Dynamic models and analysis of key factors influencing stick–slip vibration in disc brake system

Abstract

The stick–slip vibration of the disc brake system at low speed is caused by the interaction of multiple factors. This paper focuses on the disc brake system of the high-speed train as the research object, establishing three- and four-degree-of-freedom (DOF) dynamic models considering wheel–rail adhesion and nonlinear friction, and the model’s accuracy was confirmed through line testing. The system stability, stick–slip bifurcation characteristics, and key factors affecting stick–slip vibration are analyzed through models simulation. The results demonstrated that compared with the three-DOF model, the over-evaluation of the system stability can be avoided after considering the normal motion. In the three-DOF model, the main factor inducing chaotic stick–slip vibration is the tangential stiffness. In the four-DOF model, the tangential stiffness mainly changes the amplitude, while the normal stiffness is the main factor causing vibration chaos. Additionally, damping has a minimal impact on the occurrence of chaotic stick–slip vibration. Optimal ranges for brake disc rotational inertia (5–9 kg·m² and 11–22 kg·m²) and friction pad mass (7–17 kg) were further identified, effectively mitigating the occurrence of chaotic stick–slip vibration.

Keywords

Disc brake / Stick–slip vibration / Dynamic model / System stability

References

[1] ZengJ, LuoR. Non-linear analysis of disc brake-induced vibrations for railway vehicles. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2011, 225148-56.

[2] GeX, ChenQ, LingL, et al. . An approach for simulating the air brake system of long freight trains based on fluid dynamics. Railw Eng Sci, 2023, 312122-134.

[3] VermaPC, CiudinR, BonfantiA, et al. . Role of the friction layer in the high-temperature pin-on-disc study of a brake material. Wear, 2016, 346: 56-65.

[4] ZhuH, LianS, JinM, et al. . Review of research on the influence of vibration and thermal fatigue crack of brake disc on rail vehicles. Eng Fail Anal, 2023, 153: 107603.

[5] OuyangH, Abu BakarAR, LiJ. A combined analysis of heat conduction, contact pressure and transient vibration of a disc brake. Int J Veh Des, 2009, 511–2190.

[6] WangZ, YangL, MoJ, et al. . A trailer car dynamics model considering brake rigging of a high-speed train and its application. Railw Eng Sci, 2023, 313269-280.

[7] ZhuQ, XieJ, ZhangW, et al. . Influence of disc brake on wheel polygonal wear of high-speed train. Wear, 2023, 524: 204814.

[8] ZouL, ZengD, LiY, et al. . Experimental and numerical study on fretting wear and fatigue of full-scale railway axles. Railw Eng Sci, 2020, 284365-381.

[9] Lorang X, Chiello O (2008) Stability and transient analysis in the modelling of railway disc brake squeal. In: Proceedings of the 9th International Workshop on Railway Noise, Munich, pp 447–453

[10] ChenG, LvJ, ZhuQ, et al. . Effect of the braking pressure variation on disc brake squeal of a railway vehicle: Test measurement and finite element analysis. Wear, 2019, 426: 1788-1796.

[11] WahlströmJ. A pin-on-disc tribometer study of friction at low contact pressures and sliding speeds for a disc brake material combination. Res Eng, 2019, 4: 100051

[12] Huemer-KalsS, KappaufJ, ZacharczukM, et al. . Advancements on bifurcation behavior and operational deflection shapes of disc brake creep groan. J Sound Vib, 2022, 534: 116978.

[13] NeisPD, FerreiraNF, PolettoJC, et al. . Quantification of brake creep groan in vehicle tests and its relation with stick-slip obtained in laboratory tests. J Sound Vib, 2016, 369: 63-76.

[14] MengD, ShenL, ZhangL, et al. . Transient dynamic analysis of vehicle brake creep groan. J Vib Eng Technol, 2019, 76591-601.

[15] LuX, ZhaoJ, MoJ, et al. . Suppression of friction-induced stick–slip behavior and improvement of tribological characteristics of sliding systems by introducing damping materials. Tribol Trans, 2020, 632222-234.

[16] NeisPD, De BaetsP, OstW, et al. . Investigation of the dynamic response in a dry friction process using a rotating stick–slip tester. Wear, 2011, 2719/102640-2650.

[17] WangX, MoJ, OuyangH, et al. . An investigation of stick-slip oscillation of Mn–Cu damping alloy as a friction material. Tribol Int, 2020, 146: 106024.

[18] ZhangQ, MoJ, XiangZ, et al. . Effect of surface micro-grooved textures in suppressing stick-slip vibration in high-speed train brake systems. Tribol Int, 2023, 189: 108946.

[19] BalaramB, SanthoshB, AwrejcewiczJ. Frequency entrainment and suppression of stick–slip vibrations in a 3 DoF discontinuous disc brake model. J Sound Vib, 2022, 538: 117224.

[20] ChoiJ, SeoH, SohnSS, et al. . Size effects of brake pads on stick-slip phenomena. Tribol Int, 2023, 189: 108944.

[21] ZhangQ, MoJ, XiangZ, et al. . The influence of interfacial wear characteristics on stick-slip vibration. Tribol Int, 2023, 185: 108535.

[22] MaegawaS, ItoigawaF. Design method for suppressing stick-slip using dynamic vibration absorber. Tribol Int, 2019, 140: 105866.

[23] CantoneL, OttatiA. A simplified pneumatic model for air brake of passenger trains. Railw Eng Sci, 2023, 312145-152.

[24] LiP, JiangZ. Bifurcation analysis of stick-slip motion of the vibration-driven system with dry friction. Math Probl Eng, 2018, 2018: 2305187

[25] WangQ, WangZ, MoJ. A hybrid friction-induced vibration form: experimental measurement and mechanism discussion. Tribol Int, 2023, 183: 108397.

[26] WangZ, MoJ, WangK, et al. . A novel vehicle-track coupled dynamics model with disc brake systems: modelling and validation. Veh Syst Dyn, 2024, 624789-812.

[27] ChenL, XiG. Stability and response of a self-amplified braking system under velocity-dependent actuation force. Nonlinear Dyn, 2014, 7842459-2477.

[28] KangJ, KrousgrillCM, SadeghiF. Oscillation pattern of stick–slip vibrations. Int J Non Linear Mech, 2009, 447820-828.

[29] ShinK, BrennanMJ, OhJE, et al. . Analysis of disc brake noise using a two-degree-of-freedom model. J Sound Vib, 2002, 2545837-848.

[30] WeiD, SongJ, NanY, et al. . Analysis of the stick-slip vibration of a new brake pad with double-layer structure in automobile brake system. Mech Syst Signal Process, 2019, 118: 305-316.

[31] WangQ, WangZ, MoJ, et al. . Nonlinear behaviors of the disc brake system under the effect of wheel−rail adhesion. Tribol Int, 2022, 165: 107263.

[32] WangH, LiuX, ShanY, et al. . Nonlinear behavior evolution and squeal analysis of disc brake based on different friction models. J Vibroeng, 2014, 16: 2593-2609

[33] DuanC, SinghR. Transient responses of a 2-dof torsional system with nonlinear dry friction under a harmonically varying normal load. J Sound Vib, 2005, 2854–51223-1234.

[34] WangQ, WangZ, MoJ, et al. . Evaluation of the dynamic behaviors of a train braking system considering disc–block interface characteristics. Mech Syst Signal Process, 2023, 192: 110234.

[35] van de VrandeBL, van CampenDH, de KrakerA. An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure. Nonlinear Dyn, 1999, 192159-171.

[36] MontenegroPA, CalçadaR. Wheel–rail contact model for railway vehicle–structure interaction applications: development and validation. Railw Eng Sci, 2023, 313181-206.

[37] OuakkaS, VerlindenO, KouroussisG. Railway ground vibration and mitigation measures: benchmarking of best practices. Railw Eng Sci, 2022, 3011-22.

[38] WangQ, WangZ, MoJ, et al. . Effect and mechanism of wheel–rail adhesion on torsional vibration and stability of the braking system. Tribol Int, 2023, 179: 108182.

[39] XuK, ZengJ, WeiL. An analysis of the self-excited torsional vibration of high-speed train drive system. J Mech Sci Technol, 2019, 3331149-1158.

[40] KimM, JangG, KimH. Stability analysis of a disc-spindle system supported by coupled journal and thrust bearings considering five degrees of freedom. Tribol Int, 2010, 4381479-1490.

[41] HuH, BatouA, OuyangH. Friction-induced vibration of a stick–slip oscillator with random field friction modelling. Mech Syst Signal Process, 2023, 183: 109572.

[42] TeohCY, RipinZM, HamidMNA. Analysis of friction excited vibration of drum brake squeal. Int J Mech Sci, 2013, 67: 59-69.

[43] WangX, MoJ, OuyangH, et al. . The effects of grooved rubber blocks on stick–slip and wear behaviours. Proc Inst Mech Eng Part D J Automob Eng, 2019, 233112939-2954.

[44] LuX, ZhaoJ, MoJ, et al. . Improvement of dynamical and tribological properties of friction systems by introducing parallel-grooved structures in elastic damping components. Compos Struct, 2018, 192: 8-19.

Funding

National Key Research and Development Program of China(2023YFB3710604)

National Natural Science Foundation of China(No.52205217，U22A20181)

Independent Research Projects of State Key Laboratory of Traction Power(No.2024RVL-T09)

China Academy of Railway Sciences Corporation Limited Research Project(2022YJ321)

RIGHTS & PERMISSIONS

The Author(s)