# Contact Analysis and Friction Prediction of Non-Gaussian Random Surfaces
## 1 Introduction
Various extensions of the GW contact model have been developed to incorporate the interaction between asperities and the effects of adhesion and plastic deformation [22; 23; 24; 25; 26]. However, such method cannot give the pressure distribution. The deterministic method can provide pressure distribution, deformation, etc. However, the deterministic method may have a convergence problem and calculation efficiency for large scale calculations. In order to cope with those problems, the discrete convolution-Fast Fourier transform (DC-FFT) [27] method is used extensively to speed up the related calculations by reducing the computational complexity. [PERSON] and [PERSON] [28] proposed an alternative numerical method based on the conjugate gradient method (CGM) to address the rough contact problem. Those improvements make this method converge for arbitrary rough surfaces. From this, it has been widely applied to investigate the contact properties of the non-Gaussian rough surface [29; 30; 31; 32]. Friction is a combined phenomenon that originates from the interaction of deformation of surface irregularities and adhesive forces between the two surfaces. Thus, the surface roughness fundamentally influences friction behavior. Many researchers [33; 34; 35; 36; 37] have investigated the impact of surface topography on the friction coefficient and found that the static friction coefficient was highly sensitive to surface roughness. However, most of them used the stochastic method which were based on simplifying assumptions about the distribution of contact pressure in and around the contact region. In addition, only the effect of adhesion force on friction was considered, while the ploughing component was ignored. It is now generally agreed that friction is attributed to the interactions of the ploughing effect and adhesion force of contact asperities. [PERSON] [38] proposed a numerical approach based on molecular and mechanical theory to investigate the sliding friction behaviors. However, the research focused on Gaussian surface. Extensive experimental work [39; 40] has been performed to investigate the correlation between roughness parameters and friction, and it was discovered that the skewness and kurtosis of non-Gaussian surface tend to have an influence on the coefficient of friction. Herein, a novel friction prediction model considering the effects of adhesion and ploughing components simultaneously is proposed and is used to derive the macroscale friction coefficient from microscale asperity interactions. Many significant works have been completed for contact problem and friction of non-Gaussian surface; however, a systematic study to investigate the impact of non-Gaussian surface properties on contact performance and friction is still desirable. In this paper, the non-Gaussian rough surfaces with specified amplitude parameters and ACF are generated based on linear transformation and the MA model. The contact analysis is conducted by a deterministic contact model to obtain deformation of asperities contact pressure and real contact area. Then, the friction coefficient of each single asperity can be derived from the friction model using the results of the contact model. Finally, the overall friction coefficient is calculated from the sum of the friction of all asperities.