2.4 Contact Problem of Rough Surface
Traditionally, surfaces were modeled analytically using assumption and simplifications. Surface produced by any conventional machiningmanufacturing processes are never
smooth. The surface irregularities are termed as asperities. Asperities were modeled as a variety of geometric shapes. In the past, a number of authors study rough surface
contact problem using analytical method Whitehouse Archad [19]; Onions Archad [20]; Bush, Gibson, et al, [8]; Hisokado [23]. Their result was very useful but their
application is limited to a relatively small range of loads. Surface asperity height and contact pattern were treated as probability
distributions. Behavior of a single pair of interacting asperities was often extrapolated to describe the behavior of a pair of interacting surfaces covered in asperities [25].
Investigation of the contact itself classically follows two types of approach, either stochastically or deterministically. One of the first models has been proposed by
Greenwood and Williamson [7], who assumed that the asperity summits are spherical with a constant radius, the asperities deform elastically and their height follows a
Gaussian distribution. Statistical models have had a considerable impact on contact analysis and have been considered by many authors [28-31]. Nevertheless, these models
do not take into account the real geometry of the surface and the interactions between the asperities. Deterministic approaches were then developed to introduce a more
precise geometric description [41]. Surface roughness can affect the performance of components and system in a
wide variety of fields including tribology, fluid sealing, heat transfer, electronic packaging, dentistry, and medicine. Although it is possible to measure the topography
of a real surface and incorporate that data into a finite element model [32-34], this practice is still relatively uncommon [35].
In fact, most analysts create probabilistic surfaces based on assumed, known, or desired surface geometry [7, 36-39], in part because the real geometry cannot always be
measured. In recent time, researchers work on real surfaces analysis by either experimentally [42] or developed rough surface model in finite element software. Finite
element modeling permits contact simulation with complex geometry, boundary condition, material properties, and material models. The finite elements method has
been used to solve the contact problem for artificial fractal surfaces [46]. Starting from roughness measurements, synthesized fractal surfaces were also used in the studies of
Vallet et al. [44-45] where they used a numerical procedure to solve the contact problem.
2.5 Modeling Rough Surface
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