Purpose

The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products.

Design/methodology/approach

The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method.

Findings

The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model.

Research limitations/implications

The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation.

Practical implications

The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly.

Originality/value

This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

中文翻译：

---

基于torsor簇模型的离散表面结构三维公差分析

目的

本文的目的是提出一种新的数学模型来呈现离散表面的三维公差，并实施一种方法来分析具有离散表面结构的组件的公差。分立面是一种大面基的特殊结构，上面装有若干分立元件，一种广泛应用于复杂机电产品中。

设计/方法/方法

根据离散单元的空间关系，将离散曲面的几何特征分离出来，并以小位移扭力为特征。通过对torsor模型进行积分，建立torsor聚类模型来表征离散曲面的积分特征变化。离散曲面装配公差的影响和累积是通过基于统一雅可比-托尔法的统计公差分析来确定的。

发现

通过相控阵天线的案例研究，成功地证明了所提出的模型在离散表面综合公差表征方面的有效性和优越性。基于torsor cluster模型对容差进行了明显直观的计算和表达。

研究限制/影响

所提出的容差分析方法对于统计模拟的计算需要大量时间和较高的计算性能。

实际影响

Torsor集群模型实现了离散曲面的三维公差表示。基于该模型的公差分析方法预测组件在物理装配之前的公差累积。

原创性/价值

本文提出了torsor cluster作为一种新的数学模型来解释离散表面的公差。