Abstract
This paper deals with the thermo-elastic processes occurring in railway wheels. The block braking is based on the frictional dissipation of kinetic energy stored in the moving vehicle. The dissipated heat energy flows partially into the wheel, and into the brake blocks, respectively. The heat energy input causes an inhomogeneous thermal process in the wheel. This leads to intensively varying tangential stresses along the whole wheel periphery, which may initiate and amplify radial cracks originated on the wheel tread. Another important thermal load of the wheel is composed by the highly concentrated thermal shocks arising from the micro- and macro-sliding contact of wheel and rail. Such effects, paired with rapid cooling of the heat affected zone, may lead to martensitic transformations in small patches on the wheel running surface. The appearance of hard martensified spots can often cause crack initiations. The finite element studies introduced in this paper were performed in order to numerically investigate the thermal and stress processes variating with time and their spatial distribution in the wheel during realistic block brake operation conditions.
Introduction
Block brake systems have been used in the railway industry for centuries. When a brake block is pressed against a rotating wheel periphery, the generated frictional heat affects the thermal and stress conditions over the whole circumference of the wheel.
Occassionally, railway wheels are also loaded by the frictional heat arising from the sliding of the wheel on the rail. This thermal load is highly concentrated to the vicinity of the wheel/rail contact patch, but – due to its capability of martensite forming – this ’thermal shock’ is of great importance when investigating the thermal fatigue of the wheel material [13]. Local thermal and wear effects, surface roughness and thermo-elastic instability increase the complexity of the phenomena, but are beyond the scope of this paper.
1. Scientific antecedents
Subsequent brake applications cause heat treatment of the wheel material, which leads to a refined micro-structure in the precincts of the tread. Martensified regions (Fig. 1) as well as cracks initiated from such regions (Fig. 2) were reported by several microscopic studies of damaged wheels ([2], [4]). A typical broken wheel is shown in Fig. 3: radial crack propagation was experienced in the wheel row, tangential one in the wheel disc.
Fig. 1: Martensified texture (N=1000x) (Fig. from [4])
Fig. 2: Cracks and re-crystalli-zations (N=16x) (Fig. from [2])
Fig. 3: Cracked mono-block wheel Investigations performed by Zobory et al. ([3]-[5], [11]) concluded that besides the brakes, the anti-slip device might also be responsible for the wheel damages mentioned above.
Vernersson [6] performed several measurements and FE simulations to observe the primary mechanisms of thermo-elastic instability, heat partitioning and the rail chill effect.
Harder, Kennedy et al. (refs. [7]-[9]) demonstrated that martensite formation in tread-braked wheels occur mainly because of wheel sliding on the rail. It was shown that the conditions for martensite generation might be satisfied in the wheel material for a depth of ca. 0.5-0.6 mm under the running surface. Similar results were found by Su et al. [10].
2. FE analyses and results
2.1. Thermo-elastic processes due to tread braking
For the sake of the quantitative description of the tread braking-induced temperature and stress distributions in a mono-block railway wheel, a 3D finite element model was constructed. The heat flux entering the wheel was supposed to be uniformly distributed around the wheel circumference. The simulation process contained a full passenger train route with length of 188 km. The details of the model and its results are given in [11].
The simulation insisted that the wheel tread temperature did not exceed 300 °C [11].
Considering the approximations mentioned above, local effects might increase the simulated peak temperatures by 30-50%. These results explain the texture refinement in the wheel row, but the austenitizing limit of the wheel steel (723 °C) is far from reached.
During braking, the frictional heat entering the wheel generates very high gradients inside the wheel row. This leads to the restricted dilatation of a thin layer in the vicinity of the wheel tread (Fig. 4). The result: excessive tangential (compressive) stresses. Von Mises equivalent stress has also high magnitudes at this location, as it is shown in Fig. 5. In the middle of the wheel disc, radial stress components are dominant. The wheel/rail contact has a concentrated effect on the Von Mises stress
Fig. 4: Momentary component was evaluated for a chosen point on the wheel tread. The high wheel/rail contact pressure proved to have significant effect also on the tangential stress, causing high amplitude cycles in every wheel rotation. A detailed evaluation of the stress
Tangential stress collective on the tread of the monoblock wheel
Frequency
Fig. 7: Tangential stress collective for passenger train operation with several stop brakings
The stress cycles for the peripheral points in question were obtained by determining the stress amplitudes and mean values. A 3D frequency diagram of the tangential stress collective is illustrated in Fig. 7. The group of high amplitude cycles (right side of Fig. 7) – the ones caused by wheel/rail contact stresses – can be considered as the main reason of radial crack propagation in the wheel row. With the knowledge of the S-N curve of the wheel steel, this load collective gives a basis for fatigue life computations.
2.2 Thermo-elastic processes due to wheel/rail contact
duration of 0.06 s. As a result, a spherical temperature field (see Fig. 8) evolved in the wheel. Analytical computations based on the formulae derived in [1] were used to evaluate the FE results.
Fig. 8: Temperature distribution in the wheel rim
Knowing that the effective part of the thermal process is very short in time, and it is concentrated to a small region, a local FE model was constructed (Fig. 9). The higher mesh density resulted in an increased accuracy of the simulated temperature data. It can be seen in Fig. 10 that the temperature of the centre-point of the contact area matched the analytical results well until 0.2 s, so the essential part of the phenomenon was captured by the model.
Fig. 10: Local FE model with high mesh density vs. analytical solution
The qualitative study pointed out an intensive heating-cooling cycle in the wheel/rail contact surface. The quick cooling is caused by the heat conduction towards the depth of the solid, but a possible stop on a cold part of the rail could further accelerate the quenching. A quantitative investigation with realistic amount of thermal power seems to be necessary for demonstrating the exact way of martensite generation on the wheel tread.
3. Conclusions drawn from the simulations
of the tread surface. The heat flow density is not sufficient to meet the conditions necessary for martensite formation on the tread.
• The simulations pointed out that thermally generated tangential mean stresses in the wheel – superimposed by wheel/rail contact stress amplitudes – may lead to plastic deformations, residual stresses and radial crack propagation in the wheel row.
• The vertical load transmitted through the wheel/rail contact surface plays a decisive role in wheel fatigue through radial cracks.
• Fatigue life computations for the mono-block wheels in question would be possible based on load collectives similar to the one illustrated in Fig. 7. Such computations require the reliable knowledge of the S-N curves of the wheel steel, determined by laboratory fatigue tests.
• The complete macro-sliding appearing on the wheel/rail contact patch can be considered as the effect of a ‘fifth brake block’ contributing to the increase of local temperature on the wheel tread, that may easily exceed the austenitizing limit. In addition, the always present lateral motion of the railway wheel-set can cause such wheel/rail contact conditions, that the overheated tread domains (strip) come into direct contact with the cool rail surface, which can contribute to the martensite formation through the intensive falling in temperature.
References
[1] Carslaw, H.S. - Jaeger, J.C.: Conduction of heat in solids (2nd ed.), Oxford, at the Clarendon Press, 1959.
[2] Rózsavölgyi, Zs. - Majoros A.: The role of material testing in investigating operational loads and root causes of wheel-tread failures, Poster for BOGIE’10, Budapest, 13-16 September, 2010
[3] Zobory, I. (Pr.M.).: Coupled investigation into the thermal and wear state of railway wheel tyres II. Research Report, Budapest University of Technology and Economics, Department of Railway Vehicles and Vehicle System Analysis, Budapest, 2009. (In Hungarian)
[4] Zobory, I. (Pr.M.).: Cause recovering investigation into the crack damage of the block-type wheel of the german carriages. Research Report, BUTE, DRVVSA, Budapest, 2009. (In Hungarian)
[5] Zobory, I. - Sábitz, L. - Kolonits, F. - Békefi, E.: Quantitative investigation into the thermal and stress processes evolving in the mono-block wheel during the brake operation process of the german railway carriages of MÁV. Research Report, BUTE, DRVVSA, Budapest, 2010. (In Hungarian)
[6] Vernersson, T.: Tread Braking of Railway Wheels – Noise-Related Tread Roughness and Dimensioning Wheel Temperatures (Field Tests, Rig Measurements and Numerical Simulations, thesis for the degree of Doctor of Philosophy, Chalmers University of Technology, Department of Applied Mechanics, Division of Dynamics, 2006, Göteborg, Sweden
[7] Kennedy, T. C. - Gonzales, S. - Harder, R. F.: Finite element analysis of martensite formation in railcar wheels during Hertzian sliding conditions, Proceedings of BOGIE’04, Budapest, 2004, p165-173.
[8] Kennedy, T. C. - Plengsaard, C. - Harder, R. F.: Transient heat partition factor for a sliding railcar wheel, Wear 261 (2006) p932–936
[9] Harder, R. F. - Kennedy, T. C.: Thermal modeling of railcar wheel braking, Proceedings of BOGIE’10, Budapest, 2010, p89-101
[10] Su, H. - Pan, T. - Li, L. - Yang, C. - Cui, Y. - Ji, H.: Frictional heat-induced phase transformation on train wheel surface, Journal of Iron and Steel Research 15(5), 2008, p49-55
[11] Sábitz, L. – Zobory, I.: Finite element modelling of the thermoelastic processes in tread-braked wheels, Proceedings of BOGIE’10, Budapest, 2010, p103-113
Acknowledgement
The work reported in the paper has been developed in the framework of the project
„Talent care and cultivation in the scientific workshops of BME" project. This project