Abstract
Many software packages for roughness analysis offer the possibility of calculating the fractal dimension D of surface profiles by techniques, which assume them to be self-similar and therefore uniquely defined by D. However, fractal profiles are not self-similar but self-affine, so that two profiles of quite different roughnesses may share the same fractal dimension. To distinguish between them requires the calculation of an additional scaling factor, the so-called topothesy Λ. Traditionally, D and Λ are derived laboriously from the slope and intercept of the profile's structure function. A quicker and more convenient derivation from standard roughness parameters has been suggested by Whitehouse. Based on this derivation, it is here shown that D and Λ depend on two dimensionless numbers: the ratio of the mean peak spacing to the rms roughness and the ratio of the mean local peak spacing to the sampling interval. Using this approach, values of D and Λ are calculated from the measurements on surface profiles produced by polishing, plateau honing, and various single-point machining processes. Different processes are shown to occupy different regions in D–Λ space, and polished surfaces show a relationship between D and Λ, which is independent of the surface material.
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