BMe Research Grant


Zwierczyk Péter Tamás

email address



BMe Research Grant - 2015

IIIrd Prize


Géza Pattantyús-Ábrahám Doctoral School of Mechanical Engineering 

BME Faculty of Mechanical Engineering, Department of Machine and Product Design

Supervisor: Dr. Váradi Károly

Thermal and Stress Analysis of a Railway Wheel-Rail Connection in Rolling-Sliding Motion 

Introduction of the research area

In the course of the intensive braking process of railway vehicles equipped with disk brakes, as a result of the inappropriate conditions of adhesion, the tread of the wheel can slide considerably on the rail. Because of the sliding, considerable heat is generated in the area of the contact. Although the wheel slide is restricted by the Wheel Slide Protection System (WSP), a 10–20% slip still remains between the rail and the wheel under braking. The thermal stresses generated by the considerable heat may lead to the occurrence of micro cracks on the surface of the railway tread as shown in Figure 1.



Figure 1. Micro cracks on the surface of the railway wheel tread, caused by heat development [1,2]

Hence the finite element analyses provide opportunity to analyse the background of the crack development procedure in the vicinity of the contact zone.  

Brief introduction of the research place

I have completed my research work at the BME Faculty of Mechanical Engineering in the Department of Product and Machine Design. This department is one of the biggest departments in the University. It has an outstanding share in the education of the BSc. and MSc. mechanical engineer students. Besides many domestic and international industrial partners, it established good relationships with the Knorr-Bremse Vasúti Járműrendszerek Hungária Kft., which allows me to work together with industrial railway professionals.

History and context of the research

When vehicles equipped with disc brake systems come to general use the surface crack problem outcrops to the surface. In case of the vehicles equipped with block brake systems, however, the value of the slip between the block and the wheel tread is bigger than that between the rail and the wheel because of the bigger size of the contact area. Consequently, heat is distributed to an extended area, which results in lower temperature on the surfaces.

With the help of numerical methods and measurements, researchers can analyse both the material phase transformation on the wheel tread, and the impact of the thermal stresses caused by the heat development on the surface of the wheel tread and the rail [3-7]. Phase transformation, which results in rigid tread surface takes place only at very high temperatures (~700-1000°C), and only in a special cooling procedure which is caused under high slip ranges. Modern railway vehicles – cars alike – are equipped with anti-block brake systems. These systems – through the brake pressure – restrict the value of sliding (~10-20%) which results in lower heat development. Nevertheless, lower temperatures can lead to residual strain which assists to the appearance or the growth of micro cracks.

Research goals, questions to answer

I have done my researches and written my dissertation with the contribution of the professionals of the Knorr-Bremse Vasúti Járműrendszerek Hungária Kft. The main goal of my work was to create a numerical analysis method to help calibrate the WSP systems which are in the design phase and which are already installed, to avoid overheating during intensive braking, restricting the value of the slip without the outstanding growth of the braking distance.

To examine this, my goal is to analyse the temperature and the thermal stress distribution in the vicinity of the contact zone. With the help of these results I can show that below temperatures needed for phase transformation, the wheel tread suffers residual strain which helps the occurrence of cracks [Z1] in case of one or more revolutions of the wheel. After the analysis of the former results I would like to make a suggestion for an optimal allowable slip rate during intensive braking which avoids damages to the surface of the wheel.


In the literature I have found several methods to examine the crack development on the wheel and on the rail. The analyses can be divided into two main groups. The first one is the experimental measurements [2], the other ones are the finite element analyses [4,6,7]. From the first group, empirical and comparative results can be obtained, while the results of the second group – due to the complexity of the problem – contains too many neglects. Therefore, a 3D FE model group (Figure 2) had be worked out which divided the complex problem into predefined phases with acceptable neglects. As a first step of my analyses, I have created a contact analysis to determine the exact size and shape of the contact zone [Z2-Z6].

As a second step of my analyses, with simplified shape, a segmented wheel model was created, which was subjected to a coupled transient thermal-elastic-plastic FE analysis. To improve the accuracy of the result, temperature dependent thermal and mechanical material properties were applied. The originally elliptical contact shape was considered to be rectangular for simpler FE discretization. This helped me define the loading condition as a moving heat source. The heat source was stepped with a pace of 1 mm according to the speed of the wheel [Z1]. The heat source was modelled as a heat flux and was previously calculated in an analytical way as a product of the wheel load, the sliding speed, the coefficient of friction and the heat partition (wheel slide). Initially, the heat partition was taken as 0.5, i.e. half of the generated heat was supposed to go into the wheel. These neglects only caused acceptable differences in case of the results [Z7].



Figure 2 The structure of the segmented FE computation method

The constructed model provides an opportunity to examine the temperature and thermal stress distributions, on and under the surface of the tread, in case of more than one revolutions of the wheel [Z8],[Z9].



The results of the analyses prove that, in rolling-sliding motion, the temperature in the contact zone rises like flash (Figure 3). The analysis was also performed for 5 continuous revolutions where the growing trend of the peak temperature could be clearly seen [Z7]. Besides the temperature distribution, the stress distribution of the lower layers under the tread surface was also investigated (Figure 4). The results pointed out that directly before and after the heat source a significant pressure stress occurs (exceeding the Yield strength of the wheel material causing residual strain). When the heat source leaves the examined surface point far beyond, the initial pressure stress transformed into tensile stress. This kind of stress state facilitates crack development. Comparison of the results of contact analysis showed that the stress coming from the sliding and from the contact distinctly separated from each other. In the first case, the thermal stresses expand our effect in the 0.2–0.5 mm deep layers [Z1,Z8,Z10], but the stresses coming from the contact causes problems in the deeper lying layers (2–4 mm) [Z9,Z11-Z12].



Figure 3 Temperature distribution in and in the vicinity of the contact zone
on the FE model of the rail, under the first passage


Figure 4 Tangential stress distribution on and under the wheel tread
(deformation scale 6000:1). The depth marked with Sd is 4 mm.
The q is the actual position of the heat source (heat flow).

Expected impacts and further research

The model I created can be used to analyse the thermal and stress state of the railway wheel-rail rolling-sliding connection. It provides an opportunity to map the thermal phenomenon during a complete intensive braking process, which occurs on and under the tread and may cause micro cracks. The results can be used to calibrate the railway WSP systems to avoid the damage of the wheel under intensive low adhesion braking.

Taking into consideration the foregoing research results, I have been searching the optimal sliding range for an average railway carriage, i.e. when the damage to the wheel and rail tread can be avoided via minimum increase in the braking distance. My further task is a more precise understanding of the mechanisms of remaining strain and stress.

Own publications, references, links

Own publications

[Z1] Zwierczyk P. T., Váradi K.: “Thermal Stress Analysis of a Railway Wheel in Sliding-Rolling      Motion” Journal of. Tribology, vol. 136, no. 3, pp. 031401–031401, 2014.

[Z2] Zwierczyk P. T., Váradi K.: “Frictional contact FE analysis in a railway wheel-rail contact” Periodica Polytechnica Mechanical Engineering, vol. 58, no. 2, pp. 93–99, 2014.

[Z3] Zwierczyk P. T., Váradi K.: “Vasúti kerékabroncs-sín kapcsolat súrlódási állapotának vizsgálata VEM analízissel” (in Hungarian), OGÉT 2012, XX. Nemzetközi Gépészeti Találkozó, Cluj Napoca, Romania, 2012.04.19-22. pp. 518-521.

[Z4] Zwierczyk P. T., Váradi K., Oroszváry L.: “Finite Element Analysis of the Friction State for Wheel-Rail Connection”, Proceedings of the PhD Conferences organised by the Doctoral Schools of the BME, in the framework of TÁMOP-4.2.2/B-10/1-2010-0009, Budapest, Hungary, pp. 56-63, 2012.

[Z5] Zwierczyk P. T., Váradi K., Oroszváry L.: "Finite Element Analysis of the Friction State for Wheel-Rail Connection”, Gépészet 2012: proceedings of the Eight International Conference on Mechanical Engineering, Budapest, Hungary, 2012.05.24-25 pp. 604-611.

[Z6] Zwierczyk P. T., Váradi K.: “Vasúti sín-kerékabroncs kapcsolat súrlódási állapotának végeselemes vizsgálata” (in Hungarian), GÉP LXIII:(12): pp. 159-162, 2012.

[Z7] Zwierczyk P. T., Váradi K.: “Thermal Analysis of a Railway Wheel-Rail Connection in Sliding/Rolling Motion” The Tenth International Symposium on Tools and Methods of Competitive Engineering (TMCE 2014), Budapest, Hungary, 2014.05.19-23., Proceedings of TMCE 2014, pp. 1405–1412.

[Z8] Zwierczyk P. T., Váradi K.: “Thermal and Stress Analysis of a Railway Wheel-Rail Connection in Disc Braking - Part 1: Temperature and Thermal Stress Development”, manuscript, under submission - 2015.

[Z9] Zwierczyk P. T., Váradi K.: “Thermal and Stress Analysis of a Railway Wheel-Rail Connection in Disc Braking - Part 2: Coupled Analysis of Macroscopic Sliding and Contact”, manuscript, under submission - 2015.

[Z10] Zwierczyk P. T., Váradi K.: “Vasúti kerékabroncs végeselemes hőtani és feszültségi vizsgálata” (in Hungarian), OGÉT 2014: XXII. Nemzetközi Gépészeti Találkozó - OGÉT 2014, Sibiu, Romania, 2014.04.24-27. pp. 438-441.

[Z11] Zwierczyk P. T., Váradi K.: “Thermal and contact FE analysis of a railway wheel in sliding-rolling motion”, 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014.07.20-25, pp. 1-2.

[Z12] Zwierczyk P. T., Váradi K.: “Coupled thermal elastic-plastic analysis of a railway wheel under intensive braking process”, European Mechanics of Materials Conference (EMMC14), Gothenburg, Sweden, 2014.08.27-08.29, p. 1.



WSP - Wheel Slide Protection System

Disc Braking  - overview



[1] Handa K., Morimoto F.: “Influence of wheel/rail tangential traction force on thermal cracking of railway wheels” Wear, vol. 289, pp. 112–118, 2012.

[2] Handa K., Kimura Y., Mishima Y.: “Surface cracks initiation on carbon steel railway wheels under concurrent load of continuous rolling contact and cyclic frictional heat” Wear, vol. 268, no. 1–2, pp. 50–58, 2010.

[3] Sábitz L., Kolonits F.: “Finite element and analytical computation of flash temperature” Periodica Polytechnica Civil Engineering, vol. 58, no. 3, pp. 267–278, 2014.

[4] Wu L., Wen Z., Li W., Jin X.: “Thermo-elastic–plastic finite element analysis of wheel/rail sliding contact”, Wear, vol. 271, no. 1–2, pp. 437–443, 2011.

[5] Fischer F. D., Werner E., Yan W.-Y.: “Thermal stresses for frictional contact in wheel-rail systems”, Wear, vol. 211, no. 2, pp. 156–163, 1997.

[6] Peng D., Jones R., Constable T.: “A study into crack growth in a railway wheel under thermal stop brake loading spectrum”, Engineering. Failure Analysis, vol. 25, pp. 280–290, 2012.

[7] Peng D., Jones R., Constable T.: “An investigation of the influence of rail chill on crack growth in a railway wheel due to braking loads” Engineering Fracture Mechanics, vol. 98, pp. 1– 14, 2013.

[8] Tian X., Francis E. Kennedy J:, “Maximum and Average Flash Temperatures in Sliding Contacts” Journal of Tribology, vol. 116, no. 1, pp. 167–174, 1994.