Calculation of wear on a corrugated rail using a three-dimensional contact model
Introduction
Rail corrugation and roughness have long been concerns in the railway industry. Rail roughness consists of broad band irregularities covering wavelengths from 10 to 500 mm on the railhead while corrugation is a quasi-periodic irregularity. Six types of corrugation have been classified by Grassie and Kalousek [2], according to different wavelength-fixing and damage mechanisms but, although much research work has been carried out, there is still inadequate knowledge of how roughness develops over time and why corrugation appears on some types of trackform in some place and not in others. Rail grinding is widely used to treat rail corrugation and roughness.
A large number of parameters influence the dynamic system of train/track interaction and thus influence the wear of the wheel and rail. The main factors are: contact geometry; normal force; traction (or creepage) and coefficient of friction. It is therefore desirable to perform wear calculations with a contact model that includes all these factors and to determine the relevance of each factor. In this paper, the wheel/rail contact is modelled in three-dimensions based on the variational method by Kalker [1]. Sinusoidal corrugations on the railhead are considered for different wavelengths and amplitudes and the normal and tangential problems are solved in a transient way using a time-stepping integration technique, taking account of non-Hertzian normal contact and non-steady tangential contact. The wear in the contact patch is calculated based on the friction work and a constant normal force and creepage are initially used to investigate any possible wavelength-fixing mechanism. A range of prescribed dynamic forces are then used to investigate the relationship between wear and force and a comparison is also carried out between Hertzian and non-Hertizan contact modelling.
Section snippets
Background
Most research work has been focused on short-pitch corrugation [3], [4], [5], [6]. The most common wavelengths of short-pitch corrugation are in the range of 20–100 mm. The main damage mechanism according to Grassie [2] for this type corrugation is wear of troughs mainly from longitudinal slip. Although different wear mechanisms exist, abrasive wear is the only mechanism accounted for and material loss due to this type of wear is assumed to be proportional to the friction work. To investigate
Wheel/rail system
Consider a free wheel rolling over a corrugated rail, as shown in Fig. 1. A global coordinate system is defined to have an x-axis corresponding to the rolling direction and y-axis corresponding to the lateral direction and a local coordinate system which moves as the wheel centre moves along the rail is defined for the potential contact area. Parameters for the wheel/rail system are given in Table 1. For a nominal load of 70 kN, the wheel/rail geometry gives an elliptical contact patch having a
Wear calculation using a constant normal force
Wear after one wheel passage was first calculated for sinusoidal roughness of wavelengths λ = 25, 30, 40, 60, 80 and 100 mm. These cover the range of typical short-pitch corrugation wavelengths. A corrugation amplitude of 10 μm was chosen to be sufficiently small to avoid the loss of the contact in the corrugation trough. Nielsen [16] gives a two-dimensional plot for characteristic wavelengths for which the corrugation is most likely to develop. It was shown that, for a given creepage, only
Wear calculation using prescribed dynamic normal forces
The wear calculation using a constant normal force in Section 4 does not reveal any mechanism for corrugation growth so in this section a dynamic normal force will be considered. A dynamic normal force is normally obtained from a vehicle/track interaction model and various such models have been developed, either in the time domain or the frequency domain. For a sinusoidal roughness, the dynamic normal force obtained from an interaction model is normally close to sinusoidal, but with certain
Conclusions
The contact problem of a wheel rolling over a rough rail has been modelled in three-dimensions using the variational method. The rolling process has been treated as transient and the wear calculated for various sinusoidal roughnesses. The contact geometry due to the roughness has significant influences on solutions of the normal and tangential wheel/rail contact. For the case where a constant normal force and creepage are present, it has been demonstrated that the maximum wear occurs near the
Acknowledgement
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) through Rail Research UK (RRUK).
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