Abstract
The unified Jacobian-Torsor model uses the torsor model for tolerance representation and the Jacobian matrix for tolerance propagation. The torsor model is composed of six components, i.e., three translational vectors and three rotational vectors. However, previous studies about this model have only considered the constraint of individual component. In fact, this constraint is the scope of a single component. It is called variation. Relations between these components are constraints which reflect the interaction between them in a tolerance zone. Integrating all limited values of components of torsors into the unified Jacobian-Torsor model may lead to an inaccurate result. Meanwhile, the variations and constraints of torsor for a feature specified by more than one tolerance have been not illustrated clearly. In this paper, a modified method of the unified Jacobian-Torsor model considering constraints between components of torsor is presented. The variations and constraints of torsors for cylindrical and planar features are proposed. These constraints are calculated by means of a modified Monte Carlo method based on the previous work. Moreover, tolerance allocation of this modified method in a statistical way is also introduced. Two case studies have been performed to demonstrate the modified method.
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Chen, H., Jin, S., Li, Z. et al. A modified method of the unified Jacobian-Torsor model for tolerance analysis and allocation. Int. J. Precis. Eng. Manuf. 16, 1789–1800 (2015). https://doi.org/10.1007/s12541-015-0234-7
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DOI: https://doi.org/10.1007/s12541-015-0234-7