Time integration algorithm in nonlinear railway vehicle system
Article Text (Baidu Translation)
-
摘要: 研究了铁路车辆系统中存在的非线性因素, 介绍了修正双步长显式法, 给出了该算法的数学表达式。基于简化的非线性车辆系统动力学模型, 利用铁路车辆系统中的5个典型非线性算例, 对比分析了修正双步长显式法、Newmark法、Wilson-θ法、Runge-Kutta法、翟方法和精细积分法, 指出了这些算法在非线性铁路车辆系统中的适用范围。研究结果表明: Newmark法和Wilson-θ法不适用于非线性铁路车辆系统; Newmark法、Wilson-θ法和Runge-Kutta法在包含非线性垂向轮轨力的车辆系统中会产生虚假振荡; 仿真时间为2 s, 时间步长分别为0.4、0.1、0.01 ms时, 修正双步长显式法的耗时分别为0.198、0.829、7.772 s, 在6种算法中耗时最短或较短; 当非线性铁路车辆系统的自由度较大时, 推荐采用修正双步长显式法和翟方法。Abstract: The nonlinear elements existing in railway vehicle system were studied, a corrected explicit method with double time steps was introduced, and the corresponding mathematical expressions were provided.Based on the simplified dynamics models of nonlinear railway vehicle system, five typical nonlinear examples of railway vehicle system were used to contrastively analyze the corrected explicit method with double time steps, Newmark method, Wilson-θmethod, Runge-Kutta method, Zhai method and the precise integration method, and the application scopes of the methods in nonlinear railway vehicle system were pointed out.Research result shows that Newmark method and Wilson-θmethod are not applicable for nonlinear railway vehicle system.Newmark method, Wilson-θ method and Runge-Kutta method can lead to spurious vibration in vehicle system including nonlinear vertical wheel-rail forces. When simulation time is 2 s and time steps are 0.4, 0.1, 0.01 ms respectively, the consumed times of corrected explicit method with double time steps are respectively 0.198, 0.829, 7.772 sthat are the shortest or the shorter in six algorithms.When the degree of freedom for nonlinear railway vehicle system is larger, the corrected explicit method with double time steps and Zhai method are recommended to use.
-
图 8 显式算法在0~1 s的轮轨相对位移
Figure 8. Relative displacements of wheel-rail for explicit algorithms at 0-1 s
图 9 显式算法在1.8~2.0 s的轮轨相对位移
Figure 9. Relative displacements of wheel-rail for explicit algorithms at 1.8-2.0 s
图 10 隐式算法的轮轨相对位移
Figure 10. Relative displacements of wheel-rail for implicit algorithms
-
[1] 赫丹, 向俊, 曾庆元. 横风作用下的列车-轨道系统空间振动响应分析[J]. 中南大学学报: 自然科学版, 2010, 41(3): 1212-1216. http://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201003066.htmHE Dan, XIANG Jun, ZENG Qing-yuan. Analysis on spatial vibration response of train-track system in cross-wind[J]. Journal of Central South University: Science and Technology, 2010, 41(3): 1212-1216. (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201003066.htm [2] 史吏, 蔡袁强, 徐长节. 轨道结构动力响应Newmark方法时间积分步长的确定[J]. 浙江大学学报: 工学版, 2014, 48(2): 228-235. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDZC201402007.htmSHI Li, CAI Yuan-qiang, XU Chang-jie. Time step length determination of Newmark method for dynamic responses of railway tracks[J]. Journal of Zhejiang University: Engineering Science, 2014, 48(2): 228-235. (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZDZC201402007.htm [3] 王少钦, 夏禾, 郭薇薇, 等. 风荷载-列车-大跨度桥梁系统非线性耦合振动分析[J]. 北京交通大学学报, 2012, 36(3): 36-40, 46. doi: 10.3969/j.issn.1673-0291.2012.03.007WANG Shao-qin, XIA He, GUO Wei-wei, et al. Nonlinear coupling vibration analysis of wind load-train-long-span bridge system[J]. Journal of Beijing Jiaotong University, 2012, 36(3): 36-40, 46. (in Chinese). doi: 10.3969/j.issn.1673-0291.2012.03.007 [4] 张健, 谭述君, 吴昌华. 车辆-轨道非线性耦合动力学的精细积分法及其应用[J]. 振动与冲击, 2012, 31(8): 5-10. doi: 10.3969/j.issn.1000-3835.2012.08.002ZHANG Jian, TAN Shu-jun, WU Chang-hua. A precise integration method for vehicle-track nonlinear coupling dynamics and its application[J]. Journal of Vibration and Shock, 2012, 31(8): 5-10. (in Chinese). doi: 10.3969/j.issn.1000-3835.2012.08.002 [5] ZHAI Wan-ming, WANG Kai-yun, CAI Cheng-biao. Fundamentals of vehicle-track coupled dynamics[J]. Vehicle System Dynamics, 2009, 47(11): 1349-1376. doi: 10.1080/00423110802621561 [6] COLE C, MCCLANACHAN M, SPIRYAGIN M, et al. Wagon instability in long trains[J]. Vehicle System Dynamics, 2012, 50(S): 303-317. http://trid.trb.org/view/1256224 [7] NAEIMI M, ZAKERI J A, SHADFAR M, et al. 3Ddynamic model of the railway wagon to obtain the wheel-rail forces under track irregularities[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2015, 229(4): 357-369. doi: 10.1177/1464419314566833 [8] ZHOU H C, WANG W B, HECHT M. Three-dimensional override analysis of crashed railway multiple units[J]. Vehicle System Dynamics, 2012, 50(4): 663-674. doi: 10.1080/00423114.2011.631552 [9] DIAS J P, PEREIRA M S. Optimization methods for crashworthiness design using multibody models[J]. Computers and Structures. 2004, 82(17-19): 1371-1380. [10] AMBRSIO J. Crash analysis and dynamical behaviour of light road and rail vehicles[J]. Vehicle System Dynamics. 2005, 43(6/7): 385-411. [11] 吕和祥, 于洪洁, 裘春航. 精细积分的非线性动力学积分方程及其解法[J]. 固体力学学报, 2001, 22(3): 303-308. doi: 10.3969/j.issn.0254-7805.2001.03.014LU He-xiang, YU Hong-jie, QIU Chun-hang. An integral equation of nonlinear dynamics and its solution method[J]. Acta Mechanica Solida Sinica, 2001, 22(3): 303-308. (in Chinese). doi: 10.3969/j.issn.0254-7805.2001.03.014 [12] XIE Y M. An assessment of time integration schemes for nonlinear dynamic equations[J]. Journal of Sound and Vibration, 1996, 192(1): 321-331. doi: 10.1006/jsvi.1996.0190 [13] FACCHINETTI A, MAZZOLA L, ALFI S, et al. Mathematical modelling of the secondary airspring suspension in railway vehicles and its effect on safety and ride comfort[J]. Vehicle System Dynamics, 2010, 48(S): 429-449. http://www.ingentaconnect.com/content/tandf/vesd/2010/00000048/a00101s1/art00026 [14] SAYYAADI H, SHOKOUHI N. A new model in rail-vehicles dynamics considering nonlinear suspension components behavior[J]. International Journal of Mechanical Sciences, 2009, 51(3): 222-232. doi: 10.1016/j.ijmecsci.2009.01.003 [15] 吴兴文, 池茂儒, 朱旻昊, 等. 空气弹簧模型对铁道车辆动力学性能的影响[J]. 交通运输工程学报, 2013, 13(2): 54-59. http://transport.gfscw.cn/article/id/201302008WU Xing-wen, CHI Mao-ru, ZHU Min-hao, et al. Influences of air spring models on dynamics performance of railway vehicle[J]. Journal of Traffic and Transportation Engineering, 2013, 13(2): 54-59. (in Chinese). http://transport.gfscw.cn/article/id/201302008 [16] 罗仁, 曾京, 邬平波. 空气弹簧对车辆曲线通过性能的影响[J]. 交通运输工程学报, 2007, 7(5): 15-18. http://transport.gfscw.cn/article/id/200705004LUO Ren, ZENG Jing, WU Ping-bo. Influence of air spring on curve negotiating property of vehicle[J]. Journal of Traffic and Transportation Engineering, 2007, 7(5): 15-18. (in Chinese). http://transport.gfscw.cn/article/id/200705004 [17] 陈燎, 周孔亢, 李仲兴. 空气弹簧动态特性拟合及空气悬架变刚度计算分析[J]. 机械工程学报, 2010, 46(4): 93-98. http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201004017.htmCHEN Liao, ZHOU Kong-kang, LI Zhong-xing. Dynamic characteristics fitting of air springs and numerical analysis of air suspensions with variant stiffness[J]. Journal of Mechanical Engineering, 2010, 46(4): 93-98. (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201004017.htm [18] 苏荣华, 彭晨宇. 振动筛橡胶弹簧非线性刚度实验及仿真研究[J]. 应用基础与工程科学学报, 2011, 19(6): 986-994. http://www.cnki.com.cn/Article/CJFDTOTAL-YJGX201106017.htmSU Rong-hua, PENG Chen-yu. Experiment and simulation research on nonlinear stiffness of vibrating screen rubber spring[J]. Journal of Basic Science and Engineering, 2011, 19(6): 986-994. (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YJGX201106017.htm [19] 杨超, 肖守讷, 鲁连涛. 基于双步长的显式积分算法[J]. 振动与冲击, 2015, 34(1): 29-32, 38. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201501008.htmYANG Chao, XIAO Shou-ne, LU Lian-tao. Explicit integration algorithm based on double time steps[J]. Journal of Vibration and Shock, 2015, 34(1): 29-32, 38. (in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201501008.htm [20] YANG Chao, XIAO Shou-ne, LU Lian-tao, et al. Two dynamic explicit methods based on double time steps[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2014, 228(3): 330-337. -
下载:
图(10) / 表(1)
计量
- 文章访问数: 1541
- HTML全文浏览量: 407
- PDF下载量: 768
- 被引次数: 0
