VIBRATION ANALYSIS OF ELECTRIC VEHICLE-ROAD COUPLING SYSTEM CONSIDERING TIRE-ROAD MULTI-POINT CONTACT
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摘要: 轮毂电机驱动电动汽车的簧下质量大, 使得轮胎动载荷增加, 且电机激励进一步加剧车轮振动. 同时, 轮胎与路面单点接触的简化模型, 其动力学计算结果与实际存在差别. 鉴于此, 考虑电机的电磁激励、胎路多点接触和非线性地基, 建立了电动汽车−路面系统机电耦合动力学模型, 通过Galerkin法推导了非线性地基梁的垂向振动, 利用积化和公式推导了非线性地基梁中非线性项积分的精确表达式, 提出了路面截断阶数选取的简易方法, 并通过路面位移响应的收敛性进行了验证. 在此基础上, 研究了胎路多点接触、非线性地基、电机激励、车速、路面不平顺幅值等对路面及车辆响应的影响. 结果表明, 非线性地基及多点接触对车辆响应的影响中, 轮胎动载荷的影响最大, 车身加速度和悬架动挠度的影响较小, 且考虑电机激励时, 二者对车辆响应的影响显著增大. 从对路面响应的影响看, 电机激励的影响最大, 非线性地基的影响次之, 多点接触的影响较小. 所建模型及研究方法可为电动汽车的垂向动力学分析提供一种新思路.Abstract: The unsprung mass of the electric vehicle driven by the hub motor is large, which makes the tire dynamic load increase, and the motor excitation further aggravates the wheel vibration. Meanwhile, the dynamic calculation results of the simplified model of single point contact between tire and road are different from the actual. Thus, considering the electromagnetic excitation of the motor, nonlinear foundation and multi-point contact between tire and road, the electromechanical coupling dynamic model of the electric vehicle-road system is established. The vertical vibration of the nonlinear foundation beam is derived by the Galerkin method, and the accurate expression of the nonlinear integral term in the nonlinear foundation beam is derived by using the integral sum formula. A simple method to select the truncation order of the road is proposed, which is verified with the convergence of road response. Accordingly, the effects of multi-point contact between tire and road, nonlinear foundation, motor excitation, vehicle speed and road roughness amplitude on vehicle response are studied. The results show that among the effects of nonlinear foundation and multi-point contact on the vehicle response, the tire dynamic load has the largest influence, and the vehicle body acceleration and suspension dynamic displacement have a small effect. Moreover, when the motor excitation is considered, the influence of the two on the vehicle response increases. From the perspective of the influence on the road response, the motor excitation has the greatest, the nonlinear foundation has the second influence, and the multi-point contact has the less. The established model and research method provide a new idea for vertical dynamics analysis of electric vehicles.
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图 2 接触点数对路面响应最大幅值的影响
Figure 2. Effects of the number of contact point on the maximum amplitude of road response
图 6 截断阶数对路面响应最大幅值的影响
Figure 6. Effects of truncation order on maximum amplitude of road response
图 7 B0 = 0.02 m时非线性地基、多点接触及电机激励对路面响应的影响
Figure 7. Effects of nonlinear foundation and multi-point contact and motor excitation on road response when B0 = 0.02 m
图 8 B0 = 0.002 m时非线性地基、多点接触及电机激励对路面响应的影响
Figure 8. Effects of nonlinear foundation and multi-point contact and motor excitation on road response when B0 = 0.002 m
图 9 非线性地基及多点接触对车身加速度的影响
Figure 9. Effects of nonlinear foundation and multi-point contact on acceleration of vehicle body
图 11 非线性地基及多点接触对轮胎动载荷的影响
Figure 11. Effects of nonlinear foundation and multi-point contact on tire dynamic load
图 12 非线性地基及多点接触对车辆响应的相对差别
Figure 12. Relative differences of nonlinear foundation and multi-point contact on vehicle response
图 10 非线性地基及多点接触对悬架动挠度的影响
Figure 10. Effects of nonlinear foundation and multi-point contact on suspension dynamic displacement
图 13 不同车速时非线性地基及胎路多点接触对路面响应最大幅值的影响
Figure 13. Effects of nonlinear foundation and multi-point contact between tire and road on the maximum amplitude of road response at different speeds
图 14 不同车速时非线性地基及胎路多点接触对路面响应的频域曲线
Figure 14. Frequency domain curves of the effects of non-linear foundation and multi-point contact between tire and road on the road response at different speeds
图 16 不同行驶速度下路面二次位移的最大幅值
Figure 16. Maximum amplitude of road secondary displacement at different speeds
图 17 不同车速下非线性地基及多点接触对车辆响应最大幅值的影响
Figure 17. Effects of NF and MP on maximum amplitude of vehicle response at different speeds
图 18 不同车速下非线性地基及多点接触对车辆响应的最大增幅
Figure 18. Maximum differences of NF and MP on vehicle response at different speeds
图 19 地基弹性系数对路面响应最大幅值的影响
Figure 19. Effects of foundation elastic coefficient on maximum amplitude of road response
图 20 地基线性弹性系数对车辆响应最大幅值的影响
Figure 20. Effects of foundation linear elastic coefficient on maximum amplitude of vehicle response
21 地基非线性弹性系数对车辆响应最大幅值影响
21. Effects of foundation nonlinear elastic coefficient on maximum amplitude of vehicle response
图 21 地基非线性弹性系数对车辆响应最大幅值影响(续)
Figure 21. Effects of foundation nonlinear elastic coefficient on maximum amplitude of vehicle response (continued)
表 1 线弹性地基梁的固有频率及相邻频率差别
Table 1. Natural frequency and relative differences of adjacent frequencies of linear elastic foundation beam
NM Frequency/Hz Difference/% 1 11.623 0 0 10 11.623 9 0.002 6 20 11.636 8 0.022 0 30 11.692 8 0.075 5 40 11.842 1 0.177 0 50 12.150 9 0.331 6 60 12.693 2 0.529 3 70 13.539 1 0.743 7 80 14.742 5 0.941 6 90 16.335 2 1.096 8 100 18.327 4 1.199 0 110 20.714 3 1.252 0 120 23.483 4 1.266 4 130 26.619 4 1.254 1 140 30.107 8 1.224 8 150 33.935 7 1.186 0 160 38.092 5 1.142 3 170 42.569 7 1.097 180 47.360 2 1.051 9 190 52.458 6 1.008 1 200 57.860 7 0.966 3 210 63.562 8 0.926 7 220 69.562 2 0.889 4 230 75.856 7 0.854 5 240 82.444 4 0.821 7 250 89.323 9 0.791 0 260 96.493 9 0.762 3 270 103.953 4 0.735 5 280 111.701 6 0.710 3 290 119.737 7 0.686 6 300 128.061 3 0.664 4 
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表 2 路面响应的最大幅值及相对增量
Table 2. Maximum amplitude of road response and relative difference
B0/m Motor excitation NF LF Difference between NF and LF yr(SP)/m yr(MP)/m difference yr(SP)/m yr(MP)/m difference SP MP 0.02 √ 2.468 6 × 10−4 2.302 2 × 10−4 −6.74% 2.593 3 × 10−4 2.580 6 × 10−4 −0.49% −4.81% −10.79% × 4.205 0 × 10−4 4.199 6 × 10−4 −0.13% 4.426 7 × 10−4 4.430 9 × 10−4 0.09% −5.01% −5.22% difference 41.29% 45.18% − 41.42% 41.76% − − − 0.002 √ 1.976 6 × 10−4 1.957 3 × 10−4 −0.98% 2.069 5 × 10−4 2.066 9 × 10−4 −0.13% −4.49% −5.30% × 3.819 7 × 10−4 3.819 1 × 10−4 −0.02% 3.846 2 × 10−4 3.846 6 × 10−4 0.01% −0.69% −0.71% difference 48.25% 48.75% − 46.19% 46.27% − − −
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