Electrical Contact Resistance Considering Multi-Scale Roughness

Surface roughness has many effects in contacting engineering surfaces and electrical connectors are no exception. In connectors, the roughness on the surfaces causes added electrical resistance (known as electrical contact resistance (ECR)). This work presents a new method for modeling ECR while considering the multi-scale nature of surfaces in the contact mechanics and electrical resistivity theory. Based on Archard's "protuberance upon protuberance" theory, this method employs sinusoids stacked into layers to represent the rough surface. However, many models already exist ranging from statistical to other forms of multi-scale methods. There is considerable debate in the field of contact mechanics as to which method is the "best". Since all methods have various advantages and disadvantages, this work makes a comparison between several different models. In particular, results from the sinusoidal multi-scale model are evaluated alongside results from statistical methods for both perfectly elastic and elastic-plastic deformation. This effort has shown qualitative similarities despite quantitative discrepancies.