行星传动多体齿轮承载接触特性分析

Loaded Tooth Contact Characteristic Analysis of Multi-gear for Planetary Transmission

根据行星齿轮功率分流传动的特点,提出多个齿轮接触的齿面加载接触分析方法。考虑了安装误差条件下的齿面准确几何形态,提出行星齿轮齿面几何接触分析(TCA)方法并获得外(内)各齿轮副的相对齿面间隙;通过一次有限元柔度系数计算获得各齿轮的柔度系数,各外(内)齿轮辐接触点的法向柔度系数通过分别插值太阳轮和行星轮(行星轮和齿圈)齿面网格节点的柔度系数并叠加获得;结合齿轮的几何分析与力学分析,将多个齿轮副受力接触转化为求解齿面有限个离散接触点的力学平衡问题,通过数学规划的方法求解非线性方程组得到加载后各齿轮副的齿面变形、啮合刚度、载荷分布、行星轮均载系数。多载荷传动误差和载荷分配进一步反映了行星传动啮合性能,为高性能行星传动齿面的修形设计、动力学分析奠定了理论基础。

An approach of loaded tooth contact analysis of muti-gear for planetary transmission was proposed to simulate gears performances. The relative tooth clearances of external(internal) gear pair were calculated based on tooth contact analysis(TCA) considering accurate topography of tooth surfaces with alignment errors. The normal flexibility matrix caused by unit normal force of tooth surface point were obtained by computing flexibility coefficients based on finite element, and based on which normal flexibility coefficient of points on tooth contact lines for external(internal) gear pairs were calculated by interpolating and summing the the flexibility coefficient from sun and planet gears(planet gears and ring gear). With geometric analysis and mechanical analysis of gears, the tooth contact problem for gear pairs under load were represented to mechanical equilibrium problem of finite contact points. Besides, deformation, meshing stiffness, loads distribution and load sharing coefficient were obtained by solving the non-linear equations applied mathematical programming. Simulation results from transmission errors and load distribution under loads show validity of the method, which contribute to design of modified tooth surfaces and dynamic analysis for high-performance planetary gears.