蜗杆斜齿轮传动副时变啮合刚度计算及非线性动力学特性分析

Calculation of time⁃varying mesh stiffness of worm and helical gear transmission pair and analysis on its nonlinear dynamic characteristics

蜗杆斜齿轮传动副作为一种交错轴点接触传动形式,掌握其时变啮合刚度及啮合侧隙与误差等引起的非线性动力学行为是减振降噪的核心。文中基于势能法修正并求解蜗杆斜齿轮传动副理论时变啮合刚度,建立考虑齿侧间隙-综合误差及时变啮合刚度的动力学模型,采用4~5阶Runge⁃Kutta法对系统动力学方程进行数值求解,得到蜗杆斜齿轮传动副动力学特性曲线。结合时域图、Poincaré图及FFT频谱图,分析齿侧间隙、阻尼比及载荷等因素对传动副振动和冲击状态的影响,结果表明:较小的误差幅值及较大的阻尼比可使系统处于稳定的周期运动状态。研究结果对优化蜗杆斜齿轮传动系统的振动噪声有指导意义。

The worm and helical gear transmission pair is a form of cross⁃axis point contact transmission.It is important to explore the nonlinear dynamic behavior caused by time⁃varying meshing stiffness,meshing backlash,and errors,which helps re⁃duce vibration and noise.In this article,the potential energy method is used to modify and solve the worm and helical gear trans⁃mission pair’s time⁃varying meshing stiffness in theory.The dynamic model is set up,with such factors as meshing backlash,comprehensive error,and time⁃varying meshing stiffness taken into consideration.The 4~5 order Runge⁃Kutta method is used to numerically solve the system’s dynamic equation,and the dynamic characteristic curve is worked out.By combining the time⁃do⁃main plots,the Poincaréplots,and the FFT spectrograms,efforts are made to explore the influence of such factors as meshing backlash,damping ratio,and load on the transmission pair’s vibration and impact state.The results show that a smaller error amplitude and a larger damping ratio ensure that the system runs steadily in constant periods.These results provide guidance to reduce the worm and helical gear transmission system’s vibration and noise.