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When a rigid rough solid slides on a rigid rough surface, it experiences arandom motion in the direction normal to the average contact plane. Here,through simulations of the separation at single-point contact betweenself-affine topographies, we characterize the statistical and spectralproperties of this normal motion. In particular, its rms amplitude is muchsmaller than that of the equivalent roughness of the two topographies, anddepends on the ratio of the slider's lateral size over a characteristicwavelength of the topography. In addition, due to the non-linearity of thesliding contact process, the normal motion's spectrum contains wavelengthssmaller than the smallest wavelength present in the underlying topographies. Weshow that the statistical properties of the normal motion's amplitude are wellcaptured by a simple analytic model based on the extreme value theoryframework, extending its applicability to sliding-contact-related topics.

Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach