Estimating the damage of railway carriage wheels equipped with disc brakes

The aim of this paper is to estimate the damage of railway carriage wheels caused by lock-up braking. First, we investigate the typical characteristics of wheel-rail contact including the parameters of contact patch, longitudinal creep and coefficient of adhesion. Then we show the current requirements concerning the wheel-slide protection systems and determine the points which should be reviewed. To predict the effect of the sliding phenomenon, material properties are needed, as well. Afterwards, a simplified thermal simulation is built to estimate where martensite formation may occur.


Introduction
Railway is one of the most used transportation facilities nowadays. Like other fields, trains are getting faster and faster every day, as well. The increased speed results in a higher demand on the requirements of the wheel-slide protection system. However, phenomenon of sliding is still difficult to eliminate. Especially when braking is too intense, and the coefficient of adhesion is low, lock-up of the wheels may occur. This means that the wheels have a sliding velocity of v but no angular velocity. As the wheel is sliding on the rail, a significant heat is being generated between the contacting bodies that results in high temperatures on the surface and near the contact patch. This may even cause changes in the microstructure of the wheel material and bring about the formation of a brittle and hard martensite layer. Thus, cracking and spalling may appear on the tread, so leading to wheel damage in the long run [1]. A simplified thermal model was used to estimate where phase changes were expected in case of lock-up braking. To predict the consequences of this type of sliding, a research was required on wheel-rail contact, wheel-slide protection system and wheel material.

Wheel-rail contact
In fact, both contacting bodies undergo elastic deformation due to the axle load. If we assume the validity of Hertzian contact mechanics, this results in an ellipseshaped contact patch, which can be divided into two segments: an adhesion and a slip region. In the slip area local pressure is not high enough to transmit tangential force without slippage. In case of lock-up braking, the slip region covers the whole contact patch.
Wheel-rail contact is usually described using the coefficient of adhesion -longitudinal creep function. Latter depicts the virtual sliding velocity caused by deformation of the wheel near the contact patch. Only approximations are available for the function mentioned above. One of these can be seen on Figure 1 [2,3].

Wheel-slide protection
The wheel-slide protection system is integrated in the basic brake equipment. Several requirements were set out regarding sliding. According to EN15595 and UIC541-05 standards, maximum sliding velocity can't exceed 30 km/h, while the duration of lock-up sliding can't be longer than 0.4 seconds. EN15595 restricts the amount of total energy  [2] per wheel, as well. This value is 26 kJ per contact point. In this paper we review whether these requirements can eliminate martensite formation completely [4,5].

Wheel material
Train wheels are mostly made of low alloy steel. For the simulation a steel with 0.5 % carbon content was used. As shown in the CCT curve in Figure 2, this material undergoes phase change at high temperatures. Above 735°C partial austenite formation can be observed, while over 780°C complete austenitization occurs. In case of rapid cooling, the martensite phase replaces the previously austenitized points [6,7]

Geometry
For modelling a simplified geometry was built. As the size of the contact patch is small compared to the dimensions of the wheel, only the parts near the contact surface were taken into consideration. Thus, volumes far from this region including the flange were neglected. Special cone shape of the tread was also disregarded as it affects the results marginally. This led to a cylinder which could be cut in half according to Figure 3 due to the symmetric arrangement of the case. The contact ellipse was replaced with an equivalent rectangle which had the same area as the original surface [1].

Meshing
The meshing of the model was implemented using tetrahedral elements. As near the contact patch large gradients were expected, denser mesh was applied in that region. The highest cell size was 0.15 mm while the smallest one we set to 1 mm.

Thermal simulation
The simulation was carried out via open source software programs. For preprocessing e.g. geometry modelling and meshing we used Salome. Elmer served as the solver for the thermal finite element equations. Results were evaluated in ParaView.
Input data were given according to the parameters of a real railway carriage. Values of velocity and duration of sliding were set as written in the requirements of WSP systems to check whether they were strict enough to prevent martensite formation.

Assumptions
During simulation several assumptions were set. For example, there was no heat loss towards the environment. We neglected the temperature dependence of material properties. Mechanical effects like stresses and strains were not taken into consideration. Coefficient of adhesion and sliding velocity were set constant. The traction was homogenous on the whole contact surface. A third layer e.g. some kind of fluid did not appear between contacting bodies.

Segments of simulation
The simulated process consists of three parts. First, the wheel goes through a rapid warm up due to the lock-up sliding condition. The wheel can be considered as a moving heat source from the rail's point of view. Therefore, the temperature of the contact patch tends to an equilibrium value. Afterwards, a significant cooling occurs when the wheel starts to rotate again [7].

Boundary Conditions
Boundary conditions were defined according to the geometrical simplifications. On the contact patch we set heat flux during sliding and convective heat transfer in the cooling interval. The tread is in contact with the environment, so convective heat transfer occurs in this region. Zero heat flux was defined on the plane of symmetry. Constant temperature was applied on the rest of the boundaries.

Input heat flux
If there is no heat dissipation, the amount of heat flux towards the wheel can be calculated from the power of friction force per area as shown in Equation 1. We assume that the normal load stems from the weight of the vehicle and it is distributed equally on each wheel. This leads to the following: where A is the contact surface, m is the mass of the vehicle, n is the number of axles, μ is the coefficient of adhesion, v is the sliding velocity and β is the partition factor. The partition factor β is due to the movement of wheel. As it is sliding, the hot front of the contact patch is permanently getting in contact with a cooler segment of the rail. Consequently, a compensational heat is going towards the rail thus reducing the amount of heat entering the wheel. This phenomenon can be described by the compensation factor which shows how many percent of the generated heat reaches the wheel. According to Kennedy [8], this parameter is a difficult function of time and the coordinates. Due to the limitations of Elmer the partition factor was approximated with linear functions as shown in Figure 7 [9].

Temperature distribution
The temperature distribution on the plane of symmetry can be seen on Figure 8. Temperature values from different depths are presented in Figure 9. It became clear based on the results that even the temperature of the points in depth of 0.5 mm reaches the region of complete austenitization.

Cooling
To check whether martensite formation would occur, the cooldown intervals of the graphs above were placed on the logarithmic-scaled CCT curves.
It became clear that in every examined point the cooling was fast enough to produce martensite, as it can be seen on Figure 10.

Region of possible martensite formation
We assumed that martensite would appear in each point where the temperature had reached the partial austenitic segment before. According to this, the region of possible martensite formation near the contact patch can be considered as a half ellipsoid. The X, Y and Z depths can be taken from the diagrams on the Figures 12, 13, 14.
The results show that current requirements of wheelslide protection system according to UIC541-05 do not prevent martensite formation near the tread. As mentioned before, EN15595 includes a limitation regarding total energy per wheel, as well. Equation 2 shows he method of calculating total energy: where t is the duration. In our case this value turned out to be according to In case of 0.3 s duration, the generated total energy is less than the prescribed value. However, it can be seen on Figure  15, that martensite formation still occurs if the lock-up braking lasts for 0.3 s.  If the speed was set to 25 km/h the total energy did not exceed 26 kJ, but according to Figure 17 appearance of martensite was still present.

Summary
It became clear that neither UIC541-05 nor EN15595 contains requirements that are strict enough to eliminate martensite formation completely. Thus, even if the WSP system operates properly, a thin layer of martensite may appear near the contact patch because of the lock-up braking. This indicates, that from a thermal point of view, a controlled martensite formation is allowed according to the standards. To estimate the damage of the wheels, a further mechanical simulation and a fatigue test will be needed.