基于齿轮时变啮合过程的修形齿面设计方法研究

Research on the Design Method of the Modified Gear Tooth Surface Based on the Gear Time-varying Meshing Process

斜齿轮啮合过程中的理想齿面为渐开螺旋面,但在实际的服役过程中,由于齿轮受载、热变形以及支承变形等因素的影响,实际齿面与理想齿面存在一定的偏差,通常采用齿面修形的方法来减小由于位置偏差引起的齿面偏载及振动。现有的修形方式往往采用考虑载荷大小的公式法计算修形量,虽然能在一定程度上提高传动性能,但仍存在设计精度不高的问题。提出一种基于齿轮时变啮合过程的拓扑修形齿面设计方法,以此来提高齿轮副传动的啮合性能。首先,通过沿斜齿轮接触迹线划分齿面的方式对石川公式进行改进,建立斜齿轮副齿面时变刚度模型;然后,根据齿轮副的实际啮合过程建立6自由度动力学方程;最后,根据动力学方程计算的齿面综合变形量设计补偿齿面拓扑修形量,并进行了动力学仿真。通过与采用传统公式法设计的修形齿轮进行仿真对比,验证了提出方法的有效性。

The ideal tooth surface in the meshing process of helical gears is an involute helical surface,but in the actual service process, there is a certain deviation between the actual tooth surface and the ideal tooth surface due to the influence of gear load, thermal deformation and support deformation. The tooth surface modification method is usually used to reduce the tooth surface eccentric load and vibration caused by position deviation. The existing modification methods often use the formula method considering the size of the load to calculate the modification amount. Although it can improve the transmission performance to a certain extent, there is still the problem of low design accuracy. Thus, a topological modification tooth surface design method based on the time-varying meshing process of gears is proposed to improve the meshing performance of gear pair transmission. Firstly, Ishikawa formula is improved by dividing the tooth surface along the contact trace of helical gears,and the time-varying stiffness model of helical gear pair tooth surface is established;then, the six-degree-offreedom dynamic equation is established according to the actual meshing process of the gear pair;finally, according to the comprehensive deformation of the tooth surface calculated by the dynamic equation, the topological modification of the compensated tooth surface is designed, and the dynamic simulation is carried out. Through the simulation comparison with the modified gear designed by the traditional formula method, the effectiveness of the proposed method is verified.