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

- 1.2k Downloads
- 177 Citations

## 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.

## Keywords

Analysis Tool Market Share Engineering Design Nonlinear Effect Major Topic## Preview

Unable to display preview. Download preview PDF.

## References

- Agarwal, M. (1981), “Optimal Synthesis of Tolerance and Clearance in Function Generating Mechanisms—A Parametric Programming Problem,” ASME Paper No. 81-DET-5Google Scholar
- Andersen, C.B. (1990), “General System for Least Cost Tolerance Allocation in Mechanical Assemblies,” ADCATS Report No. 90–2, Brigham Young UniversityGoogle Scholar
- ASME (1990), “Research Needs and Technological Opportunities in Mechanical Tolerancing,” ASME Publication No. CRTD-15Google Scholar
- ASME (1983), “Dimensioning and Tolerancing,” ANSI Y14.5M-1982, ASME PublicationGoogle Scholar
- 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. 71–76Google Scholar - Bender, A., Jr. (1968), “Statistical Tolerancing as it Relates to Quality Control and the Designer,” SAE Paper No. 680490Google Scholar
- Bennett, G. and L.C. Gupta (1969), “Least Cost Tolerances—I and II,”
*International J. of Production Research*, v 8, pp. 65–74 and 169–181Google Scholar - Beohar, S. and A. Rao (1980), “Optimum Stochastic Synthesis of Four Bar Spatial Function Generators,” ASME Paper No. 80-DET-32Google Scholar
- Bjorke, O. (1989),
*Computer-Aided Tolerancing*, Second Ed., ASME PressGoogle Scholar - Byrne, D. and S. Taguchi (1987), “The Taguchi Approach to Parameter Design,”
*Quality Progress*, pp. 19–26, DecemberGoogle Scholar - Chase, K.W. (1991), “A Bibliography on Tolerance Analysis of Mechanical Assemblies,” ADCATS Report No. 91-2, Brigham Young UniversityGoogle Scholar
- Chase, K.W. and W.H. Greenwood (1988), “Design Issues in Mechanical Tolerance Analysis,”
*Manufacturing Review*, ASME, v 1, n 1, pp. 50–59, MarchGoogle 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, MarchGoogle 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. 73–80Google Scholar
- Chun, K. (1988), “Development of Two-Dimensional Tolerance Modeling Methods for CAD Systems,” ADCATS Report No. 88-7, Brigham Young UniversityGoogle Scholar
- Chung, J.C.H. and M.D. Schussel (1990), “Technical Evaluation of Variational and Parametric Design,”
*Computers in Engineering—1990*, ASME, 1, pp. 289–298Google Scholar - Cox, N.D. (1979), “Tolerance Analysis by Computer,”
*J. of Quality Technology*, v 11, n 2, pp. 80–87, AprilGoogle Scholar - Cox, N.D. (1986), “How to Perform Statistical Tolerance Analysis,” ASQC Series Vol 11, Basic References in Quality ControlGoogle Scholar
- Craig, M. (1989), “Managing Variation by Design Using Simulation Methods,”
*Failure Prevention and Reliability—1989*, ASME Publ. No. DE—Vol 16, pp. 153–163Google Scholar - DeDoncker, D. and A. Spencer (1987), “Assembly Tolerance Analysis with Simulation and Optimization Techniques,” SAE Paper No. 870263Google Scholar
- 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. 672–676Google Scholar - Dhande, S. and J. Chakraborty (1978), “Mechanical Error Analysis of Spatial Linkages,”
*J. of Mechanical Design*, ASME, v 100, pp. 732–738Google 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. 131–138Google Scholar - 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. 139–144Google Scholar - Eaton, F. (1975), “Computer Model of a Three-Dimensional Assembly,” ASME Paper No. 75-DE-21Google Scholar
- 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. 36–38Google Scholar - 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, SeptemberGoogle Scholar - Etesami, F. (1987), “On the Theory of Geometric Tolerancing,”
*Computers in Engineering—1987*, ASME, 2, pp. 327–334Google Scholar - Evans, D.H. (1967), “An Application of Numerical Integration Techniques to Statistical Tolerancing,”
*Technometrics*, v 9, n 3, pp. 441–456, AugustGoogle Scholar - Evans, D.H. (1970), “A Statistical Tolerancing Formulation,”
*J. of Quality Technology*, v 2, n 4, pp. 226–231, OctoberGoogle 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, MayGoogle 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, FebruaryGoogle 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, OctoberGoogle 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, JanuaryGoogle 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, AprilGoogle 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, DecemberGoogle 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, DecemberGoogle Scholar - Fortini, E. (1967),
*Dimensioning for Interchangeable Manufacture*, Industrial PressGoogle Scholar - Fortini, E. (1985), “Dimensions and Tolerances,”
*Mechanical Design and Systems Handbook*, Second Ed., H. Rothbart editor, McGraw-HillGoogle Scholar - Foster, L.W. (1986),
*Geometrics II—The Application of Geometric Tolerancing Techniques*. Addison-WesleyGoogle Scholar - Fu, J., W. Cleghorn, and R. Fenton (1987), “Synthesis of Dimensional Tolerances of a Slider Crank Mechanism,”
*10th Applied Mechanisms Conference*, Oklahoma State UniversityGoogle Scholar - 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, FebruaryGoogle Scholar - Gladman, C.A. (1980), “Applying Probability in Tolerance Technology,”
*Trans. Inst. Eng. Austral. Mech. Eng.*, v ME5, n 2, p. 82Google 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, MarchGoogle Scholar - Greenwood, W.H. (1987), “A New Tolerance Analysis Method for Designers and Manufacturers,” (Dissertation), ADCATS Report No. 87-2, Brigham Young University.Google Scholar
- 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, MayGoogle 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, AugustGoogle 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, NovemberGoogle 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, MayGoogle Scholar
- Harry, M. (1987), “The Nature of Six Sigma Quality,” Motorola CorporationGoogle Scholar
- Harry, M. and J. Lawson (1990), “Six Sigma Producibility Analysis and Process Characterization,” Publication No. 6σ-3-03/88, Motorola CorporationGoogle Scholar
- Harry, M. and R. Stewart (1988), “Six Sigma Mechanical Design Tolerancing,” Publication No. 6σ-2-10/88, Motorola CorporationGoogle Scholar
- Haugen, E. (1980),
*Probabilistic Mechanical Design*, John WileyGoogle Scholar - 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, MarchGoogle Scholar - Kackar, R., (1986), “The Power of Taguchi Methods,”
*Quality Progress*, pp. 21–29, DecemberGoogle Scholar - Kendrick, J. (1991), “Customers ‘Win’ in Baldrige Award Selections,”
*Quality*, pp. 23–31, JanuaryGoogle Scholar - Lee, W. and T.C. Woo (1989), “Optimum Selection of Discrete Tolerances,”
*J. Mechanisms, Transmissions, and Automation in Design*, v 111, pp. 243–251, JuneGoogle Scholar - Lee, W. and T.C. Woo (1990), “Tolerances: Their Analysis and Synthesis,”
*J. of Engineering for Industry*, v 112, pp. 113–121, MayGoogle Scholar - Levy, S. (1974),
*Applied Geometric Tolerancing*, TAD Products Corp., Beverly, MAGoogle Scholar - Light, R. and D. Gossard (1982), “Modification of Geometric Models Through Variational Geometry,”
*Computer-Aided Design*, v 14, n 4, pp. 209–214, JulyGoogle 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. 115–123Google 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. 29–51Google Scholar - Marler, J. (1988), “Nonlinear Tolerance Analysis Using the Direct Linearization Method,” ADCATS Report No. 88-6, Brigham Young UniversityGoogle Scholar
- 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. 19–27Google Scholar - 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. 79–84Google Scholar - 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, OctoberGoogle 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, OctoberGoogle 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. 1–28Google Scholar - Monte, M.E. and P. Datseris, (1982), “Optimum Tolerance Selection for Minimum Manufacturing Cost and Other Criteria,” ASME Paper No. 82-DET-35, pp. 1–9Google Scholar
- Ostwald, P.F. and J. Huang (1977), “A Method for Optimal Tolerance Selection,”
*J. of Engineering for Industry*, ASME, 99, pp. 558–565, AugustGoogle 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, SeptemberGoogle Scholar - Parkinson, D.B. (1982), “The Application of Reliability Methods to Tolerancing,”
*J. of Mechanical Design*, v 104, pp. 612–618, JulyGoogle Scholar - Parkinson, D.B. (1985), “Assessment and Optimization of Dimensional Tolerances,”
*Computer-Aided Design*, 17, 4, pp. 191–199, MayGoogle Scholar - Patel, A.M. (1980), “Computer-Aided Assignment of Manufacturing Tolerances,”
*Proc. of the 17th Design Automation Conf.*, Minneapolis, MN, JuneGoogle Scholar - Peters, J. (1970), “Tolerancing the Components of an Assembly for Minimum Cost,”
*J. of Engineering for Industry*, ASME, pp. 677–682, AugustGoogle Scholar - Placek, C. (1989a), “Motorola, Westinghouse Nuclear Fuel Unit, Globe Metallurgical Named Malcolm Baldrige National Quality Award Winners,”
*Quality,*pp. 13–14, JanuaryGoogle Scholar - Placek, C. (1989b), “Mechanical Tolerancing Workshop,”
*Quality,*pp. 16–17, DecemberGoogle Scholar - Placek, C. (1990), “Milliken and Xerox Garner 1989 Baldrige National Quality Awards,”
*Quality,*pp. 13–14, JanuaryGoogle Scholar - Rao, S., and S. Gavane (1980), “Analysis and Synthesis of Mechanical Error in Cam-Follower Systems,” ASME Paper No. 80-DET-22Google Scholar
- Requicha, A.A.G. (1983), “Toward a Theory of Geometric Tolerancing,”
*Int. J. of Robotics Research*v 2, no 4, pp. 45–60, WinterGoogle 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, SeptemberGoogle Scholar - Robison, R.H. (1989), “A Practical Method for Three-Dimensional Tolerance Analysis Using a Solid Modeler,” ADCATS Report No. 89-3, Brigham Young UniversityGoogle Scholar
- Schade, R. (1980), “Probabilistic Models in Computer Automated Slider-Crank Function Generator Design,” ASME Paper No. 80-DET-48Google Scholar
- Schade, R. (1982), “A Probabilistic Model of Four-Bar Mechanisms,” ASME Paper No. 82-DET-43Google Scholar
- Shapiro, S. and A. Gross (1981),
*Statistical Modeling Techniques,*Marcel DekkerGoogle Scholar - 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, FebruaryGoogle Scholar - Speckhart, F.H. (1972), “Calculation of Tolerance Based on a Minimum Cost Approach,”
*J. of Engineering for Industry*ASME, v 94, pp. 447–453, MayGoogle Scholar - Spence, R. and R. Sion (1988),
*Tolerance Design of Electronic Circuits,*Addison-WesleyGoogle Scholar - Spotts, M.F. (1973), “Allocation of Tolerances to Minimize Cost of Assembly,”
*J. of Engineering for Industry*ASME, v 95, pp. 762–764, AugustGoogle Scholar - Spotts, M.F. (1975), “Probability Theory for Assemblies with Piece Part Errors Concentrated Near End of Tolerance Limit,” ASME Paper No. 75-DE-1Google Scholar
- Spotts, M.F. (1978), “How to Use Wider Tolerances, Safely, in Dimensioning Stacked Assemblies,”
*Machine Design,*pp. 60–63, AprilGoogle Scholar - Spotts, M. F. (1983),
*Dimensioning and Tolerancing for Quantity Production,*Prentice-Hall.Google Scholar - Srikanth, S. and J. Turner (1990), “Toward a Unified Representation of Mechanical Assemblies,”
*Engineering with Computers*v 6, pp. 103–112Google Scholar - Srinivasan, V. and R. Jayaraman (1989), “Geometric Tolerancing: 2 Conditional Tolerances,
*IBM J. of Research and Development*33, 2, pp. 105–124, MarchGoogle 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, FebruaryGoogle Scholar - Taguchi, G. (1986),
*Introduction to Quality Engineering,*Asian Productivity OrganizationGoogle Scholar - Taguchi, G., E. Elsayed and T. Hsiang, (1989),
*Quality Engineering in Production Systems,*McGraw-HillGoogle Scholar - Turner, J. (1990), “Relative Positioning of Parts in Assemblies Using Mathematical Programming,”
*Computer-Aided Design*v 22, n 7, pp. 393–400, SeptemberGoogle Scholar - Turner, J. and S. Srikanth (1990), “Constraint Representation and Reduction in Assembly Modeling and Analysis,” Rensselear Design Research Center, Tech. Report No. 90027.Google Scholar
- Turner, J. and M. Wozny (1987), “Tolerances in Computer-Aided Geometric Design,”
*The Visual Computer,*n 3, pp. 214–226Google Scholar - 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. 217–225Google 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, NovemberGoogle Scholar - Wirtz, A. (1988), “Vectorial Tolerancing,” Tech. Paper CH 9470, New-Technikum Buchs, Gallen, SwitzerlandGoogle Scholar