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The Greenwood and Williamson (GW) statistical approach of characterizing rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution. A key parameter that is used to characterize asymmetry is the skewness, and the corresponding Weibull parameters are investigated for a range of practical skewness values. The Weibull distribution is then adopted to model the asperity heights, and once normalized, is used to calculate the contact load, real area of contact and number of contacting asperities using the CEB elastic-plastic model of an equivalent rough surface in contact with a smooth plane. The effect of skewness on different levels of surface roughness, ranging from very smooth surfaces encountered in microtribological applications to rougher surfaces encountered in macrotribological applications is investigated, and also compared to the symmetric Gaussian case. Also, to allow for closed-form solution of the contact equations, simpler exponential distributions are curved-fitted to the contact side of the Weibull distribution, and the analytical results are favorably compared with the numerical results using the Weibull distribution.

Modeling of contact interfaces that inherently include roughness such as joints, clamping devices, and robotic contacts, is very important in many engineering applications. Accurate modeling of such devices requires knowledge of contact parameters such as contact stiffness and contact damping, which are not readily available. In this paper, an experimental method based on contact resonance is developed to extract the contact parameters of realistic rough surfaces under lightly loaded conditions. Both Hertzian spherical contacts and flat rough surfaces in contact under normal loads of up to 1000 mN were studied. Due to roughness, measured contact stiffness values are significantly lower than theoretical values predicted from smooth surfaces in contact. Also, the measured values favorably compare with theoretical values based on both Hertzian and rough contact surfaces. Contact damping ratio values were found to decrease with increasing contact load for both Hertzian and flat surfaces. Furthermore, Hertzian contacts have larger damping compared to rough flat surfaces, which also agrees with the literature. The presence of minute amount of lubricant and wear debris at the interface was also investigated. It was found that both lubricant and wear debris decrease the contact stiffness significantly though only the lubricant significantly increases the damping.