基于蒙特卡洛模拟与响应面方法的公差建模

中国机械工程 ›› 2015, Vol. 26 ›› Issue (4): 427-434.

基于蒙特卡洛模拟与响应面方法的公差建模

余治民;刘子建;董思科;李斯明;艾彦迪

湖南大学汽车车身先进设计制造国家重点实验室,长沙,410082

出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金资助项目（51175161,51301532）;国家科技重大专项（2011ZX04003-011）

Tolerance Modeling Based on Monte-Carlo Simulation and Response Surface Method

Yu Zhimin;Liu Zijian;Dong Sike;Li Simin;Ai Yandi

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body,Hunan University,Changsha,410082

Online:2015-02-25 Published:2015-02-25
Supported by:
National Natural Science Foundation of China（No. 51175161,51301532）;National Science and Technology Major Project ( No. 2011ZX04003-011)

摘要/Abstract

摘要：

针对现有机床精度设计方法实用性不强的问题,提出了一种基于蒙特卡洛模拟与响应面方法的公差建模方法。采用基于数学定义的公差分析理论建立公差的变动不等式与约束不等式;运用蒙特卡洛模拟法进行仿真试验，模拟实际公差表面的变动，生成公差变动要素的实际变动区间;以公差与试验得到的公差变动要素实际变动区间带宽值为建模样本，运用响应面方法建立两者间的响应面模型;对一个典型实例进行分析,分析结果表明,该方法符合工程实际，具有较高的建模精度及技术经济性。

关键词: 蒙特卡洛模拟, 响应面法, 小位移旋量, 约束不等式, 变动不等式

Abstract:

For the poor practicability of existing precision design method of machine tool,a new method about tolerance modeling based on MCS and response surface method was proposed herein.Firstly,the constraint inequality and change inequality were established using tolerance analysis based on mathematic definition theory.And then the simulated tests with MCS method were conducted to simulate the change of actual tolerance surface,and get the actual change interval of the tolerance factor.With the samples based on the tolerance and the bandwidth value of actual change interval obtained above,the response surface modeling between the tolerance and bandwidth was constructed by response surface method.Finally,a typical example was analyzed and the results indicate the method is consistent with engineering practice, and has high modeling precision and technical economics.

Key words: Monte-Carlo simulation(MCS), response surface method, small displacement torsor, constraint inequality, change inequality

中图分类号:

TH115

余治民, 刘子建, 董思科, 李斯明, 艾彦迪. 基于蒙特卡洛模拟与响应面方法的公差建模[J]. 中国机械工程, 2015, 26(4): 427-434.

Yu Zhimin, Liu Zijian, Dong Sike, Li Simin, Ai Yandi. Tolerance Modeling Based on Monte-Carlo Simulation and Response Surface Method[J]. China Mechanical Engineering, 2015, 26(4): 427-434.

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