This paper presents a mathematical model used to obtain the vertical vibration of a ballasted railway track when a wheel is passing at a certain speed over a fixed location of the rail. The aim of this simulation is to compare calculated root-mean-square (RMS) values of the vertical vibration velocity with measured RMS values. This comparison is the basis for a proposed time domain methodology for detecting potential wheel flats or any other singular defect on the wheel rolling bands of metropolitan trains. In order to reach this goal, a wheel–rail contact model is proposed; this model is described by the track vertical impulse response and the vertical impulse response of the wheel with the primary suspension, both linked through a Hertz nonlinear stiffness. To solve the model for obtaining the wheel–rail contact force, a double convolution method is applied. Several kinds of wheel flats are analyzed, from theoretical round edged wheel flats to different real wheel profile irregularities. Afterward, the vertical vibration velocity at a fixed point on the rail is obtained using a variable kernel convolution method. Running different simulations for different wheel flats, a study of the vertical vibration attenuation along the rail is carried out. Finally, it is proceeded to obtain the temporary evolution of the RMS value for the rail vertical vibration velocity in order to be used as a reference for detecting wheel flats or any other defect. This last aspect will be presented in more detail in a second paper.
Issue Section:
Research Papers
References
1.
Wu
, T. X.
, and Thompson
, D. J.
, 2002
, “A Hybrid Model for the Noise Generation Due to Railway Wheel Flats
,” J. Sound Vib.
, 251
(1
), pp. 115
–139
.2.
Mazilu
, T.
, Dumitriu
, M.
, Tudorache
, C.
, and Sebesan
, M.
, 2011
, “Using the Green's Functions Method to Study Wheelset/Ballasted Track Vertical Interaction
,” Math. Comput. Modell.
, 54
(1–2
), pp. 261
–279
.3.
Hertz
, H.
, 1895
, Gesamelte Werke Band I: Shriften Vermishen Inhalts
, P.
Lenard
, ed., Vol. 1
, Leipzig
, Barth, Germany
, p. 155
.4.
Yan
, W.
, and Fischer
, F. D.
, 2000
, “Applicability of the Hertz Contact Theory to Rail-Wheel Contact Problems
,” Arch. Appl. Mech.
, 70
(4
), pp. 255
–268
.5.
Fernández-Díaz
, E.
, 2000
, “Study of the Detection and Analysis of Vibrations Produced by a Railway Bogie
,” Ph.D. thesis, Universitat Politècnica de Catalunya, Barcelona, Spain.6.
Remington
, P.
, and Webb
, J.
, 1996
, “Estimation of Wheel/Rail Interaction Forces in the Contact Area Due to Roughness
,” J. Sound Vib.
, 193
(1
), pp. 83
–102
.7.
Carter
, F. W.
, 1926
, “On the Action of a Locomotive Driving Wheel
,” Proc. R. Soc. Ser. A
, 113
(760
), pp. 151
–157
.8.
Johnson
, K. L.
, and Vermeulen
, P. J.
, 1964
, “Contact of Non-Spherical Bodies Transmitting Tangential Forces
,” ASME J. Appl. Mech.
, 31
(2
), pp. 338
–340
.9.
Kalker
, J. J.
, 1967
, “On the Rolling Contact for Two Elastic Bodies in the Presence of Dry Friction
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.10.
Kalker
, J. J.
, 1983
, “A Fast Algorithm for the Simplified Theory of Rolling Contact
,” Veh. Syst. Dyn.
, 11
(1
), pp. 1
–13
.11.
Wu
, T. X.
, and Thompson
, D. J.
, 2000
, “Theoretical Investigation of Wheel/Rail Non-Linear Interaction Due to Roughness Excitation
,” Veh. Syst. Dyn.
, 34
(4
), pp. 261
–282
.12.
Cardona
, S.
, Martínez
, J.
, Fernàndez-Díaz
, E.
, and De los Santos
, M. A.
, 1998
, “Determination of the Vibrations Produced by the Profile Irregularities of the Wheels of a Metropolitan Railway Bogie in a Rail Location
,” Anales de Ingeniería Mecánica (in Spanish)
, 12
(4
), pp. 454
–459
.13.
Clark
, R. A.
, Dean
, P. A.
, Elkins
, J. A.
, and Newton
, S. G.
, 1982
, “An Investigation Into the Dynamic Effects of Railway Vehicles Running on Corrugated Rails
,” J. Mech. Eng. Sci.
, 24
(2
), pp. 65
–76
.14.
Zougari
, A.
, Martínez
, J.
, and Cardona
, S.
, 2016
, “Numerical Models of Railway Tracks for Obtaining Frequency Response. Comparison With Analytical Results and Experimental Measurements
,” J. Vibroeng.
, 18
(2
), pp. 1104
–1114
.https://jvejournals.com/article/1654615.
Tran
, L. H.
, Hoang
, T.
, Duhamel
, D.
, Foret
, G.
, Messad
, S.
, and Loaec
, A.
, 2018
, “A Fast Analytic Method to Calculate the Dynamic Response of Railways Sleepers
,” ASME J. Vib. Acoust.
, 141
(1
), p. 011005
.16.
Zougari
, A.
, 2014
, “Study of the Vibrational Behaviour of Different Tracks Using Finite Element Model
,” Ph.D. thesis (in Spanish), Universitat Politècnica de Catalunya, Barcelona, Spain.17.
Martínez
, J.
, De los Santos
, M.
, and Cardona
, S.
, 1995
, “A Convolution Method to Determine the Dynamic Response in a Railway Track Submitted to a Moving Vertical Excitation
,” Mach. Vib.
, 4
(1), pp. 142
–146
.18.
Otero
, J.
, Martínez
, J.
, De los Santos
, M. A.
, and Cardona
, S.
, 2012
, “A Mathematical Model to Study Railway Track Dynamics for the Prediction of Vibration Levels Generated by Rail Vehicles
,” J. Rail. Rapid Transit.
, 226
(1
), pp. 62
–71
.19.
Thompson
, D.
, 1993
, “Wheel-Rail Noise Generation. Part III: Rail Vibration
,” J. Sound Vib.
, 161
(3
), pp. 421
–446
.20.
Grassie
, S. L.
, Gregory
, R. W.
, Harrison
, D.
, and Johnson
, K. L.
, 1982
, “The Dynamic Response of Railway Track to High Frequency Vertical Excitation
,” J. Mech. Eng. Sci.
, 24
(2
), pp. 77
–90
.21.
Iwnicki
, S.
, 2006
, Handbook of Railway Vehicle Dynamics
, CRC Press
, Boca Raton, FL
, pp. 279
–325
.22.
Mazilu
, T.
, 2017
, “Interaction Between Moving Tandem Wheels and an Infinite Rail With Periodic Supports—Green's Matrices of the Track Method in Stationary Reference Frame
,” J. Sound Vib.
, 401
, pp. 233
–254
.23.
Thompson
, D.
, Wu
, T. X.
, and Armstrong
, T.
, 2003
, “Wheel/Rail Rolling Noise—The Effects of Non-Linearities in the Contact Zone
,” Tenth International Congress on Sound and Vibration
, Stockholm, Sweden, July 7–10.https://www.southampton.ac.uk/assets/imported/transforms/content-block/UsefulDownloads_Download/223F9A5BFBAD4A0885B7790738D08585/icsv10_240.pdf24.
Kawaguchi
, K.
, Seko
, N.
, Nagai
, T.
, and Ookita
, Y.
, 2006
, “Development of a Wheel Slip Prevention (WSP) System for Freight Trains
,” Seventh World Congress on Railway Research
, Montréal, QC, Canada
, June 4–8
, p. 77.25.
Newton
, S. G.
, and Clark
, R. A.
, 1979
, “An Investigation Into the Dynamic Effects on the Track of Wheel Flats on Railway Vehicles
,” J. Mech. Eng. Sci.
, 21
(4
), pp. 287
–297
.26.
Dings
, P. C.
, and Dittrich
, M. G.
, 1996
, “Roughness on Dutch Railway Wheels and Rails
,” J. Sound Vib.
, 193
(1
), pp. 103
–112
.27.
Squicciarini
, G.
, Toward
, M. G.
, Thompson
, D. J.
, and Jones
, C. J. C.
, 2013
, “Statistical Description of Wheel Roughness
,” 11th International Workshop on Railway Noise
, Uddevalla, Sweden
, Sept. 9–13
.28.
Tomov
, M.
, Kuzinovski
, M.
, and Trajcevski
, N.
, 2010
, “Function on Gaussian and 2RC Filters to Determine the Roughness Profile in Real Non-Periodic and Periodic Surface
,” 14th International Research/Expert Conference
, Mediterranean Cruise
, Sept. 11–18
.29.
Yuan
, Y. B.
, Vorburger
, Y. B.
, Song
, J. F.
, and Renegar
, T. B.
, 2000
, “A Simplified Realization for the Gaussian Filter in Surface Metrology
,” Tenth International Colloquium on Surfaces
, Chemnitz, Germany
, pp. 133
–144
.30.
Amick
, H.
, 1999
, “A Frequency-Dependency Soil Propagation Model
,” Conference on Current Developments in Vibration Control for Optomechanical Systems
, Denver, CO
, July 20–23
.31.
Telford
, W. M.
, Geldart
, L. P.
, and Sheriff
, R. E.
, 1990
, Applied Geophysics, Seismic Methods
, Cambridge University Press
, Cambridge, UK
, p. 770
.32.
Florez
, E.
, 2009
, “Identification and Characterization of Wheel Flats of a Train Using the Signal Analysis of the Rail Vertical Vibration Generated by the Wheel-Rail Contact
,” Ph.D. thesis, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain (in Spanish).33.
Colaço
, A.
, Costa
, P. A.
, Amado-Mendes
, P.
, and Godinho
, L.
, 2017
, “Prediction of Vibrations and Reradiated Noise Due to Railway Traffic: A Comprehensive Hybrid Model Based on a Finite Element Method and Method of Fundamental Solutions Approach
,” ASME J. Vib. Acoust.
, 139
(6
), p. 061009
.Copyright © 2019 by ASME
You do not currently have access to this content.
