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A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears.pdf

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A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears.pdf

Mechanism and Machine Theory 109 (2017) 155–170 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: /locate/mechmachtheory A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears Han Ding, Yuansheng Zhou?, Jinyuan Tang?, Jue Zhong, Zhenyu Zhou, Guoxin Wan State Key Laboratory of High-performance Complex Manufacturing, Central South University, Changsha 410083, China MARK ARTICLE INFO Keywords: ETCA Spiral bevel and hypoid gear Initial contact point Initial values Matching strategy BFGS algorithm ABSTRACT Tooth contact analysis with errors (ETCA) has been widely applied to simulate the meshing process of a pair of spiral bevel or hypoid gears. In the computation of ETCA, all contact points of the meshing process are calculated based on application of numerical methods. To start the computation procedure, an initial contact point should be ?rstly calculated, and the result of ETCA is sensitive to this initial contact point. In this paper, a new systematic methodology using a novel operation strategy and an optimization algorithm is proposed to accurately identify the initial contact point for ETCA. First, the nonlinear equations of ETCA are established by a universal model of the real tooth ?ank using universal machine settings. Second, the matching strategy of candidate points on the discrete tooth ?ank is proposed to determine the target points with the minimum distance. And then the discretization optimization based on the subdivision rule and the numbering of target matching points is described to perform an accurate and e?ective matching. After the target points are obtained as the initial values, the BFGS algorithm is applied to solve the initial contact point, as well as ETCA results. Finally, numerical examples are provided to verify the accuracy and e?ciency of the proposed systematic method. 1. Introduction Tooth contact analysis technology (TCA