Synthesis of engineering surfaces using representative elementary patterns of roughness

Synthesis of surface roughness is a long-standing problem that has many practical applications. Here novel algorithms for the synthesis of rough surfaces at nano/micro scales are proposed. The algorithms are based on introduction and development of two new concepts, namely the representative elementary pattern of roughness (REPR) and the statistically representative pattern of surface roughness (SRPSR). From the statistical point of view, the REPR is the smallest interval (or area) over which a measurement can be made that represents statistically the whole surface. However, synthesis of surfaces by the direct use of the REPR may cause some artificial singularities. To avoid this drawback and to incorporate the synthetic surface in a numerical scheme of the contact solver, one needs to extend the REPR to a non-singular SRPSR that satisfies additional conditions of the scheme used. Our findings indicate that specific time-series analysis techniques, such as the moving window approach, can be effectively utilized to extract the REPR from experimental data. The representativeness may be justified by the use of the Kolmogorov–Smirnov statistic. Extraction of REPRs of surfaces and constructions of appropriate SRPSRs are demonstrated on experimental data obtained by stylus and atomic-force microscopy at micro and atomic/nano scales, respectively.