考虑支撑间隙的齿轮系统动力学响应分析

以两轴式变速器三档传动齿轮为研究对象,对于通过花键与输出轴连接的从动齿轮,由于制造误差和装配误差,在其中心处所存在的支撑间隙必将影响齿轮传递动态特性,对此以二状态模型描述从动齿轮支撑处间隙副的接触状态及碰撞摩擦特性,建立考虑时变啮合刚度,齿侧间隙,综合齿频误差等非线性特性因素的运动微分方程,采用变步长Runge-Kutta法对状态方程进行数值求解,结合相图、Poincare截面和功率谱密度图,综合分析间隙值大小等因素对齿轮系统的动力学特性的影响。数值算例分析表明,随着间隙值的增大,齿轮啮合线的传递误差从单周期运动逐渐过渡到混沌运动,从动轮的位移响应经历了单周期-准周期-单周期的变化;间隙值过大时,间隙副出现明显的单边接触状态。

Dynamic Response Analysis of Gear Systems with Support Clearance Considered

The third gear pair of the twin-shaft transmission was taken as the research object, the driven gear and the output shaft were connected by a spline, due to the manufacturing error and the assembly error, the support clearance in the center of the driven gear would affect the dynamic characteristics of gear transmission, therefore the contact state and the friction characteristics between the gear and the transmission shaft were simulated by the two-state model. The dynamic differential equations were established while considering the nonlinear factors such as time-varying meshing stiffness, backlash and comprehensive tooth frequency error. The state equations were solved by the variable step size Runge-Kutta method. With the help of the phase diagram, Poincare section and power spectrum density diagram, the influence of clearance on the dynamic characteristics of the gear system were analyzed. With the increase of clearance, the transmission error on gear meshing line changed gradually from single periodic motions to chaotic motions, the displacement of driven wheel changed from single periodic motions to quasi periodic motions ,and then exhibited single periodic motions. The clearance pair showed obvious unilateral contact state when the clearance value was too large.