Validation of three-dimensional multi-body system approach for modelling track flexibility

Abstract

The objective of this investigation is to examine the results and demonstrate the validity of a proposed multi-body railroad vehicle system formulation that accounts for the dynamic coupling between three-dimensional (3D) contact parameters and the rail structural flexibility. This formulation allows building complex track models that include significant details at a finite-element preprocessing stage. The data of the detailed track model can be used as an input to a general purpose flexible multi-body computer program for a non-linear analysis that accounts for the dynamic coupling between the track flexibility, 3D wheel—rail contact, and the vehicle dynamics. The simulations are performed using the methods of multi-body system dynamics that employ 3D wheel—rail contact methodology capable of finding the wheel—rail contact points online. The effect of the structural flexibility of the rails is included in the equations of motion using the finite-element floating frame of reference formulation. While this formulation allows for an arbitrary reference displacement for the track, this reference displacement is constrained in order to be able to compare the results with those results obtained using simplified approaches. The results obtained by applying the proposed multi-body system/finite-element formulation to a simple railroad vehicle travelling on a deformable tangent track are compared with the results of a moving load on a Winkler foundation. In addition to the simple moving load model used, a second model that accounts for the effect of the vehicle inertia is also used in this study. The comparative study presented in this article shows a good agreement between the results obtained using the two different methods. Furthermore, the results obtained in the case of a flexible track are compared with the results obtained using a rigid track in order to examine the effect of the track structural flexibility on the non-linear dynamics of the rail system.

Keywords

railroad vehicles track structural flexibility multi-body system dynamics

Get full access to this article

View all access options for this article.

References

Fryba

Vibration of solids and structures under moving loads (Groningen, The Netherlands: Noordhoff International Publishing 1972)

Kerr

A. D.

‘Continuously supported beams and plates subjected to moving loads - a survey’

Solid Mech. Arch. 6 (1981): 401–449

Grassie

S. L.

Cox

S. J.

‘The dynamic response of railway to high frequency vertical excitation’

J. Mech. Engng Sci. 242 (1982): 77–90

Duffy

D. G.

‘The response of an infinite railroad track to a moving vibrating mass’

Trans. ASME, J. Appl. Mech. 57 (1990): 66–73

Ilias

Muller

‘A discrete-continuous track-model for wheelsets rolling over shot wavelength sinusoidal rail irregularities’

In Proceedings of the 13th IAVSD Symposium, The Dynamics of Vehicles on Roads and on Tracks, Chengdu, Sichuan, China, 23–27 August 1993, vol. 23(S1), pp. 221–233.

Cai

Raymond

G. P.

‘Modeling the dynamic response of railway track to wheel-rail impact loading’

Struct. Eng. Mech. 21 (1994): 95–112

Ishida

Miura

Kono

‘The influence of track stiffness on track dynamic behaviour’

Quart. Reports Railw. Techn. Res. Inst. 383 (1997): 129–134

Lin

Y. H.

Trerhewey

M. W.

‘Finite element analysis of elastic beams subjected to moving dynamic loads’

J. Sound Vibr. 1362 (1988): 323–342

Thompson

D. J.

‘Theoretical modeling of wheel-rail noise generation’

Proc. Ind. Mech. Eng., Part F 205 (1991): 137–149

10.

Dong

R. G.

Sankar

Dukkipati

R. V.

‘A finite element model of railway track and its application to the wheel flat problem’

Proc. Ind. Mech. Eng. 208 (1994): 61–72

11.

Luo

H. Y.

Hua

‘The dynamic response of railway ballast to the action of trains moving at different speeds’

Proc. Ind. Mech. Eng. 210 (1996): 95–101

12.

Knothe

K. L.

Grassie

S. L.

‘Modeling of railway track and vehicle-track interaction at high frequencies’

Veh. Syst. Dyn. 22 (1993): 209–262

13.

Popp

Kruse

Kaiser

‘Vehicle-track dynamics in the mid-frequency range’

Veh. Syst. Dyn. 315-6 (1999): 423–464

14.

Iwnicki

Handbook of railway vehicle dynamics (Boca Raton, FL: CRC Press 2006)

15.

Sato

Matsumoto

Knothe

‘Review on rail corrugation studies’

Wear 2531-2 (2002): 130–139

16.

Grassie

S. L.

Cox

S. J.

‘The dynamic response of railway track with flexible sleepers to high frequency vertical excitation’

Proc. IMechE, Part D: Transport Engineering 198(D7) (1984): 117-124 DOI: 10.1243/PIME_PROC_1984_198_137_02

17.

Dahlberg

Nielsen

J. C. O.

‘Dynamic behavior of free-free and in-situ concrete railway sleepers’

In Proceedings of the International Symposium on Precast Concrete Railway Sleepers, Madrid, Spain, 8–11 April 1991, pp. 393–416.

18.

Zhai

Cai

‘Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track’

Comput. Struct. 635 (1997): 987–997

19.

Shabana

A. A.

Chamorro

Rathod

‘A multibody system approach for finite element modeling of rail flexibility in railroad vehicle applications’

Proc. IMechE, Part K: J Multi-body Dynamics 222 (2008): 1-15 DOI: 10.1243/14644193JMBD117

20.

Dukkipati

R. V.

Amyot

J. R.

Computer-aided simulation in railway dynamics (New York: Mercel-Dekker 1988)

21.

Shabana

A. A.

Zaazaa

K. E.

Sugiyama

Railroad vehicle dynamics: a computational approach (Boca Raton, Florida: Taylor & Francis (CRC) 2008)

22.

Shabana

A. A.

Computational continuum mechanics (Cambridge: Cambridge University Press 2008)

23.

Yakoub

R. Y.

Shabana

A. A.

‘Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications’

ASME J. Mech. Des. 1234 (2001): 614–621

24.

Shabana

A. A.

‘Resonance conditions and deformable body coordinate systems’

J. Sound Vibr. 1921 (1996): 389–398

25.

Shabana

A. A.

Dynamics of multibody systems (Cambridge: Cambridge University Press 2005)

26.

Shabana

‘Automated analysis of constrained inertia- variant flexible systems’

ASME J. Vibr., Acoust., Stress, Reliab. Des. 1074 (1985): 431–440

27.

Mallik

A. K.

Chandra

Singh

A. B.

‘Steady-state response of an elastically supported infinite beam to a moving load’

J. Sound Vibr. 291 (2006): 1148–1169

28.

Dukkipati

R. V.

Dong

‘Idealized steady state interaction between railway vehicle and track’

Proc. IMechE, Part F: J. Rail and Rapid Transit 213(F1) (1999): 15-29 DOI: 10.1243/0954409991530994