Research on the Truncated Asperity Size Distribution Function for the Two-dimensional Fractal Profiles

doi:10.3901/JME.2025.21.329

Abstract

Abstract: The accuracy of fractal model of contact between rough surfaces depends on the truncated asperity size distribution function which is obtained by derivative of the Korcak formula. The form of relationship between number of truncated asperities and diameter of section of truncated asperities is developed based on the Korcak formula, namely N(Λ>l)=λ(l_max/l)^B. The fractal profiles generated by Weierstrass-Mandelbrot function, Fourier transform and machining treatment, respectively are used to validate the developed form. The expressions for the parameters λ、B and l_max covering whole height of fractal profile are obtained. Then a revised truncated asperity size distribution function is given. The results show that the parameter B is related to the fractal dimension D and truncated interference. As the truncated interference is equal to the mean height of fractal profile, the value of B is D?1 approximatively. The parameters λ and l_max depend on the characteristics of profile, such as the reference sample length, the sample length, the parameters of profile etc. The expressions of λ and l_max are different for different profiles. The revised truncated asperity size distribution function and classic truncated asperity size distribution function are applied respectively to calculate the real truncated area of fractal profiles generated by Weierstrass-Mandelbrot function and machining treatment, and the values of real truncated area obtained by the revised truncated asperity size distribution function are really close to measured values of truncated area. As the sample length of fractal profile simulated by Weierstrass-Mandelbrot function equals γ^-n_min, the results of real truncated area obtained by the classic truncated asperity size distribution function are valid.

Key words: fractal profile, asperity, the truncated asperity size distribution function, sample length, truncation height

CLC Number:

TH117

LIU Shuai, YUAN Yuan, LIU Chenxi, QIAO Luqun. Research on the Truncated Asperity Size Distribution Function for the Two-dimensional Fractal Profiles[J]. Journal of Mechanical Engineering, 2025, 61(21): 329-344.

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