The assembly precision prediction of industrial products with numerous tolerance information and complex assembly relations is a challenge for existing deviation analysis methods since their dimensional chains usually form parallel connections. The parallel connection chain is often transformed into a serial connection chain by discarding some tolerance information and physical constraints in practical application, which leads to amplifying the range of predicted results and reducing the predicted accuracy. In this paper, a virtual functional element method is proposed to simplify the parallel connection chain by integrating the tolerance information into the torsor parameters of specified virtual functional elements. A general Jacobian-Torsor model is developed to solve the simplified parallel connection chain, in which the Boolean intersection operation on torsor parameters is used to obtain comprehensive deviation results for multiple branches in a parallel connection chain. Meanwhile, the locking effect and leverage activation effect are proposed to characterize the effect of the invariant degree in parallel connection chain. Finally, an assembly case of a power plant is applied to validate the proposed method, and the results show that it has a high potential to improve the prediction accuracy of assembly deviation compared to three conventional methods.

中文翻译：

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并行连接链装配结构偏差预测的虚拟功能元新方法

具有大量公差信息和复杂装配关系的工业产品的装配精度预测对现有偏差分析方法来说是一个挑战，因为它们的尺寸链通常形成并行连接。实际应用中常常通过丢弃一些容差信息和物理约束将并行连接链转变为串行连接链，导致预测结果的范围放大，预测精度降低。本文提出了一种虚拟功能单元方法，通过将容差信息集成到指定虚拟功能单元的扭转参数中来简化并联连接链。提出了一种通用的Jacobian-Torsor模型来求解简化的并联链，该模型通过对torsor参数进行布尔交集运算来获得并联链中多个分支的综合偏差结果。同时，提出了锁定效应和杠杆激活效应来表征并联链中不变度的影响。最后，应用电厂装配案例对所提出的方法进行验证，结果表明，与三种传统方法相比，该方法有很大潜力提高装配偏差的预测精度。