Tolerance Analysis of a Deformable Component Using the Probabilistic Approach and Kriging-Based Surrogate Models
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4, Issue 3
Abstract
Tolerance analysis is a key issue in proving the compatibility of manufacturing uncertainties with the quality level of mechanical systems. For rigid and isostatic systems, multiple methods (worst case, statistical, or probabilistic approaches) are applicable and well established. Recent scientific developments have brought enhancements for rigid overconstrained systems using probabilistic and optimization-based methods. The consideration of nonrigid systems is more complex since a large-scale numerical model must be taken into account for an accurate prediction of the quality. The aim of the present paper is the illustration of the probabilistic tolerance analysis approach for an industrial application involving deformable parts. The distributions associated with the dimensions of the components were identified using real components collected from the assembly lines. A nonlinear finite-element model was used to predict the mechanical behavior. A reliability analysis was performed in order to compute the defect probability and estimate the quality of the products. A kriging-based surrogate model was used to reduce the numerical efforts required for the reliability analysis.
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Acknowledgments
This research is partially supported by the French Science Agency (ANR) under Contract No. ANR-11-MONU-013, which is gratefully acknowledged by the authors. The authors are grateful to Laurent André-Masse and Sébastien Jallet, Valeo VWS, for their collaboration on this study and their assistance with the finite-element model. David Turner is gratefully acknowledged for the proofreading of the manuscript.
References
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Bucher, C., and U. Bourgund. 1990. “A fast and efficient response surface approach for structural reliability problems.” J. Struct. Saf. 7 (1): 57–66. https://doi.org/10.1016/0167-4730(90)90012-E.
Chase, K. W., and A. R. Parkinson. 1991. “A survey of research in the application of tolerance analysis to the design of mechanical assemblies.” Res. Eng. Des. 3 (1): 23–37. https://doi.org/10.1007/BF01580066.
Dahlström, S., and L. Lindkvist. 2006. “Variation simulation of sheet metal assemblies using the method of influence coefficients with contact modeling.” J. Manuf. Sci. Eng. 129 (3): 615–622. https://doi.org/10.1115/1.2714570.
Dantan, J.-Y., and A.-J. Qureshi. 2009. “Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation.” Comput.-Aided Des. 41 (1): 1–12. https://doi.org/10.1016/j.cad.2008.11.003.
Dumas, A., N. Gayton, J.-Y. Dantan, and B. Sudret. 2015. “A new system formulation for the tolerance analysis of overconstrained mechanisms.” Probab. Eng. Mech. 40: 66–74. https://doi.org/10.1016/j.probengmech.2014.12.005.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
Echard, B., N. Gayton, M. Lemaire, and N. Relun. 2013. “A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models.” Reliability Eng. Syst. Saf. 111 (2): 232–240. https://doi.org/10.1016/j.ress.2012.10.008.
Evans, D. 1975. “Statistical tolerancing: The state of the art. Part II, methods for estimating moments.” J. Qual. Technol. 7 (1): 1–12. https://doi.org/10.1080/00224065.1975.11980657.
Fauriat, W., and N. Gayton. 2014. “AK-SYS: An adaptation of the AK-MCS method for system reliability.” Reliability Eng. Syst. Saf. 123: 137–144. https://doi.org/10.1016/j.ress.2013.10.010.
Gayton, N., P. Beaucaire, J.-M. Bourinet, E. Duc, M. Lemaire, and L. Gauvrit. 2011. “APTA: Advanced probability-based tolerance analysis of products.” Mécanique et Industrie 12 (2): 71–85. https://doi.org/10.1051/meca/2011014.
Gordis, J., and W. Flannelly. 1994. “Analysis of stress due to fastener tolerance in assembled components.” AIAA J. 32 (12): 2440–2446. https://doi.org/10.2514/3.12311.
Greenwood, W., and K. Chase. 1987. “A new tolerance analysis method for designers and manufacturers.” J. Eng. Ind. 109 (2): 112–116. https://doi.org/10.1115/1.3187099.
Hong, Y., and T. Chang. 2002. “A comprehensive review of tolerancing research.” Int. J. Prod. Res. 40 (11): 2425–2459. https://doi.org/10.1080/00207540210128242.
Karhunen, K. 1947. “Über lineare Methoden in der Wahrscheinlichkeitsrechnung.” Am. Acad. Sci., Fennicade, Ser. A 37: 3–79.
Lemaire, M. 2010. Structural reliability. New York: Wiley.
Li, Z., J. Yue, M. Kokkolaras, J. A. Camelio, P. Papalambros, and J. S. Hu. 2004. “Product tolerance allocation in compliant multistation assembly through variation propagation and analytical target cascading.” In Proc., ASME 2004 Int. Mechanical Engineering Congress and Exposition. New York: American Society of Mechanical Engineers.
Lindau, B., S. Lorin, L. Lindkvist, and R. Söderberg. 2015. “Efficient contact modeling in nonrigid variation simulation.” J. Comput. Inf. Sci. Eng. 16 (1): 011002. https://doi.org/10.1115/1.4032077.
Liu, P.-L., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Liu, S., and S. Hu. 1996. “Variation simulation for deformable sheet metal assemblies using finite element methods.” J. Manuf. Sci. Eng. 119 (3): 368–374. https://doi.org/10.1115/1.2831115.
Liu, S. C., and S. J. Hu. 1997. “Variation simulation for deformable sheet metal assemblies using finite element methods.” J. Manuf. Sci. Eng. 119 (3): 368–374. https://doi.org/10.1115/1.2831115.
Loève, M. 1977. Probability theory. 4th ed. New York: Springer.
Mai, J.-F., and M. Scherer. 2012. Simulating copulas (stochastic models, sampling algorithms and applications). Vol. 4 of Series in quantitative finance. Singapore: World Scientific.
Myers, R. H., D. C. Montgomery, and C. M. Andersson-Cook. 2008. Response surface methodology: Process and product optimization using designed experiments. Hoboken, NJ: Wiley.
Nigam, S., and J. Turner. 1995. “Review of statistical approaches to tolerance analysis.” Comput.-Aided Des. 27 (1): 6–15. https://doi.org/10.1016/0010-4485(95)90748-5.
Qureshi, A.-J., J.-Y. Dantan, V. Sabri, P. Beaucaire, and N. Gayton. 2012. “A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation.” Comput.-Aided Des. 44 (2): 132–142. https://doi.org/10.1016/j.cad.2011.10.004.
Roy, U., C. Liu, and T. Woo. 1991. “Review of dimensioning and tolerancing: representation and processing.” Comput.-Aided Des 23 (7): 466–483. https://doi.org/10.1016/0010-4485(91)90045-X.
Scholtz, F. 1995. Tolerance stack analysis methods. Seattle: Boeing Information & Support Services.
Schölzel, C., and P. Friederichs. 2008. “Multivariate non-normally distributed random variables in climate research—Introduction to the copula approach.” Nonlinear Processes Geophys. 15 (5): 761–772. https://doi.org/10.5194/npg-15-761-2008.
Söderberg, R., L. Lindkvist, and S. Dahlström. 2006. “Computer-aided robustness analysis for compliant assemblies.” J. Eng. Des. 17 (5): 411–428. https://doi.org/10.1080/09544820500275800.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4 • Issue 3 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 6, 2017
Accepted: Mar 15, 2018
Published online: Jun 22, 2018
Published in print: Sep 1, 2018
Discussion open until: Nov 22, 2018
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