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This paper presents a two-scale analytical approach to study the normal contact of deformable bodies, taking into account their surface roughness. This approach makes it possible to evaluate the influence of roughness on both real contact characteristics (microscale) and nominal ones (macroscale). The advantage of the presented approach is demonstrated by solving several contact problems. At microscale, contacts of rigid rough surfaces with elastic and viscoelastic half-spaces are considered based on periodic and probabilistic roughness descriptions. The interaction of asperities is taken into account by the localization method. At macroscale, contacts of punches of various macroshapes, which have rough contact surfaces, and deformable homogeneous and inhomogeneous bases are studied. It is shown that roughness parameters determine the additional compliance of deformable bodies. In turn, the additional compliance function influences the distribution of nominal pressures, as well as the size of the nominal contact area. The presented solutions can be used to control the contact characteristics by selecting a suitable microrelief of the contacting surfaces and to predict the durability of contact pairs based on analysis of internal stresses and wear processes.
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