A survey of research in the application of tolerance analysis to the design of mechanical assemblies
 Kenneth W. Chase,
 Alan R. Parkinson
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Tolerance analysis is receiving renewed emphasis as industry recognizes that tolerance management is a key element in their programs for improving quality, reducing overall costs, and retaining market share. The specification of tolerances is being elevated from a menial task to a legitimate engineering design function. New engineering models and sophisticated analysis tools are being developed to assist design engineers in specifying tolerances on the basis of performance requirements and manufacturing considerations. This paper presents an overview of tolerance analysis applications to design with emphasis on recent research that is advancing the state of the art. Major topics covered are (1) new models for tolerance accumulation in mechanical assemblies, including the Motorola Six Sigma model; (2) algorithms for allocating the specified assembly tolerance among the components of an assembly; (3) the development of 2D and 3D tolerance analysis models; (4) methods which account for nonnormal statistical distributions and nonlinear effects; and (5) several strategies for improving designs through the application of modern analytical tools.
 Agarwal, M. (1981), “Optimal Synthesis of Tolerance and Clearance in Function Generating Mechanisms—A Parametric Programming Problem,” ASME Paper No. 81DET5
 Andersen, C.B. (1990), “General System for Least Cost Tolerance Allocation in Mechanical Assemblies,” ADCATS Report No. 90–2, Brigham Young University
 ASME (1990), “Research Needs and Technological Opportunities in Mechanical Tolerancing,” ASME Publication No. CRTD15
 ASME (1983), “Dimensioning and Tolerancing,” ANSI Y14.5M1982, ASME Publication
 Baumgarten, J. and K. Van der Werff (1985), “A Probabilistic Study Relating to Tolerancing and Path Generation Error,”J. of Mechanism and Machine Theory, v 20, n 1, pp. 71–76
 Bender, A., Jr. (1968), “Statistical Tolerancing as it Relates to Quality Control and the Designer,” SAE Paper No. 680490
 Bennett, G. and L.C. Gupta (1969), “Least Cost Tolerances—I and II,”International J. of Production Research, v 8, pp. 65–74 and 169–181
 Beohar, S. and A. Rao (1980), “Optimum Stochastic Synthesis of Four Bar Spatial Function Generators,” ASME Paper No. 80DET32
 Bjorke, O. (1989),ComputerAided Tolerancing, Second Ed., ASME Press
 Byrne, D. and S. Taguchi (1987), “The Taguchi Approach to Parameter Design,”Quality Progress, pp. 19–26, December
 Chase, K.W. (1991), “A Bibliography on Tolerance Analysis of Mechanical Assemblies,” ADCATS Report No. 912, Brigham Young University
 Chase, K.W. and W.H. Greenwood (1988), “Design Issues in Mechanical Tolerance Analysis,”Manufacturing Review, ASME, v 1, n 1, pp. 50–59, March
 Chase, K.W. and W.H. Greenwood, B.G. Loosli, and L.F. Hauglund (1990), “Least Cost Tolerance Allocation for Mechanical Assemblies with Automated Process Selection,”Manufacturing Review, ASME, v 3, n 1, pp. 49–59, March
 Chase, K., C. Sorensen, and C. Andersen (1989), “Recent Developments in Tolerance Analysis Software for Mechanical Assemblies, Part A: TwoDimensional Modeling,” Proceedings of the ASQC Western Regional Conference—1989, pp. 73–80
 Chun, K. (1988), “Development of TwoDimensional Tolerance Modeling Methods for CAD Systems,” ADCATS Report No. 887, Brigham Young University
 Chung, J.C.H. and M.D. Schussel (1990), “Technical Evaluation of Variational and Parametric Design,”Computers in Engineering—1990, ASME, 1, pp. 289–298
 Cox, N.D. (1979), “Tolerance Analysis by Computer,”J. of Quality Technology, v 11, n 2, pp. 80–87, April
 Cox, N.D. (1986), “How to Perform Statistical Tolerance Analysis,” ASQC Series Vol 11, Basic References in Quality Control
 Craig, M. (1989), “Managing Variation by Design Using Simulation Methods,”Failure Prevention and Reliability—1989, ASME Publ. No. DE—Vol 16, pp. 153–163
 DeDoncker, D. and A. Spencer (1987), “Assembly Tolerance Analysis with Simulation and Optimization Techniques,” SAE Paper No. 870263
 Dhande, S. and J. Chakraborty (1973), “Analysis and Synthesis of Mechanical Error in Linkages—A Stochastic Approach,”J. of Engineering for Industry, ASME, v 105, pp. 672–676
 Dhande, S. and J. Chakraborty (1978), “Mechanical Error Analysis of Spatial Linkages,”J. of Mechanical Design, ASME, v 100, pp. 732–738
 Doepker, P.E. and D. Nies (1989), “Designing Brake Components Using Variation Simulation Modeling,”Failure Prevention and Reliability—1989, ASME Publ. No. DE—Vol 16, pp. 131–138
 Early, R. and J. Thompson (1989), “Variation Simulation Modeling—Variation Analysis Using Monte Carlo Simulation,”Failure Prevention and Reliability—1989, ASME Publ. No. DE—Vol 16, pp. 139–144
 Eaton, F. (1975), “Computer Model of a ThreeDimensional Assembly,” ASME Paper No. 75DE21
 Edel, D.H. and T.B. Auer (1965), “Determine the Least Cost Combination for Tolerance Accumulations in a Drive Shaft Seal Assembly,”General Motors Engineering Journal, Fourth Quarter, 1964, pp. 37–38, First Quarter, pp. 36–38
 Eggert, R.J. and R.W. Mayne, (1990), “Probabilistic Optimization Using Successive Surrogate Probability Density Function,Proc. of ASME 16th Design Automation Conf., Chicago, IL, DE—Vol 231, p. 129, September
 Etesami, F. (1987), “On the Theory of Geometric Tolerancing,”Computers in Engineering—1987, ASME, 2, pp. 327–334
 Evans, D.H. (1967), “An Application of Numerical Integration Techniques to Statistical Tolerancing,”Technometrics, v 9, n 3, pp. 441–456, August
 Evans, D.H. (1970), “A Statistical Tolerancing Formulation,”J. of Quality Technology, v 2, n 4, pp. 226–231, October
 Evans, D.H. (1971), “An Application of Numerical Integration Techniques to Statistical Tolerancing, II—A Note on the Error,”Technometrics, v 13, n 2, pp. 315–324, May
 Evans, D.H. (1972), “An Application of Numerical Integration Techniques to Statistical Tolerancing, III—General Distributions,”Technometrics, v 14, n 1, pp 23–25, February
 Evans, D.H. (1974), “Statistical Tolerancing: State of the Art, Part 1. Background,”J. of Quality Technology, v 6, n 4, pp. 188–195, October
 Evans, D.H. (1975a), “Statistical Tolerancing: State of the Art, Part 2. Methods of Estimating Moments,”J. of Quality Technology, v 7, n 1, pp. 1–12, January
 Evans, D.H. (1975b), “Statistical Tolerancing: State of the Art, Part 3. Shifts and Drifts,”J. of Quality Technology, v 7, n 2, pp. 72–76, April
 Faux, I.D. (1986), “Reconciliation of Design and Manufacturing Requirements for Product Description Data Using Functional Primitive Part Features,” CAMI Report No. R86ANC/GM/PP01.1, CAMI Inc, Arlington, TX, December
 Fenton R., W. Cleghorn, and J. Fu (1989), “Allocation of Dimensional Tolerances for Multiple Loop Assemblies,”J. of Mechanisms, Transmissions, and Automation in Design, v 111, pp. 465–470, December
 Fortini, E. (1967),Dimensioning for Interchangeable Manufacture, Industrial Press
 Fortini, E. (1985), “Dimensions and Tolerances,”Mechanical Design and Systems Handbook, Second Ed., H. Rothbart editor, McGrawHill
 Foster, L.W. (1986),Geometrics II—The Application of Geometric Tolerancing Techniques. AddisonWesley
 Fu, J., W. Cleghorn, and R. Fenton (1987), “Synthesis of Dimensional Tolerances of a Slider Crank Mechanism,”10th Applied Mechanisms Conference, Oklahoma State University
 Garrett, R. and A. Hall, Jr. (1969), “Effect of Tolerance and Clearance in Linkage Design,”J. of Engineering for Industry, ASME, v 91, pp. 198–202, February
 Gladman, C.A. (1980), “Applying Probability in Tolerance Technology,”Trans. Inst. Eng. Austral. Mech. Eng., v ME5, n 2, p. 82
 Gossard, D.C., R.P. Zuffante, and H. Sakurai (1988), “Representing Dimensions, Tolerances, and Features in MCAE Systems,”IEEE Computer Graphics & Applications, v 8, n 2, pp. 51–59, March
 Greenwood, W.H. (1987), “A New Tolerance Analysis Method for Designers and Manufacturers,” (Dissertation), ADCATS Report No. 872, Brigham Young University.
 Greenwood, W.H. and K.W. Chase (1987), “A New Tolerance Analysis Methods for Designers and Manufacturers,”J. of Engineering for Industry, ASME, v 109, pp. 112–116, May
 Greenwood, W.H. and K.W. Chase (1988a), “Worst Case Tolerance Analysis with Nonlinear Problems,”J. of Engineering for Industry, ASME, v 110, pp. 232–235, August
 Greenwood, W.H. and K.W. Chase (1990), “Root Sum Squares Tolerance Analysis with Nonlinear Problems,”J. of Engineering for Industry, ASME, v 112, pp. 382–384, November
 Grossman, D. (1976), “Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacture,” Stanford Artificial Intelligence Laboratory, Memo AIM280, Computer Science Dept. Report No. STANCS76555, May
 Harry, M. (1987), “The Nature of Six Sigma Quality,” Motorola Corporation
 Harry, M. and J. Lawson (1990), “Six Sigma Producibility Analysis and Process Characterization,” Publication No. 6σ303/88, Motorola Corporation
 Harry, M. and R. Stewart (1988), “Six Sigma Mechanical Design Tolerancing,” Publication No. 6σ210/88, Motorola Corporation
 Haugen, E. (1980),Probabilistic Mechanical Design, John Wiley
 Jayaraman, R. and V. Srinivasan (1989), “Geometric Tolerancing: 1 Virtual boundary requirements,IBM J. of Research and Development, v 33, n 2, pp. 90–104, March
 Kackar, R., (1986), “The Power of Taguchi Methods,”Quality Progress, pp. 21–29, December
 Kendrick, J. (1991), “Customers ‘Win’ in Baldrige Award Selections,”Quality, pp. 23–31, January
 Lee, W. and T.C. Woo (1989), “Optimum Selection of Discrete Tolerances,”J. Mechanisms, Transmissions, and Automation in Design, v 111, pp. 243–251, June
 Lee, W. and T.C. Woo (1990), “Tolerances: Their Analysis and Synthesis,”J. of Engineering for Industry, v 112, pp. 113–121, May
 Levy, S. (1974),Applied Geometric Tolerancing, TAD Products Corp., Beverly, MA
 Light, R. and D. Gossard (1982), “Modification of Geometric Models Through Variational Geometry,”ComputerAided Design, v 14, n 4, pp. 209–214, July
 Mallik, A. and S. Dhande (1987), “Analysis and Synthesis of Mechanical Error in PathGenerating Linkages Using a Stochastic Approach,”J. of Mechanism and Machine Theory, v 22, n 2, pp. 115–123
 Mansoor, E. (1963), “The Application of Probability to Tolerances Used in Engineering Designs,”Proc. of the Inst. of Mech. Engineers, v 178, pt 1, n 1, pp. 29–51
 Marler, J. (1988), “Nonlinear Tolerance Analysis Using the Direct Linearization Method,” ADCATS Report No. 886, Brigham Young University
 Martino, P.M. and G.A. Gabriele (1989a), “Application of Variational Geometry to the Analysis of Mechanical Tolerances,”Failure Prevention and Reliability—1989, ASME Paper No. DE—Vol 16, pp. 19–27
 Martino, P.M. and G.A. Gabriele (1989b), “Estimating Jacobian and Constraint Matrices in Variational Geometry Systems,”Failure Prevention and Reliability—1989, ASME Paper No. DE—Vol 16, pp. 79–84
 Michael, W. and J.N. Siddall (1981), “The Optimization Problem with Optimal Tolerance Assignment and Full Acceptance,”J. of Mechanical Design, ASME, 103, pp. 842–848, October
 Michael, W., J.N. Siddall (1982), “The Optimal Tolerance Assignment with Less Than Full Acceptance,”J. of Mechanical Design, ASME, 104, pp. 855–860, October
 Mischke, C.R., (1989), “Stochastic Methods in Mechanical Design, Parts 1–4,”Failure Prevention and Reliability—1989, ASME Publ. No. DE—Vol 16, pp. 1–28
 Monte, M.E. and P. Datseris, (1982), “Optimum Tolerance Selection for Minimum Manufacturing Cost and Other Criteria,” ASME Paper No. 82DET35, pp. 1–9
 Ostwald, P.F. and J. Huang (1977), “A Method for Optimal Tolerance Selection,”J. of Engineering for Industry, ASME, 99, pp. 558–565, August
 Parkinson, A.R., C. Sorensen, J. Free, and B. Canfield, (1990), “Tolerances and Robustness in Engineering Design Optimization,”Proc. of ASME 16th Design Automation Conf., Chicago, IL, DE—Vol 231, p. 121, September
 Parkinson, D.B. (1982), “The Application of Reliability Methods to Tolerancing,”J. of Mechanical Design, v 104, pp. 612–618, July
 Parkinson, D.B. (1985), “Assessment and Optimization of Dimensional Tolerances,”ComputerAided Design, 17, 4, pp. 191–199, May
 Patel, A.M. (1980), “ComputerAided Assignment of Manufacturing Tolerances,”Proc. of the 17th Design Automation Conf., Minneapolis, MN, June
 Peters, J. (1970), “Tolerancing the Components of an Assembly for Minimum Cost,”J. of Engineering for Industry, ASME, pp. 677–682, August
 Placek, C. (1989a), “Motorola, Westinghouse Nuclear Fuel Unit, Globe Metallurgical Named Malcolm Baldrige National Quality Award Winners,”Quality, pp. 13–14, January
 Placek, C. (1989b), “Mechanical Tolerancing Workshop,”Quality, pp. 16–17, December
 Placek, C. (1990), “Milliken and Xerox Garner 1989 Baldrige National Quality Awards,”Quality, pp. 13–14, January
 Rao, S., and S. Gavane (1980), “Analysis and Synthesis of Mechanical Error in CamFollower Systems,” ASME Paper No. 80DET22
 Requicha, A.A.G. (1983), “Toward a Theory of Geometric Tolerancing,”Int. J. of Robotics Research v 2, no 4, pp. 45–60, Winter
 Requicha, A.A.G. (1986), “Representation of Geometric Features, Tolerances and Attributes in Solid Modelers Based on Constructive Solid Geometry,”IEEE J. of Robotics and Automation RA2 no 3, pp. 156–166, September
 Robison, R.H. (1989), “A Practical Method for ThreeDimensional Tolerance Analysis Using a Solid Modeler,” ADCATS Report No. 893, Brigham Young University
 Schade, R. (1980), “Probabilistic Models in Computer Automated SliderCrank Function Generator Design,” ASME Paper No. 80DET48
 Schade, R. (1982), “A Probabilistic Model of FourBar Mechanisms,” ASME Paper No. 82DET43
 Shapiro, S. and A. Gross (1981),Statistical Modeling Techniques, Marcel Dekker
 Sorensen, C., D. Nielsen, and K. Chase (1991), “Improved Methods for Tolerance Analysis of Mating Hole Patterns,”Proc. of the Internat. Design Productivity Conf., Honolulu, Hawaii, February
 Speckhart, F.H. (1972), “Calculation of Tolerance Based on a Minimum Cost Approach,”J. of Engineering for Industry ASME, v 94, pp. 447–453, May
 Spence, R. and R. Sion (1988),Tolerance Design of Electronic Circuits, AddisonWesley
 Spotts, M.F. (1973), “Allocation of Tolerances to Minimize Cost of Assembly,”J. of Engineering for Industry ASME, v 95, pp. 762–764, August
 Spotts, M.F. (1975), “Probability Theory for Assemblies with Piece Part Errors Concentrated Near End of Tolerance Limit,” ASME Paper No. 75DE1
 Spotts, M.F. (1978), “How to Use Wider Tolerances, Safely, in Dimensioning Stacked Assemblies,”Machine Design, pp. 60–63, April
 Spotts, M. F. (1983),Dimensioning and Tolerancing for Quantity Production, PrenticeHall.
 Srikanth, S. and J. Turner (1990), “Toward a Unified Representation of Mechanical Assemblies,”Engineering with Computers v 6, pp. 103–112
 Srinivasan, V. and R. Jayaraman (1989), “Geometric Tolerancing: 2 Conditional Tolerances,IBM J. of Research and Development 33, 2, pp. 105–124, March
 Sutherland, G. H. and Roth, B. (1975), “Mechanism Design: Accounting for Manufacturing Tolerances and Costs in Function Generating Problems,”J. of Engineering for Industry ASME, v 97, pp. 283–286, February
 Taguchi, G. (1986),Introduction to Quality Engineering, Asian Productivity Organization
 Taguchi, G., E. Elsayed and T. Hsiang, (1989),Quality Engineering in Production Systems, McGrawHill
 Turner, J. (1990), “Relative Positioning of Parts in Assemblies Using Mathematical Programming,”ComputerAided Design v 22, n 7, pp. 393–400, September
 Turner, J. and S. Srikanth (1990), “Constraint Representation and Reduction in Assembly Modeling and Analysis,” Rensselear Design Research Center, Tech. Report No. 90027.
 Turner, J. and M. Wozny (1987), “Tolerances in ComputerAided Geometric Design,”The Visual Computer, n 3, pp. 214–226
 Turner, J. and M. Wozny (1990), “The MSpace Theory of Tolerances,”Advances in Design Automation1990 v 1, ASME Publication No. DEVol 231, pp. 217–225
 Turner, J., M. Wozny, and D. Hoh (1987), “Tolerance Analysis in a Solid Modeling Environment,”Computers in Engineering1987 ASME, v 2, pp. 169–175.
 Wilde, D. and Prentice, E. (1975), “Minimum Exponential Cost Allocation of SureFit Tolerances,”J. of Engineering for Industry ASME, v 97, pp. 1395–1398, November
 Wirtz, A. (1988), “Vectorial Tolerancing,” Tech. Paper CH 9470, NewTechnikum Buchs, Gallen, Switzerland
 Title
 A survey of research in the application of tolerance analysis to the design of mechanical assemblies
 Journal

Research in Engineering Design
Volume 3, Issue 1 , pp 2337
 Cover Date
 19910301
 DOI
 10.1007/BF01580066
 Print ISSN
 09349839
 Online ISSN
 14356066
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Kenneth W. Chase ^{(1)}
 Alan R. Parkinson ^{(1)}
 Author Affiliations

 1. Mechanical Engineering Department, Brigham Young University, 84602, Provo, UT, USA