Spectral Analysis of Two-Dimensional Contact Problems

Abstract

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.

Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques

“…Björklund and Andersson (Andersson & S. Björklund, 1994) extended the conventional matrix inversion approach by incorporating friction induced deformations. Alternative techniques that aim to solve the elastic contact of rough surfaces are the Fast Fourier Transform (FFT)-based method introduced by Ju and Farris (Ju & Farris, 1996) and a follow-up extension, based on a varia-tional principle (Kalker, 1977), proposed by Stanley and Kato (Stanley & Kato, 1997). The contact between solids with realistic surface topographies under relatively small loads usually leads to plastic deformations.…”

An experimentally validated thermo-mechanical model for the prediction of thermal contact conductance

“…The radii of curvature and peak density in a surface profile are dependent on the sampling interval of the scanning instrument [21]. As the sampling interval for a given instrument decreases, more details of the surface are captured.…”

Characterization of Rough Engineering Surfaces for Use in Thermal Contact Conductance Modeling

“…Thomas [7] showed that these properties are not unique for a given surface, but change with the sampling rate of the instrument used to characterize the surface. Ju and Farris [8] also demonstrated the dependence of RMS curvature and slope on the sampling frequency. They showed that the RMS curvature can vary by more than three orders of magnitude and the RMS slope can vary by almost two orders of magnitude while the RMS height stays essentially constant as the sampling interval goes from 0.1 to 0.0001 mm.…”