# Enhancing Railway Network Safety by Reproducing Wheel-Rail Electrical Contact on a Laboratory Scale
## 3 Results
### Dependence of the Resistance on the Applied Force  
This section focuses on the effect of applied force on the contact resistance. In [PERSON]'s theory, the contact resistance as a function of force is predicted to follow a power-law behavior \(R_{c}\ \sim\ F^{-\frac{1}{3}}\).  
The contact resistance was evaluated with a constant DC current of 0.1 A. The applied load was progressively increased from 30 N to 430 N (maximum force as explained in Section 2.2.2), then decreased to 30 N.  
Initially the tests were conducted on three zones under normal conditions, in ambient air. In Figure 7, we present the \(R_{c}-F\) characteristics obtained from one of these zones.  
These force tests conducted in ambient air reveal unexpected contact resistance behaviors far from those predicted by [PERSON]. At lower forces (<230 N), the resistance decreases very slowly, following a power-law \(R_{c}\ \sim\ F^{-0.09}\). Beyond 230 N, the resistance exhibits a much more pronounced decrease, following a power-law \(R_{c}\ \sim\ F^{-1.24}\) with an exponent greater than one. When decreasing the force from 430 N to 30 N the resistance follows a \(R_{c}\ \sim\ F^{-0.47}\) power-law. These observations may reflect the extreme difficulty of obtaining perfectly smooth, clean surfaces on both wheel and rail. Surface roughness, contamination and possible oxidation make it impossible to achieve ideal Hertz's conditions.  
To address these unexpected results and evaluate the potential impact of oxidation on the contact resistance, the test was replicated on three other zones using a nitrogen jet to create a controlled environment. In Figure 8, we present the \(R_{c}-F\) characteristics obtained from one zone with nitrogen exposure. When increasing the force from 30 N to 230 N, the resistance closely follows a power-law \(R_{c}\ \sim\ F^{-0.31}\), thus approaching the Hertzian law. This indicates that the application of the nitrogen jet effectively eliminated some external factors and thus allowed for approaching Hertz conditions in this force range. However, beyond 230 N, the resistance evolution again deviates as for the ambient air experiment, following a greater power-law, \(R_{c}\ \sim\ F^{-2}\). When decreasing the force from 430 N to 30 N, the resistance follows a \(R_{c}\ \sim\ F^{-0.76}\) power-law.  
This change in resistance behavior for forces beyond 230 N can be attributed to the occurrence of permanent deformation (plasticity of asperities). A similar behavior was  
Figure 7: In air—\(Log-logR_{c}-F\) characteristics at imposed DC current I = 0.1 A. Increasing the load (\(\bullet\)) then decreasing it (\(\bigtriangledown\)). (–): experimental fits of the various sections.  
observed in a previous study [14], which focused on a single electrical contact between two grains of copper powder subjected to a mechanical pressure \(P\) in the plastic regime. In this study, it was found that the resistance demonstrated a power-law dependence on the force, with an exponent greater than one. This peculiar behavior was attributed to the presence of microchannels at the contact area between the two grains, characterized by wide-ranging conductances.  
During the return phase (decreasing force), for both air and nitrogen conditions, the resistance follows a different path, which can be explained by the persistent asperity flattening [15].