摆线钢球行星传动啮合副非线性力学性能研究  

RESEARCH ON NONLINEAR MECHANICAL PROPERTIES FOR ENGAGEMENT PAIR OF CYCLOID BALL PLANETARY TRANSMISSION

作　　者：张鹏[1] 安子军[1,2] 杨作梅[1] 

机构地区：[1]燕山大学机械工程学院,河北秦皇岛066004 [2]重庆大学机械传动国家重点实验室,重庆400030

出　　处：《工程力学》2010年第3期186-192,共7页Engineering Mechanics

基　　金：河北省教育厅科技计划项目(20050097);重庆大学机械传动国家重点实验室访问学者项目(200816)

摘　　要：摆线钢球啮合副为空间曲面啮合结构,啮合副承载与变形之间的非线性关系以及啮合副接触区扩展均会对其力学性能产生较大的影响。该文首先利用超静定方法建立了啮合副非线性力学模型,根据啮合力与阻力矩作功相等的原理推导出时变的啮合力函数。然后将啮合力转换为啮合接触区上的椭球状分布载荷,利用叠加法对接触区微元在集中力作用下的变形与应力结果进行积分,给出了接触区变形挠曲面方程、接触表面下各应力函数,以及最大切应力的深度位置。最后根据钢球位置方程,建立了啮合副不同啮合位置的有限元模型,对钢球与摆线槽的啮合过程进行了数值模拟,分析了啮合副应力分布状态以及啮合点等效应力的变化规律。结果表明:采用啮合副非线性力学模型和接触区分布载荷减少了线弹性和集中力简化处理造成的误差,为啮合副承载状态提供了更符合实际的计算结果。The cycloid ball engagement pair has a configuration of spatial surface engagement,and the mechanical properties of engagement pair are affected by the nonlinear relationship between load and deformation as well as the extension of contact zone.Firstly,this paper establishes the nonlinear mechanical model of engagement pair using the hyperstatic method,and the time-variant engagement force is derived according to the equal work between engagement force and resistance moment.Then,the engagement force is converted to an ellipsoidal distributed load acting on contact zone.The deformed deflection surface of contact zone,the stresses under contact surface,and the depth of maximum shear stress are obtained using the superposition method,which integrates the deformation and stress of infinitesimal contact zone acted by concentrated forces.Finally,based on the position equation of balls,the finite element models of engagement pair are established with different engagement positions.The engagement process is simulated by the finite element method,and the stress distribution of engagement pair as well as the equivalent stress on engagement point is analyzed.The results show that the nonlinear mechanical model and the distributed load reduce the error caused by the simplification of linear elasticity and concentrated forces,and offer a more practical loading condition of engagement pair.

关 键 词：行星传动 非线性力学性能 赫兹接触 有限元 摆线 钢球 啮合副 

分 类 号：TH132.4[机械工程—机械制造及自动化]