A review of two models for tolerance analysis of an assembly: Jacobian and torsor
A review of two models for tolerance analysis of an assembly: Jacobian and torsor
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DOI：
10.1080/0951192x.2010.531286
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发表时间：
2011-01
影响因子：
4.1
通讯作者：
M. Marziale;W. Polini
中科院分区：
文献类型：
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作者：
M. Marziale;W. Polini
装配的每个部件的尺寸和几何变化必须受到公差的限制，以确保标准化生产和一定水平的质量，这是通过满足功能要求来定义的。在装配的不同部件之间适当分配公差是确保装配以较低成本正确工作的基本工具。因此，有一个强烈的需要开发公差分析，以满足装配要求的公差施加在单个零件上。该工具必须基于能够评估单个公差累积效应的数学模型。实际上，文献中使用或提出了一些不同的模型来对由刚性零件组成的装配体进行公差分析，但没有一种模型是完全和统一接受的。一些作者把注意力集中在解决这些模型中发现的单个问题或在计算机辅助公差系统中的实际应用上。但都没有对它们进行客观、全面的比较，分析它们的优缺点，为它们的选择和应用提供一个标准。本文简要介绍了公差分析的两种主要模型——雅可比矩阵和扭量模型。本文对这些模型进行了简要描述，并对其进行了比较。并给出了这两种模型的演化过程，即统一雅可比-托子模型。
The dimensional and geometrical variations of each part of an assembly have to be limited by tolerances able to ensure both a standardised production and a certain level of quality, which is defined by satisfying functional requirements. The appropriate allocation of tolerances among the different parts of an assembly is the fundamental tool to ensure assemblies that work correctly at lower costs. Therefore, there is a strong need to develop a tolerance analysis to satisfy the requirements of the assembly by the tolerances imposed on the single parts. This tool has to be based on a mathematical model able to evaluate the cumulative effect of the single tolerances. Actually there are some different models used or proposed by the literature to make the tolerance analysis of an assembly constituted by rigid parts, but none of them is completely and univocally accepted. Some authors focus their attention on the solution of single problems found in these models or in their practical application in computer-aided tolerancing systems. But none of them has done an objective and complete comparison among them, analysing the advantages and the weakness and furnishing a criterion for their choice and application. This paper briefly introduces two of the main models for tolerance analysis, the Jacobian and the torsor. These models are briefly described and then compared showing their analogies and differences. The evolution of these two models, known as unified Jacobian-torsor model, is presented too.