Contact problems can be converted into the spatial frequency domain using Fast Fourier Transform (FFT) techniques. Spectral analysis is used to develop an algebraic relationship between the surface displacement and the contact pressure. This relationship can be used to find the contact pressure or displacement for the contact of smooth surfaces or the complete contact of rough surfaces. In addition to providing rapid, robust solutions to contact problems, the algebraic relationship contains details of the relationship between surface displacement and contact pressure on different length scales. In particular, it is shown that the frequency composition of pressure is similar to that for slope of the surface displacement. Thus, the high frequency content of the surface profile gives rise to high localized contact pressure, in some cases singular pressure for complete contact. However, measurement limitations always lead to the omission of certain high frequency components of the surface profile. Assuming that the high frequency content of the surface profile obeys a power law, spectral analysis is also used to estimate partial contact parameters. This result relates the exponent of the power law to the contact pressure and implied surface integrity. It is concluded that spectral analysis can be combined with the FFT to provide a useful technique for classifying rough surface contacts.

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A numerical model for the elastic contact of three-dimensional real rough surfaces has been developed and applied to the study of the variations in contact stress distribution in running-in process. The specimens for calculation and experiment are washers with nominally flat grinding surfaces. The stresses of real contact between specimens at each stage of running-in are calculated and the contact stress distributions are given. It is shown that the contact stress distribution is in an exponential form which could be characterized by one dimensionless parameter: λ, the index of contact stress distribution. The proportion of plastic deformation β may be expressed as a function of λ. The results of the present work confirm the reasonableness of the early opinion that the running-in process can be considered as a gradual increase in the elastic component of deformation of the contact area and a decrease in the proportion of plastic deformation.