Fractal Characterization Of Worn Surface Topography And Its Variation During Wear Process

Wear is a dynamic process in which a large amount of materials are continuously lost from the working surface due to the mechanical interaction between a tribopair in frictional sliding contact.The wear process is often accompanied by the variation of surface topography.Based on the monofractal and multifractal theories,the variation law of two-dimensional surface profile and three-dimensional surface topography are studied to enrich the theoretical study of tribology,reveal the mechanism of friction and wear,provide theoretical basis for identification wear stage and prediction fault diagnosis.A new method termed as three-dimensional root-mean-square method(3D-RMS),is proposed to accurately calculate the fractal dimension of three-dimensional surface topography.The measure of this method is the root-mean-square value of surface data,and the scale is the side length of square in the projection plane.In order to evaluate the calculation accuracy of the proposed method,the isotropic surfaces with deterministic fractal dimensions are generated based on two-dimensional fractional Brownian motion function and Weierstrass-Mandelbrot fractal surface,and two kinds of anisotropic surfaces are generated by stretching or rotating a Weierstrass-Mandelbrot fractal curve.Grey images with deterministic fractal dimensions are generated based on the isotropic surfaces.Their fractal dimensions are estimated by the proposed method,as well as differential boxing-counting method,triangular prism surface area method and variation method.The results show that 3D-RMS method performs better than the other methods with a lower relative error for isotropic surfaces,anisotropic surfaces and grey images.Wear experiments are carried out on a ring-on disc tribometer by multi-stage tests under different cutting conditions.Three-dimensional laser confocal microscope is used to measure the three-dimensional surface topographies of disc and ring.Fractal dimensions of surface topographies of tribopair are calculated by 3D-RMS method.The results show that the surface roughness of disc decreases at first,then maintains at a small value,finally increase significantly during the wear process.The surface roughness of ring increases in the running-in wear stage,fluctuates at a large value in the steady wear stage,and increase gradually in the severe wear stage.Fractal dimensions of disc surfaces increase at first,then fluctuate in a small range and finally decrease during the wear process.Fractal dimensions of ring surfaces decrease at first,then maintain at a certain value,finally decrease during the wear process.In contrast to the variation of three-dimensional surface topography and surface roughness of tribopair,it is found that the three variation regions of fractal dimensions correspond to the running-in wear stage,steady wear stage and severe wear stage of the tribopair,respectively.A reposition-measurement apparatus is designed to measure the profile of brass surface at the same areas throughout the wear process.The wear experiments are performed on a ring-on-disc tribometer.The maximum peak-to-valley height and fractal parameters are used to characterize the variation law of surface profile during the wear process.The maximum peak-to-valley height decreases in the running-in wear stage,fluctuates within a narrow range in the steady wear stage,and increases significantly in the severe wear stage.Fractal dimension and characteristic roughness increase gradually at first,then stabilize at a large value,finally decrease rapidly.In contrast to the variation of surface profile,it is found that the increase,stabilization and decrease of fractal parameters correspond to the running-in wear stage,the steady wear stage,and the severe wear stage,respectively.Multifractal spectrum and its parameters are applied to describe the localized fractal characteristic of two-dimensional surface profile and three-dimensional surface topography.The multifractal spectrums present a hook-like shape with different fractal dimensions at different singularity exponents,which suggests that the two-dimensional profile and three-dimensional topography possess multifractal properties.In running-in wear stage,the width of the spectrum of surface profile becomes narrow,indicating that the fluctuation range of surface profile decreases.In the steady wear stage,the width of the spectrum of surface profile maintains at a small value,indicating that the surface profile keeps smooth.In the severe wear stage,the width of the spectrum increases rapidly,indicating the failure of the worn surface.For the three-dimensional topography of disc sample,the width of the spectrum and the difference between fractal dimensions of the subset with the largest singularity exponent and that with the smallest singularity exponent decrease in the running-in wear stage,remain stable at a small value in the steady wear stage,and increase in the severe wear stage.The multifractal parameters of the three-dimensional topography of ring sample increase at first,then tend to stabilize at a certain value,finally increase significantly during the wear process.Recurrence plot and recurrence quantification analysis are introduced to study the nonlinear dynamic evolution of brass surfaces when sliding against steel.The recurrence plots depict conditions before wear testing,during steady-state wear,and after severe wear begins.These sequential plots evolve from a periodic-like pattern,to a partially homogeneous pattern,and then to a disrupted pattern.During wear,average diagonal length first decreases,then stabilizes at a small value,and finally increases significantly,corresponding,respectively,to the running-in wear stage,the steady-wear stage,and the severe wear stage.By contrast,the correlation dimension tends toward two dimensions at first,then fluctuates around a large value and then rapidly decreases toward one dimension.The computation of average diagonal length and correlation dimension reveal changes in randomness and complexity as wear passes through three wear stages.Nonlinear characteristic parameters of worn surface and clustering analysis are applied to wear state recognition.Nonlinear state coordinates are established in three-dimensional space by fractal dimension,average diagonal line length and the width of mutifractal spectrum.Surface profiles are characterized by monofractal parameters,multifractal parameter and recurrence parameters from different perspectives.These parameters are complementary and irreplaceable of each other,and they are used at the same time to analyze the variation of worn surface comprehensively.The nonlinear state points of surface profiles converge in running-in wear stage,remain stable in a certain space in steady wear stage,and diverge in rapid wear stage.Spherical surface in steady wear stage can be plotted by clustering analysis.Wear state for the same tribopair and under the same experimental conditions can be recongnized based on the relative space position relations between the spherical surface and the nonlinear state points of surface profiles.