次摆线滚轮齿条传动啮合副力学性能研究

Research of Mechanical Property of Trochoid Roller Pinion Rack Transmissions

面向机器人移动系统对高精度、高速及大行程传动装置的需求,针对次摆线滚轮齿条传动啮合力及接触应力进行了综合研究。首先,考虑多齿啮合的静不定问题,建立了啮合副力学模型,根据啮合副变形协调条件和滚轮力矩平衡条件,结合齿廓压力角分析,推导出啮合力公式,并分析了啮合力的变化规律及啮合滚柱间的载荷分配;其次,基于弹性力学赫兹理论,结合啮合点处齿形曲率分析,给出了啮合副接触应力公式,并分析了接触应力的变化规律;最后,结合算例,建立了啮合副有限元模型,通过滚柱与次摆线齿啮合过程的有限元仿真,验证了啮合副力学建模方法与分析结果的合理性。

It is important to meet drive requirements of the high precision,high speed and long-stroke for robotic driving system. An investigation on meshing force and contact stress of trochoid roller pinion rack transmission is carried out. Firstly,the mechanical model of meshing pair is established when considering statically indeterminate problem of multi-tooth meshing transmission,and the time-variant calculating formula and change of meshing force is derived,and force distribution between rollers is analyzed according to the equilibrium conditions of moment and the analysis of pressure angle. Then,the calculating formula and change of stress is concluded based on the Hertz formula of elastic mechanics and radius of curvature of the contacting point. Finally,a example is given and the finite element models of meshing pair are established. Through the finite element simulation of the meshing process of roller and trochoid tooth,the rationality of the mechanics modeling method and the analysis results of the meshing pair are verified.