The peak identification scheme based method (three-point definition) and the spectral moments based method (spectral moment approach) are both widely used for asperity peak modeling in tribology. To discover the differences between the two methods, a great number of rough surface profile samples with various statistical distributions are first randomly generated using FFT. Then the distribution parameters of asperity peaks are calculated for the generated samples with both methods. The obtained results are compared and verified by experiment. The variation rules of the differences between the two methods with statistical characteristics of rough surfaces are investigated. To explain for the discovered differences, the assumptions by spectral moment approach that the joint distribution of surface height, slope and curvature is normal and that the height distribution of asperities is Gaussian, are examined. The results show that it is unreasonable to assume a joint normal distribution without inspecting the correlation pattern of [z], [z'] and [z"], and that the height distribution of asperities is not exactly Gaussian before correlation length of rough surface increases to a certain extent, 20 for instance.
Wei Zhou
,
Daiyan Zhao
,
Jinyuan Tang
,
Jun Yi
. A Comparative Study on Asperity Peak Modeling Methods[J]. Chinese Journal of Mechanical Engineering, 2021
, 34(4)
: 61
-61
.
DOI: 10.1186/s10033-021-00584-1
The peak identification scheme based method (three-point definition) and the spectral moments based method (spectral moment approach) are both widely used for asperity peak modeling in tribology. To discover the differences between the two methods, a great number of rough surface profile samples with various statistical distributions are first randomly generated using FFT. Then the distribution parameters of asperity peaks are calculated for the generated samples with both methods. The obtained results are compared and verified by experiment. The variation rules of the differences between the two methods with statistical characteristics of rough surfaces are investigated. To explain for the discovered differences, the assumptions by spectral moment approach that the joint distribution of surface height, slope and curvature is normal and that the height distribution of asperities is Gaussian, are examined. The results show that it is unreasonable to assume a joint normal distribution without inspecting the correlation pattern of [z], [z'] and [z"], and that the height distribution of asperities is not exactly Gaussian before correlation length of rough surface increases to a certain extent, 20 for instance.
[1] V L Popov, R Pohrt. Friction and Wear: From Elementary Mechanisms to Macroscopic Behavior. Lausanne: Frontiers Media, 2019.
[2] Y Q Wen, J Y Tang, W Zhou. Influence of distribution parameters of rough surface asperities on the contact fatigue life of gears. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2019, 234(6): 821-832.
[3] K Komvopoulos. A multiscale theoretical analysis of the mechanical, thermal, and electrical characteristics of rough contact interfaces demonstrating fractal behavior. Frontiers in Mechanical Engineering, 2020, 6: 36.
[4] J A Greenwood, J B P Williamson. Contact of nominally flat surfaces. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1966, 295: 300-319.
[5] Y Q Wen, J Y Tang, W Zhou, et al. A reconstruction and contact analysis method of 3-D rough surface based on ellipsoidal asperity. Journal of Tribology, 2020, 142: 041502.
[6] Y Q Wen, J Y Tang, W Zhou, et al. An improved simplified model of rough surface profile. Tribology International, 2018, 125: 75-84.
[7] H Deng, Z Xu, L Q Wang, et al. Laser micro-structuring of a coarse-grained diamond grinding wheel. International Journal of Advanced Manufacturing Technology, 2019, 101: 2947-2954.
[8] M S Longuet-Higgins. Statistical properties of an isotropic random surface. Philosophical Transactions of the Royal Society A Mathematical Physical & Engineering Sciences, 1957, 250: 157-174.
[9] P R Nayak. Random process model of rough surfaces. Journal of Lubrication Technology, 1971, 93: 398-407.
[10] J I McCool. Comparison of models for the contact of rough surfaces. Wear, 1986, 107: 37-60.
[11] G Pawar, P Pawlus, I Etsion. The effect of determining topography parameters on analyzing elastic contact between isotropic rough surfaces. Journal of Tribology, 2013, 135: 011401.
[12] W Zhou, J Y Tang, Y F He. Formulae of roughness peak distribution parameters with standard deviation and correlation length. Proceedings of the Institution of Mechanical Engineers, Part J Journal of Engineering Tribology, 2015, 229: 1395-1408.
[13] A Poga?nik, M Kalin. How to determine the number of asperity peaks, their radii and their heights for engineering surfaces: A critical appraisal. Wear, 2013, 300: 143-154.
[14] M Kalin, A Poga?nik, I Etsion. Comparing surface topography parameters of rough surfaces obtained with spectral moments and deterministic methods. Tribology International, 2016, 93: 137-141.
[15] S Panda, A Panzade, M Sarangi, et al. Spectral approach on multiscale roughness characterization of nominally rough surfaces. Journal of Tribology, 2016, 139: 031402.
[16] W R Chang, I Etsion, D B Bogy. An elastic-plastic model for the contact of rough surfaces. Journal of Tribology, 1987, 109: 257-263.
[17] S Hu, W Huang, N Brunetiere, et al. Stratified effect of continuous bi-Gaussian rough surface on lubrication and asperity contact. Tribology International, 2016, 104: 328-341.
[18] X Zhang, Y Xu, R L Jackson. An analysis of generated fractal and measured rough surfaces in regards to their multi-scale structure and fractal dimension. Tribology International, 2017, 105: 94-101.
[19] D J Whitehouse, J F Archard. The properties of random surfaces of significance in their contact. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1970, 16: 97-121.
[20] W Hirst, A E Hollander. Surface finish and damage in sliding. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1974, 337: 379-394.
[21] H Aramaki, H S Cheng, Y W Chung. The contact between rough surfaces with longitudinal texture. I: Average contact pressure and real contact area. Journal of Tribology, 1993, 115: 419-424.
[22] A Francisco, N Brunetiere. A hybrid method for fast and efficient rough surface generation. Proceedings of the Institution of Mechanical Engineers, Part J Journal of Engineering Tribology, 2016, 230(7): 747-768.
[23] Y F He, J Y Tang, W Zhou. Research on the obtainment of topography parameters by rough surface simulation with fast Fourier transform. Journal of Tribology, 2015, 137: 031401.
[24] B Sista, K Vemaganti. Estimation of statistical parameters of rough surfaces suitable for developing micro-asperity friction models. Wear, 2014, 316: 6-18.
[25] T R Thomas. Rough surfaces. London: Imperial Coll Press, 1999.
[26] A Sklar. Random variables, joint distribution functions, and copulas. Kybernetika Praha, 1973, 9: 449-460.
[27] U Cherubini, B Luciano, W Vecchiato. Copula methods in finance. England: John Wiley & Son, 2004.
[28] P R Nayak. Random process model of rough surfaces in plastic contact. Wear, 1973, 26: 305-333.
[29] J A Greenwood. A note on Nayak's third paper. Wear, 2007, 262: 225-227.
