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摘要: 利用有限元方法得到高速列车齿轮传动系统时变啮合刚度, 利用傅里叶级数模拟啮合刚度和传动误差, 用多项式拟合齿侧间隙, 建立考虑时变啮合刚度、传动误差与齿侧间隙等多种非线性因素的高速列车斜齿轮传动系统弯扭耦合动力学模型。结合非线性多尺度法, 推导了高速列车齿轮传动系统谐波共振频率因子, 利用数值积分法对齿轮传动系统动力学方程进行求解, 得到了齿轮传动系统的频率响应曲线, 分析了静态载荷、动态载荷与阻尼对系统谐振响应的影响。分析结果表明: 齿轮传动系统中存在多种谐振频率因子, 超谐共振会发生跳跃现象, 谐波振动会引发系统倍频振动。当相对激励频率低于1.00时, 系统波动剧烈。在列车实际运营中应制定合理的运营速度, 以避免谐振的发生。Abstract: The time-varying mesh stiffness of gear transmission system for high-speed train was calculated by using finite element method, the mesh stiffness and the transmission error were expressed by using Fourier series, the tooth backlash was fitted by using polynomial expression, and a bending-torsion coupling dynamics model of cylindrical helical gear transmission system was developed based on considering some nonlinear factors such as the time-varying mesh stiffness, the transmission error, the tooth backlash, etc.The nonlinear method of multiple scales was used to derive the harmonic resonance frequency factors of gear transmission system.The frequency response curves of gear transmission system were obtained by using numerical integration method to solve the dynamics equations of gear transmission system.The influences of static loads, dynamic loads and dampings on the harmonic resonance responses of gear transmission system were analyzed.Analysis result indicates that there are many harmonic resonance frequency factors in gear transmission system.A jumping phenomenon is found in thesuper-harmonic resonance response of gear transmission system.The double frequency vibrations are found under the harmonic excitations.The gear system has intense vibration when the meshing frequency is lower than the natural frequency.The reasonable operating speed of train should be set to avoid the harmonic resonances.
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