Determination of the optimum sampling interval for rough contact mechanics

It is well known that roughness parameters such as slopes, asperity densities and curvatures, which are needed to calculate contact mechanics, are not intrinsic properties of the surface but depend on the sampling interval. A method for choosing this sampling interval is proposed, based on Archard's observation that repetitive contact must be elastic. From a description of the rough surface as a self-affine fractal, the second moment of the power spectrum can be expressed in terms of fractal parameters which are intrinsic properties of the surface. The moment integral is then solved for its lower limit, which defines the tribologically appropriate sampling interval. Thus a relationship can be derived between three dimensionless numbers: the ratio of this critical wavelength to the topothesy; the fractal dimension; and the material property ratio. Measurements on two commercial hard disk drives are interpreted in terms of the model, and it is predicted that under realistic operating loads the real separation between slider and disk at rest is about 100 nm, with between 40,000 and 80,000 discrete contacts of 12–15 nm radius.