Research into the application of fractal geometry in characterising machined surfaces

Many machined surfaces such as those processed by turning, drilling, electrical discharging machining, grinding and rubbing, which have the property of self similarity or self-affinity, can be characterised with fractal geometry. Up to now the emphasis of most researchers has been on isotropic surfaces with a profile of several fractal parameters. In this paper, we first review the characterisation of a profile with fractal geometry and the relation between fractal parameters of the profile and that of a three-dimensional machined surface. Afterward, we propose a concise method based on two-dimensional Fourier transform to compute the surface fractal dimension and to analyse the anisotropy along three-dimensional machined surfaces. The precise three-dimensional topography of a machined surface is taken with atomic force microscopy. After spatial power spectrum obtained by two-dimensional fast Fourier transform, surface fractal parameters are acquired by averaging power spectrum along every direction with nominal same amplitude and anisotropy is analysed according to spectrum amplitude within a certain direction. The results show that this has some advantages over other three-dimensional fractal characterisation methods. It is also obvious this method can be used for either an isotropic surface or an anisotropic one.