Optimization design on suspension parameters of equipment mounted under car body via analytical target cascading method
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摘要: 为改善高速列车运行舒适度和车下悬挂设备的振动水平，建立了车辆-设备系统垂向动力学模型，推导了车辆系统振动加速度频率响应函数；结合轨道不平顺激励谱函数计算了车下悬挂设备振动加速度均方根，联合人体舒适度加权滤波函数计算了车体振动参考点的垂向舒适度指标；引入目标级联分析(ATC)法逐层分解车辆-设备系统振动指标，构建了车辆-设备系统两层指标分解数学模型，采用指数罚函数策略协调两层振动指标之间的耦合问题；提出了以车辆运行舒适度和车下悬挂设备振动加速度为指标的多目标优化方法，建立了以车下设备悬挂刚度和阻尼为设计变量的优化模型；联合车下设备悬挂参数动力吸振器(DVA)设计法对比探讨了ATC法在复杂车辆系统参数优化设计中的应用效果。分析结果表明：与DVA设计法相比，ATC法优化后车辆中部舒适度在300 km·h-1工况下提高了8.5%，设备振动水平减小了约20%；在全速域区间，ATC法对车体中部的振动衰减是DVA设计法的2倍，且对设备的振动衰减比DVA设计法大4.5 dB；与优化前相比，ATC法优化后车辆中部舒适度指标最大提升了15%，设备振动加速度减小了0.18 m·s-2。由此可见，ATC法可以运用于复杂轨道车辆结构参数优化设计中，能有效改善车辆系统的振动水平，也可为车下设备悬挂参数优化设计提供指导。Abstract: To improve the running comfort in high-speed trains and reduce the vibration of the equipment mounted under the car body, a vertical dynamics model was constructed for the vehicle-equipment system, and a frequency response function related to the vibration acceleration of vehicle system was derived. The root-mean-square of vibration acceleration of the equipment mounted under the car body was calculated using a function for the track irregularity excitation spectrum. The vertical running comfort indices were calculated for the car body reference points by applying a human comfort weighting filter function. The analytical target cascading (ATC) method was used to hierarchically decompose the vibration indices of vehicle-equipment system to construct a two-level index decomposition mathematical model for the vehicle-equipment system. An exponential penalty function strategy was used to coordinate the interlevel coupling problems in the vibration indices. A multi-objective optimization method was developed to maximize the running comfort of vehicle and minimize the vibration acceleration of equipment mounted under the car body, and an optimization model for the stiffness and damping of the equipment mounted under the car body was constructed. The efficacy of the ATC method for the parameters optimization in complex vehicle systems was investigated via a comparison with the design method of dynamic vibration absorber (DVA). Analysis results show that compared with the design method of DVA, during the operation at 300 km·h-1, the optimization by the ATC method improves the running comfort at the vehicle center by 8.5% and decreases the equipment vibration level by approximately 20%. Over the full range of operating speeds, the vibration attenuation of ATC method is twice as that of DVA design method for the vehicle center, and 4.5 dB better for the equipment. Compared with the unoptimized state, the ATC method improves the running comfort at the vehicle center by a maximum of 15% and reduces the equipment vibration acceleration by 0.18 m·h-2. Therefore, the ATC method can be used for the optimization design of structure parameters in complex railway vehicles to significantly reduce the vibration level in vehicle systems, and is also a guidance for the parameters optimization design of the equipment mounted under car body. 2 tabs, 10 figs, 30 refs.
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图 4 车辆设备系统指标分解数据流
Figure 4. Vehicle-equipment system indexes decomposition data stream
图 8 两种优化方法所得车辆-设备系统振动指标变化百分比
Figure 8. Percentage changes in vibration indexes of vehicle-equipment system obtained by two optimization methods
图 10 车辆乘坐舒适度指标和设备振动加速度曲线
Figure 10. Curves of riding comfort indexes of vehicle and vibration accelerations of equipment
表 1 车辆系统参数
Table 1. Vehicle system parameters
参数 数值 参数 数值 mc/kg 2.6×104 kzc/(MN·m-1) 0.8 mb/kg 2.5×103 kzb/(MN·m-1) 1.4 me/kg 400 czc/(kN·s·m-1) 30 ab/m 1.25 czb/(kN·s·m-1) 15 ac/m 8.75 Ic/(kg·m2) 1.3×106 l/m 24.5 Ib(kg·m2) 1.5×103 le/m 14.25 
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表 2 采用DVA设计法和ATC法获得的最优设计变量
Table 2. Optimal design variables obtained via design method of DVA and ATC method
悬挂参数 设计变量 初始值 ATC DVA 刚度 kze/(MN·m-1) 0.55 0.65 0.81 阻尼 cze/(kN·s·m-1) 1.00 2.99 2.11
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