考虑偏转的斜齿轮啮合刚度及其振动分析

Meshing stiffness calculation and vibration analysis of helical gear considering deflection

结合啮合接触线长度变化规律,根据斜齿轮啮合存在轴向偏转角时载荷沿轴向分布变化引起的啮合力矩的变化规律,推导了包含时变刚度和偏转刚度的斜齿轮啮合刚度解析表达式,并通过算例与现有实验数据对比验证。研究了不同齿宽和传递扭矩下,新啮合刚度模型的振动响应规律;进一步提出了考虑齿隙的斜齿轮啮合动力学方程,并研究了扭矩和齿隙大小的影响规律。结果显示,给出的斜齿轮啮合刚度解析公式能够较快速、准确地获取啮合刚度波动变化规律,能够很好地反映斜齿轮啮合振动;时变刚度和偏转刚度对斜齿轮传动系统的影响主要表现在具有工程意义的中低转速,随着齿宽增大其影响更明显,随着扭矩增大啮合刚度的时变引起的参数激振响应也随之增大;考虑齿隙的齿轮啮合振动,随着激励增大会经历稳定周期运动、概周期运动再回到稳定周期运动的过程。

Based on the change rule of the length of the contact line of the helical gear,the deflection moment under different load distributions along the axial direction is analyzed,and a novel model of the helical gear considering the time-varying stiffness and the deflection stiffness is proposed.The response of an example helical gear system with different tooth widths and torques is studied and compared with the existing experimental data.The lumped-parameter model accounting for backlash is also introduced to analyze the influence of torque and backlash.The results reveal that the proposed model is effective and advanced for general gear systems,especially at low and medium speeds.As the tooth width increases,the effect of the deflection stiffness becomes more significant.With increasing torque,the meshing stiffness of the helical gear increases,and the response of the gear system under parametric excitation caused by time-varying stiffness also increases.As the unbalanced force increases,the motion of the gear system considering backlash develops from periodic motion into pseudo-periodic motion and then back into periodic motion.