INTRODUCTION: Contact between rough surfaces is a ubiquitous problem that can be applied to numerous phenomena such as friction, wear, and contact resistance. It can be modeled in many ways such as statistical1-2, fractal, and multi-scale3 models. In the statistical model, the surface is generalized by using mathematical parameters to calculate probabilities to determine the contact area and force. Fractal based models account for different scales of surface features neglected by statistical models. Due to their limitations, they are not considered here. The multi-scale model more accurately incorporates deformation mechanics and does not result in zero area of contact at the smallest scales, which occurs if perfect fractal surfaces are assumed.
In this work, three different rough surface contact models are considered. The first two models were based on the Greenwood-Williamson (GW) statistical model, which assumes a Gaussian distribution of asperities. One model assumed the asperities were spherical in nature, while the other assumed sinusoidal asperities. Both assumed identical radius of curvature for each peak and a lack of interaction between adjacent asperities. However, the sinusoidal asperity model includes a periodic boundary condition which includes interactions with adjacent asperities. The final model was the full multi-scale model with asperities assumed to be sinusoidal in shape and no underlying statistical distribution required because the surface would be analyzed in the frequency domain. The rough surface contact models were applied to reference surfaces to compare them to a deterministic model solved with finite elements.
METHODS: A profilometer was used to measure the surface heights of the cylinder wall. The surface heights were converted to statistical asperity parameters using methods from McCool3. The Greenwood-Williamson (GW) statistical model was applied to a rough surface-rigid flat interface using them, and they were converted to an amplitude and a wavelength. These two quantities were employed in the sinusoidal asperity model, which replaced spherical asperities in the GW model. The interface was then transformed to the frequency domain and analyzed using the multi-scale method of Jackson and Streator4. These steps were repeated for a interface of two rough surfaces and for the reference surfaces in contact with a rigid flat.
RESULTS: Figure 1 illustrates the linear trend between contact area and applied load for all three models when they were applied to the interface of two rough surfaces. Even though the models predict similar trends, the statistical model with sinusoidal asperities predicts a larger contact area for a given load and predicts complete contact at a smaller load. On the other hand, the multiscale model and the statistical model with spherical asperities predict identical contact areas for a given load. Figure 2 illustrates the differences in predicted contact pressure for varied surface separations for the same interface. All three models predict a decreasing contact pressure as surface separation is increased. However, the multiscale model predicts a larger change.