电动驱动桥是由行星轮系、轴系、轴承和壳体等多种零部件构成的大型复杂柔性系统, 不可避免的齿轮偏心误差激励会产生信号调制现象, 严重影响系统振动特性。采用空间梁单元建立的系统等效动力学模型能够有效求解振动响应, 但对于大型复杂系统而言计算时间仍然较长。该文提出了一种考虑齿轮偏心误差激励的电动驱动桥高效动力学计算方法。该方法在有限元模型基础上, 进一步采用模态综合法对各部件的刚度和质量矩阵进行维度缩减, 系统自由度下降45.7%, 显著提高了计算效率。与试验结果对比表明, 各车速下, 该方法在加速度时域和频域响应中均能有效体现出偏心误差激励对振动响应的显著影响, 且与试验结果一致, 证明了其正确性和考虑齿轮偏心误差激励的必要性。

Objective: The electric drive axle is a big and complex flexible system composed of a planetary gear system, an axle system, bearings and housing, etc. The unavoidable excitation of gear eccentricity error and the time-varying meshing stiffness of gears cause signal modulation, which severely affects the vibration characteristics of the system. Although an equivalent dynamics model of the system established by using spatial beam units can effectively solve the vibration response, it requires a long computation time for large and complex systems. Methods: An efficient dynamics calculation method for electric drive axles is proposed herein. This method considers the excitation of gear eccentricity error. First, the beam element of each component in the driveline was used to reduce the dimensions of the stiffness and mass matrices using the modal synthesis method. Only the essential connection nodes and the main modal order were retained. Since the housing was not suitable for beam unit modeling due to its complex structure, the bearing connection nodes and test measurement nodes were retained on the basis of the housing finite element solid element to obtain the reduced housing stiffness matrix and mass matrix. Second, the magnitude of the eccentricity error for each gear in the planetary gear system was determined using the results of the gear detection accuracy. It was assumed that the magnitude of the eccentricity error of each planetary gear was consistent, but the direction was random; the eccentricity error state of the planetary gear was regarded as consistent when the same planetary gear was in the sun-planet and ring-planet gear pairs simultaneously. Accordingly, the detailed expression of eccentricity error excitation for sun-planet n and ring-planet n gear pair was deduced. Finally, using the reduced stiffness matrix and mass matrix of each component, which considered the eccentric error excitation of each gear pair of the planetary gear system, a combined modal integrated dynamics model of the electric drive axle system was obtained. The vibration response was solved by using the Newmark method. Results: The analysis results revealed the following: (1) Compared with the finite element model of the beam element with an unreduced system, the proposed model had fewer degrees of freedom—2 788×2 788 for the former model but only 1 515×1 515 for the latter model (an effective reduction of 45.7%)—and significantly higher computational efficiency. (2) Pronounced side-frequency phenomena were observed in the frequency-domain response of the system calculated by the proposed method. In addition, amplitude fluctuations were observed in the time-domain response. These phenomena are consistent with the experimental measurement results. These phenomena did not arise when the eccentricity error excitation was not considered. Conclusions: In summary, this study proposed an efficient dynamic modeling and analysis method for overcoming the problem of time-consuming dynamics solution and signal modulation in determining the dynamic response of large and complex systems, such as electric drive axles. The accuracy of the method was verified, and the necessity of considering the excitation of eccentricity error through numerical calculation and experimental measurement was established.