Abstract. 1 Introduction

Transcription

1 Simulation of severe wheel-rail wear Zi-Li Li & Joost J. Kalker Delft University of Technology Subfaculty of Technical Mathematics and Informatics Faculty ofinformation Technology and Systems MeWweg 4 262(9 CD D(# The Netherlands Z.L Li@math.tidelft.nl J.J. Kalker@math.tudelft.nl Abstract Wear is inherent to wheel-rail system. Severe wear is a problem for heavy haul railways. Based on experimental results, knowledge in vehicle-track system dynamics and advances in rolling contact mechanics, computer aided wheel-rail wear simulation is possible. It provides a fast and cheap means for prediction of wear life, optimal profile design and more realistic vehicle-track dynamical analysis. In this paper, a method for the simulation of severe wheel-rail wear by non-hertz contact is presented, it is fast and robust. Combining it with vehicle dynamical simulation is desired. 1 Introduction Rail systems exploit friction to transmit power, therefore wear is inevitable. Severe wear has long been a problem, particularly in curves, the wheel flange and rail gauge face are subject to intensive wear. It causes early reprofiling of wheels, prematured rail replacement, increases vehicle-track dynamical interaction, worsens vehicle performance, causes rolling contact noise, fastens track deterioration,

2 394 Computers in Railways increases operation and maintenance costs. With the development of heavy haul railways, those problems are attracting attention from many researchers. Over the years, wheel-rail wear has been extensively studied experimentally [1,2]. Some of them were laboratory tests, full-scale rigs and simpler Amsler machines were employed, they have the control of the experimental variables, the ability to test a wide range of materials and lower costs. Some were field research, they are expensive and difficult to control, but realistic. From the experimentally accumulated knowledge, it is established that wheel-rail wear is mainly related to vehicle-track dynamical behaviour, wheel-rail contact mechanics, and the materials. A number of wear models have been proposed[1,3], which make digital simulation possible. Computer aided wheel-rail wear simulation has been carried out by many authors [4,5,6]. They mainly fall into two classes. The first class concentrates on vehicle dynamics, with the operation conditions probably included, while contact mechanics is much simplified and may rely on parameter identification on the basis of field tests[5,6]. The second class pay more attention on contact mechanics, while the vehicle-track dynamics as well as operation conditions are treated with some neglection[4]. This state is because that both the solution of large number of contact problems for wear and the vehicle-track dynamical simulation require large amount of computing time. Even in the second class, only Hertz contact was employed. Although non-hertz contact is common in reality, it was not employed because of its long computing time and unknown contact area: for Hertz contact the shape and size of the contact area are analytically available and the normal pressure is easily known, which makes the trend of tangential solution predictable and the discretization easy. The use of Hertz contact can cause a number of problems. First, to solve a Hertz problem, the radii of curvature of the bodies must be known. In wear simulation, the wheel and rail profiles are changing. To obtain a reasonably accurate estimation of the radii by curve fitting, the wear step must be very small[4], the actual overall simulation speed is therefore greatly reduced. Secondly, multiple point contact can not be included. Though in a multiple point contact a sub- contact area may look like a Hertz contact, the overall behaviour is strongly non-hertz. Thirdly, severe wear can not be simulated. The

3 Computers in Railways 395 contact between severely worn wheel and rail is usually non-hertz. In the flange and gage face area, conformal contact may occur. Spin due to the strongly warped geometry is large, which causes severe abrasive wear, conformal contact should be employed. In the present work, the most comprehensive wear model by now established, the frictional work model, is employed. Non-Hertz solution is used for the the frictional work. To speed up the calculation, the procedure proposed in [10] is incorporated. 2 Wear Model There are by mechanism four main types of wear[7], namely abrasive, adhesive, corrosive wear and surface fatigue wear. Corrosive wear rate is very low under normal environmental conditions. It is established [1,3,7] that the amount of material worn away by adhesive wear, abrasive wear, and by surface delamination fatigue wear are proportional to the tangential force, to the sliding distance, and inversely proportional to the hardness. Therefore, we may express wheel-rail wear irrespective of its nature in the following way: V = k,^ = kw (1) rt where V is the volume of material worn away, k\ is a coefficient, d is the distance slided over, T is the frictional force, H is the hardness of the material, k = ki /H is the wear coefficient, W = F d is the frictional work. This is the most comprehensive model by now used in wheel-rail wear simulation concerning most of the contact mechanics variables. k depends on the materials of the wheel and rail, their hardness and relative hardness, lubrication and the properties of the lubricants, the pressure and traction in the contact, and the magnitude of slip, etc. It may be different at different part on the same wheel and rail, and can be decided by laboratory tests simulating the loading conditionsfl], or can be identified from data collected from field experiments or field survey[4]. In rolling contact area, some of the contact area is in slip and some in adhesion. The contact area is discretized into equal boundary elements with area da, tangential traction p^., relative slip velocity s. The the friction power in the element is

4 396 Computers in Railways Replace s in (2) with w s/v, V is the rolling velocity, and divide it with the modulus of rigidity G and da, the following dimensionless frictional power density is defined: P = «(3) It can be computed from contact mechanics, the influence of load, geometry, coefficient of friction, creepage and spin are all included. 3 Contact Mechanics An exact non-hertz solution of rolling contact is em ployed [8,9,10]. The problem is formulated in the maximisation of complementary energy, and discretized in the potential contact area. A special boundary element method making use of Green's influence function is employed[10]. For concentrated contact, half-space approximation is used, and for conformal contact, finite element solution is sought for the influence number [9]. Multiple point contact is very important in the transition from tread contact to flange contact. The usual way by searching for the minimum wheel-rail distance can only find explicit multiple point contactflo] from their rigid body geometry, and requires very intensive search. In [10] a method is presented which can also find the implicit multiple point contact due to elastic deformation, and it is incorporated in the non-hertz solution method. Solution of rolling contact is time consuming, especially for non- Hertz contact because its boundary is not known a priori. The situation is even worse when spin is large or when it is conformal contact, which are the cases with severe wheel-rail wear involving flange-gage face contact. Much effort is made to speed up the solution by using various numerical techniques, making good initial estimation and reducing the number of elements while maintaining the required accuracy. For successful continuous simulation, robustness is also vital. It is achieved by perturbation and by turning to the robust but slower contact solution method whenever the fast one diverges. The results shown infig.land 2 are computed from the Chinese TB wheel and TB 50 kg/m rail, the modulus of rigidity is 0.8 X 10*1 Fa, the Poisson ratio is 0.28, the normal wheel load is 10^ N. Fig.l shows a two point contact between the wheel and rail. It can

5 Computers in Railways 397 be seen that the contact area on the flange is very slender, while its frictional power density is far greater than that on the tread, this can explain the cutting effect of two point contact for wheel-rail wear. In fig.2, the contact is on the flange of the new profile. The contact area is non-hertz, and the frictional power density is very high due to the large geometrical spin. It should be noticed that in fig.2 the contact area is also very slender in rolling direction though it does not look so from the appearance in the figure. 4 The Simulation Process The flow chart of the simulation is shown in fig. 3. The given starting profiles can be new, worn, analytically expressed or discrete measured data. They can be different for the left and right wheels and rails. The search for the initial contact point(s) is carried out three-dimensionally, the inputed independent variables are the lateral displacement and yaw angle of the wheelset, roll of the wheelset is taken into account, perturbation due to track irregularities can be included. The lateral displacement and yaw angle, the creepages and loads should come from vehicle-track dynamics analysis simulating the operational conditions. The frictional work done at a contact point is proportional both to the frictional power density and the number of contacts taking place at this point. The later is decided by the contact distribution which should also come from vehicle dynamics. 5 Some Results In fig. 4 some simulated results are shown. The original profiles, the normal wheel load and the elastic constants are the same as for fig.l and 2. The longitudinal creepage is , lateral creepage 0.0, and spin due to geometry only, the rail profile is fixed. A constant k is chosen such that in a wear step, a maximum depth of 0.1 mm material is worn. In obtaining the results in fig 4(a), a maximum of 78* on the flange is used as the termination criterion. It can be seen that with yaw angle equal to 0.3*, the wheel is worn fast on the flange. In figure 4(b), the same number of wear step is taken for the two worn profiles. It shows that on the profile with the larger rail bottom cant more is worn on the tread.

6 398 Computers in Railways the element divisions rolling direction = 0 deg. to positive x-axis double line around adhesion, single line around contact area (a) f riclional power density y-axis rolling direction = 0 deg. to positive x-axis (b) Figure 1: (a) Contact area division. Double line around adhesion area, single line around slip area, coordinate units in meter; (b) Frictional power density, the vertical coordinate is demensionless, the other coordinate units in meter. Wheelset lateral displacement y 6.9 mm, longitudinal creepage is

7 the element divisions Computers in Railways rolling direction = 0 deg. to positive x-axle frictional power density y-axis rolling direction = 0 deg. to positive x-axi (b) Figure 2: (a) Contact area division. Double line around adhesion area, single line around slip area, coordinate units in meter; (b) Frictional power density, the vertical coordinate is dimensionless, the other coordinate units in meter. Wheelset lateral displacement y 11 mm, geometrical spin only

8 400 Computers in Railways Figure 3: The simulation flow chart Obviously the dynamical behaviour of the vehicle has strong influence on wheel-rail wear. Without consideration of it, the wear simulation is not realistic. On the other hand, vehicles are running on more or less worn wheels and rails. It is well known that the wheel and rail profiles have very important effect on the vehicle dynamical behaviour and on the vehicle-track interaction. Hence including the change of wheel and rail profiles due to wear in the vehicle-track system dynamical analysis is desired. In view of the fact that severely worn wheel and rail may cause derailment and rail fracture, this seems very important. Combining wear and vehicle dynamical analysis in one simulation is under way. 6 Conclusion Severe wheel-rail wear is a problem, especially in curves of heavy haul railways. Simulation of severe wear should be carried out using non-hertz contact. The proposed method is fast and robust, it is accurate and realistic in the sense of contact mechanics. Combining it with vehicle-track system dynamical analysis is desired. The wear coefficient can be obtained from laboratory experiment or from

9 Computers in Railways (a) (b) Figure 4: Simulated worn wheel profile. The coordinate is the position of the profile in the wheelset in mm. (a) The rail bottom cant is 0.025, the yaw angle is 0.0 for the solid lower line, and 0.3 degree for the dashed line. The upper line is the original profile; (b) The rail bottom cant is 0.05 for the dashed line, and for the solid lower line. The upper line is the original profile

10 402 Computers in Railways identification of field collected data. References [1] P. Clayton, Tribological aspects of wheel-rail contact: a review of recent experimental research, wear, 191 (1996) [2] S. Zakharov, I. Komarovsky, I. Zharov, Wheel flange/rail head wear simulation, wear, 219 (1998) [3] R.H. Fries and C.G. Davila, Analytical Methods for Wheel and Rail Wear Prediction, Proc. of 10th IAVSD Symposium, pp [4] J.J. Kalker, Simulation of the development of a railway wheel profile through wear, MFeor, 150 (1991) [5] T.G. Pearce and N.D. Sherratt, Prediction of Wheel Profile Wear, Wear, 144 (1991) pp [6] I. Zobory, Prediction of Wheel/Rail Profile Wear, Vehicle System zca, 28 (1997), pp [7] E. Rabinowicz, Friction and Wear of Materials, John Wiley and Sons, New York, (1965) [8] J.J. Kalker, Three Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Dordrect, 1990 [9] Z.L. Li and J.J. Kalker, The Computation of Wheel-Rail Conformal Contact, Proc. of the 4th World Congress on Computational Mechanics, 29 June - 2 July, 1998, Buenos Aires, Argentina (to be published) [10] Z.L. Li and J.J. Kalker, Adaptive Solution of Rolling Contact Using Boundary Element Method, submitted for the 20th World Conference on the Boundary Element Method, August 1998, Orlando, Florida, USA