A New Approach of Constraints Establishment and Optimization for Matrix Tolerance Model

doi:10.3901/JME.2016.01.123

Abstract

Abstract: The constraints of traditional matrix tolerance model are constructed by virtue of vertexes of features. Differences of locations and numbers of these vertexes may result in different computational accuracy and efficiency. Meanwhile, traditional algorithm of optimization is incapable of dealing with the situations where a large number of nonlinear inequalities exist. Therefore, the general variations and constraints of features are brought into the matrix model. Monte Carlo simulation is used to take these random numbers satisfying the constraints into computation process. This approach enhances the reliability and efficiency of the matrix model, and reduces its difficulty of the optimization. Comparative results of a simple assemble show the practicability and effectiveness of this approach.

Key words: constraints, matrix model, Monte Carlo, optimization, tolerance

CLC Number:

TP391

CHEN Hua, LIN Guansheng, TANG Tao, YANG Jia, JIN Sun. A New Approach of Constraints Establishment and Optimization for Matrix Tolerance Model[J]. Journal of Mechanical Engineering, 2016, 52(1): 123-129.

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http://www.cjmenet.com.cn/EN/Y2016/V52/I1/123

References

[1] SHEN Z，AMETA G，SHAH J J，et al. A comparative study of tolerance analysis method[J]. ASME Journal of Computing and Information Science in Engineering，2005，5：247-256.
[2] AMETA G，SERGE S，GIORDANO M. Comparison of spatial math models for tolerance analysis：Tolerance-maps，deviation，domain，and TTRS[J]. ASME Journal of Computing and Information Science in Engineering，2011，11：012004-1-8.
[3] CHEN H，JIN S，LI Z，et al. A comprehensive study of three dimensional tolerance analysis methods[J]. Computer-Aided Design，2014，53：1-13.
[4] GAO J，CHASE K W，MAGLEBY S P. General 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments[J]. IIE Transactions，1998，30：367-377.
[5] DAVIDSON J K，MUJEZINOVIC′ A，SHAH J J. A new mathematical model for geometric tolerances as applied to round faces[J]. ASME Journal of Mechanical Design，2002，124：609-622.
[6] DESROCHERS A，GHIE W，LAPERRIèRE L. Application of a unified Jacobian-Torsor model for tolerance analysis[J]. ASME Journal of Computing and Information Science in Engineering，2003，3：1-13.
[7] DESROCHERS A，RIVIèRE A. A matrix approach to the representation of tolerance zones and clearances[J]. International Journal of Advanced Manufacturing Technology，1997，13：630-636.
[8] CLéMENT A，RIVIèRE A，SERRé P，et al. The TTRSs：13 constraints for dimensioning and tolerancing[J]. Geometric Design Tolerancing：Theories，Standards and Applications，1998，122-131.
[9] PRISCO U，GIORLEO G. Overview of current CAT systems[J]. Integrated Computer-Aided Engineering，2002，9：373-387.
[10] WHITNEY D E，GILBERT O L，JASTRZEBSKI M. Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies[J]. Research in Engineering Design，1994，6(4)：191-210.
[11] SALOMONS O W. Computer support in the design of mechanical products[D]. University of Twente，The Netherlands，1995.
[12] ROY U，LI B. Representation and interpretation of geometric tolerances for polyhedral objects. II. Size，orientation and position tolerances[J]. Computer-Aided Design，1999，31(4)：273-285.
[13] 蔡敏. 基于数学定义的圆柱要素公差数学建模与分析技术的研究[D]. 杭州：浙江大学，2002.CAI Ming. Study on mathematical modeling and analysis of cylindrical feature[D]. Hangzhou：Zhejiang University，2002.
[14] 王正林，龚纯，何倩. 精通MATLAB科学计算[M]. 北京：电子工业出版社，2007. WANG Zhenglin，GONG Chun，HE Qian. Proficiency of scientific calculation with MATLAB[M]. Beijing：Publishing House of Electronics Industry，2007.
[15] 杜比. 蒙特卡洛方法在系统工程中的应用[M]. 西安：西安交通大学出版社，2007. DU Bi. Monte Carlo applications in systems engineering[M]. Xi’an：Xi’an Jiaotong University Press，2007.
[16] NIGAM S D，TURNER J U. Review of statistical approaches to tolerance analysis[J]. Computer-Aided Design，1995，27(1)：6-15.