基于分段间隙函数的螺旋锥齿轮时变啮合参数分析

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Meshing parameters including stiffness and damping are key factors of nonlinear vibration of spiral bevel gears. Considering the time-varying characteristics of meshing stiffness and meshing damping, adopting a second-order Fourier series, vibration equation of a pair of spiral bevel gears was established. Based on the variation of clearance function under different meshing states, the effects of meshing stiffness and meshing damping on meshing features of a pair of spiral bevel gears under three meshing states were studied. Using Matlab, the vibration displacement curves of the meshing point were given when mean meshing damping, harmonic meshing damping, major harmonic meshing stiffness and sub-harmonic meshing stiffness were considered. The results showed that increasing mean meshing damping and decreasing major harmonic meshing stiffness can drop vibration displacement peaks and improve transmission stability.刚度和阻尼等啮合参数是螺旋锥齿轮非线性振动的主要影响因素。考虑啮合刚度和啮合阻尼的时变性，采用二次谐波形式展开，建立了螺旋锥齿轮副振动平衡方程。基于不同啮合状态下间隙函数的变化，研究了啮合刚度及啮合阻尼在三种啮合状态下对螺旋锥齿轮副啮合特性的影响规律。采用Matlab进行分析，给出了平均啮合阻尼、谐波啮合阻尼、主谐波啮合刚度和次谐波啮合刚度对啮合点振动位移的影响曲线。结果表明增大平均啮合阻尼和降低主谐波啮合刚度会降低振动位移峰值，提高齿轮传动平稳性。