Modares Mechanical Engineering

Modares Mechanical Engineering

Nonlinear computer-aided tolerance analysis of mechanical assemblies using improved second-order method

Authors
Omid Sadikhani 1
Seyed Ali Hashemian 2
1 Department of Mechanical Engineering, Hakim Sabzevari University, Sabzevar, Iran
2 Department of Mechanical EngineeringFaculty of EngineeringHakim Sabzevari University
Abstract
Tolerance analysis plays a crucial role in predicting the quality of products and reducing production costs. This procedure is generally complex and available methods for analyzing different types of assemblies are not always applicable. Accordingly, having a comprehensive approach to assess the effect of tolerances on the quality and cost of products is a fundamental requirement in the manufacturing industry. This paper proposes the improved second-order method for tolerance analysis of complex assemblies. The conventional second-order tolerance analysis (SOTA) is an accurate and applicable method for obtaining the statistical specifications of the assembly’s key characteristic. However, determining the assembly function in SOTA entails forming vector loops and therefore, this method is limited to simple assemblies. On the other hand, in mechanical assemblies that are usually complex, creating vector loop may encounter some difficulties in practice. In this study, the mentioned issues have been overcome by linking SolidWorks and MATLAB software to employ the proposed methodology for any mechanical assemblies without creating vector loops. For this purpose, MATLAB software makes necessary changes in the SolidWorks model and calculates the derivatives of the assembly function, which are required for the analysis. Then, the statistical moments are computed and the probability distribution of the key characteristic is obtained using the Pearson system. The present study is appropriate for analyzing either linear or nonlinear assembly functions with any statistical distribution. Finally, the applicability of the proposed approach is investigated by some practical examples and the accuracy of results is confirmed by Monte Carlo simulation.
Keywords
Nonlinear tolerance analysis
Sensitivity Analysis
improved second-order method
statistical moments

Subjects

1] K. W. Chase, A. R. Parkinson, A survey of research in the application of tolerance analysis to the design of mechanical assemblies, Research in Engineering design, Vol. 3, No. 1, pp. 23-37, 1991.
[2] P. Franciosa, S. Gerbino, A. Lanzotti, S. Patalano, Automatic evaluation of variational parameters for tolerance analysis of rigid parts based on graphs, International Journal on Interactive Design and Manufacturing (IJIDeM), Vol. 7, No. 4, pp. 239-248, 2013.
[3] J.-Y. Dantan, N. Gayton, A. J. Qureshi, M. Lemaire, A. Etienne, Tolerance analysis approach based on the classification of uncertainty (aleatory/epistemic), Procedia CIRP, Vol. 10, pp. 287-293, 2013.
[4] B. Schleich, S. Wartzack, Evaluation of geometric tolerances and generation of variational part representatives for tolerance analysis, The International Journal of Advanced Manufacturing Technology, Vol. 79, No. 5-8, pp. 959-983, 2015.
[5] S. Khodaygan, M. Movahhedy, A comprehensive fuzzy feature-based method for worst case and statistical tolerance analysis, International Journal of Computer Integrated Manufacturing, Vol. 29, No. 1, pp. 42-63, 2016.
[6] K. Chase, Basic tools for tolerance analysis of mechanical assemblies, Manufacturing engineering handbook, 2004.
[7] C.-Y. Lin, W.-H. Huang, M.-C. Jeng, J.-L. Doong, Study of an assembly tolerance allocation model based on Monte Carlo simulation, Journal of Materials Processing Technology, Vol. 70, No. 1-3, pp. 9-16, 1997.
[8] P. Varghese, R. N. Braswell, B. Wang, C. Zhang, Statistical tolerance analysis using FRPDF and numerical convolution, Computer-Aided Design, Vol. 28, No. 9, pp. 723-732, 1996.
[9] R. E. Caflisch, Monte carlo and quasi-monte carlo methods, Acta numerica, Vol. 7, pp. 1-49, 1998.
[10] K. W. Chase, J. Gao, S. P. Magleby, General 2-D tolerance analysis of mechanical assemblies with small kinematic adjustments, Journal of Design and Manufacturing, Vol. 5, pp. 263-274, 1995.
[11] J. Gao, K. W. Chase, S. P. Magleby, Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments, IIE transactions, Vol. 30, No. 4, pp. 367-377, 1998.
[12] H. S. Seo, B. M. Kwak, Efficient statistical tolerance analysis for general distributions using three-point information, International journal of production research, Vol. 40, No. 4, pp. 931-944, 2002.
[13] R. H. Myers, D. C. Montgomery, C. M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments: John Wiley & Sons, 2016.
[14] M. .Nighikhani, H. R. A. Mohammadi, Using Response Surface Method (RSM) in the Optimal Allocation of Tolerances, Space Science &Technology, Vol. 4, No. 2, 2011(In Persian).
[15] R. Cvetko, Characterization of Assembly Variation Analysis Methods, Thesis, Brigham Young University. Department of Mechanical Engineering, 1997.
[16] J. Zhou, A. S. Nowak, Integration formulas to evaluate functions of random variables, Structural safety, Vol. 5, No. 4, pp. 267-284, 1988.
[17] H. Xu, S. Rahman, A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics, International Journal for Numerical Methods in Engineering, Vol. 61, No. 12, pp. 1992-2019, 2004.
[18] S. Rahman, H. Xu, A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics, Probabilistic Engineering Mechanics, Vol. 19, No. 4, pp. 393-408, 2004.
[19] B. D. Youn, Z. Xi, P. Wang, Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis, Structural and Multidisciplinary Optimization, Vol. 37, No. 1, pp. 13-28, 2008.
[20] A. Hashemian, B. M. Imani, An improved sensitivity-free probability analysis in variation assessment of sheet metal assemblies, Journal of Engineering Design, Vol. 25, No. 10-12, pp. 346-366, 2014.
[21] S. A. Hashemian, B. Moetakef, Effect of Flexible-Body Assembly Errors on Appearance Quality of Automotive Bodies, Modares Mechanical Engineering, Vol. 16, No. 9, pp. 375-386, 2016.
[22] C. G. Glancy, K. W. Chase, A second-order method for assembly tolerance analysis, in Proceeding of, 21-44.
[23] N. Cox, Tolerance analysis by computer, Journal of Quality Technology, Vol. 11, No. 2, pp. 80-87, 1979.
[24] S. Khodaygan, M. Movahhedy, Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic, The International Journal of Advanced Manufacturing Technology, Vol. 53, No. 5-8, pp. 777-788, 2011.
[25] K. W. Chase, Tolerance analysis of 2-d and 3-d assemblies, ADCATS Report, Vol. 94, No. 4, 1999.
[26] S. A. Hashemian, B. M. Imani, Tolerance analysis of flexible sheet metal structures including effects of contact interaction and surface continuity of components, Modares Mechanical Engineering, Vol. 14, No. 12, pp. 199-208, 2014 (In Persian).
Modares Mechanical Engineering
Volume 18, Issue 5
September 2018
Pages 192-201