Development and Validation of the Statistical Elastic and Elastic-plastic Rough Surface Contact Model for Small Contact to Complete Contact

Contact mechanics models are widely used to analyze electrical contact behavior. Greenwood and Williamson (GW model) first developed a rough surface contact model to solve the problem of electrical contact. The original GW model used the Hertz single asperity model and a Gaussian distribution of the surface roughness. However, in many of the electrical contact cases, contact area surpasses the Hertz small contact region. For medium to complete contact cases, asperity interactions become very important and the Hertz model cannot predict this behavior. Besides asperity interaction, the probability distribution function (PDF) of the asperities of the rough surface is very important as not all the surfaces are Gaussian in nature. This work has shown the effect of asperity models to predict the asperity interaction behavior. Then the asperity models are applied with different PDF of the asperities of the rough surface in the framework of the statistical model. For the elastic case, the newly proposed rough surface models are compared with a Boundary Element Method (BEM) simulation result and the Persson model. For the elastic-plastic case, electrical contact resistance has been measured between two rough surfaces using the four-wire resistance method and then the newly proposed rough surface models are compared with the experimental results. Comparisons suggest that sinusoidal asperity model and the proper choice of the PDF of the asperity of the rough surface can effectively model the contact resistance behavior.