# Railway Axle and Wheel Assembly Press-Fitting Force Characteristics and Holding Torque Capacity
## 5 Effect of the Interference on the Holding Torque Capacity
### Finite Element Analysis of the Holding Torque Capacity  
Finite element analysis was used to examine the effect of the interference on the holding torque capacity for the wheel and axle assembly. The geometry of the 3D models and materials properties were similar to those for the press-fitting finite element analysis. During this analysis, surface-to-surface contact interaction was set between the wheel and axle interface with a contact interference fit option. A penalty frictional coefficient, 0.1, and hard contact were set as the contact properties. It was necessary to define the reference points on the axle at both end sides of the centre point and coupling to the surface that defined the coupling nodes. To obtain more accurate results, a refined mesh was used at  
Figure 17: Holding torque capacity vs contact length.  
the contact area with a coarse mesh for the other areas. The torque loading was applied to the reference node at the end of the axle, and the outer surface of the wheel was fixed (Figure 18). The value of the applied torque was increased until rotation or'slip' occurred in the interface.  
The torque capacity analysis simulated the wheel and axle assemblies to obtain the curves of the torque and rotational angle, which determined the maximum holding torque capacity for different interference values. The torque and rotational angle curves were needed to decide the torque required to resist the slip between the interference assemblies. In Figure 19, \(\mathrm{T_{E}}\) was the maximum elastic torque, and yielding started at that point. Within the elastic torque region, the shear stress in the axle varied linearly, and the axle showed only elastic deformation. When the torque increased to the plastic region, \(\mathrm{T_{P}}\), the axle rotated continuously with no further increase in the torque. The maximum elastic torque was equal to 75% of the maximum holding torque capacity at the fully plastic region [22; 23]. Therefore, it was evident that the maximum holding torque capacity or plastic torque, \(\mathrm{T_{P}}\), before slipping was 75 kNm at the twist angle 0.15 rad, and the maximum elastic torque \(\mathrm{T_{E}}\) was 56 kNm at the twist angle 0.029 rad for the interference of 240 \(\mathrm{\SIUnitSymbolMicro m}\). \(\mathrm{T_{E}}\) did not exceed the 75% of \(\mathrm{T_{P}}\) for 240 \(\mathrm{\SIUnitSymbolMicro m}\), and others were also less than 75% of the maximum holding torque capacity. When the torque increased beyond the maximum holding torque capacity, the axle started slipping. The curves for the torque capacity simulated with different interferences are shown in Figure 20. Table 3 compares the maximum holding torque capacity with theoretical and finite element results. The deviations between the estimated maximum holding torque capacities from the theory and finite element analyses were 15% for 200 \(\mathrm{\SIUnitSymbolMicro m}\) interference, 12% for 240 \(\mathrm{\SIUnitSymbolMicro m}\), 8% for 280 \(\mathrm{\SIUnitSymbolMicro m}\), and 6% for 320 \(\mathrm{\SIUnitSymbolMicro m}\). Thus, the finite element results agreed with the theory.  
Figure 18: Loading and boundary conditions for the torque analysis.