Sampling-based tolerance analysis: the key to establish tolerance-cost optimization in the product development process

Abstract Tolerance allocation during detail design aims to identify a combination of tolerances which are tight enough to ensure total product functionality but also as wide as possible to minimize the resultant manufacturing costs. Optimization techniques automatize and thus significantly accelerate the complex search for suitable tolerance values taking both the design and manufacturing perspective into account. While sampling techniques became well-established for tolerance analysis, statistical approximative approaches, e.g. the root sum square method, are still commonly used for tolerance-cost optimization. However, this leads to a limited applicability and validity of the optimization which currently prevents its successful implementation in industry. Thus, the article discusses the direct and indirect effects of sampling methods on the definition and solution of the optimization problem and reveals the benefits and drawbacks of sampling-based tolerance-cost optimization in terms of effectiveness and efficiency using an illustrative case study. In addition, guidelines as well as recommendations for its proper application in research and industry are given. In doing so, this article shows that the use of sampling-based techniques can significantly contribute to a shift of tolerance-cost optimization from an expert tool for tolerance specialists with in-depth knowledge in statistics, optimization and programming, to a user-friendly engineering design tool with an enhanced usability, which enables solving problems of industrial complexity.

[1]  Y. S. Hong,et al.  A comprehensive review of tolerancing research , 2002 .

[2]  Zuomin Dong,et al.  New Production Cost-Tolerance Models for Tolerance Synthesis , 1994 .

[3]  E. Sandgren,et al.  Tolerance Optimization Using Genetic Algorithms: Benchmarking with Manual Analysis , 1996 .

[4]  Stefan Goetz,et al.  Mapping of GD&T information and PMI between 3D product models in the STEP and STL format , 2019, Comput. Aided Des..

[5]  Joshua U. Turner,et al.  Estimating gradients for statistical tolerance synthesis , 1996, Comput. Aided Des..

[6]  L. F. Hauglund,et al.  Least Cost Tolerance Allocation for Mechanical Assemblies with Automated Process Selection , 1990 .

[7]  Giovanni Moroni,et al.  Tolerancing: Managing uncertainty from conceptual design to final product , 2018 .

[8]  P K Singh,et al.  Important issues in tolerance design of mechanical assemblies. Part 1: Tolerance analysis , 2009 .

[9]  S. Khodaygan,et al.  Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation , 2011 .

[10]  Sandro Wartzack,et al.  Sampling-based Tolerance-Cost Optimization of Systems with Interrelated Key Characteristics , 2020 .

[11]  Yanlong Cao,et al.  A comprehensive review of tolerance analysis models , 2018 .

[12]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[13]  Martin Ebro,et al.  The Applicability of CAT tools in industry – boundaries and challenges in tolerance engineering practice observed in a medical device company , 2018 .

[14]  R. Alan Bowman.  Efficient Gradient-Based Tolerance Optimization Using Monte Carlo Simulation , 2009 .

[15]  Kenneth W. Chase,et al.  A survey of research in the application of tolerance analysis to the design of mechanical assemblies , 1991 .

[16]  Glen E. Johnson,et al.  Optimal tolerance allotment using a genetic algorithm and truncated Monte Carlo simulation , 1993, Comput. Aided Des..

[17]  Rikard Söderberg,et al.  Virtual Geometry Assurance Process and Toolbox , 2016 .

[18]  Antonio Armillotta,et al.  A method for computer-aided specification of geometric tolerances , 2013, Comput. Aided Des..

[19]  Sandro Wartzack,et al.  Towards a more Comprehensive Understanding of Tolerance Engineering Research Importance , 2015 .

[20]  Jhareswar Maiti,et al.  A review on dimensional tolerance synthesis: paradigm shift from product to process , 2012 .

[21]  Peng Wang,et al.  An effective strategy for improving the precision and computational efficiency of statistical tolerance optimization , 2017 .

[22]  Joseph K. Davidson,et al.  Toward Automatic Tolerancing of Mechanical Assemblies: First-Order GD&T Schema Development and Tolerance Allocation , 2015, J. Comput. Inf. Sci. Eng..

[23]  Sandro Wartzack,et al.  Comparison of different methods for scrap rate estimation in sampling-based tolerance-cost-optimization , 2018 .

[24]  Sandro Wartzack,et al.  Geometrical Variations Management 4.0: towards next Generation Geometry Assurance , 2018 .

[25]  Joseph K. Davidson,et al.  A Comparative Study Of Tolerance Analysis Methods , 2005, J. Comput. Inf. Sci. Eng..

[26]  Jean-Yves Dantan,et al.  Improved algorithm for tolerance allocation based on Monte Carlo simulation and discrete optimization , 2009, Comput. Ind. Eng..

[27]  M. M. Sfantsikopoulos.  A cost-tolerance analytical approach for design and manufacturing , 1990 .

[28]  Sandro Wartzack,et al.  On Connected Tolerances in Statistical Tolerance-Cost-Optimization of Assemblies with Interrelated Dimension Chains , 2016 .

[29]  Sandro Wartzack,et al.  From tolerance allocation to tolerance-cost optimization: a comprehensive literature review , 2020, The International Journal of Advanced Manufacturing Technology.

[30]  Wolfgang Ernst Eder,et al.  Design Engineering and Needs for Methodology , 2009 .

[31]  Joseph K. Davidson,et al.  Automated Tolerance Analysis of Mechanical Assemblies from a CAD Model with PMI , 2019 .

[32]  Sandro Wartzack,et al.  How to consider Over-constrained Assemblies with Gaps in Tolerance-Cost Optimization? , 2020 .