Parametric Tolerance Analysis of Mechanical Assembly by Developing Direct Constraint Model in CAD and Cost Competent Tolerance Synthesis

ABSTRACT

The objective of tolerance analysis is to check the extent and nature of variation of an analyzed dimension or geometric feature of interest for a given GD & T scheme. The parametric approach to tolerance analysis is based on parametric constraint solving. The accuracy of simulation results is dependent on the userdefined modeling scheme. Once an accurate CAD model is developed, it is integrated with tolerance synthesis model. In order to make it cost competent, it is necessary to obtain the costtolerance relationships. The neural network recently has been reported to be an effective statistical tool for determining relationship between input factors and output responses. This study deals development of direct constraint model in CAD, which is integrated to an optimal tolerance design problem. A backpropagation (BP) network is applied to fit the costtolerance relationship. An optimization method based on Differential Evolution (DE) is then used to locate the combination of controllable factors (tolerances) to optimize the output response (manufacturing cost plus quality loss) using the equations stemming from the trained network. A tolerance synthesis problem for a motor assembly is used to investigate the effectiveness and efficiency of the proposed methodology.

The objective of tolerance analysis is to check the extent and nature of variation of an analyzed dimension or geometric feature of interest for a given GD & T scheme. The parametric approach to tolerance analysis is based on parametric constraint solving. The accuracy of simulation results is dependent on the userdefined modeling scheme. Once an accurate CAD model is developed, it is integrated with tolerance synthesis model. In order to make it cost competent, it is necessary to obtain the costtolerance relationships. The neural network recently has been reported to be an effective statistical tool for determining relationship between input factors and output responses. This study deals development of direct constraint model in CAD, which is integrated to an optimal tolerance design problem. A backpropagation (BP) network is applied to fit the costtolerance relationship. An optimization method based on Differential Evolution (DE) is then used to locate the combination of controllable factors (tolerances) to optimize the output response (manufacturing cost plus quality loss) using the equations stemming from the trained network. A tolerance synthesis problem for a motor assembly is used to investigate the effectiveness and efficiency of the proposed methodology.

Cite this paper

nullG. Jayaprakash, K. Sivakumar and M. Thilak, "Parametric Tolerance Analysis of Mechanical Assembly by Developing Direct Constraint Model in CAD and Cost Competent Tolerance Synthesis,"*Intelligent Control and Automation*, Vol. 1 No. 1, 2010, pp. 1-14. doi: 10.4236/ica.2010.11001.

nullG. Jayaprakash, K. Sivakumar and M. Thilak, "Parametric Tolerance Analysis of Mechanical Assembly by Developing Direct Constraint Model in CAD and Cost Competent Tolerance Synthesis,"

References

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[2] J. Guilford, M. Sethi and J. Turner, “Worst Case and Statistical Tolerance Analysis of the Daughter Card Assembly,” Proceedings of the 1992 ASME International Computers in Engineering Conference, San Francisco, 26 August 1992, pp. 343350.

[3] Y. Wu, J. Shah and J. Davidson, “Computer Modeling of Geometric Variations in Mechanical Parts and Assemblies,” ASME Journal Computing and Information Science in Engineering, Vol. 3, No. 1, 2003, pp. 5463.

[4] T. M. K. Pasupathy, E. P. Morse and R. G. Wilhelm, “A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 6475.

[5] P. Martino, “Simplification of Feature Based Models for Tolerance Analysis”, Proceedings of the 1992 ASME International Computers in Engineering Conference & Exposition, San Francisco, 26 August 1992, pp. 329341.

[6] Y.J. Tseng and Y.S. Terng, “Alternative Tolerance Allocations for Machining Parts Represented with Multiple Sets of Features,” International Journal of Production Research, Vol. 37, No. 7, 1999, pp. 15611579.

[7] B. K. A. Ngoi and J. M. Ong, “A Complete Tolerance Charting System in Assembly,” International Journal of Production Research, Vol. 37, No. 11, 1999, pp. 2477 2498.

[8] U. Prisco and G. Giorleo, “Overview of Current CAT Systems,” Integrated ComputerAided Engineering, Vol. 9, No. 4, 2002, pp. 373387.

[9] Z. Shen, “Software ReviewTolerance Analysis with EDS/VisVSA,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 95–99.

[10] F. Chiesi and L. Governi, “Software ReviewTolerance Analysis with eTolMate,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 100105.

[11] C. X. Feng and A. Kusiak, “Design of Tolerances for Quality,” Design Theory and MethodologyDTM’ 94, Vol. 668, ASME, 1994, pp. 1927.

[12] A. Jeang, “Tolerance Chart Optimisation for Quality and Cost,” International Journal of Production Research, Vo. 36. No. 11, 1998, pp. 29692983.

[13] A. Jeang, “Optimal Tolerance Design by Response Surface Methodology,” International Journal of Production Research, Vol. 37, No. 14, 1999, pp. 32753288.

[14] C. C. Wu and G. R. Tang, “Tolerance Design for Products with Asymmetric Quality Losses,” International Journal of Production Research, Vol. 36, No. 9, 1998, pp. 25292541.

[15] S. C. Diplaris and M. M. Sfantsikopoulos, “Tolerancing for Enhanced Quality and Optimum Cost,” Proceedings of the 33rd International MATADOR Conference, Manchester, 1999, pp. 539544.

[16] A. Jeang, “An Approach of Tolerance Design for Quality Improvement and Cost Reduction”, International Journal of Production Research, Vol. 35, No. 5, 1997, pp. 1193 1211.

[17] F. H. Speckhart, “Calculation of Tolerance Based on Minimum Cost Approach,” Journal of Engineering for IndustryTransactions of the ASME, Vol. 94, No. 2, 1972, pp. 447453.

[18] M. F. Spotts, “Allocation of Tolerances to Minimize Cost of Assembly,” Journal of Engineering for IndustryTransactions of the ASME, Vol. 95, No. 3, 1973, pp. 762764.

[19] K. W. Chase, W. H. Greenwood, B. G. Loosli and L. F. Hauglund, “Least Cost Tolerance Allocation for Mechanical Assemblies with Automated Process Selection,” Manufacturing Review, Vol. 3, No. 1, 1990, pp. 4959.

[20] Z. Dong, W. Hu and D. Xue, “New Production Cost Tolerance Models for Tolerance Synthesis,” Journal of the Engineering Industry, Vol. 116, 1994, pp. 199205.

[21] R. Soderberg, “Robust Design by Tolerance Allocation Considering Quality and Manufacturing Cost,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 219 226.

[22] M. Krishnasawamy and R. W. Mayne, “Optimizing Tolerance Allocation Based on Manufacturing Cost,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 211217.

[23] E. M. Mansoor, “The Application of Probability to Tolerances Used in Engineering Design,” Proceedings of the Institution of Mechanical Engineers, Vol. 178, No. 1, 1963, pp. 2944.

[24] E. Santoro, “Probabilistic Model for Tolerance Synthesis: An Analytical Solution, Structural Safety and Reliability,” Balkema, Rotterdam, 1994.

[25] V. J. Skowronski and J. U. Turner, “Estimating Gradients for Statistical Tolerance Synthesis,” ComputerAided Design, Vol. 28, No. 12, 1996, pp. 933941.

[26] C. Zhang, J. Luo and B. Wang, “Statistical Tolerance Synthesis Using Distribution Function Zones,” International Journal of Production Research, Vol. 37, No. 17, 1999, pp. 39954006.

[27] M. H. Gaddalah and H.A. ElMaraghy, “The Tolerance Optimization Problem Using a System of Experimental Design,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 251264.

[28] V. J. Skowronski and J. U. Turner, “Using Monte–Carlo Variance Reduction in Statistical Tolerance Synthesis,” ComputerAided Design, Vol. 29, No. 1, 1997, pp. 6369.

[29] H. S. Stern, “Neural Networks in Applied Statistics (with Discussion),” Technometrics, Vol. 38, No. 3, 1996, pp. 205220.

[30] H.C. Zhang, H. Huang, “Applications of Neural Networks in Manufacturing: AStateoftheArt Survey,” International Journal of Production Research, Vol. 33, No. 3, 1995, pp. 705728.

[31] D. E. Rumelhart and J. L. McClelland, “Parallel Distributed Processing Explorations in the Microstructure of Cognition,” MIT Press, Cambridge, 1989.

[32] R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Magazine, Vol. 4, No. 2, 1987, pp. 422.

[33] K. Price and R. Storn, “Differential Evolution–A Simple Evolution Strategy for Fast Optimization,” Dr. Dobb’s Journal, Vol. 22, No. 4, pp.1824 and 78.

[1] J. Turner and A. B. Gangoiti, “Tolerance Analysis Approaches in Commercial Software,” Concurrent Engineering, Vol. 1, No. 2, 1991, pp.1123.

[2] J. Guilford, M. Sethi and J. Turner, “Worst Case and Statistical Tolerance Analysis of the Daughter Card Assembly,” Proceedings of the 1992 ASME International Computers in Engineering Conference, San Francisco, 26 August 1992, pp. 343350.

[3] Y. Wu, J. Shah and J. Davidson, “Computer Modeling of Geometric Variations in Mechanical Parts and Assemblies,” ASME Journal Computing and Information Science in Engineering, Vol. 3, No. 1, 2003, pp. 5463.

[4] T. M. K. Pasupathy, E. P. Morse and R. G. Wilhelm, “A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 6475.

[5] P. Martino, “Simplification of Feature Based Models for Tolerance Analysis”, Proceedings of the 1992 ASME International Computers in Engineering Conference & Exposition, San Francisco, 26 August 1992, pp. 329341.

[6] Y.J. Tseng and Y.S. Terng, “Alternative Tolerance Allocations for Machining Parts Represented with Multiple Sets of Features,” International Journal of Production Research, Vol. 37, No. 7, 1999, pp. 15611579.

[7] B. K. A. Ngoi and J. M. Ong, “A Complete Tolerance Charting System in Assembly,” International Journal of Production Research, Vol. 37, No. 11, 1999, pp. 2477 2498.

[8] U. Prisco and G. Giorleo, “Overview of Current CAT Systems,” Integrated ComputerAided Engineering, Vol. 9, No. 4, 2002, pp. 373387.

[9] Z. Shen, “Software ReviewTolerance Analysis with EDS/VisVSA,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 95–99.

[10] F. Chiesi and L. Governi, “Software ReviewTolerance Analysis with eTolMate,” ASME Journal Computing and Information Science in Engineering, Special Issue on GD & T, Vol. 3, No. 1, 2003, pp. 100105.

[11] C. X. Feng and A. Kusiak, “Design of Tolerances for Quality,” Design Theory and MethodologyDTM’ 94, Vol. 668, ASME, 1994, pp. 1927.

[12] A. Jeang, “Tolerance Chart Optimisation for Quality and Cost,” International Journal of Production Research, Vo. 36. No. 11, 1998, pp. 29692983.

[13] A. Jeang, “Optimal Tolerance Design by Response Surface Methodology,” International Journal of Production Research, Vol. 37, No. 14, 1999, pp. 32753288.

[14] C. C. Wu and G. R. Tang, “Tolerance Design for Products with Asymmetric Quality Losses,” International Journal of Production Research, Vol. 36, No. 9, 1998, pp. 25292541.

[15] S. C. Diplaris and M. M. Sfantsikopoulos, “Tolerancing for Enhanced Quality and Optimum Cost,” Proceedings of the 33rd International MATADOR Conference, Manchester, 1999, pp. 539544.

[16] A. Jeang, “An Approach of Tolerance Design for Quality Improvement and Cost Reduction”, International Journal of Production Research, Vol. 35, No. 5, 1997, pp. 1193 1211.

[17] F. H. Speckhart, “Calculation of Tolerance Based on Minimum Cost Approach,” Journal of Engineering for IndustryTransactions of the ASME, Vol. 94, No. 2, 1972, pp. 447453.

[18] M. F. Spotts, “Allocation of Tolerances to Minimize Cost of Assembly,” Journal of Engineering for IndustryTransactions of the ASME, Vol. 95, No. 3, 1973, pp. 762764.

[19] K. W. Chase, W. H. Greenwood, B. G. Loosli and L. F. Hauglund, “Least Cost Tolerance Allocation for Mechanical Assemblies with Automated Process Selection,” Manufacturing Review, Vol. 3, No. 1, 1990, pp. 4959.

[20] Z. Dong, W. Hu and D. Xue, “New Production Cost Tolerance Models for Tolerance Synthesis,” Journal of the Engineering Industry, Vol. 116, 1994, pp. 199205.

[21] R. Soderberg, “Robust Design by Tolerance Allocation Considering Quality and Manufacturing Cost,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 219 226.

[22] M. Krishnasawamy and R. W. Mayne, “Optimizing Tolerance Allocation Based on Manufacturing Cost,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 211217.

[23] E. M. Mansoor, “The Application of Probability to Tolerances Used in Engineering Design,” Proceedings of the Institution of Mechanical Engineers, Vol. 178, No. 1, 1963, pp. 2944.

[24] E. Santoro, “Probabilistic Model for Tolerance Synthesis: An Analytical Solution, Structural Safety and Reliability,” Balkema, Rotterdam, 1994.

[25] V. J. Skowronski and J. U. Turner, “Estimating Gradients for Statistical Tolerance Synthesis,” ComputerAided Design, Vol. 28, No. 12, 1996, pp. 933941.

[26] C. Zhang, J. Luo and B. Wang, “Statistical Tolerance Synthesis Using Distribution Function Zones,” International Journal of Production Research, Vol. 37, No. 17, 1999, pp. 39954006.

[27] M. H. Gaddalah and H.A. ElMaraghy, “The Tolerance Optimization Problem Using a System of Experimental Design,” Advances in Design Automation, Vol. 691, ASME, 1994, pp. 251264.

[28] V. J. Skowronski and J. U. Turner, “Using Monte–Carlo Variance Reduction in Statistical Tolerance Synthesis,” ComputerAided Design, Vol. 29, No. 1, 1997, pp. 6369.

[29] H. S. Stern, “Neural Networks in Applied Statistics (with Discussion),” Technometrics, Vol. 38, No. 3, 1996, pp. 205220.

[30] H.C. Zhang, H. Huang, “Applications of Neural Networks in Manufacturing: AStateoftheArt Survey,” International Journal of Production Research, Vol. 33, No. 3, 1995, pp. 705728.

[31] D. E. Rumelhart and J. L. McClelland, “Parallel Distributed Processing Explorations in the Microstructure of Cognition,” MIT Press, Cambridge, 1989.

[32] R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Magazine, Vol. 4, No. 2, 1987, pp. 422.

[33] K. Price and R. Storn, “Differential Evolution–A Simple Evolution Strategy for Fast Optimization,” Dr. Dobb’s Journal, Vol. 22, No. 4, pp.1824 and 78.