Experimental study on the characterization of worn surface topography with characteristic roughness parameter

doi:10.1016/S0043-1648(03)00215-1

Wear

Volume 255, Issues 1–6, August–September 2003, Pages 309-314

https://doi.org/10.1016/S0043-1648(03)00215-1 Get rights and content

Abstract

The fractal dimension and scale coefficient of surface profiles were calculated using the structure function method. Studies show that fractal dimension or scale coefficient is not optimum in characterizing rough surfaces. In consideration of this case, a fractal parameter called the characteristic roughness is put forward by combining the profile fractal dimension and the scale coefficient. Its definition and calculation expression are given. Running-in wear tests were conducted by using a thrustwasher type tester, and surface topographies were measured in the same area of the test specimens at different wear times. Experimental results show that the characteristic roughness parameter is not only more objective but also more sensitive to characterize wear surfaces during the running-in process than fractal dimension or scale coefficient.

Introduction

The wear of machine parts is an important problem in the operating life of machines. Studying the characteristics of the worn surfaces of machine parts is helpful in judging wear conditions, in predicting wear behavior and controlling wear processes. For this reason, the objective characterization of rough surface topography has been an important investigation subject for many decades.

Traditionally, statistical parameters, such as the standard deviation of the surface height, slope and curvature are used for characterizing surface roughness. However, since the deviation of a surface from its mean plane is a non-stationary random process and rough surfaces have the feature of geometric self-affinity, these parameters depend strongly on the resolution and sampling length of the roughness-measuring instrument and are therefore not unique for a surface [1], [2], [3], [4], [5]. It is difficult for conventional tribological models based on statistical roughness parameters to reflect internal law of engineering problems in a scale-independent manner. Therefore, it is necessary to characterize rough surfaces by intrinsic scale-independent parameters.

The foundation of fractal geometry provides an opportunity to characterize rough surfaces objectively [6], [7]. It has been shown that surfaces formed by electric discharge machining [8], cutting or grinding [9], [10], and worn surfaces [11], [12] have fractal structures, and fractal parameters can reflect the intrinsic properties of surfaces to overcome the disadvantages of conventional roughness parameters. This paper applies fractal geometry to characterize worn surface topography during the running-in period. Fractal dimension and scale coefficient of surface profiles are calculated using the structure function method. Considering the imperfection of fractal dimension or scale coefficient in characterizing rough surfaces, a fractal parameter called the characteristic roughness τ^∗ is put forth by combining fractal dimension D and scale coefficient C in a power law relationship of structure function. Its definition, geometric meaning and mathematical express are given, and its validity and objectivity in characterizing worn surfaces are verified by experimental investigations. Advantages in characterizing surfaces are compared with that of fractal dimension D and scale coefficient C.

Section snippets

Fractal dimension and scaling coefficient of rough surfaces

The profiles of machined or worn surfaces appear random, multi-scale, and disordered. The mathematical properties of such profiles are continuous everywhere but non-differentiable at all points. Such surface profiles are also known to be self-affine in roughness structure [2], [3]. It was found that the Weierstrass–Mandebrot (W–M) fractal function satisfies these properties of continuity, non-differentiability, and self-affinity, and is therefore used to characterize and simulate such profiles

Definition of the characteristic roughness parameter

Fig. 1 shows log–log plots of the structure function. It is seen, from the figure, that the fractal dimension D can only reflect the slope of the straight line. The location of the straight line must be determined by the scale coefficient C. For this reason, the fractal surfaces cannot be completely characterized by only either the fractal dimension D or the scale coefficient C, as illustrated in Fig. 2, Fig. 3. By combining the fractal dimension D and the scale coefficient C, there is the

Experimental details

Running-in experiments were carried out on a thrustwasher type tester in order to check the validity and objectivity in characterizing worn surfaces by the characteristic roughness parameter τ^∗. The thrustwasher type tester system consists of the tester, a T1000 type stylus profilometer and a computer data-collecting system, as shown in Fig. 4. The surface profile measurements were made in the setup. The continuous analogous electric signal of a surface profile of the test samples measured by

Conclusion

The characterizations of the worn surface topographies of friction pairs during running-in process have been studied with fractal theory. While the fractal dimension or scale coefficient can reflect the roughness level of surfaces, they cannot completely characterize the surface. The characteristic roughness parameter τ^∗ proposed in this paper combines both fractal dimension and scale coefficient of rough surfaces, so it is better able to characterize rough surface topography. It was found that

Acknowledgements

The authors would like to thank National Natural Science Foundation of China (Grant No. 50225519), Province Natural Science Foundation of Jiangsu (Grant No. BK2002116) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, PR China. They provided financial support for researches on the performance improvements of materials and the tribology issues of machinery.

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CommunicationExperimental study on the characterization of worn surface topography with characteristic roughness parameter

Abstract

Introduction

Section snippets

Fractal dimension and scaling coefficient of rough surfaces

Definition of the characteristic roughness parameter

Experimental details

Conclusion

Acknowledgements

The digitization of surface profiles

Wear

Measurement and characterization of multiscale surface

Wear

Fractal characterization and simulation of rough surfaces

Wear

Fractal model of elastic–plastic contact between rough surfaces

ASME J. Tribol.

Comprehensive study of parameters for characterizing three-dimensional surface topography. II. Statistical properties of parameter variation

Wear

The fractal behavior and fractal characterization of rough surfaces

Tribology

Communication
Experimental study on the characterization of worn surface topography with characteristic roughness parameter