Abstract
The unified Jacobian-Torsor model has been developed for deterministic (worst case) tolerance analysis. This paper presents a comprehensive model for performing statistical tolerance analysis by integrating the unified Jacobian-Torsor model and Monte Carlo simulation. In this model, an assembly is sub-divided into surfaces, the Small Displacements Torsor (SDT) parameters are used to express the relative position between any two surfaces of the assembly. Then, 3D dimension-chain can be created by using a surface graph of the assembly and the unified Jacobian-Torsor model is developed based on the effect of each functional element on the whole functional requirements of products. Finally, Monte Carlo simulation is implemented for the statistical tolerance analysis. A numerical example is given to demonstrate the capability of the proposed method in handling three-dimensional assembly tolerance analysis.
Highlights
With the release of new generation GPS tolerancing standards, geometric tolerances are generally accepted as industry practices [1]
Geometric tolerances and dimensional tolerances, as well as the interaction between them in the tolerance zone can be taken into consideration by 3D tolerance analysis methods
This paper focuses on the development of an analysis method to realize the statistical tolerance analysis of a mechanical assembly by integrating the unified Jacobian-Torsor model with Monte Carlo simulation
Summary
With the release of new generation GPS tolerancing standards, geometric tolerances are generally accepted as industry practices [1]. Geometric tolerances and dimensional tolerances, as well as the interaction between them in the tolerance zone can be taken into consideration by 3D tolerance analysis methods. Desrochers et al [2] proposed the unified Jacobian-Torsor model for deterministic tolerance analysis by the unifying of two existing models: the torsor model and the Jacobian matrix model in which the torsor model is used for tolerance representation and the Jacobian matrix for tolerance propagation. The research on combinations of 3D tolerance analysis technology and statistical analysis method is attracting the attention of many researchers [3, 4]. This paper focuses on the development of an analysis method to realize the statistical tolerance analysis of a mechanical assembly by integrating the unified Jacobian-Torsor model with Monte Carlo simulation. The designation of a surface is made up of two numbers separated by a “,”: (1, 1) means surface 1 of part 1
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