controlling geometric variability in design and manufacturing. Both evolved from shop and drafting practice and are partially codified in standards. In recent years, the introduction of new technology - notably Coordinate Measuring Machines (CMMs) and CAD systems - exposed gaps, ambiguities, and inconsistencies in current practice. These findings triggered a wave of effort to formalize tolerancing and metrology, by 'mathematizing' the American tolerancing standard and by producing a new companion standard for measurement. These two developments are unlikely to be the end of teh story, however, because other gaps and issues remain. Thus tolerancing and metrology currently stand at a waterhed: the era of evolutionary practice seems to be endin, and a new era based on lmathematically defined techniques and standards seems to be dawning.This paper sets a context for the Proceedings papers that address these matters, by surveying the major approaches to tolerancing and metrology and the issues they engender. The paper concludes with brief discussions of issues not addressed well or at all in the Proceedings, and some speculations on the future.
Voelcker, Herbert, Parratt, Steffen, Robinson, Dean Session 10, The Current State of Affairs Michigan, June 17-19, 1993, CRTD-Vol.27, International Forum on Dimensional Tolerancing and Metrology, ASME, pp. 297-308 This session, the last in the scheduled series, opened with short, invited presentations by a Panel representing four communities involved with tolerancing and metrology, specifically: the Industrial User community, the Standards Community, the Research Community, and the CAD/CAM Vendor Community. These talks, and the questions they stimulated, were followed by questions and discussion pertinent to Session 9, and then by general discussion.
The Panelists provided teh statements printed below, and the Reporters produced the remaining text from written notes and tape recordings; all of this material has been edited lightly by Herb Voelcker, acting for teh Proceedings Editor, Vijay Srinivasan. The questions, responses, and remarks attributed to individuals have not been checked by those individuals because of the compressed publication schedule for the Proceedings. The Reporters and Editor apologize for any misinterpretations.
Wade, O.R. Tolerance Control in Design and Manufacturing Industrial Press Inc., 1967, pp. 176-177, Chapter 18. Tolerance Charting, Manufacturing This textbook is designed to provide a single, cost-cutting, unified technique for computing tolerance buildups and thereby simpligying the task of determining optimum tolerances for use in product design and manufacturing.
Walker, Richard K., Srinivasan, Vijay Creation and Evolution of the ASME Y 14.5.1M Standard Michigan, June 17-19, 1993, CRTD-Vol. 27, International Forum on Dimensional Tolerancing and Metrology, ASME,pp. 19-30 The forthcoming ASME Y 14.5M-1993 standard will soon have a mathematical companion in the form of ASME Y 114.5.1M-1993 standard. Effort on this mathematical document began in early 1989. This paper describes the origin, workings, and accomplishments of the Y14.5.1 subcommittee that was responsible for this new standard.
Wallace, J.R., and J.L. Grant A Least Squares Method for Computing Statistical Tolerance Limits Water Resources Research, Vol 13, No 5, pp. 819-823 Statistics, Fitting distributions Statistical analysis often requires the fitting of a probability density function to sample data in order to estimate either the population parameters or a particular percentile point of the population. In either case the exact determination of the population. The theories of statistical confidence regions and tolerance limits allow inferences to be drawn regarding relationships between the estimates and the corresponding unknown population values. A least squares procedure has been devised which allows the construction of cofidence regions and tolerance limits for arbitrary distribution functions. The class errors, ie, are defined as the difference between the sample histogram and the expected frequency based upon the density function. The confiendence region is defined by the relation Ra = (-:[R1(e)/R2(e)]< [m/(N-m)]F(a,m,N - m)}, where - represents the m-dimensional parameter vector of the distribution function, R1(e) and R2(e) represent decompositions of Žei2 of ranks m and N - m, respectively, and F is Snedecor's F statistic. The n tolerance limit of the - percentile point is found from the relation v,-- = max--"Rn{v:švp(x,-) dx = -}.
Wampler, C., Buffinton, K., Shu-hui, J. Formulation of Equations of Motion for Systems Subject to Constraints Journal of Applied Mechanics,June 1985,Vol. 52/465-47 Kinematics, Dynamics A method for constructing equations of motion governing constrained systems is presented. The method, which is particularly useful when equations of motion have already been formulated, and new equations of motion, reflecting the presence of additional constraints are needed, allow the new equations to be written as a recombination of terms comprising the original equations. An explicit form in which the new dynamical equations may be cast for the purpose of numerical integration is developed, along with special cases that demonstrate how the procedure may be simplified in two commonly occurring situations. An illustrative example from the field of robotics is presented, and several areas of application are identified.
Wang, Nanxin, Ozsoy, Tulga M. Automatic Generation of Tolerance Chains from Mating Relations Represented in Assembly Models Advances in Design Automation -1990, Vol. 1, ASME Publication No. DE-Vol. 23-1 pp. 227-233 This paper presents an algorithm for generating tolerance chains from the mating relations between components of assemblies. The algorithm is developed upon a feature-based assembly modeling strategy that represents each component in close relation to its mating features, dimensions and tolerances. The mating relations within an assembly are described by a mating graph. Tolerance chains together with their dimensions and tolerances are generated automatically by searching through a mating graph for matching mating geatures. A prototype program package based on the presented algorithm has been developed, and several examples of various complexity have been tested with success.
Wang, Nanxin, Ozsoy, Tulga M. Representation of Assemblies for Automatic Tolerance Chain Generation Engineering with Computers 6, 121-126 (1990) A scheme of representing assemblies and an algorithm for the tolerance chain generation are developed so that tolerance chains of assemblies can be generated automatically to accommodate tolerance analysis at the assembly level. In the hierarchical data structure representing an assembly the connectivity information is carried by the instances of components and subassemblies, and the mating relations between each pair of mating entities are described by mating links, mating paths, mating conditions, and mating features. Mating graphs are derived from the mating links before they are searched for the generation of tolerance chains. The scheme has been implemented in a prototype interactive package that allows the user to model assemblies directly without detailed object modeling. Several examples of various complexity have been tested with success.
Wang, Nanxin, Ozsoy, Tulga M. A Scheme to Represent Features, Dimensions, and Tolerances in Geometric Modeling Journal of Mfg. Systems,V. 10, N 3,pp. 233-240 CAD, Data Stucture, Feature Dimension, Tolerance This paper presents a scheme for representing features, demensions, and tolerances in geometric models. The scheme combines a modified CSG tree with a face-edge based B-rep data structure to represent high-level form features and low-level primitve features. Dimensions and tolerances are treated as constraints. The dimensional relations within a machine part are described by constraining operators from which the position and orientation of form fetures are derived automatically. The modification of geometry can be achieved by directly changing dimensions. The representation promises a new engineering tool for design and manufacturing engineers and provides the important foundation for supporting engineering applications such as tolerance analysis and dimensioning checking. The scheme has been implemented in a prototype system.
Wearring, Colin, Cola, Gary Identifying Sources of Build Variation Using VSA Audit Applied Computer Solutions - 911644 This paper outlines the use of VSA Audit procedures to identify sources of build variation in an assembly operation. VSA Audit isolates the effects of component variation from variation incurred during the assembly process. (wear of fixtures, fixture breakage, etc.) This approach provides significant advantages when troubleshooting dimensional variation issues in an assembly plant evnironment.
Wehage, R.A. Solution of Multibody Dynamics Using Natural Factors and Iterative Refinement - Part 1: Open Kinematic Loops Advances in Design Automation, ASME Publication.DE 19-3, Sept. 17-21, 1989, pp. 125-132 Open loop, Dynamics, Recursive Algorithm, Kinematics, Loop Constraint An O(n) methodology employing block matix partioning and recursive projection to solve multibody equations of motion coupled by a sparse connectivity matrix was developed in (Wehage, 1988, 1989, Wehage and Shabana, 1989). These primitive equations, which include all joint generalized and absolute coordinates and constraint reaction forces, are easily obtained form free body diagrams. The corresponding recursive algorithms isolate the generalized joint accelerations for numerical integration and offer the best computational advantage when solving long kinematic chains on serial processors. Recursion, however, precludes effective exploitation of vector or parallel processors. Therefore this paper explores less recursive algorithms by applying the inverse of joint connectivity to eliminate absolute accelerations and constraint forces yielding a generalized system of equations. The resulting positive definite generalized inertia matrix is first represented symbolically as a product of sparse matrices, or which some are singular and then as the product of nonsingular factors obtained recursively. This algorithm has overhead ranging from O(n2) to O(n) depending on the degree of system parallelism. Incorporating iterative refinement and exploiting parallel and vector processing makes this approach competitive for many applications.
Wehage, R.A. Solution of Multibody Dynamics Using Natural Factors and Iterative Refinement - Part II: Closed Kinematic Loops Advances in Design Automation, ASME Publication DE 19-3, Sept. 17-21, 1989, pp. 133-139. Kinematics, Loop Constraint, Closed loop, Dynamics, Recursive Algorithm A symbolic algorithm exploiting natural factors of generalized inertia matrices and iterative refinement to compute the dynamics of open kinematic-loop systems was developed in Part I of this paper. The general equations of motion for open and closed loop systems were derived in an earlier paper (Wehage, 1988) and it was shown that algorithms for open loop dynamics could be used to solve closed loop problems by cutting the secondary joints. In this paper it is shown that secondary joint forces can be obtained either from a dynamic force balance or from constraint surface deformations. Closed kinematic loops create additional numerical problems and require substantially more computational overhaed. Therefore, the iterative refinement algorithm developed in Part I is extended to address some of these problems. Exploitation of iterative refinement and computer architecture can substantially improve overall algorithm performances.
Wei-Liang, Xu and Zhang Qi-Xian Probabilistic Analysis and Monte Carlo Simulation of The Kinematic Error in a Spatial Linkage Mech. Mach. Theory Vol. 24, No. 1, pp. 19-27, 1989. Linkage Tolerances, Monte Carlo The stochastic models of the usual joints are first established through introducing the concepts of "clearance characteristic element" and "clearance space". After deriving the probability density function of the joint clearance and making the probabilistic analysis of the resulted kinematic errors, the sampling formulas of the independent variables of the joint clearances are further deduced. Through Monte Carlo simulation, the statistical characteristics and frequency histograms of the kinematic errors are then analysed on computer. For illustration, the spatial RCST linkage is taken as a numerical example.
Weill, R., Clement, A., Hocken, R., Farmer, L.E., Gladman, C.A., Wirtz, A., Bourdet, P., Freckleton, J.E., Kunzmann, H., Ham, I., Trumpold, H., Matthias, E. Tolerancing for Function Annals of the CIRP Vol. 37/2/1988,pp. 603-610 Tolerancing, Dimensioning, Computerized Measuring Machines, Mechanical Design Although the basic objective of design is to create mechanical systems which are first of all suitable for function, the way to achieve this aim is usually an indirect one. The designer has to observe a certain number of standards and technical rules relating to mechanical tolerances, geometrical and dimensional, which will enable to produce a design which is not only consistent with the function of the part, but also with manufacturing constraints, assembly limitations, and inspection possibilities. These latter conditions determine essentially the economy of the industrial production of components. It is therefore a central concern of the design and manufacturing functions in industry to strive for a tolerancing system which would support the designer in finding an optimal way from functional requirements and production constraints to a comprehensive tolerance assessment of mechanical features composing the parts. This review is therefore concerned with identifying the remaining problems in tolerancing, their relations with functions and to suggest approach directions for their future practical solutions.
Wesley, Michael A., Markowsky, George Generation of Solid Models from Two-Dimensional Data Solid Modeling by Computer: From Theory to Application,Plenum Press,NY,1984,pp. 23-51,MS Pickett & JW Boyse,eds CAD, Solid Model Many important CAD data bases exist only in wire frame (three-dimensional edge and vertex) or projection (two-dimensional planarview) form. In order to exploit the many advantqges of compter-based solid modeling, the data descriptors of the objects in these data bases must be converted to solid form. This paper surveys methods for performing the transformation automatically, describes one polyhedral algorithm in some detail, and explores the degree of automation that is both possible and practicable.
Wilde, D., and Prentice, E. Minimum Exponential Cost Allocation of Sure-Fit Tolerances J. of Engineering for Industry, ASME, vol 97, Nov. 1975, pp. 1395-1398. Optimization, Cost The least cost allocation of sure-fit machine tolerances for Speckhart's exponential cost model is solved in closed form, without numerical iteration, as a geometric program with zero desgrees of difficulty. The results show the importance of an exponential cost sensitivity parameter defined as the "characteristic tolerance." The theoretical minimum cost tolerances can be computed later in closed form. Potential cost servings are significant.
Wilde, Doug Simplifying Discrete Tolerance Assignment ASME Paper 75-DET-106 A discrete tolerance assignment problem exposed by Smathers and Ostwald is subjected to rigorous siplifications suggested by pseudo-boolean programming. The solution to the simplified example is immediate, whereas previous solution by dynamic programming required evaluation of 10 percent of the 1296 possibiliies. The simplifications involve first transforming to excess tolerance and cost saving, then identifying and deleting redundant inequalities, and finally using the remaining constraint to eliminate a variable and expose profitable possibilities. The unsimplified problem has 20 bivalent (zero-one) variables constrained by eight equalities and two upper bound inequalities. Simplified, the problem has only four variables and a single constraint function bounded in a unit interval, to which the solution is apparent by inspection.
Wilkinson, Roger, I. The Combination of Probability Curves in Engineering American Institue of Electrical Engineering, Vol. 61, 1942, pp. 953-962. Statistics, Probability Distribution Engineers are quite familiar with simple probability distributions showing the relative likelihoods of occurence of the different values which a varying physical or electrical quantity may assume. As the complexities of machines and circuits in modern design increase, it becomes highly desirable toobe able tostimate the probability distribution resulting from the joint presence of two or more sources of variation. This paper will undertake to present something of the theory of making such combinations, and its application to a number of practical examples.
Wirsching, P.H. On the Behavior of Statistical Models Used for Design Transactions of the ASME, May 1976, pp. 601-606. Probabilistic Design In probablistic design, it is common practice to use two parameter statistical models (e.g., normal lognormal) to describe random factors. However, given a ramdom sample of data, it is often difficult to distinguish which of several competing models rovides the best description. It is demonstrated herein that the choice of model has a profound effect on probabioity estimates, particularly in the tails fo the distributions. Given only the mean and standard deviation of a random variable, the Tchebycheff or Champ-Meidell inequalities can be used to provide upper-bound estimates of probabilities. However, the inequalities are usually too weak for design purposes. Probability models which yield more reasonable results are proposed. The two parameter exponential and power models are proposed for quasi-upper bounds of right and left tail probabilities, respectively. The exponential and ower models are used for stress and strength, respectively, to derive from inference theory, quasi-upper bounds for probability of failure of a structural element.
Wirsching, P.H., Haugen, E.B. Probabilistic Design of Helical Springs ASME paper 74-WA/DE-21 Probabilistic Design In summary, the probabilistic approach promises to provide a more rational description of design than does the conventional approach. A disadvantage of probabilistic design is that the algorithms are more complicated.
Wirsching, P.H., Jones, L.H. On the Use of the Extreme Value Distribution in Reliability Anlysis and Design Journal of Engineering for Industry, Transactions of the ASME, Aug. 1976, pp. 1080-1085 Reliability, Analysis and Design, Statistics Use of the Type 1 Extreme Value Distribution of Maxima to design engineerig problems is reviewed. Results of a Monte Carlo study of the statistical behavior of the distribution parameter estimators are summarized. The study compares behavior of the method of moment estimators, a simpler algorithm, is but slightly less efficient than the maximum likelihood estimators. An example is given to illustrate how a design engineer uses these results to translate observations into an estimate of "reliability" or "risk." Moreover, a scheme for obtaining approximate confidence intervals on reliability is presented..
Wirtz, Adolf Vectorial Tolerancing Neu-Technikum Buchs, Buchs, Switzerland Most features defined in the ISO-Tolerance System combine different geometrical attributes. For production process control it is necessary to have exact geometrical deviations, as different deviations are caused by different components of the machine tool. When the attributes are given in a pure mathematical description, this information is given in a computer conform way. Therefore it is possible to send the data in the same format from CAD to CAM to CMM.
Wirtz, Adolf Vectorial Tolerancing A Baic Element for Quality Control Proceeding of 3rd CIRP Seminars on Computer Aided Tolerancing, Cachan, France, April 27-28, 1993,pp. 115-128 ISO-Tolerances, Vectorioal Tolerancing, Process Control This paper shows the advantage of Vectorial Tolerancing in the manufacturing and designing process. It is based on a exact geometrical description of the workpiece shape. This description allows the automation in machining and measuring.
Wolff, E.R. Graph Sets Safe Tolerance for Cumulative Dimensions Product Engineering, Jan. 2, 1961. pp. 40-43 Statistical Methods, RSS Non-Normal When design keeps adding on dimensions (poor practice, but not always avoidable) this graph will help establish an over-all tolerance that is neither too conservative nor too risky.
Xue, Deyi, Dong, Zuomin Automated Concurrent Design Based on Combined Feature, Tolerance, Production Process and Cost Models DE-Vol. 65-2, Advances in Design Automation-Volume 2 ASME 1993 This paper presents a method for conducting automated concurrent design using combined feature, tolerance, production process and cost models. The introduced features are defined and examined in terms of design function, manufacturing method, and geometric shape and accuracy. The integrated design model has three functions: (a) facilitating the generation of all feasible designs by design feature-based knowledge reasoning using an intelligent CAD system; (b) representing various design information using the geometric primitives of a concventional CAD system; (c) describing a design using production process-oriented manufactuing features for evaluating manufacturability and production costs. This approach can incorporate manufacturing consideration into design phase and identify a cost-effective design satisfying given design functions and achieving minimum production costs. Functions of a prototype system are illustrated using an example.
Zhang, Chun, Hsu-Pin, Wang The Discrete Tolerance Optimization Problem Manufacturing Review, July 1991 Tolerance, Optimization Tolerance design and synthesis is a major task of product and process design and is in a period of extensive study due both to increased demands for quality products and to increasing automation of machining and assembly. Optimum tolerance design and synthesis ensures good quality product at low cost.This paper gives and analysis of the tolerance optimization problem. Three studies were conducted. First, the tolerance sythesis problem was formulated as a nonlinear discrete optimization model, which has as its objective the minimum manufacturing cost. Second, the discrete optimization model was treated as a continuous optimization model and solved with the swquential quadratic programming (SQP) method. Optimality of the continuous model was examined to understand the characteristics of the problem. Third, a simulated annealing algorithm was coded to solve the discrete tolerance optimization model, and the algorithm was compared with the SQP method on a range of problems. The simulated annealing algorithm appears to be rather effective, in particular, for problems with a wide process capability range or nonoverlapping cost curves.