Wide frequency range 3D power spectral density analysis of plunger’s topography of brake system

Power spectral density (PSD) analysis is an efficient tool of “full length scale” characterisation of topographies of engineering surfaces. In case of self-affine surfaces the fractal dimension of topography can be calculated from the slope of logarithmic scaled PSD curve.
Topographic measurements of plunger were performed by stylus instrument and atomic force microscope (AFM). The sampling distance was in the range 20 nm-3 m, while the largest measuring area was 3x3 mm2, thus the whole frequency range - five orders of magnitude - of surface roughness measurement was investigated.
3D PSD analysis of measured topographies was carried out with software developed by the authors. After transforming the 3D PSD topographies to 2D PSD curve the fractal dimension representing the surfaces was calculated.
The results show that, in case of surfaces studied, the linear approximation of PSD curve can not be used, because the slope of the curve changes depends on frequency. Based on our observations the PSD curve – after a constant part – can be substituted with two lines having different slopes. The slopes of these two lines give the characteristic fractal dimension of the micro- and nano-topography.