公差分析中的非理想表面模型技术研究现状与展望

doi:10.3901/JME.260024

摘要/Abstract

摘要： 由于实际加工的零件表面不可避免地与设计的理想表面存在差异，因此如何快速准确地建立能够描述这种差异的几何误差模型，一直是公差分析的难题。当前几何误差模型通常将几何误差简化为理想表面的刚性平移和旋转，忽略了表面形貌对零件之间相对位置关系的影响，进而制约了公差分析结果的精确性。非理想表面模型(Skin model shapes, SMS)作为一种基于离散数学的几何误差模型，能够在公差分析中更加真实地反映零件表面包括表面形貌等在内的几何误差，因此SMS一出现就得到了学者们的广泛关注。但是，当前SMS的研究还缺乏系统性，其重要性也未达成共识。系统性回顾了SMS的起源，在此基础上进一步明确了SMS的特征和内涵，并提出了非理想表面模型技术的技术体系，提炼出SMS的非理想表面定义、几何误差分布规律与多物理场作用机理等三个技术问题，以及特征表面操作方法、几何误差生成方法与多物理场表征方法等三项关键技术，然后重点分析了非理想表面模型技术现有几何误差生成方法及其典型应用；并指出了当前非理想表面模型技术在理论层面、技术层面和应用层面面临的三大核心挑战，最后给出了非理想表面模型技术未来发展的三个方向。

关键词: 非理想表面模型, 公差分析, 计算机辅助公差设计, 建模与仿真

Abstract: As the actual surfaces of manufactured parts are inevitably different from the designed ideal ones, how to quickly and accurately establish a model that can describe such differences as geometric defects, has always been challenging in tolerance analysis. Current geometric defect models usually simplify geometric errors into rigid translation and rotation of ideal surfaces, ignoring the influence of surface topography on the relative position among parts, which in turn restricts the accuracy of tolerance analysis results. As a model of geometric defects based on the discrete geometry framework, skin model shapes (SMS) enable to reflect the geometric deviations more realistically in tolerance analysis. Therefore, the emergence of SMS has attracted widespread attention from scholars. However, the current research on SMS is characterized by a lack of systematic organization, and there is no consensus regarding its relative importance. This study systematically reviews the origin of SMS. The characteristics and connotations of SMS are further clarified. A technical framework of SMS technology is proposed, extracting three technical issues of SMS, including the definition of non-ideal surfaces, the law of geometric error distribution and the mechanism of multi-physical fields. Three types of methods, in the context of feature operations, geometric error modelling and multi-physical field characterization, are summarized as key enablers in the framework. Then, existing modelling methods for geometric defects and their typical applications are analysed in detail. Three core challenges currently faced by SMS at the theoretical level, technical level and application level are pointed out. Finally, three directions for the future development of SMS technology are highlighted.

Key words: skin model shapes(SMS), tolerance analysis, computer-aided tolerancing, modelling and simulation

中图分类号:

TH124

郄一帆, 艾泽凯, 刘检华, ANWER Nabil. 公差分析中的非理想表面模型技术研究现状与展望[J]. 机械工程学报, 2026, 62(1): 329-346.

QIE Yifan, AI Zekai, LIU Jianhua, ANWER Nabil. Skin Model Shapes for Tolerance Analysis: State of the Art and Prospects[J]. Journal of Mechanical Engineering, 2026, 62(1): 329-346.

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