Bifurcation control and complex motion analysis of high-speed bogie based on active yaw damper
Article Text (Baidu Translation)
-
摘要: 为保障高速动车组蛇行稳定性并提升临界速度，开展基于主动抗蛇行减振器的车辆系统分岔特性控制研究，建立了包含刚性转向架横移/摇头与车体横移的动力学简化模型，结合实测磨耗后期的车轮踏面数据给出了非线性轮轨关系；在传统被动悬挂的基础上并联主动抗蛇行减振器，基于转向架摇头控制分析了车辆系统的Hopf分岔及分岔后的复杂运动。分析结果表明：线性刚度与线性阻尼控制均能延后Hopf分岔点，即能够直接提高车辆系统的蛇行临界速度，从被动状态下247 km·h-1提高至328 km·h-1；线性刚度控制不影响分岔后的轮对横移量，将蛇行频率从5 Hz提高至7 Hz，线性阻尼控制能有效降低分岔后的极限环幅值与蛇行频率；非线性刚度与阻尼控制不改变车辆的临界速度，且二次项控制增益将引起车辆系统产生不稳定的极限环；三次项控制增益均可以降低分岔后的极限环幅值，其中三次项刚度控制会提高蛇行频率，三次项阻尼控制能够抑制蛇行频率；传统被动悬挂下车辆在发生Hopf分岔后，系统将经历极限环运动进入倍周期分岔进而通向混沌态，而线性控制在车速为386 km·h-1时发生超临界Hopf分岔后能维持稳定的极限环单周期运动，其最大李雅普诺夫指数始终小于0，可以有效避免车辆系统产生复杂的混沌运动，但非线性控制的作用效果有限。Abstract: In order to ensure the hunting stability of high-speed trains and improve critical speed, a study on control of the bifurcation characteristics of vehicle system based on active yaw dampers was carried out. A simplified dynamics model containing the lateral/yaw motion of a rigid bogie and the lateral motion of the car body was established, and a nonlinear wheel-rail relationship was given by combining the measured wheel tread data at the end-worn stage. Active yaw dampers were connected in parallel on the basis of traditional passive suspension, and the Hopf bifurcation and complex motion of the vehicle system after bifurcation were analyzed based on the yaw motion control of bogie. Research results show that the Hopf bifurcation point can be delayed, and the critical speed of vehicle system can be directly increased from 247 km·h-1 in passive state to 328 km·h-1 through linear stiffness and damping control. The lateral wheelset displacement after bifurcation is not affected by linear stiffness control, increasing the hunting frequency from 5 Hz to 7 Hz, while the limit cycle amplitude and hunting frequency after bifurcation are effectively reduced via linear damping control. The critical speed is not changed by nonlinear stiffness and damping control, and quadratic control gain will cause the vehicle system to produce an unstable limit cycle. The amplitude of the limit cycle after bifurcation can be reduced through cubic control gain, of which the cubic stiffness control can increase the hunting frequency, while the cubic damping control can inhibit hunting frequency. Meanwhile, after Hopf bifurcation of the vehicle under traditional passive suspension, the system will go through the limit cycle motion into period doubling bifurcation and then lead to the chaotic state, whereas the linear control can maintain the stable single-cycle motion of the limit cycle after the supercritical Hopf bifurcation occurs at the speed of 386 km·h-1, and its maximum Lyapunov exponent is always less than 0, which can effectively avoid the generation of complex chaotic motion of vehicle system, but the effect of nonlinear control is limited.
-
Key words:
- vehicle engineering /
- yaw damper /
- active control /
- hunting stability /
- high-speed bogie /
- Hopf bifurcation
-
图 6 二次项控制下车辆系统分岔特性
Figure 6. Bifurcation characteristics of vehicle system under quadratic control
图 9 被动悬挂状态下车辆系统复杂行为分析
Figure 9. Complex behavior analysis of vehicle system under passive suspension
图 10 线性控制状态下车辆系统复杂行为分析
Figure 10. Complex behavior analysis of vehicle system under linear control
图 11 非线性控制状态下车辆系统复杂行为分析
Figure 11. Complex behavior analysis of vehicle system under nonlinear control
表 1 车辆系统参数
Table 1. Vehicle system parameters
参数 取值 mb/kg 2 200 mc/kg 18 000 Ib/(kg·m2) 2 336 ls/m 0.95 lyaw/m 1.275 kyaw/(kN·m-1) 6 000 cyaw/(kN·s·m-1) 200 b/m 0.746 5 lb/m 1.25 r0/m 0.46 ksy/(kN·m-1) 166 ksx/(kN·m-1) 166 csy/(kN·s·m-1) 50 
下载: 导出CSV
-
[1] GUO Jin-ying, SHI Huai-long, ZENG Jing, et al. Double-parameter Hopf bifurcation analysis of a high-speed rail vehicle with an alternative wheel/rail contact approximation[J]. Vehicle System Dynamics, 2023, 61(2): 530-549. [2] SHI Huai-long, LUO Ren, GUO Jin-ying. Improved lateral-dynamics-intended railway vehicle model involving nonlinear wheel/rail interaction and car body flexibility[J]. Acta Mechanica Sinica, 2021, 37(6): 997-1012. [3] WANG Qun-sheng, ZENG Jing, MAO Ran-cheng, et al. Parameters optimum of multiple underframe suspended equipment on high-speed railway vehicle carbody vibration control by using an improved genetic algorithm[J]. Journal of Vibration and Control, 2023, DOI: 10.1177/10775463231225552. [4] 黄彩虹, 曾京, 魏来. 铁道车辆蛇行稳定性主动控制综述[J]. 交通运输工程学报, 2021, 21(1): 267-284. doi: 10.19818/j.cnki.1671-1637.2021.01.013HUANG Cai-hong, ZENG Jing, WEI Lai. Review on active control of hunting stability for railway vehicles[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 267-284. doi: 10.19818/j.cnki.1671-1637.2021.01.013 [5] 黄彩虹, 曾京, 宋春元. 高速列车抗蛇行减振器的简化物理参数模型[J]. 铁道学报, 2021, 43(7): 47-56. doi: 10.3969/j.issn.1001-8360.2021.07.007HUANG Cai-hong, ZENG Jing, SONG Chun-yuan. Simplified physical parameter model of high-speed train yaw damper[J]. Journal of the China Railway Society, 2021, 43(7): 47-56. doi: 10.3969/j.issn.1001-8360.2021.07.007 [6] SHI Huai-long, ZENG Jing, QU Sheng. Linear stability analysis of a high-speed rail vehicle concerning suspension parameters variation and active control[J]. Vehicle System Dynamics, 2023, 61(11): 2976-2998. [7] SHI Huai-long, ZENG Jing, GUO Jin-ying. Disturbance observer-based sliding mode control of active vertical suspension for high-speed rail vehicles[J]. Vehicle System Dynamics, 2024, 62(11): 2912-2935. [8] VON WAGNER U. Nonlinear dynamic behaviour of a railway wheelset[J]. Vehicle System Dynamics, 2009, 47(5): 627-640. [9] 曾京. 车辆系统的蛇行运动分叉及极限环的数值计算[J]. 铁道学报, 1996, 18(3): 13-19. doi: 10.3321/j.issn:1001-8360.1996.03.003ZENG Jing. Numerical computations of the hunting bifurcation and limit cycles for railway vehicle system[J]. Journal of the China Railway Society, 1996, 18(3): 13-19. doi: 10.3321/j.issn:1001-8360.1996.03.003 [10] 史禾慕, 曾晓辉, 吴晗. 轮对非线性动力学系统蛇行运动的解析解[J]. 力学学报, 2022, 54(7): 1807-1819.SHI He-mu, ZENG Xiao-hui, WU Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1807-1819. [11] ZBOINSKI K, DUSZA M. Bifurcation approach to the influence of rolling radius modelling and rail inclination on the stability of railway vehicles in a curved track[J]. Vehicle System Dynamics, 2008, 46(S1): 1023-1037. [12] ZBOINSKI K, DUSZA M. Extended study of railway vehicle lateral stability in a curved track[J]. Vehicle System Dynamics, 2011, 49(5): 789-810. [13] 王鹏, 杨绍普, 刘永强, 等. 轮对非线性动力学模型稳定性和分岔特性研究[J]. 力学学报, 2023, 55(2): 462-475.WANG Peng, YANG Shao-pu, LIU Yong-qiang, et al. Investigation of stability and bifurcation characteristics of wheelset nonlinear dynamic model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 462-475. [14] 王鹏, 杨绍普, 刘永强, 等. 轮对非线性随机动力学模型稳定性及分岔研究[J]. 机械工程学报, 2023, 59(10): 210-225.WANG Peng, YANG Shao-pu, LIU Yong-qiang, et al. Research on stability and bifurcation of nonlinear stochastic dynamic model of wheelset[J]. Journal of Mechanical Engineering, 2023, 59(10): 210-225. [15] CHRISTIANSEN L E, TRUE H. Dynamics of a railway vehicle on a laterally disturbed track[J]. Vehicle System Dynamics, 2018, 56(2): 249-280. doi: 10.1080/00423114.2017.1372584 [16] BUSTOS A, TOMAS-RODRIGUEZ M, RUBIO H, et al. On the nonlinear hunting stability of a high-speed train bogie[J]. Nonlinear Dynamics, 2023, 111(3): 2059-2078. doi: 10.1007/s11071-022-07937-y [17] LIANG Ya-ru, LUO Ren, ZENG Jing, et al. Study on dynamic performance of high-speed railway vehicle using roller rig and numerical simulation[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2024, 238(16): 7963-7976. doi: 10.1177/09544062241237905 [18] FU B, GIOSSI R L, PERSSON R, et al. Active suspension in railway vehicles: a literature survey[J]. Railway Engineering Science, 2020, 28(1): 3-35. doi: 10.1007/s40534-020-00207-w [19] 高国生, 杨绍普, 郭京波. 轮对蛇行运动Hopf分岔的非线性控制[J]. 铁道学报, 2002, 24(3): 23-26. doi: 10.3321/j.issn:1001-8360.2002.03.006GAO Guo-sheng, YANG Shao-pu, GUO Jing-bo. Nonlinear control for Hopf bifurcation of hunting motion in rail wheelset[J]. Journal of the China Railway Society, 2002, 24(3): 23-26. doi: 10.3321/j.issn:1001-8360.2002.03.006 [20] YAO Yuan, LI Guang, SARDAHI Y, et al. Stability enhancement of a high-speed train bogie using active mass inertial actuators[J]. Vehicle System Dynamics, 2019, 57(3): 389-407. doi: 10.1080/00423114.2018.1469776 [21] YAO Yuan, WU Guo-song, SARDAHI Y, et al. Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control[J]. Vehicle System Dynamics, 2018, 56(2): 297-318. doi: 10.1080/00423114.2017.1375128 [22] 晏永, 曾京, 翟玉江, 等. 轨道车辆蛇行运动GA-LQR主动控制研究[J]. 铁道科学与工程学报, 2020, 17(10): 2642-2648.YAN Yong, ZENG Jing, ZHAI Yu-jiang, et al. Active control analysis of railway vehicle hunting motion based on LQR and genetic algorithm[J]. Journal of Railway Science and Engineering, 2020, 17(10): 2642-2648. [23] WANG Qun-sheng, JIANG Xue-song, ZENG Jing, et al. Innovative method for high-speed railway carbody vibration control caused by hunting instability using underframe suspended equipment[J]. Journal of Vibration and Control, 2024, DOI: 10.1177/10775463241272954. [24] MAO Ran-cheng, ZENG Jing, WANG Qun-sheng, et al. Hunting stability control of high-speed bogie based on active yaw damper[J]. Journal of Low Frequency Noise Vibration and Active Control, 2024, 43(4): 1827-1841. [25] ABOOD K, KHAN R A. Investigation to improve hunting stability of railway carriage using semi-active longitudinal primary stiffness suspension[J]. Journal of Mechanical Engineering Research, 2010, 2(5): 97-105. [26] DIANA G, BRUNI S, CHELI F, et al. Active control of the runningbehaviour of a railway vehicle: stability and curving performances[J]. Vehicle System Dynamics, 2002, 37(S1): 157-170. [27] BRAGHIN F, BRUNI S, RESTA F. Active yaw damper for the improvement of railway vehicle stability and curving performances: simulations and experimental results[J]. Vehicle System Dynamics, 2006, 44(11): 857-869. [28] 张恒, 凌亮, 昌超, 等. 基于线性轨道涡流制动器的高速列车风致安全主动控制研究[J]. 机械工程学报, 2022, 58(8): 195-203.ZHANG Heng, LING Liang, CHANG Chao, et al. Active control of crosswind safety of high-speed trains with linear track eddy current brake system[J]. Journal of Mechanical Engineering, 2022, 58(8): 195-203. [29] ZHANG Heng, LING Liang, ZHAI Wan-ming. Adaptive nonlinear damping control of active secondary suspension for hunting stability of high-speed trains[J]. Applied Mathematical Modelling, 2024, 133: 79-107. [30] KALKER J J. Wheel rail rolling-contact theory[J]. Wear, 1991, 144(1/2): 243-261. [31] SHI Huai-long, WANG Jian-bin, WU Ping-bo, et al. Field measurements of the evolution of wheel wear and vehicle dynamics for high-speed trains[J]. Vehicle System Dynamics, 2018, 56(8): 1187-1206. doi: 10.1080/00423114.2017.1406963 [32] GUO Jin-ying, SHI Huai-long, LUO Ren, et al. Bifurcation analysis of a railway wheelset with nonlinear wheel-rail contact[J]. Nonlinear Dynamics, 2021, 104(2): 989-1005. doi: 10.1007/s11071-021-06373-8 [33] DHOOGE A, GOVAERTS W, KUZNETSOV Y A. MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs[J]. ACM Transactions on Mathematical Software, 2003, 29(2): 141-164. [34] 曾京, 邬平波. 高速列车的稳定性[J]. 交通运输工程学报, 2005, 5(2): 1-4. https://transport.chd.edu.cn/article/id/200502001ZENG Jing, WU Ping-bo. Stability of high-speed train[J]. Journal of Traffic and Transportation Engineering, 2005, 5(2): 1-4. https://transport.chd.edu.cn/article/id/200502001 -
点击查看大图
图(11) / 表(1)
计量
- 文章访问数: 26
- HTML全文浏览量: 28
- PDF下载量: 4
- 被引次数: 0
