Fast Simulation Method for Rigid Pantograph and Overhead Conductor Rail System
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摘要:
针对当前刚性接触网-受电弓系统有限元模型仿真速度慢、计算时间成本高的问题，本文对采用三维接触算法的弓网仿真方法与流程进行改进. 首先，采用中心差分思想，将求解弓网接触副相对运动速度时需迭代计算的方程转换为可直接计算的显式方程；然后，将刚性接触网在静平衡处进行线性化处理，以避免刚度矩阵组装耗时，并加快刚性网内力计算；其次，对弓网接触状态进行惰性判断以减少计算量；最后，对本文所提快速仿真方法在不同情况下的计算效率与精度进行分析. 研究结果表明：在30跨8 m跨距的刚性接触网-受电弓仿真算例中，快速仿真方法相比标准仿真方法节省97.67%的仿真时间，且接触力结果最大偏差仅为0.48%；随着模型规模的增大，其节省的时间迅速增加，计算效率优势愈发显著，同时接触力结果偏差均小于1.0%；且随着运行速度的提高，所节省的时间占比基本不变，接触力结果偏差略有增大趋势，在230 km/h以下的速度工况中，接触力标准差偏差均小于1.0%.
Abstract:Finite element model simulation of the rigid pantograph and overhead conductor rail (OCR) system is slow, and the time cost of calculation is high. Therefore, the simulation method and process of the pantograph and OCR system using three-dimensional contact formulation were improved. Firstly, the equation that needs to be calculated iteratively when solving the relative velocity of the contact pair between the pantograph and the OCR was replaced with an explicit equation that can be calculated directly based on the central difference method. Then, the rigid OCR model was linearized at the static equilibrium state to avoid the time-consuming rigidity matrix assembly procedure and increase the efficiency when calculating the internal force of the OCR. Next, a lazy judgment strategy was used to estimate the contact state of the pantograph and the OCR to reduce the computational load. Finally, the computational efficiency and accuracy of the fast simulation method in different cases were analyzed. The results show that compared with the standard simulation method, the proposed fast simulation method can save 97.67% of computational time in the example of rigid pantograph and OCR with 30 spans of 8 m, and the maximum error of contact force results is only 0.48%. With the increase in the model scale, the time saved by the fast simulation method increases sharply, and its computational efficiency advantage becomes more and more significant. Meanwhile, the errors of contact force results are all less than 1%. With the increase in the operation speed, the proportion of time saved by the fast simulation method remains stable, and the errors of contact force results increase slightly. At speeds under 230 km/h, the standard deviation errors of contact force are all less than 1%.
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图 2 刚性接触网-受电弓系统整体仿真流程
Figure 2. Simulation flowchart of rigid pantograph and OCR system
图 4 替换后仿真方法各环节耗时占比
Figure 4. Time proportion of each procedure in simulation method after replacing
图 6 刚性接触网-受电弓系统快速仿真流程
Figure 6. Fast simulation flowchart of rigid pantograph and OCR system
图 7 快速仿真方法与标准方法结果对比
Figure 7. Comparison of results from fast simulation method and standard method
图 8 快速仿真方法环节耗时占比
Figure 8. Time proportion of each procedure in fast simulation method
图 9 不同规模模型中快速仿真方法节省时间对比
Figure 9. Time saved for models in different scales by fast simulation method
图 11 不同速度下快速仿真方法节省时间对比
Figure 11. Time saved for models at different speeds by fast simulation method
图 12 不同速度下快速仿真方法结果偏差对比
Figure 12. Result error comparison for models at different speeds by fast simulation method
表 1 受电弓参数
Table 1. Parameters of pantograph
参数 质量/kg 刚度/（N·m−1） 阻尼/（N·s·m−1） 自由度1 7.12 9430.00 20 自由度2 6.00 14100.00 20 自由度3 5.80 0.01 70 
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表 2 各改进措施效果
Table 2. Effect of different improvement measures
改进方法 总接触力 仿真时间 最大相对偏差/% 平均相对偏差/% 标准差相对偏差/% 耗时/s 节省时间比/% 标准方法 2092.89 1 3.50 × 10−4 4.80 × 10−5 5.90 × 10−5 960.13 54.12 1 + 2 0.48 0.10 0.06 496.64 76.27 1 + 2 + 3 0.48 0.10 0.06 116.83 94.42 1 + 2 + 3 + 4 0.48 0.10 0.06 56.53 97.30 1 + 2 + 3 + 4 + 5 0.48 0.10 0.06 48.75 97.67
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