锥齿行星齿轮传动模态特性分析

Modal properties for bevel planetary gear trains

根据相对质心的动量矩定理,建立了锥齿行星齿轮传动的多维动力学模型,采用归纳方法研究了模态特性。结果表明:该传动系统的模态可归结为4种典型振动模式,即:轴向平移-扭转、径向平移-扭摆、行星轮及轴向平移振动模式。在轴向平移-扭转振动模式下,中心构件呈现沿轴线方向的平移振动及绕该轴的扭转振动;在径向平移-扭摆振动模式下,中心构件呈现沿径向的平移振动及绕该方向的扭摆振动;在行星轮振动模式下,中心构件均不振动,仅行星轮在振动;在轴向平移振动模式下,中心构件仅呈现沿轴线方向的平移振动,其他方向不存在振动。与上述4种典型振动模式对应的固有频率的重数分别为1,2,N-3及N-2。该研究为锥齿行星传动的动态特性优化奠定了理论基础。

Based on the theory of angular momentum relative to mass center,an analytical model of bevel planetary gear trains is developed including the gyroscopic effect to investigate the dynamic characteristics of the gear system.According to the inductive method,the free vibration properties of the system are studied.And the results show that the vibration modes can be classified into four groups： axial translational and rotational modes in which the center components exhibit translation motion in the direction of the axis and the rotational motion around it,the radial translational and torsional modes in which the center components exhibit translation motion in the radial direction and the torsional motion around it,planet modes in which the center components have no motion and only the planets deflect,and axial translational modes in which the center members only exhibit translation motion in the direction of the axis.The multiplicity of the associated natural frequencies for the four vibration modes is 1,1 or 2,N-3 and N-2.This work lays a foundation for the optimization of the dynamic properties for the bevel planetary gears trains.