Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of the Model
2.1.1. Contact Forces
2.1.2. Equations of Motion
2.2. Stability Analysis of the Self-Excited System
2.3. Derivation of the Initial Conditions
2.3.1. Initial Condition on Velocity
2.3.2. Initial Condition on Displacement
2.3.3. Modal-Derived Initial Conditions
3. Results and Discussion
3.1. System’s Parameters
3.2. Stability Results
3.3. Initial Conditions
3.3.1. Initial Condition on Velocity
3.3.2. Initial Condition on Displacement
3.3.3. Modal-Derived Initial Conditions and Summary of the Test Cases
- All unstable modes
- Mode 0Ln, with
3.4. Time Integration Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Thompson, D.J.; Squicciarini, G.; Ding, B.; Baeza, L. A State-of-the-Art Review of Curve Squeal Noise: Phenomena, Mechanisms, Modelling and Mitigation. In Noise and Vibration Mitigation for Rail Transportation Systems; Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Springer: Cham, Switzerland, 2018; pp. 3–41. [Google Scholar] [CrossRef]
- Rudd, M.J. Wheel/rail noise—Part II: Wheel squeal. J. Sound Vib. 1976, 46, 381–394. [Google Scholar] [CrossRef]
- van Ruiten, C.J.M. Mechanism of squeal noise generated by trams. J. Sound Vib. 1988, 120, 245–253. [Google Scholar] [CrossRef]
- Fingberg, U. A model of wheel-rail squealing noise. J. Sound Vib. 1990, 143, 365–377. [Google Scholar] [CrossRef]
- de Beer, F.G.; Janssens, M.H.A.; Kooijman, P.P. Squeal noise of rail-bound vehicles influenced by lateral contact position. J. Sound Vib. 2003, 267, 497–507. [Google Scholar] [CrossRef]
- Chiello, O.; Ayasse, J.B.; Vincent, N.; Koch, J.R. Curve squeal of urban rolling stock—Part 3: Theoretical model. J. Sound Vib. 2006, 293, 710–727. [Google Scholar] [CrossRef]
- Hoffmann, N.; Fischer, M.; Allgaier, R.; Gaul, L. A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations. Mech. Res. Commun. 2002, 29, 197–205. [Google Scholar] [CrossRef]
- Glocker, C.; Cataldi-Spinola, E.; Leine, R.I. Curve squealing of trains: Measurement, modelling and simulation. J. Sound Vib. 2009, 324, 365–386. [Google Scholar] [CrossRef]
- Pieringer, A. A numerical investigation of curve squeal in the case of constant wheel/rail friction. J. Sound Vib. 2014, 333, 4295–4313. [Google Scholar] [CrossRef]
- Ding, B.; Squicciarini, G.; Thompson, D. Effect of rail dynamics on curve squeal under constant friction conditions. J. Sound Vib. 2019, 442, 183–199. [Google Scholar] [CrossRef]
- Lai, V.V.; Chiello, O.; Brunel, J.F.; Dufrénoy, P. The critical effect of rail vertical phase response in railway curve squeal generation. Int. J. Mech. Sci. 2020, 167, 105281. [Google Scholar] [CrossRef]
- Jiang, J.; Anderson, D.C.; Dwight, R. The Mechanisms of Curve Squeal. In Noise and Vibration Mitigation for Rail Transportation Systems; Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Springer: Berlin/Heidelberg, Germany, 2015; pp. 587–594. [Google Scholar] [CrossRef]
- Meehan, P.A. Prediction of wheel squeal noise under mode coupling. J. Sound Vib. 2020, 465, 115025. [Google Scholar] [CrossRef]
- Huang, Z.Y.; Thompson, D.J.; Jones, C.J.C. Squeal Prediction for a Bogied Vehicle in a Curve. Noise and Vibration Mitigation for Rail Transportation Systems; Springer: Berlin/Heidelberg, Germany, 2008; pp. 313–319. [Google Scholar] [CrossRef]
- Ding, B.; Squicciarini, G.; Thompson, D.; Corradi, R. An assessment of mode-coupling and falling-friction mechanisms in railway curve squeal through a simplified approach. J. Sound Vib. 2018, 423, 126–140. [Google Scholar] [CrossRef]
- Charroyer, L.; Chiello, O.; Sinou, J.J. Self-excited vibrations of a non-smooth contact dynamical system with planar friction based on the shooting method. Int. J. Mech. Sci. 2018, 144, 90–101. [Google Scholar] [CrossRef]
- Coudeyras, N.; Nacivet, S.; Sinou, J.J. Periodic and quasi-periodic solutions for multi-instabilities involved in brake squeal. J. Sound Vib. 2009, 328, 520–540. [Google Scholar] [CrossRef]
- Zenzerovic, I. Time-Domain Modelling of Curve Squeal: A Fast Model for One- and Two-Point Wheel/Rail Contact. Ph.D Thesis, Chalmers University of Technology, Gothenburg, Sweden, 2017. ISBN 9789175976471. [Google Scholar]
- Ding, B. The Mechanism of Railway Curve Squeal. Ph.D Thesis, University of Southampton, Southampton, UK, 2018. [Google Scholar]
- Loyer, A.; Sinou, J.J.; Chiello, O.; Lorang, X. Study of nonlinear behaviors and modal reductions for friction destabilized systems. Application to an elastic layer. J. Sound Vib. 2012, 331, 1011–1041. [Google Scholar] [CrossRef]
- Lai, V.V.; Anciant, M.; Chiello, O.; Brunel, J.F.; Dufrénoy, P. A nonlinear FE model for wheel/rail curve squeal in the time-domain including acoustic predictions. Appl. Acoust. 2021, 179, 108031. [Google Scholar] [CrossRef]
- Heckl, M.A.; Abrahams, I.D. Curve squeal of train wheels, part 1: Mathematical model for its generation. J. Sound Vib. 2000, 229, 669–693. [Google Scholar] [CrossRef]
- Giner-Navarro, J.; Martínez-Casas, J.; Denia, F.D.; Baeza, L. Study of railway curve squeal in the time domain using a high-frequency vehicle/track interaction model. J. Sound Vib. 2018, 431, 177–191. [Google Scholar] [CrossRef]
- Schneider, E.; Popp, K.; Irretier, H. Noise generation in railway wheels due to rail-wheel contact forces. J. Sound Vib. 1988, 120, 227–244. [Google Scholar] [CrossRef]
- Thompson, D.J. Railway Noise and Vibration: Mechanisms, Modelling and Means of Control; Elsevier: Amsterdam, The Netherlands, 2009. [Google Scholar]
- Ding, B.; Squicciarini, G.; Thompson, D.J. Effects of rail dynamics and friction characteristics on curve squeal. J. Phys. Conf. Ser. 2016, 744, 012146. [Google Scholar] [CrossRef]
- Kalker, J.J. Wheel-rail rolling contact theory. Wear 1991, 144, 243–261. [Google Scholar] [CrossRef]
- Shen, Z.Y.; Hedrick, J.K.; Elkins, J.A. A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis. Vehicle System Dynamics; Taylor & Francis: Abingdon, UK, 1983; Volume 12, pp. 79–83. [Google Scholar] [CrossRef]
- Newmark, N.M.; Asce, F. A method of computation for structural dynamics. J. Eng. Machanics Div. 1959, 85, 67–94. [Google Scholar] [CrossRef]
- Géradin, M.; Rixen, D. Mechanical Vibrations: Theory and Application to Structural Dynamics, 2nd ed.; Wiley: Hoboken, NJ, USA, 1997. [Google Scholar]
Parameter [Units] | Description | Value |
---|---|---|
[km/h] | Rolling speed | 30 |
[mrad] | Angle of attack | 11 |
N [kN] | Normal load per wheel | 51 |
[m] | Wheel diameter | 0.86 |
[mm] | Lateral offset of the contact point | 15 |
[rad] | Contact plane angle | −0.0145 |
[m] | Rail transverse radius | 0.3 |
E [Gpa] | Young modulus | 210 |
[-] | Poisson’s ratio | 0.3 |
[-] | Static friction coefficient | 0.3 |
[-] | Parameter for friction law | 0.05 |
[-] | Falling ratio on saturated regime | 0.2 |
Free Modes | Stability Analysis | ||||
---|---|---|---|---|---|
Mode | Denomination | Frequency [Hz] | Damping Ratio [-] | Frequency [Hz] | Equivalent Damping Ratio [-] |
5 | 0L0 | 304.43 | 304.43 | ||
6 | 0L2 | 386.38 | 386.35 | ||
9 | 0L3 | 1028.8 | 1028.79 | ||
12 | 0L4 | 1853.9 | 1853.91 | ||
16 | - | 2369.8 | 2369.8 | ||
17 | 0L5 | 2776.3 | 2776.3 | ||
22 | 0L6 | 3752.6 | 3752.59 | ||
26 | - | 4561.5 | 4561.5 | ||
28 | 0L7 | 4762.2 | 4762.19 | ||
33 | 0L8 | 5794.7 | 5794.69 |
Case Name | ||
---|---|---|
Modal-derived initial conditions | ||
All_unstable_V0.1 | With Unstable modes and | |
All_unstable_V1.0 | ⋯ Unstable modes and | |
All_unstable_V2.0 | ⋯ Unstable modes and | |
0L0 | ⋯ “mode 0L0” | |
0L1 | ⋯ “mode 0L1” | |
0L2 | ⋯ “mode 0L2” | |
0L3 | ⋯ “mode 0L3” | |
0L4 | ⋯ “mode 0L4” | |
0L5 | ⋯ “mode 0L5” | |
0L6 | ⋯ “mode 0L6” | |
0L7 | ⋯ “mode 0L7” | |
0L8 | ⋯ “mode 0L8” | |
Physically-derived initial conditions | ||
V_-1.0 | With | |
V_-0.5 | ||
V_0.01 | ||
V_0.1 | ||
V_0.2 | ||
V_0.3 | ||
V_0.5 | ||
V_1.0 | ||
U_0.5 | With | |
U_-0.5 |
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Arango Montoya, J.; Chiello, O.; Sinou, J.-J.; Tufano, R. Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Appl. Sci. 2025, 15, 509. https://doi.org/10.3390/app15020509
Arango Montoya J, Chiello O, Sinou J-J, Tufano R. Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Applied Sciences. 2025; 15(2):509. https://doi.org/10.3390/app15020509
Chicago/Turabian StyleArango Montoya, Jacobo, Olivier Chiello, Jean-Jacques Sinou, and Rita Tufano. 2025. "Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal" Applied Sciences 15, no. 2: 509. https://doi.org/10.3390/app15020509
APA StyleArango Montoya, J., Chiello, O., Sinou, J.-J., & Tufano, R. (2025). Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Applied Sciences, 15(2), 509. https://doi.org/10.3390/app15020509