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摘要: 为改善传统稳定域在评价铰接列车非稳态转向稳定性方面的不足, 提出了一种适用于半挂汽车列车的高速变道稳定域的估计方法; 建立了包含Pacejka魔术公式的半挂汽车列车四自由度非线性动力学模型, 通过半挂汽车列车高速变道的仿真和实车试验对比验证了所建模型的有效性; 在构建车辆系统Jacobian矩阵的基础上, 应用特征根法分析了车辆在高速阶跃转向和正弦转向2种情况下的稳定性; 基于Lyapunov稳定性定理, 通过构建Lyapunov能量函数, 分析了车辆极限状态时的系统能量与能量变化阈值, 获得了车辆高速变道稳定域, 并利用半挂汽车列车30m·s-1变道试验验证稳定域。分析结果表明: 高速变道过程中车辆系统Jacobian矩阵特征根大于0, 但最终收敛至小于0, 系统仍可保持稳定; 车辆高速变道稳定域为近似凹形曲面, 能量越接近中心区的低点, 车辆系统越稳定, 而一旦接近甚至超过能量阈值, 车辆系统将临近或发生失稳; 在半挂汽车列车30m·s-1变道试验中, 当Lyapunov能量接近阈值3.863 6J时, 车辆系统处于临近失稳状态。可见, 确定的半挂汽车列车高速变道稳定域, 能够较好地表征车辆系统在高速瞬态连续转向状态下的稳定性, 可为半挂汽车列车操纵稳定性评价和控制提供有益参考。Abstract: To improve the deficiency of the traditional vehicle stability region for evaluating the unsteady steering stability of articulated train, a stability region estimation method for lane change on a highway for tractor-semitrailer was proposed. A four-degree-of-freedom nonlinear dynamics model of tractor-semitrailer with Pacejka's magic formula was established and verified by comparing the tractor-semitrailer lane change simulation and test on a highway. Though establishing the vehicle system Jacobian matrix, the vehicle stabilities in high-speed step steeringand sinusoidal steering were analyzed by using an eigenvalue method. Based on the Lyapunov stability theorem, the Lyapunov energy function was derived. The energy and energy change thresholds of the vehicle system in critical situations were analyzed, and the vehicle stability region for lane change on a highway was obtained. The stability region was verified by tractorsemitrailer lane change test at 30 m·s-1. Analysis result shows that the eigenvalues of the vehicle system Jacobian matrix are greater than 0 during lane change on a highway, but the values finally converge to less than 0, so the system can remain stable. The vehicle stability region for lane change on a highway is an approximate concave surface, so the closer to the low point in the central area, the more stable the vehicle system is, and the vehicle system will approach instability or become unstable once approaching or even exceeding the energy threshold. A vehicle lane change test at 30 m·s-1 indicates that the vehicle system is in critical instability when the Lyapunov energy is close to the threshold of 3.863 6 J. Therefore, the determined stability region for lane change on a highway for a tractor-semitrailer can better characterize the stability of vehicle system in the condition of high-speed transient continuous steering, and offer a valuable reference for tractor-semitrailer handling stability evaluation and control.
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图 13 工况1牵引车质心侧偏角输出
Figure 13. Output of side slip angle of tractor centroid in condition 1
图 15 工况2牵引车质心侧偏角输出
Figure 15. Output of side slip angle of tractor centroid in condition 2
图 18 工况3牵引车质心侧偏角输出
Figure 18. Output of side slip angle of tractor centroid in condition 3
图 20 工况4牵引车质心侧偏角输出
Figure 20. Output of side slip angle of tractor centroid in condition 4
图 22 工况3车辆前轮转角与Lyapunov能量
Figure 22. Front wheel angles and Lyapunov energies in condition 3
图 23 工况4牵引车横摆角速度与Lyapunov能量
Figure 23. Tractor yaw rates and Lyapunov energies in condition 4
图 25 牵引车质心侧偏角-横摆角速度能量等势面
Figure 25. Energy equipotential surfaces of tractor centroid side slip angle and yaw rate
图 26 牵引车质心侧偏角-铰接角能量等势面
Figure 26. Energy equipotential surfaces of tractor centroid side slip angle and splice angle
图 27 牵引车质心侧偏角-横摆角速度稳定域
Figure 27. Stability region of side slip angle of tractor centroid and yaw rate
图 28 牵引车质心侧偏角-铰接角稳定域
Figure 28. Stability region of side slip angle of tractor centroid and splice angle
图 29 牵引车质心侧偏角-横摆角速度分布
Figure 29. Distribution of side slip angle of tractor centroid and yaw rate
图 30 牵引车质心侧偏角-铰接角分布
Figure 30. Distribution of side slip angle of tractor centroid and splice angle
表 3 不同前轮转角对应车辆状态参量与Lyapunov能量
Table 3. Vehicle state parameters and Lyapunov energies with different front wheel angle
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