斜齿轮传动的啮合刚度计算及其主共振分析

斜齿轮是机械装备的重要传动元件，其啮合刚度的准确计算和传动系统的稳定性分析具有重要的实际意义。根据斜齿轮轮齿接触线的变化规律，结合斜齿轮单对齿单位长度啮合刚度变化规律和ISO刚度计算准则，提出一种斜齿轮啮合刚度计算方法，分析了不同参数下斜齿轮传动的啮合刚度波动特性；基于分析所得的啮合刚度变化规律建立了斜齿轮传动的动力学模型，并利用多尺度法对动力学模型进行了求解，研究了外加载荷和啮合刚度波动对斜齿轮传动主共振的影响。结果表明：给出的斜齿轮啮合刚度计算方法能够较快速、准确地获取啮合刚度波动变化规律，将其引入斜齿轮动态特性分析中，能够更加准确地反映斜齿轮啮合刚度波动和载荷波动对系统主共振稳定性的影响规律；在其他条件不变时，斜齿轮主共振稳定性随静载荷和啮合刚度波动增加而增加，但较大静载荷会导致主共振频率增大，而且在高频激励下，即使较小的啮合刚度波动也会触发主共振的不稳定；载荷波动增加会使斜齿轮主共振幅值增大，使系统稳定性变差。

Meshing Stiffness Calculation and Main Resonance Analysis of Helical Gear Transmission

Helical gear is an important element of mechanical equipment. The accurate calculation of meshing stiffness and the stability analysis of the transmission system have important practical significance. Based on the change rule of tooth contact line of helical gear, the change law of mesh stiffness about single gear pair in unit length and the ISO calculation method of mesh stiffness, a kind of approximate method was put forward for calculating the mesh stiffness of helical gear and used to study effects of the structural parameters of helical gear on mesh stiffness fluctuation. A dynamic model of helical gear transmission which included the change rule of mesh stiffness obtained from the analysis was established and solved by using multi-scale method. The influence of the loads and meshing stiffness fluctuation of helical gear on the primary resonance was analyzed. The results showed that the calculation method of meshing stiffness could be used to determine the meshing stiffness fluctuation rule of helical gear quickly and accurately. By applying the meshing stiffness fluctuation obtained to study the dynamic characteristics of helical gear transmission, some more accurate variation rules of primary resonance caused by meshing stiffness fluctuations and load fluctuation were gained. When other parameters remained unchanged, the increase of the static load and meshing stiffness fluctuate could improve the primary resonance stability accordingly. But larger static loads resulted in higher primary resonant frequencies and very small meshing stiffness fluctuations could cause the primary resonance unstable under the condition of high-frequency excitation. The amplitude of primary resonance increased with the load fluctuation and the stability of helical gear transmission deteriorates. Through the proposed calculation method of meshing stiffness and the dynamic analysis of helical gear transmission by multi-scale method, the general characteristics of helical gear transmission had been revealed more universally.