ADCATS Research Bibliography M through R
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Bibliography Abstracts M through R
Home : Tolerancing Bibliography : M through R : Abstracts M through R

Machining Tolerances
Machining Tolerances Product Engineering, May 1957, p. 219

Keywords: Machining Tolerances

Abstract: 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

Keywords: Feature modeling, Degree of freedom, Vector tolerancing, Assignment

Abstract: 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

Keywords: Software interface, Geometric Model, AIS

Abstract: 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.

Keywords: Linkage Tolerances

Abstract: 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

Abstract: 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

Keywords: Case Studies, Manufacturing Distributions, RSS, Non-Normal

Abstract: 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.

Keywords: Geometric Tolerance, Specification

Abstract: 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.

Abstract: 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

Keywords: Quality Assurance

Abstract: 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

Abstract: 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.

Keywords: 3-D, Solid Models, Constructive Variational Geometry

Abstract: 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

Abstract: 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

Keywords: Tolerance, Deviation, Vector, Co-ordinate systems

Abstract: 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

Keywords: Vectorial Tolerancing, Milling, Multivariate Statistical Process Control

Abstract: 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

Keywords: Statistical Methods

Abstract: 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

Abstract: 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

Abstract: 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

Keywords: Tolerance, Safety, Quality

Abstract: 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

Keywords: Optimization, Tolerance Allocation

Abstract: 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.

Abstract: 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

Abstract: 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.

Abstract: 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

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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.

Abstract: 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.

Keywords: Probabalistic design

Abstract: 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

Abstract: 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

Keywords: Optimum Tolerancing, Linkages,

Abstract: 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

Keywords: Optimum Tolerancing

Abstract: 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

Abstract: 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

Keywords: Geometric Tolerancing, Tolerance Synthesis, Genetic Algorithms

Abstract: 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

Abstract: 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.

Keywords: 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.

Abstract: 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

Abstract: 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.

Keywords: Machine Tolerances

Abstract: 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.

Keywords: Manufacturing Tolerances

Abstract: 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

Abstract: 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

Keywords: Kinematics, Loop constraint

Abstract: 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

Abstract: 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.

Abstract: 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

Keywords: Monte Carlo, Simulation, Geometric Tolerance, Gauge

Abstract: 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

Keywords: Statistical Methods, Monte Carlo

Abstract: 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.

Keywords: Optimization, Discrete Cost, Zero-one

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Keywords: 2-D Application Reliability Method, Tolerance, Statistics

Abstract: 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

Keywords: Reliability, Structural Safety, Index of Reliability, Limit States, Structural Systems, Modes of Failure

Abstract: 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.

Abstract: 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.

Keywords: tolerances, optimize, probabilistic methods, CAD

Abstract: 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.

Keywords: Empirical Distributions, Moments, Adv. Statistical Methods (other)

Abstract: 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

Keywords: Reliability Index, Reliability Method, Statistics

Parkinson, D.B.
Reliability Indices Employing Measures of Curvature Reliability Engineering 6 (1983) p. 153-179

Abstract: 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.

Keywords: Empirical Distributions, Moments, Adv Stat (other)

Abstract: 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"

Abstract: 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

Keywords: 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

Abstract: 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

Keywords: 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

Abstract: 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.

Keywords: Statistical Methods, Cost, Allocation

Abstract: 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.

Keywords: Statistics, Tolerance

Abstract: 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

Abstract: 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.

Abstract: 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

Keywords: machine kinematics, accuracy, higher order approximation

Abstract: 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

Keywords: Tolerancing, Dimensional chain, Compensation, Accuracy evalaluation, Accuracy optimization.

Abstract: 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

Keywords: Monte Carlo, Simulation, Tolerance, Crawler Track Chain/Shoe

Abstract: 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.

Keywords: Empirical Distributions, Moments

Abstract: 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

Keywords: Solid Model, Tolerance

Abstract: 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.

Keywords: Tolerance Analysis & Synthesis: Can-follower, Kinematics, Dynamics

Abstract: 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

Abstract: 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.

Abstract: 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

Keywords: 3-D, Solid Modeling, Tolerance Theory

Abstract: 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

Keywords: Solid Model, Review

Abstract: 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

Keywords: Statistical Methods

Abstract: 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

Keywords: Tolerancing, Tolerance modeling, Tolerance analysis, Tolerance transfer, Tolerancing standards

Abstract: 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.

Abstract: 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

Keywords: Solid modelling, quadric surfaces, constraints, rigid motions, computer graphics, CSG, Solid Model

Abstract: 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

Abstract: 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

Abstract: 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.

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