Computing and Library Services - delivering an inspiring information environment

On Quasi-Newton Method Applied To 2D Wheel-Rail Contact Models

Pislaru, Crinela and Anyakwo, Arthur (2014) On Quasi-Newton Method Applied To 2D Wheel-Rail Contact Models. International Journal of Engineering Research & Technology, 3 (3). pp. 1962-1971. ISSN 2278-0181

[img] Microsoft Word - Accepted Version
Restricted to Registered users only

Download (1MB)


Reliable and proficient numerical methods are required to determine the contact points between wheel and rail. This paper presents the use of Quasi-Newton method for determining the solution of a reduced number of non-linear wheel-rail contact geometry equations that arise as a result of the interaction of wheel and rail on the track.
A novel two dimensional (2D) wheel-rail contact model is developed by using the wheel-rail contact co-ordinates to calculate the wheel-rail normal contact forces without approximating the contact angle. The simulated results are stored in a lookup table and accessed during the simulation of the bogie dynamic behaviour thus reducing the computational time. The reduced number of non-linear wheel-rail contact geometry equations and employment of Quasi-Newton method enable the proposed 2D wheel-rail contact model to be used for fast and real time simulations of complex and non-linear wheel-rail contact mechanics.

Item Type: Article
Uncontrolled Keywords: wheel-rail interface; lateral displacement; yaw angle; wheel-rail contact model; railway vehicle dynamics; normal forces
Subjects: T Technology > TJ Mechanical engineering and machinery
Schools: School of Computing and Engineering
School of Computing and Engineering > Institute of Railway Research
Related URLs:

[1] P. Kornerup and J.-M. Muller, “Choosing starting values for certain Newton–Raphson iterations,” Theoretical Computer Science, vol. 351, no. 1, pp. 101–110, Feb. 2006.
[2] F. J., Zeleznik, "Quasi-Newton Methods for Nonlinear Equations", Journal of the association for Computing Machinery, Vol. 15, No. 2, pp. 265-271, 1968.
[3] A.H. Wickens, Fundamentals of Rail Vehicle Dynamics, 1st ed. Taylor & Francis, 2007.
[4] H. Sugiyama and Y. Suda, ‘On the Contact Search Algorithms for Wheel/Rail Contact Problems’, Journal of Computational and Nonlinear Dynamics, vol. 4, no. 4, p. 041001, 2009.
[5] A. Anyakwo, C. Pislaru, and A. Ball, ‘A new method for modelling and simulation of the dynamic behaviour of the wheel-rail contact’, International Journal of Automation and Computing, vol. 9, no. 3, pp. 237–247, Jul. 2012.
[6] J. Zeng and P. Wu, ‘Study on the wheel/rail interaction and derailment safety’, Wear, vol. 265, no. 9–10, pp. 1452–1459, Oct. 2008.
[7] S. Iwnicki, ‘Simulation of wheel–rail contact forces’, Fatigue & Fracture of Engineering Materials & Structures, vol. 26, no. 10, pp. 887–900, 2003.
[8] Powell, M. J. D., "A Fortran Subroutine for Solving Systems of Nonlinear Algebraic Equations," Numerical Methods for Nonlinear Algebraic Equations, Ch.7, 1970.
[9] Broyden, C. G., "A Class of Methods for Solving Nonlinear Simultaneous Equations". Mathematics of Computation (American Mathematical Society) 19 (92): 577–593, 1965.
[10] J. Sinclair, ‘Feasibility of reducing the number of standard wheel profile designs’, Railway Safety & Standard Boards, ITLR/T11299/001, Aug. 2002.
[11] BS1, ‘British Standard Specification for Railways’, BS 11:1985, Jul. 2004.
[12] J. Bhaskar, K. L. Johnson, and J. Woodhouse, ‘Wheel-rail dynamics with closely conformal contact Part 2: Forced response, results and conclusions’, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, vol. 211, no. 1, pp. 27–40, Jan. 1997.
[13] Y. Gharaibeh, C. Ennaceur, P. Mudge, and W. Balachandran, ‘Modelling guided waves in complex structures - Part 1: Rail’, presented at the Non-Destructive Testing (NDT) conference, 2009, Blackpool, UK,, Blackpool, UK,.
[14] A. A. Shabana, K. E. Zaazaa, and H. Sugiyama, Railroad Vehicle Dynamics: A Computational Approach. Taylor & Francis, 2007.
[15] S.-Y. Lee and Y.-C. Cheng, ‘A New Dynamic Model of High-Speed Railway Vehicle Moving on Curved Tracks’, Journal of Vibration and Acoustics, vol. 130, no. 1, p. 011009, 2008.
[16] A. Anyakwo, C. Pislaru, A. Ball, and F. Gu, ‘Modelling and simulation of dynamic wheel-rail interaction using a roller rig’, Journal of Physics: Conference Series, vol. 364, p. 012060, May 2012.
[17] M. S. Engelman, G. Strang and K.-J. Bathe, "The application of quasi Newton methods in fluid mechanics, International Journal for Numerical Methods in Engineering Volume 17, Issue 5, May 1981, Pages: 707–718.
[18] Rosen, E. M., A review of quasi-Newton methods in nonlinear equation solving and unconstrained optimization. Proc, 21st Nat. Conference of the ACM. Thompson Book Co., Washington, D. C. 1966, pp. 37-41.

Depositing User: Crinela Pislaru
Date Deposited: 03 Apr 2014 15:46
Last Modified: 03 Apr 2014 15:51


Downloads per month over past year

Repository Staff Only: item control page

View Item View Item

University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©