An iterative statistical tolerance analysis procedure to deal with linearized behavior models

Tolerance analysis consists of analyzing the impact of variations on the mechanism behavior due to the manufacturing process. The goal is to predict its quality level at the design stage. The technique involves computing probabilities of failure of the mechanism in a mass production process. The various analysis methods have to consider the component’s variations as random variables and the worst configuration of gaps for over-constrained systems. This consideration varies in function by the type of mechanism behavior and is realized by an optimization scheme combined with a Monte Carlo simulation. To simplify the optimization step, it is necessary to linearize the mechanism behavior into several parts. This study aims at analyzing the impact of the linearization strategy on the probability of failure estimation; a highly over-constrained mechanism with two pins and five cotters is used as an illustration for this study. The purpose is to strike a balance among model error caused by the linearization, computing time, and result accuracy. In addition, an iterative procedure is proposed for the assembly requirement to provide accurate results without using the entire Monte Carlo simulation.摘要目的分析由制造过程产生的变化对机构行为造成的影响。 主要分析线性化方法对失败率估计的影响, 从而平衡模型线性化造成的误差、 计算时间和结果准确性。创新点简化优化步骤, 将机构行为线性化为几个部分, 取代整体蒙特卡洛法, 并采用一种迭代算法得到更加精确的结果。方法1. 采用带有非线性约束条件的几何线性化方法和基于失败率置信区间的算法 (图3、 4 和 5); 2. 以一个器件连接器为例, 验证该算法在估计装配失败率上的作用。结论1. 线性化方法不影响蒙特卡洛仿真时间; 2. 线性化次数对计算时间和失败率估计准确率有很大影响 (表1); 3. 线性化迭代统计方法相对于蒙特卡洛法在计算时间、 计算精度和计算效率上有很大的优越性。