Many numerical surface topography analysis methods exist today. However, even for the moderately complicated topography of a tribological surface these methods can provide only limited information. The reason is that tribological surfaces often exhibit a non-stationary and multi-scale nature while the numerical methods currently used work well with surface data exhibiting a stationary random process and provide surface descriptors closely related to a scale at which surface data were acquired. The suitability of different methods, including Fourier transform, windowed Fourier transform, Cohen's class distributions (especially the Wigner-Ville distribution), wavelet transform, fractal methods and a hybrid fractal-wavelet method, for the analysis of tribological surface topographies is investigated in this paper. The method best suited to this purpose has been selected.
WhitehouseD. J.Handbook of Surface Metrology, 1994 (Institute of Physics, Bristol).
2.
DongW. P.SullivanP. J.StoutK. J.Comprehensive study of parameters for characterizing three-dimensional surface topography. I: Some inherent properties of parameter variationWear, 1992, 159, 161–171.
3.
DongW. P.SullivanP. J.StoutK. J.Comprehensive study of parameters for characterizing three-dimensional surface topography. II: Statistical properties of parameter variationWear, 1993, 167, 9–21.
4.
DongW. P.SullivanP. J.StoutK. J.Comprehensive study of parameters for characterizing three-dimensional surface topography. III: Parameters for characterising amplitude and some functional propertiesWear, 1994, 178, 29–43.
5.
DongW. P.SullivanP. J.StoutK. J.Comprehensive study of parameters for characterizing three-dimensional surface topography. IV: Parameters for characterising spatial and hybrid propertiesWear, 1994, 178, 45–60.
6.
PodsiadloP.StachowiakG. W.Fractal and wavelet transform for characterization of tribological surfaces—a preliminary studyTribology Lett., 2002 (in press).
7.
AkayM. (Ed.) Time-frequency and Wavelets in Biomedical Signal Processing, IEEE Press Series in Biomedical Engineering, 1997 (IEEE, New York).
8.
ChenX.RajaJ.SimanapalliS.Multiscale analysis of engineering surfacesInt. J. Mach. Tools Mfg, 1995, 35, 231–238.
9.
OppenheimA. V.SchaferR. W.BuckJ. R.Discrete-time Signal Processing, 2nd edition, 1999 (Prentice-Hall, Englewood Cliffs, New Jersey).
10.
LimJ. S.Two Dimensional Signal and Image Processing, 1990 (Prentice-Hall, Englewood Cliffs, New Jersey).
11.
DuhamelP.VetterliM.Fast Fourier transform: A tutorial review and a state of the artSignal Processing, 1990, 19, 259–299.
12.
ThomasT.Rough Surfaces, 2nd edition, 1999 (Imperial College Press, London).
13.
Le BosseJ. C.HansaliG.LopezL.DumasJ. C.Characterization of surface roughness by laser light scattering: Diffusely scattered intensity measurementWear, 1999, 224, 236–244.
14.
StoutK. J.Three-Dimensional Surface Topography—Measurement, Interpretation, and Applications: A Survey and Bibliography, 1994 (Penton Press, Bristol).
15.
TsaiD.-M.TsengC.-F.Surface roughness classification for castingsPattern Recognition, 1999, 32, 389–405.
16.
TomitaF.TsujiS.Computer Analysis of Visual Textures, 1990 (Kluwer, Dordrecht).
17.
XieH. C.ChenD. R.KongX. M.An analysis of the three-dimensional surface topography of textured cold-rolled steel sheetsTribology Intl, 1999, 32, 83–87.
18.
PengZ.KirkT. B.Two-dimensional fast Fourier transform and power spectrum for wear particle analysisTribology Intl, 1997, 30, 583–590.
19.
GaborD.Theory of communicationsJ. Inst. Electl Engrs, 1946, 93, 429–457.
GrossmannA.MorletJ.Decomposition of Hardy functions into square integrable wavelets of constant shapeSIAM J. Mathl Analysis, 1984, 15, 723–736.
24.
DaubechiesI.The wavelet transform, time-frequency localization and signal analysisIEEE Trans. Infn Theory, 1990, 36, 961–1005.
25.
KaiserG.A Friendly Guide to Wavelets, 1994 (Birkhäuser, Boston, Massachusetts).
26.
MallatS.A Wavelet Tour of Signal Processing, 2nd edition, 1999 (Academic Press, San Diego, California).
27.
BrislawnC. M.Classification of nonexpansive symmetric extension transforms for multirate filter banksAppl. Comput. Harmonic Analysis, 1996, 3, 337–357.
28.
ChakrabartiC.MumfordC.Efficient realizations of analysis and synthesis filters based on the 2-D discrete wavelet transform. In Proceedings of the IEEE International Conference onAcoustics, Speech, and Signal Processing, 1996, pp. 3256–3259 (IEEE, New York).
29.
JiangX. Q.BluntL.StoutK. J.Three-dimensional surface characterization for orthopaedic joint prosthesesProc. Instn Mech. Engrs, Part H: J. Engineering in Medicine, 1999, 213, 49–68.
30.
WangY.MoonK. S.A methodology for the multi-resolution simulation of grinding wheel surfaceWear, 1997, 211, 218–225.
31.
JiangX. Q.BluntL.StoutK. J.Development of a lifting wavelet representation for surface characterizationProc. R. Soc. Lond. A, 2001, 456, 2283–2313.
32.
LeeS.-H.ZahouaniH.CateriniR.MathiaT. G.Morphological characterisation of engineered surfaces by wavelet transformInt. J. Mach. Tools Mfg, 1998, 38, 581–589.
33.
CohenL.Generalized phase-space distribution functionsJ. Mathl Physics, 1966, 7, 781–788.
CohenL.Time-Frequency Analysis, 1995 (Prentice-Hall, Englewood Cliffs, New Jersey).
36.
WignerE. P.On the quantum correction for thermodynamic equilibriumPhys Rev. Lett., 1932, 40, 749–759.
37.
VilleJ.Theorie et application de la notion de signal analytiqueCables Transmissions A, 1948, 2, 61–74.
38.
JacobsonL.WechslerH.The Wigner distribution and its usefulness for 2D images processing. In Proceedings of the International Conference onPattern Recognition, Munich, Germany, 1982, pp. 538–541.
39.
HuangZ.ChanK. L.HuangY.Local spectra features extraction based-on 2D Pseudo-Wigner distribution for texture analysis. In Proceedings of the International Conference onPattern Recognition, 2000, Vol. 3, pp. 913–916.
40.
ZhangK. G.WhitehouseD. J.The application of the Wigner distribution function to machine tool monitoringProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 1992, 206, 249–264.
41.
WhitehouseD. J.ZhangK. G.The use of dual space-frequency functions in machine tool monitoringMeasmt Sci. Technol., 1992, 3, 796–808.
42.
HlawatschF.Interference terms in the Wigner distributionDigital Signal Processing, 1984, 84, 363–367.
43.
JeongJ.WilliamsW. J.Mechanism of the cross terms in the spectrogramIEEE Trans. Signal Processing, 1992, 40, 2608–2613.
44.
HormigoJ.CristóbalG.High resolution spectral analysis of images using the pseudo-Wigner distributionIEEE Trans. Signal Processing, 1998, 46, 1757–1763.
45.
HlawatschF.Boudreaux-BartelsG. F.Linear and quadratic time-frequency signal representationsIEEE Signal Processing Mag., April 1992, 21–67.
46.
ChoiH. I.WilliamsW. J.Improved time-frequency representation of multicomponent signals using exponential kernelsIEEE Trans. Acoust., Speech Signal Processing, 1989, 37, 862–871.
47.
RihaczekW.Signal energy distribution in time and frequencyIEEE Trans. Infn Theory, 1968, 14, 369–374.
48.
ZhaoY.AtlasL. E.MarksR.The use of cone shaped kernels for generalized time-frequency representations of nonstationary signalsIEEE Trans. Acoust., Speech Signal Processing, 1990, 38, 1084–1091.
GangepainJ. J.Roques-CarmesC.Fractal approach to two dimensional and three dimensional surface roughnessWear, 1986, 109, 119–126.
51.
RussJ. C.Fractal Surfaces, 1994 (Plenum, New York).
52.
ClarkeK. C.Computation of the fractal dimension of topographic surfaces using the triangular prism surface area methodComputers Geosci., 1986, 12, 713–722.
53.
LopezJ.HansaliG.ZahouaniH.Le BosseJ. C.MathiaT.3D fractal-based characterisation for engineered surface topographyInt. J. Mach. Tools Mfg, 1995, 35, 211–217.
54.
ThomasT. R.RosenB. G.AminiN.Fractal characterisation of the anisotropy of rough surfacesWear, 1999, 232, 41–50.
55.
PodsiadloP.StachowiakG. W.The development of the modified Hurst orientation transform for the characterization of surface topography of wear particlesTribology Lett., 1998, 3-4, 215–229.
56.
PodsiadloP.StachowiakG. W.Applications of Hurst orientation transform to the characterization of surface anisotropyTribology Int., 1999, 32, 387–392.
57.
SkandsU. P. V.RussJ. C.ConradsenK.Fractal surface investigation using iterated functional systemsJ. Computer-Assisted Microsc., 1995, 7, 191–210.
58.
StachowiakG. W.PodsiadloP.Surface characterization of wear particlesWear, 1999, 225-229, 1171–1185.
59.
PodsiadloP.StachowiakG. W.Scale-invariant analysis of wear particle morphology. I: Theoretical background, computer implementation and technique testingWear, 2000, 242, 160–179.
