Integration of bio-inspired limb-like structure damping into motor suspension of high-speed trains to enhance bogie hunting stability

Abstract

Hunting stability is an important performance criterion in railway vehicles. This study proposes an incorporation of a bio-inspired limb-like structure (LLS)-based nonlinear damping into the motor suspension system for traction units to improve the nonlinear critical speed and hunting stability of high-speed trains (HSTs). Initially, a vibration transmission analysis is conducted on a HST vehicle and a metro vehicle that suffered from hunting motion to explore the effect of different motor suspension systems from on-track tests. Subsequently, a simplified lateral dynamics model of an HST bogie is established to investigate the influence of the motor suspension on the bogie hunting behavior. The bifurcation analysis is applied to optimize the motor suspension parameters for high critical speed. Then, the nonlinear damping of the bio-inspired LLS, which has a positive correlation with the relative displacement, can further improve the modal damping of hunting motion and nonlinear critical speed compared with the linear motor suspension system. Furthermore, a comprehensive numerical model of a high-speed train, considering all nonlinearities, is established to investigate the influence of different types of motor suspension. The simulation results are well consistent with the theoretical analysis. The benefits of employing nonlinear damping of the bio-inspired LLS into the motor suspension of HSTs to enhance bogie hunting stability are thoroughly validated.

Keywords

High-speed train / Hunting stability / Bio-inspired limb-like structure / Motor suspension / Nonlinear damping

References

[1.] Gong D, Liu G, Zhou J. Research on mechanism and control methods of carbody chattering of an electric multiple-unit train. Multibody Syst Dyn, 2021, 53(2): 135-172,

[2.] Chang C, Ding X, Ling L, et al.. Mechanism of high-speed train carbody shaking due to degradation of wheel-rail contact geometry. Int J Rail Transp, 2022, 11(3): 289-316,

[3.] Xia Z, Zhou J, Gong D, et al.. On the modal damping abnormal variation mechanism for railway vehicles. Mech Syst Signal Process, 2019, 122: 256-272,

[4.] Li Y, Chi M, Guo Z, et al.. An abnormal carbody swaying of intercity EMU train caused by low wheel–rail equivalent conicity and damping force unloading of yaw damper. Railw Eng Sci, 2023, 31(3): 252-268,

[5.] Sawley K, Urban C, Walker R. The effect of hollow-worn wheels on vehicle stability in straight track. Wear, 2005, 258(7–8): 1100-1108,

[6.] Alizadeh KJ, Ghajar R, Tavakkoli H. Modelling of nonlinear hunting instability for a high-speed railway vehicle equipped by hollow worn wheels. Proc Inst Mech Eng K J Mul, 2016, 230(4): 553-567

[7.] Carter FW. The electric locomotive. Min Proc Inst Civ Eng, 1916, 201(1916): 221-252

[8.] Huilgol RR. Hopf-Friedrichs bifurcation and the hunting of a railway axle. Q Appl Math, 1978, 36(1): 85-94,

[9.] Wickens AH. The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels. Int J Solids Struct, 1965, 1(3): 319-341,

[10.] Polach O, Nicklisch D. Wheel/rail contact geometry parameters in regard to vehicle behaviour and their alteration with wear. Wear, 2016, 366(15): 200-208,

[11.] Guo J, Shi H, Luo R et al (2021) Bifurcation analysis of a railway wheelset with nonlinear wheel–rail contact. Nonlin Dyn 104(2):989–1005

[12.] Zhang T, Dai H (2016) Bifurcation analysis of high-speed railway wheel-set. Nonlin Dyn 83(3):1511–1528

[13.] Yan Y, Zeng J (2018) Hopf bifurcation analysis of railway bogie. Nonlin Dyn 92(1):107–117

[14.] Bustos A, Tomas-Rodriguez M, Rubio H, et al.. On the nonlinear hunting stability of a high-speed train bogie. Nonlinear Dyn, 2023, 111(3): 2059-2078,

[15.] Zhang T, Dai H. On the nonlinear dynamics of a high-speed railway vehicle with nonsmooth elements. Appl Math Model, 2019, 76: 526-544,

[16.] Luo G, Shi Y, Zhu X, et al.. Hunting patterns and bifurcation characteristics of a three-axle locomotive bogie system in the presence of the flange contact nonlinearity. Int J Mech Sci, 2018, 136: 321-338,

[17.] Miao P, Li D, Yin S, et al.. Double grazing bifurcations of the non-smooth railway wheelset systems. Nonlin Dyn, 2023, 111(3): 2093-2110,

[18.] Zhang X, Liu Y, Liu P, et al.. Nonlinear dynamic analysis of a stochastic delay wheelset system. Appl Math Model, 2023, 119: 486-499,

[19.] Lee S, Cheng Y. Influences of the vertical and the roll motions of frames on the hunting stability of trucks moving on curved tracks. J Sound Vib, 2006, 294(3): 441-453,

[20.] Zboinski K, Dusza M. Self-exciting vibrations and Hopf’s bifurcation in non-linear stability analysis of rail vehicles in a curved track. Eur J Mech A Solid, 2010, 29(2): 190-203,

[21.] Zhai W, Wang K. Lateral hunting stability of railway vehicles running on elastic track structures. J Comput Nonlin Dyn, 2010, 5(4): 041009,

[22.] Ling L, Jiang P, Wang K, et al.. Nonlinear stability of rail vehicles traveling on vibration-attenuating slab tracks. J Comput Nonlin Dyn, 2020, 15(7): 071005,

[23.] Kaiser I, Poll G, Voss G, et al.. The impact of structural flexibilities of wheelsets and rails on the hunting behaviour of a railway vehicle. Veh Syst Dyn, 2019, 57(4): 564-594,

[24.] Alfi S, Mazzola L, Bruni S. Effect of motor connection on the critical speed of high-speed railway vehicles. Veh Syst Dyn, 2008, 46(1): 201-214,

[25.] Huang C, Zeng J. Suppression of the flexible carbody resonance due to bogie instability by using a DVA suspended on the bogie frame. Veh Syst Dyn, 2022, 60(2022): 3051-3070,

[26.] Yao Y, Wu G, Sardahi Y, et al.. Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control. Veh Syst Dyn, 2018, 56(2): 297-318,

[27.] Yao Y, Li G, Sardahi Y, et al.. Stability enhancement of a high-speed train bogie using active mass inertial actuators. Veh Syst Dyn, 2019, 57(3): 389-407,

[28.] Jin T, Liu Z, Sun S, et al.. Theoretical and experimental investigation of a stiffness-controllable suspension for railway vehicles to avoid resonance. Int J Mech Sci, 2020, 187: 105901,

[29.] Xia Z, Zhou J, Liang J, et al.. Online detection and control of car body low–frequency swaying in railway vehicles. Veh Syst Dyn, 2021, 59(1): 70-100,

[30.] Shaw AD, Gatti G, Goncalves P, et al.. Design and test of an adjustable quasi-zero stiffness device and its use to suspend masses on a multi-modal structure. Mech Syst Signal Process, 2021, 152: 107354,

[31.] Ye K, Ji JC, Brown T. A novel integrated quasi-zero stiffness vibration isolator for coupled translational and rotational vibrations. Mech Syst Signal Process, 2021, 149: 107340,

[32.] Wu Z, Jing X, Bian J, et al.. Vibration isolation by exploring bio-inspired structural nonlinearity. Bioinspir Biomim, 2015, 10(5): 056015,

[33.] Feng X, Jing X. Human body inspired vibration isolation: beneficial nonlinear stiffness, nonlinear damping & nonlinear inertia. Mech Syst Signal Process, 2019, 117: 786-812,

[34.] Bian J, Jing X. Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mech Syst Signal Process, 2019, 125: 21-51,

[35.] National Standardization Committee of the People’s Republic of China. GB/T 5599–2019, Specification for dynamic performance assessment and testing verification of rolling stock. National Standardization Press of the People’s Republic of China.

[36.] Zhang H, Ding X, Chang C et al (2022) A study on the mechanism of carbody shaking phenomenon of high-speed trains. In: Proceedings of the 27th Symposium of the International Association of Vehicle System Dynamics, IAVSD 2021. Saint Petersburg, pp 208–216

[37.] Wagner U. Nonlinear dynamic behaviour of a railway wheelset. Veh Syst Dyn, 2009, 47(5): 627-640,

[38.] Dhooge A, Govaerts W, Kuznetsov Y. MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans Math Softw, 2003, 29(2): 141-164,

[39.] Zhai W. . Vehicle–Track coupled dynamics: theory and applications, 2020 Singapore Springer,

[40.] Polach O. Comparability of the non-linear and linearized stability assessment during railway vehicle design. Veh Syst Dyn, 2006, 44(1): 129-138,

Funding

National Natural Science Foundation of China(U2268210)