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AutoCAD 2D Analyzer:
CHAPTER 1: INTRODUCTION
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Increased international competition has made it clear that U.S. industry can no longer continue to produce products by old 1950's and 60's manufacturing methods. It is not enough to excel in research and innovation of new products. Our products must be built to competitive quality standards at competitive costs.
In the past, the engineer's design goal was to produce a working prototype, usually without considering future steps such as manufacturing. But this is short-sighted, comparable to driving a car along a dark rural highway at night with the headlights on low beam. The problems ahead cannot be seen. Today's designer must be far-sighted, like driving with the high beams on. He must look ahead to the manufacturing and long term consequences of his design decisions.
Figure 1.1. Short- and far- sighted engineering.
Tolerance design is an engineering function with an immense influence on the final cost of a manufactured product. The seemingly trivial task of assigning tolerances to each component dimension of an engineering drawing is not just a make-work exercise. Excessively tight tolerances can require costly machines, tooling or secondary processes. Extensive inspection, gauging and statistical quality control procedures must then be set up to monitor production and assure that tolerance specifications are met.
Tolerance analysis is often detested by engineering designers. Sometimes it is avoided or procrastinated until no time is left to do an adequate job. Yet, tolerance analysis can do more to reduce manufacturing cost, improve quality and retain market share than almost any other design activity. Even modest efforts in this area can yield significant benefits for very little capital investment.
1.1 Sources of Variation
The three major sources of variation in mechanical assemblies are illustrated in Figure 1.2:
Figure 1.2. Sources of variation in mechanical assemblies.
Manufactured parts are seldom used in isolation. They are used in assemblies of parts. The dimensional variations which occur in an assembly accumulate statistically and propagate kinematically, causing the overall assembly dimensions to vary with each contributing source of variation. Critical clearances and fits which affect the assembly's performance are thus subject to variation.
AutoCATS is an engineering tool which uses statistical methods to enable a designer to predict the effects of manufacturing variation on design performance and to improve this performance.
1.2 CATS Overview
CATS is a family of Computer-Aided Tolerancing Software developed at Brigham Young University for assembly tolerance analysis and the production design of mechanical assemblies.
AutoCATS is an AutoCAD-based version of CATS. It provides a powerful CAE environment in which mathematical models of 2-D assemblies may be created and used for predicting the design consequences of manufacturing variations.
Analysis tools available in the AutoCATS 2-D Analyzer include models for:
Several levels of tolerance selection aids are also available (see Fig. 1-3):
Figure 1-3. CATS Tolerance Selection Aids.
The AutoCATS 2-D Analyzer user interface is well suited to design iteration. Neutral files of tolerance analysis models created by the AutoCATS 2-D Modeler may be stored and retrieved for further modification. The Analyzer features full screen data editing and is menu-driven with local/global menus. An optional command-driven mode is available for experienced users, with a command buffer which allows chaining commands to bypass the prompts. Command scripts of frequently repeated tasks can also be stored and retrieved.
1.3 Tolerance Analysis vs. Tolerance Allocation
Tolerance analysis and tolerance allocation differ in their inputs and outputs. In tolerance analysis, the component tolerances are all known and the resulting assembly limits are calculated directly using a worst case or statistical model of an assembly. In tolerance allocation, an assembly tolerance is specified by the design requirements and must be distributed among the component parts. How the tolerances are distributed depends on the allocation rule applied and whether a worst case or statistical assembly model is used.
Fig. 1.4. Tolerance Analysis vs. Tolerance Allocation.
In tolerance analysis, the calculated assembly limits are compared to the specified assembly limits and the yield or percent of acceptable assemblies is predicted. In tolerance allocation, however, the designer specifies the yield then determines a set of component tolerances which will assure that the specified yield will be met.
Direct tolerance analysis is principally intended for parts and assemblies that are currently in production. Tolerance allocation is the typical problem encountered in design, long before production has begun. It is a much more difficult problem because of the number of design variables to be determined and a lack of manufacturing data.
1.4 Tolerance Analysis Models
To obtain the resulting assembly tolerance, the component tolerances are summed by the Analyzer using one of the following three models:
1. Worst Case Analysis. The specified component tolerances are summed arithmetically (Linear Sum) to determine the extreme cases of assembly dimensions. If these calculated extremes fall within specified assembly limits, 100% of the assemblies created from components with the specified tolerances can be expected to be within spec.
2. Statistical Analysis. Component tolerances are summed statistically by the root-summed-square (RSS) method to determine the probable variation in critical assembly dimensions. If the +/-3[[sigma]] limits of the normal distribution for an assembly's critical dimension fall on the specified assembly limits, these component tolerances can be expected to produce 99.73% of assemblies within spec. An acceptance fraction greater or less than 99.73% may also be selected.
3. Six Sigma Analysis. During any production process, the mean of the process may not be centered between the assembly tolerance limits. Tool wear, setup error, fixture bias, etc. can cause the mean to drift or shift off center. Mean shifts of the several components in an assembly can accumulate similar to the way tolerances accumulate, resulting in significant increases in the number of rejects. The Six Sigma model is a mathematical model for tolerance accumulation which accounts for both mean shifts and statistical tolerance stackups. This model was developed by the Motorola Corporation as part of their award-winning Six Sigma program for quality assurance. It allows more realistic estimates of the effects of process variations, but it requires better information about each process.
1.5 Tolerance Allocation Options
When an assembly tolerance is specified by the designer, the sum of the component tolerances is compared to the specified assembly tolerance. If they do not agree, a set of "Allocated Tolerances" can be computed by one of the Analyzer's built-in allocation rules to assure that both assembly tolerance and yield specifications are met.
1. Tolerance Allocation by Proportional Scaling. This is the default allocation rule in the AutoCATS 2D Analyzer. The Allocated Tolerances are calculated by scaling each component tolerance up or down by a constant proportionality factor, such that the resulting assembly tolerance meets a given specification. By scaling, the relative magnitudes of the initial set of component tolerances are preserved. This method can be applied to both worst case and statistical assembly models. Choosing a statistical analysis model will result in considerably larger component tolerances than worst case.
2. Tolerance Allocation by Weight Factors. This is an allocation method in which the designer assigns weight factors to individual component tolerances. If the component tolerances sum to less than the assembly tolerance, then one or more of the component tolerances are increased until the sum is equal to the assembly limit. The weight factors determine which tolerances should be increased and in what proportion.
3. Tolerance Allocation by Precision Factors. It is well known that tolerances increase with the size of the parts being produced. A common rule of thumb assumes that for a constant level of precision, the tolerance increases with the cube root of the nominal dimension. For example, to machine an 8.0 in. diameter part to the same precision as a 1.0 in. diameter part, the tolerance would be doubled (cube root of 8). The Precision Factor Allocation rule in the Analyzer is based on this rule of thumb. Proportional scaling is then automatically used to meet assembly requirements.
4. Least Cost Tolerance Allocation by Optimization. An optimization algorithm is used to determine the least cost allocation of tolerances among component parts. Tolerances are loosened on dimensions produced by expensive processes and tightened for cheaper processes. The tolerance allocation which will result in the lowest production costs for the complete assembly is determined subject to the constraint that the sum of the tolerances can not exceed the specified assembly tolerance. Either a worst case or a statistical model may be selected as the constraint. An empirical cost-vs-tolerance curve must be supplied by the designer for each part. Appendix E contains some suggested cost-vs-tolerance data for common processes.
1.6. Cost-vs-Tolerance Options
The optimum cost allocation option requires user-supplied cost-vs-tolerance data in the form of an empirical algebraic function. The general cost-tolerance model has the form:
Cost =A + (B . tolk ), where k is usually between -0.5 and -1.5.
Thus, manufacturing costs are assumed to vary as 1 / tolk. The coefficient A in the cost model is the "delivery cost," which may include the cost of materials, set-up, and prior production operations, computed on a per-part basis. B is a scale factor which describes how expensive each process is and includes the charge rate of the machine. When tighter tolerances are called for, speeds and feeds may be reduced and the number of passes increased, requiring more time and higher costs. The exponent k describes how sensitive the process cost is to changes in tolerance specifications.
1.7 Additional Design Features
Several valuable design tools are included in this version of the AutoCATS Analyzer:
1. Fixed Tolerance Flag. Selected tolerances may be designated as "fixed" by setting a flag in the edit screens. This allows the designer to hold individual component tolerances from being modified by the built-in allocation or optimization options. Such action may be necessary for:
a) Vendor-supplied components
b) Critical component tolerances
c) Interdependent assemblies, where the same component appears in more than one assembly and may have previously been optimized or re-scaled.
2. Report Generator. When analysis output is displayed, the user is prompted whether to save the output to a .OUT file. This file can be used to store output for all analysis results as a record of design history. Each time a neutral file is analyzed, an entry is appended to its .OUT file.
1.8 Reference Handbook
An on-line Tolerance Reference Handbook has been initiated in this version of AutoCATS. It contains tables and graphs to help the designer select reasonable tolerances for components. It may be referenced from within any menu of the program by typing /REF. Useful options include:
1. Drilled Hole Tolerances. As shown in Appendix A, a graph which gives curves for the average, maximum, and minimum tolerance as a function of the drill diameter. Currently, this option gives tolerances for drill diameters from 0 to 1 inch.
2. Typical Machine Tolerances. As shown in Appendix B, a bar chart and table showing the range of tolerances typically produced by common machining operations. The tolerances are dependent upon the basic dimension of the part being machined. The range for different size parts is reflected in the table.
3. Range of Surface Finish. As shown in Appendix C, a chart showing average and less frequent surface finishes which can be achieved by some of the most common production methods.
4. Cylindrical Fits. An interactive program has been implemented for selecting tolerances for cylindrical fits according to ANSI standards. Tables and fit diagrams may be displayed for RC, LC, LT, LN, and FN fits. In addition, the designer may be prompted for data to construct a specific fit diagram for a selected class of fit. A graph of the tolerance bands and resulting maximum and minimum expected clearance or interference is displayed. In addition, the tolerances specified in the standards can be modified to accommodate a vendor-supplied component. An RC fit diagram is featured in Appendix D.
1.9 AutoCATS 2-D Modeler
The AutoCATS 2-D Modeler is a graphical preprocessor designed to be used hand in hand with the AutoCATS 2-D Analyzer. The Modeler provides a powerful environment in which a kinematic assembly model may be created graphically and prepared for tolerance analysis. A vector assembly model is overlaid on an existing CAD model, extracting the geometry directly from the CAD database, and storing it as part of the CAD model. A menu-driven user-interface commands the modeler and appends the assembly tolerance model to the CAD database just as the CAD system itself accesses geometry from its database. All of the CAD system functions for constructing or modifying the model are available at any time. Errors due to re-entering geometry are eliminated, and keyboard entry is minimized. The modeler passes information on to the AutoCATS 2-D Analyzer via a "neutral file". Algebraic assembly equations may be then be generated by the Analyzer directly from the vector model, set up and solved with little human intervention.
Figure 1.5 Integrated AutoCATS modeling system for assembly tolerance analysis.
Modeler: Title | Overview | Modeling | Commands
Analyzer: Title | Overview | Analysis | Allocation | Interface
Modeler: Title | Overview | Modeling | Commands
Analyzer: Title | Overview | Analysis | Allocation | Interface
Verification: Title | Overview
Modeler: Title | Overview | Modeling | Commands | Building a Tolerance Model
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