# Derating of Electrical Contacts with Varying Surface Roughness
## 1 Introduction
Turned surfaces, due to their microstructure, may exhibit lower thermal conductivity efficiency compared to surfaces produced by other methods, such as polishing or precision grinding. Reduced heat dissipation from the contact increases the risk of overheating and necessitates further reductions in the maximum operating parameters of contacts to ensure their reliability [23]. Finally, turning affects the quality and homogeneity of the material in the contact, which is also significant in the context of derating. Machining processes can introduce structural defects such as microcracks or internal stresses that reduce the material's resistance to mechanical and thermal fatigue. Under real-world operating conditions, these defects can lead to premature contact failure. Therefore, derating incorporates an additional safety margin to counteract these effects [21]. At the microscopic level, surfaces are never perfectly smooth, meaning that when two rough surfaces make contact, the actual area of contact is much smaller than the apparent contact area. The real contact area is determined by the flat regions of the asperities that physically touch, which typically constitute a much smaller proportion of the surface compared to the apparent area. This reduction in contact area leads to an increase in the electrical contact resistance because the resistance is inversely proportional to the contact area. As the contact area decreases due to surface roughness, the resistance increases. This effect is particularly pronounced in cases of higher roughness, where fewer microscopic junctions form between the two surfaces. Consequently, more electrical energy is dissipated as heat at these contact points, leading to an increase in the local temperature [3]. The physical mechanism underlying this is the theory of asperity contacts, which posits that the real contact area between two rough surfaces is a function of the heightsand distribution of the asperities. As the contact force increases, more asperities come into contact, reducing the contact resistance. However, when the surfaces are rougher, fewer asperities actually make contact, which increases resistance and, consequently, heat generation. The increased resistance results in a greater power loss at the junction, contributing to a rise in temperature. This phenomenon can be modeled using the Greenwood and Williamson theory, which describes how surface roughness influences the electrical contact area and resistance, and provides insights into how temperature rises at contact points due to resistive heating [3]. The relationship between contact resistance and temperature rise can also be explained by the thermal contact resistance, which arises from microscopic imperfections in the interface. As the temperature increases, the physical properties of the materials, such as electrical conductivity, may change, further complicating the contact behavior. This thermal effect is an important consideration in applications where electrical contacts experience high currents and elevated temperatures. A notable study by [PERSON] discusses how surface roughness and contact resistance contribute to the overall heat dissipation and degradation of electrical contacts with prolonged operation [24]. Furthermore, heat dissipation at the contact interface depends not only on the contact resistance but also on the heat conductivity of the materials involved and the size of the contact area. When the contact area is small, it creates localized hotspots, which can accelerate wear, corrosion, or even complete failure of the electrical connection. This issue is particularly important in power electronics and connectors, where thermal management is critical for reliability and long-term operation. Experimental investigations, such as those conducted by [PERSON] (2019), further support these theories by showing that rougher contacts lead to significantly higher resistive heating, which in turn accelerates the degradation of the electrical connection [25].