考虑时变效应的等相对曲率齿轮动力学分析

Dynamics Analysis of Gears with Constant Relative Curvature Considering Time-varying Effect

为了研究等相对曲率齿轮的动力学特性,通过实时调用啮合点几何参数,建立了考虑法向啮合力方向、滑动摩擦因数及啮合刚度等时变效应的齿轮系统的平移-扭转耦合动力学模型,采用龙格-库塔法求解了动力学方程;通过与有限元仿真相关结果比较,验证了模型的正确性。对比分析等相对曲率齿轮与渐开线齿轮的动力学特性,结果表明,两者的动态传递误差、平均机械效率接近;等相对曲率齿轮的滑动摩擦力、滑动摩擦因数较小。建立的动力学模型能够反映等相对曲率齿轮的动力学特性,建模方法对其他非渐开线圆柱齿轮传动同样适用。

In order to investigate the dynamics characteristics of gears with constant relative curvature(CRC gears),a translation-torsional coupling dynamics model of the gear transmission system is established by instantly invoking the geometric parameters of the meshing points,considering the time-varying effects such as the direction of normal meshing force,sliding friction coefficient and meshing stiffness.The Range-Kutta meth⁃od is utilized to solve the dynamics equations numerically;the model is verified to be correct by comparing with the finite element simulation results.The results show that the dynamic transmission error and the average me⁃chanical efficiency of the two gears are close to each other;the sliding friction force and sliding friction coeffi⁃cient of the CRC gear are smaller.The dynamics model can reflect dynamics characteristics of the CRC gear,which also applies to other non-involute cylindrical gear drives.