# Thermo-Mechanical Response of Train Wheels

2016-11-11 Karl Du PlessisTransnet Freight Rail South Africa use FloEFD in the thermo-mechanical response investigations of train wheels. New train wheel designs are governed by design codes such as UIC 510-5 and EN 13979-1. One specific requirement is under braking. Heat is generated while the brake is applied which increases the wheel temperature and consequently causes thermal expansion. The lateral deflections resulting from the thermal expansion are required to be within prescribed limits. Additionally the residual hoop stress after the cool down period at the end of the test must also not exceed the yield stress of the material.

ESTEQ have proposed an approach to solving this problem with minimal effort and within short turnaround time, as outlined in the blog article: Thermo-mechanical response according to UIC510-5. Subsequent to the mentioned article, Transnet Freight Rail have adopted this approach and put it to good use recently in a real-world application where a specific wheel had to be investigated for compliance with UIC 510-5 code specifications. The modelling approach and results are discussed and presented below, however the final outcome of the investigation can unfortunately not be shared. Below follows a description of the drag braking rig test as outlined in the UIC 510-5, 2007 code.

**Drag Braking Rig Test:**

This test simulates the train travelling at a speed of 80km/h and the brake being applied for a period of 45 minutes. Thereafter there is a cool down period of 45 minutes with the train still traveling at 80km/h. Convection from the external wind is simulated by means of forced rig ventilation and is prescribed by the code as Vventilation = Vtrain/2. In this particular case with the wheel considered, the heat generated by the brake was calculated at 15.7kW. See figure 1 below which illustrates these conditions.

Figure 1. Drag brake test conditions.

**Modelling approach:**

In order to obtain accurate deflections due to thermal expansion under these conditions one requires an accurate distribution of temperature throughout the wheel and axle assembly. Considering the fact that the train is traveling at 80km/h there is forced convection taking place, and since the wheel is turning the air flow around the wheel would be disrupted and would therefore not be symmetric around the wheel. Therefore, ideally a detailed CFD simulation needs to be performed, solving the conjugate heat transfer problem, i.e. the bidirectional effects of conduction within the solid and the forced convection at the outer surfaces of the wheel, in order to obtain accurate temperature distributions.

However, although FloEFD is very capable of solving the conjugate heat transfer problem, because a 90 minute transient simulation is required as per the drag braking test description, performing the full external flow and solid heat conduction would require excessive computational time. When having to do various brake rig tests for various levels of wheel wear, shorter calculation times are desirable. Thus, to speed up the calculation time the analysis is split into two separate steps. Firstly a steady-state analysis of the external flow without heat conduction in the wheel assembly is performed from which the heat transfer coefficients (HTC) on the surfaces of the wheel and axle assembly are obtained, as shown in figure 2 and figure 3 respectively. The HTCs are then averaged circumferentially and subsequently applied as the boundary conditions of the transient analysis described hereafter. The circumferential averaging of parameters in this case is deemed acceptable since the wheel is rotating at approximately 700 rpm for which a single revolution occurs in less than 0.1 seconds, hardly enough time for any measurable temperature changes to occur.

Figure 2. External flow analysis – Velocity streamlines.

Figure 3. External flow analysis – Heat transfer coefficients.

Secondly a transient internal heat conduction analysis is performed that ultimately produces the temperature distributions required for the finite element analysis then. During this step the external flow is neglected but accounted for by the outer wall HTCs boundary condition from step one. The 15.7kW heat generated from braking is applied to the braking surface by means of a surface heat source. Figure 4 shows the thermal response of the wheel and axle temperatures with respect to time during the heating and cool down phases of the drag braking test. The resulting temperature distributions from the hot (45 min) and cold (90 min) states are then seamlessly mapped onto an existing Nastran finite element mesh of the wheel assembly. Consider figure 5 which shows the finite element mesh of the wheel assembly. Figures 6 and 7 show the resulting temperature distributions from FloEFD and the subsequent exported temperatures on the Nastran mesh in the hot and cold states respectively. It is clear from these two figures that the mapping was very successful.

Figure 4. Transient thermal response of the train wheel assembly.

Figure 5. MSC.Nastran finite element mesh, created in MSC.Patran.

Figure 6. FloEFD to Nastran export – Hot state temperature distribution.

Figure 7. FloEFD to Nastran export – Cold state temperature distribution.

Finally, the thermo-structural analysis is conducted by applying the solid temperature distribution in addition to the interference fit between the wheel and axle as prescribed by the UIC 510-5 code. The hot state deformation and cold state residual hoop stresses are shown in figures 8 & 9 respectively. The lateral displacement in both the positive and negative directions have to be within the limits prescribed by the code for a wheel to pass the specification and be accepted, whether this particular wheel passed the test or not cannot be revealed, however, it can be seen from figure 9 that the residual hoop stresses are well below the yield stress of the material. The code requires further structural and fatigue assessments, but these are pure mechanical loads and are outside of the scope of this discussion.

Figure 8. Hot state – Deformation.

Figure 9. Cold state – Residual hoop stress.

*“FloEFD has been instrumental in enabling Transnet Freight Rail to do such thermo-mechanical response investigations with the minimum effort and within the shortest possible time, minimising the reliance on physical tests, resulting in significant time and cost savings.”* – Hendrik Esterhuyse, Transnet Freight Rail.