考虑弹性支撑边界条件的电动汽车-路面系统机电耦合振动特性分析

轮毂电机驱动电动汽车的簧下质量大导致轮胎动载荷增加，并且电机电磁力和转矩波动对车轮造成电机激励，进一步加剧车轮振动引起垂向振动负效应的问题。鉴于此，考虑电机的电磁激励，建立了电动汽车-路面系统的机电耦合动力学模型，推导了弹性支撑边界条件下路面结构的模态频率和振型表达式，以及路面振动引起的二次激励。计算了简支与弹性支撑边界条件下的路面模态频率，根据频率分布进行了截断阶数选取，并分析了边界条件、电机激励和车速对路面响应的影响。在此基础上，研究了不同行驶速度、路基反应模量及路面不平顺幅值下，激励形式对汽车车身加速度、悬架动挠度和轮胎动载荷的影响。结果表明：路面不平顺幅值越小，弹性支撑对路面响应的影响越大，弹性支撑边界条件下的路面响应较小，电机激励会引起路面响应的增加；弹性支撑边界条件下，路面不平顺幅值和路基反应模量越小，考虑路面不平顺、路面二次激励和电机激励的三重综合激励对电动汽车响应的影响越大，激励形式对轮胎动载荷的影响最大，对车身加速度的影响次之，对悬架动挠度的影响最小；电机激励导致轮胎动载荷增加，对路面破坏和寿命产生的负效应不容忽视。所建电动汽车-路面系统机电耦合模型及研究思路可为电动汽车垂向动力学分析提供参考与理论支持。

Analysis of Electromechanical Coupling Vibration Characteristics of Electric Vehicle-road System Considering Elastically Supported Boundary Conditions

In an electric vehicle, the hub motor drives the large unsprung mass of the vehicle, increasing the dynamic tire load. Additionally, the fluctuation of the electromagnetic force and torque of the motor results in wheel excitation, which further aggravates the vertical vibration of the wheel. Considering the electromagnetic excitation of the motor, the electromechanical coupling dynamic model of the electric vehicle-road system was established in this study. The expressions for the modal frequency and mode shape of the road structure (under the elastically supported boundary condition), and the secondary excitation caused by the road vibration, were also derived. The modal frequencies of the pavement under the boundary conditions of simple and elastic supports were calculated, and the cut-off order was selected according to the frequency distribution. The influence of boundary conditions, motor excitation, and vehicle speed on the response of the pavement were analyzed. Accordingly, the influence of driving speed, foundation response modulus, and road roughness amplitude on the vehicle body acceleration, dynamic suspension displacement, and dynamic tire load was studied. The results show that the smaller the amplitude of road roughness, the greater the influence of elastic support on the response of the road. The response of the road is smaller under the boundary condition of elastic support. The excitation of the motor results in an increase in the response of the pavement. Under the boundary condition of elastic support, the smaller the amplitude of road roughness and foundation response modulus, the greater the influence of vehicle response, considering the comprehensive excitations, including road roughness, secondary road excitation, and motor excitation. The form of excitation has the greatest influence on the dynamic tire load, followed by its influence on the acceleration of the vehicle body, and the least on the dynamic suspension displacement. The motor excitation leads to an increase in the dynamic tire load, and the negative effect on the road damage and life cannot be ignored. The electromechanical coupling model and research ideas of the electric vehicle-road system can provide reference and theoretical support for the vertical dynamic analysis of electric vehicles.