Skip to main content
SpringerLink
Log in

A survey of research in the application of tolerance analysis to the design of mechanical assemblies

  • Published:
Research in Engineering Design Aims and scope Submit manuscript

Abstract

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 2-D and 3-D tolerance analysis models; (4) methods which account for non-normal statistical distributions and nonlinear effects; and (5) several strategies for improving designs through the application of modern analytical tools.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agarwal, M. (1981), “Optimal Synthesis of Tolerance and Clearance in Function Generating Mechanisms—A Parametric Programming Problem,” ASME Paper No. 81-DET-5

  • 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. CRTD-15

  • ASME (1983), “Dimensioning and Tolerancing,” ANSI Y14.5M-1982, 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

    Google Scholar 

  • 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

    Google Scholar 

  • Beohar, S. and A. Rao (1980), “Optimum Stochastic Synthesis of Four Bar Spatial Function Generators,” ASME Paper No. 80-DET-32

  • Bjorke, O. (1989),Computer-Aided 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. 91-2, 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

    Google Scholar 

  • 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

    Google Scholar 

  • Chase, K., C. Sorensen, and C. Andersen (1989), “Recent Developments in Tolerance Analysis Software for Mechanical Assemblies, Part A: Two-Dimensional Modeling,” Proceedings of the ASQC Western Regional Conference—1989, pp. 73–80

  • Chun, K. (1988), “Development of Two-Dimensional Tolerance Modeling Methods for CAD Systems,” ADCATS Report No. 88-7, 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

    Google Scholar 

  • Cox, N.D. (1979), “Tolerance Analysis by Computer,”J. of Quality Technology, v 11, n 2, pp. 80–87, April

    Google Scholar 

  • 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

    Google Scholar 

  • Dhande, S. and J. Chakraborty (1978), “Mechanical Error Analysis of Spatial Linkages,”J. of Mechanical Design, ASME, v 100, pp. 732–738

    Google Scholar 

  • 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 Three-Dimensional Assembly,” ASME Paper No. 75-DE-21

  • 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 23-1, p. 129, September

    Google Scholar 

  • Etesami, F. (1987), “On the Theory of Geometric Tolerancing,”Computers in Engineering—1987, ASME, 2, pp. 327–334

    Google Scholar 

  • Evans, D.H. (1967), “An Application of Numerical Integration Techniques to Statistical Tolerancing,”Technometrics, v 9, n 3, pp. 441–456, August

    Google Scholar 

  • Evans, D.H. (1970), “A Statistical Tolerancing Formulation,”J. of Quality Technology, v 2, n 4, pp. 226–231, October

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Faux, I.D. (1986), “Reconciliation of Design and Manufacturing Requirements for Product Description Data Using Functional Primitive Part Features,” CAM-I Report No. R-86-ANC/GM/PP-01.1, CAM-I Inc, Arlington, TX, December

    Google Scholar 

  • 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

    Google Scholar 

  • 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, McGraw-Hill

  • Foster, L.W. (1986),Geometrics II—The Application of Geometric Tolerancing Techniques. Addison-Wesley

  • 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

    Google Scholar 

  • Gladman, C.A. (1980), “Applying Probability in Tolerance Technology,”Trans. Inst. Eng. Austral. Mech. Eng., v ME5, n 2, p. 82

    Google Scholar 

  • 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

    Google Scholar 

  • Greenwood, W.H. (1987), “A New Tolerance Analysis Method for Designers and Manufacturers,” (Dissertation), ADCATS Report No. 87-2, 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Grossman, D. (1976), “Monte Carlo Simulation of Tolerancing in Discrete Parts Manufacture,” Stanford Artificial Intelligence Laboratory, Memo AIM-280, Computer Science Dept. Report No. STAN-CS-76-555, 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. 6σ-3-03/88, Motorola Corporation

  • Harry, M. and R. Stewart (1988), “Six Sigma Mechanical Design Tolerancing,” Publication No. 6σ-2-10/88, 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

    Google Scholar 

  • 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

    Google Scholar 

  • Lee, W. and T.C. Woo (1990), “Tolerances: Their Analysis and Synthesis,”J. of Engineering for Industry, v 112, pp. 113–121, May

    Google Scholar 

  • Levy, S. (1974),Applied Geometric Tolerancing, TAD Products Corp., Beverly, MA

    Google Scholar 

  • Light, R. and D. Gossard (1982), “Modification of Geometric Models Through Variational Geometry,”Computer-Aided Design, v 14, n 4, pp. 209–214, July

    Google Scholar 

  • Mallik, A. and S. Dhande (1987), “Analysis and Synthesis of Mechanical Error in Path-Generating Linkages Using a Stochastic Approach,”J. of Mechanism and Machine Theory, v 22, n 2, pp. 115–123

    Google Scholar 

  • 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

    Google Scholar 

  • Marler, J. (1988), “Nonlinear Tolerance Analysis Using the Direct Linearization Method,” ADCATS Report No. 88-6, 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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. 82-DET-35, 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

    Google Scholar 

  • 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 23-1, p. 121, September

  • Parkinson, D.B. (1982), “The Application of Reliability Methods to Tolerancing,”J. of Mechanical Design, v 104, pp. 612–618, July

    Google Scholar 

  • Parkinson, D.B. (1985), “Assessment and Optimization of Dimensional Tolerances,”Computer-Aided Design, 17, 4, pp. 191–199, May

    Google Scholar 

  • Patel, A.M. (1980), “Computer-Aided 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 Cam-Follower Systems,” ASME Paper No. 80-DET-22

  • Requicha, A.A.G. (1983), “Toward a Theory of Geometric Tolerancing,”Int. J. of Robotics Research v 2, no 4, pp. 45–60, Winter

    Google Scholar 

  • 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 RA-2 no 3, pp. 156–166, September

    Google Scholar 

  • Robison, R.H. (1989), “A Practical Method for Three-Dimensional Tolerance Analysis Using a Solid Modeler,” ADCATS Report No. 89-3, Brigham Young University

  • Schade, R. (1980), “Probabilistic Models in Computer Automated Slider-Crank Function Generator Design,” ASME Paper No. 80-DET-48

  • Schade, R. (1982), “A Probabilistic Model of Four-Bar Mechanisms,” ASME Paper No. 82-DET-43

  • 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

    Google Scholar 

  • Spence, R. and R. Sion (1988),Tolerance Design of Electronic Circuits, Addison-Wesley

  • Spotts, M.F. (1973), “Allocation of Tolerances to Minimize Cost of Assembly,”J. of Engineering for Industry ASME, v 95, pp. 762–764, August

    Google Scholar 

  • Spotts, M.F. (1975), “Probability Theory for Assemblies with Piece Part Errors Concentrated Near End of Tolerance Limit,” ASME Paper No. 75-DE-1

  • 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, Prentice-Hall.

  • Srikanth, S. and J. Turner (1990), “Toward a Unified Representation of Mechanical Assemblies,”Engineering with Computers v 6, pp. 103–112

    Google Scholar 

  • Srinivasan, V. and R. Jayaraman (1989), “Geometric Tolerancing: 2 Conditional Tolerances,IBM J. of Research and Development 33, 2, pp. 105–124, March

    Google Scholar 

  • 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

    Google Scholar 

  • Taguchi, G. (1986),Introduction to Quality Engineering, Asian Productivity Organization

  • Taguchi, G., E. Elsayed and T. Hsiang, (1989),Quality Engineering in Production Systems, McGraw-Hill

  • Turner, J. (1990), “Relative Positioning of Parts in Assemblies Using Mathematical Programming,”Computer-Aided Design v 22, n 7, pp. 393–400, September

    Google Scholar 

  • 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 Computer-Aided Geometric Design,”The Visual Computer, n 3, pp. 214–226

  • Turner, J. and M. Wozny (1990), “The M-Space Theory of Tolerances,”Advances in Design Automation-1990 v 1, ASME Publication No. DE-Vol 23-1, pp. 217–225

    Google Scholar 

  • Turner, J., M. Wozny, and D. Hoh (1987), “Tolerance Analysis in a Solid Modeling Environment,”Computers in Engineering-1987 ASME, v 2, pp. 169–175.

    Google Scholar 

  • Wilde, D. and Prentice, E. (1975), “Minimum Exponential Cost Allocation of Sure-Fit Tolerances,”J. of Engineering for Industry ASME, v 97, pp. 1395–1398, November

    Google Scholar 

  • Wirtz, A. (1988), “Vectorial Tolerancing,” Tech. Paper CH 9470, New-Technikum Buchs, Gallen, Switzerland

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Kenneth W. Chase & Alan R. Parkinson

Authors
  1. Kenneth W. Chase
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan R. Parkinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chase, K.W., Parkinson, A.R. A survey of research in the application of tolerance analysis to the design of mechanical assemblies. Research in Engineering Design 3, 23–37 (1991). https://doi.org/10.1007/BF01580066

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01580066

Keywords

Search

Navigation