雅可比-旋量模型在三维统计公差再设计中的应用研究  

Application of the Jacobian-Torsor Model in 3D Statistical Tolerance Redesign

作　　者：彭和平[1] 闵珉[1] 彭卓群 PENG He-ping;MIN Min;PENG Zhuo-qun(School of Electromechanical&Architectural Engineering,Jianghan University,Hubei Wuhan430056,China;School of Machinery and Automation,Wuhan University of Science and Technology,Hubei Wuhan430081,China)

机构地区：[1]江汉大学机电与建筑工程学院,湖北武汉430056 [2]武汉科技大学机械自动化学院,湖北武汉430081

出　　处：《机械设计与制造》2019年第11期158-162,166,共6页Machinery Design & Manufacture

基　　金：国家自然科学基金资助项目(51575235)

摘　　要：在确定产品功能要求(Functional Requirement,FR)和相应尺寸链的功能要素(Functional Element,FE)副之后,可以推导雅可比-旋量模型的数学表达式。蒙特卡罗模拟使用大量随机数值作为输入来反复运行该模型,使这个确定性的公差分析模型能执行三维统计公差分析。为了实现三维统计公差再设计,提出了在统计条件下雅可比-旋量模型中每个FE对总FR的贡献百分率的计算方法,以帮助设计者确定哪些公差需要收紧或是放松。经过几轮的公差再设计,直到计算出的FR值满足产品所要求的FR,三维统计公差的再设计得以实现。将该方法应用于活塞式发动机装配的曲柄连杆机构以验证其有效性,并通过与确定性公差设计方法比较表明,这里方法能显著降低所需的精度,从而大大降低产品生产和检验成本。After having identified the product functional requirement(FR)and the functional elements(FEs)of the corresponding dimension chain,the expression of Jacobian-Torsor model can be derived.Monte Carlo simulation is employed to repeatedly evaluate the model using a large number of random values as inputs so that this deterministic tolerance analysis model can perform 3D statistical tolerance analysis.In order to realize 3D statistical tolerance redesign,the method for calculating the percentage contribution of each FE to total FR in the Jacobian-Torsor model under statistical conditions is proposed to help designers determine which tolerances need to tighten or loosen.This iteration procedure is repeated several times until the calculated FR satisfies the FR required by the product,the desired tolerance values can be obtained and the statistical tolerance redesign is realized.The proposed method is tested on a crank-connecting rod mechanism of piston engine assembly.Compared with the deterministic tolerancing method,the results show that the proposed method can relax significantly the precision required,manufacturing and inspection costs can then be reduced considerably.

关 键 词：雅可比-旋量模型 统计公差设计 尺寸链 蒙特卡罗模拟 功能要求 

分 类 号：TH16[机械工程—机械制造及自动化] TG801[金属学及工艺—公差测量技术]