基于空间啮合理论的摆线钢球行星传动根切研究

Research on Undercutting in Cycloid Ball Planetary Transmission Based on Space Meshing Theory

介绍了摆线钢球行星传动的结构组成和传动原理,提出了利用锥形铣刀包络内、外摆线封闭槽的数学模型,建立了摆线槽齿面的包络面方程。根据空间啮合理论推导出摆线槽齿面的根切界限函数,分析了根切界限函数随基本设计参数的变化规律。结果表明,随着基本设计参数的变化,内、外摆线封闭槽齿面会按一定的先后顺序发生根切,并且总是内摆线槽内侧齿面最先根切,从而得到了不发生根切必须满足的不等式方程,并通过具体实例及计算机图形仿真进行验证。本研究为摆线钢球行星传动的设计制造提供了理论依据。

The structure and drive principle of the cycloid ball planetary transmission was introduced.The mathematic models for the tooth surfaces of epitrochoid and hypotrochoid enclosed grooves generated by cone milling cutter were proposed.According to space meshing theory,the meshing equations and the undercut limit functions were deduced.The variational regularity of undercut limit functions with the fundamental design parameters were analyzed through the numerical method.The analytical results showed that the undercutting phenomenon of the tooth surfaces of hypotrochoid and epitrochoid enclosed grooves occurred orderly corresponding to the variation of fundamental design parameters, and the first undercut point always occurred on inside tooth surface of hypotrochoid groove. Consequently, a simpler dimensionless inequality which can avoid the undercut was derived from the proposed analysis. Then, the conclusion was verified by the design examples and the computer simulations. The research results offer a theoretical basis for designing and manufacturing of the cycloid ball planetary transmission.