Statistical Variation Analysis Using Pearson Distribution Family Based on Jacobian-Torsor Model

¹ State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China
² Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China

^* Corresponding author: jinsun@sjtu.edu.cn

Abstract

Assembly variations are unavoidable due to parts’ geometrical errors. Statistical variation analysis is an effective method to quantitatively predict product quality in the original design stage. However, traditional methods can’t handle the problem of abnormal distribution of the actual variation variables. Meanwhile, they are underdeveloped in regard to the complex geometrical errors in spatial 3D state. To overcome this problem, firstly, Jacobian-Torsor model is used to build the variation propagation, which is well suited to a complex assembly that contains large numbers of joints and geometric tolerances; secondly, Pearson distribution family is adopted to determine probability distribution pattern and build probability density function. By comparing results of the suggested method to the Monte Carlo method, it is observed that this novel method has the same accuracy, but much higher efficiency. The results also demonstrate that probability distribution types of the parts variations have a significant impact on the final assembling variation.