ABSTRACT Tolerance analysis aims to evaluate the functional requirement of mechanical assemblies in the design stage. As one of the typical tolerance analysis methods, the polytope model has shown great potential in Computer-Aided Tolerancing (CAT) field based on a series of constraints. However, existing research outcomes on this topic rarely consider form defects and the combined effects of form defects and surface deformations. This limitation may cause inaccuracy of tolerance analysis results. Hence, this paper integrates form defects and surface deformations in polytope-based tolerance analysis. Specifically, form defects are considered based on the concept of Skin Model Shapes and surface deformations are calculated based on a Conjugate Gradient-Fast Fourier Transform (CG-FFT) method. Then, the modeling method of the new polytope model is elaborated based on surface types and different types of constraints. Moreover, a case study is conducted to explain the procedure of polytope-based tolerance analysis. Through operations of the polytopes, tolerance analysis results are obtained, and the comparison with conventional polytope analysis results shows the considerable effects of form defects and surface deformations. It is expected that the proposed method can have a more realistic and accurate analysis result because of its consideration of real surface contact status.

中文翻译：

---

考虑形状缺陷和表面变形的基于多面体的公差分析

摘要 公差分析旨在评估机械组件在设计阶段的功能要求。多面体模型作为典型的公差分析方法之一，基于一系列约束条件，在计算机辅助公差（CAT）领域显示出巨大的潜力。然而，关于该主题的现有研究成果很少考虑形状缺陷以及形状缺陷和表面变形的综合影响。此限制可能会导致公差分析结果不准确。因此，本文在基于多面体的公差分析中整合了形状缺陷和表面变形。具体而言，基于皮肤模型形状的概念考虑形状缺陷，并基于共轭梯度-快速傅立叶变换（CG-FFT）方法计算表面变形。然后，根据表面类型和不同类型的约束，阐述了新的多面体模型的建模方法。此外，还进行了一个案例研究来解释基于多胞胎的公差分析的过程。通过对多面体的操作，得到公差分析结果，与常规多面体分析结果的比较显示了形状缺陷和表面变形的显着影响。由于考虑了真实的表面接触状态，预计所提出的方法可以获得更真实和准确的分析结果。与传统多面体分析结果的比较显示了形状缺陷和表面变形的显着影响。由于考虑了真实的表面接触状态，预计所提出的方法可以获得更真实和准确的分析结果。与传统多面体分析结果的比较显示了形状缺陷和表面变形的显着影响。由于考虑了真实的表面接触状态，预计所提出的方法可以获得更真实和准确的分析结果。