Summary: | 博士 === 國立成功大學 === 機械工程學系碩博士班 === 94 === Abstract
There are two theories applied to deal with the microcontacts of two contact surfaces. One is the conventional G-W model established in the statistical form and the other is the fractal theory, in which the rough surface follows self-repetition over all length scales. In previous studies, the roughness parameters used in the statistical model or the fractal model were taken as invariant. However, this is unrealistic when two rough surfaces experience contact deformations, because the topography of each surface will be changed. Thus, these parameters should be varied with the different mean separation between the two contact surfaces. Instead of considering the fractal dimension (D) and the topothesy (G) as two invariants in the fractal analysis of surface asperities, in the present study, these two roughness parameters were varied by changing the mean separation (d) of the two contact surfaces, based on the logarithmic relationship between the total number of asperities N(a) with areas larger than a particular area and a. The relationship between the fractal dimension and the mean separation can be found theoretically. Two kinds of methods are proposed in this dissertation to find the relationships among the fractal dimension, the topothesy, and the mean separation. First, the variation of the topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained at different mean separations. Second, using the equality of the real contact area formulae expressed in two different forms, the topothesy evaluated at different deformation regimes can be expressed as a function of the fractal dimension and the mean separation. A numerical scheme is developed in this study to determine the convergent values of the fractal dimension and the topothesy corresponding to a given mean separation. The theoretical results of the contact spot number predicted by the present model show good agreement with the reported experimental results.
In the present study, the modified fractal theory model is applied to modify the conventional model (G-W model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the area density of asperities ( ) are no longer taken as constants, but are taken as variables as functions of related parameters, including the fractal dimension, the topothesy, and the mean separation of two contact surfaces. The fractal dimension and the topothesy which were varied by changing the mean separation of two contact surfaces were obtained solely using the theoretical model. The mean radius of curvature and the density of asperities were also varied by changing the mean separation. The topographies of a surface, obtained from theory, of different separations show the probability density function of asperity heights to be no longer a Gaussian distribution. Two kinds of methods were proposed to find the varied form of a non-Gaussian distribution function of asperities corresponding to the different mean separation (d). Both the fractal dimension and the topothesy are increased by increasing the mean separation. The density of asperities is reduced by decreasing the mean separation. The contact load and contact area results predicted by a variable D, G*, , and a non-Gaussian distribution are always higher than those with a constant D, G*, , and a Gaussian distribution.
Finally, the elastic-plastic microcontact model of a sphere in contact with a flat plate is also developed in the present study to investigate the effect of surface roughness on the total contact area and contact load. From the results of the finite element method, the dimensionless asperity contact area, average contact pressure, and contact load in the elastoplastic regime are assumed to be in a power form as a function of the dimensionless interference . The coefficients and exponents of the power form expressions can be determined by the boundary conditions set at the two ends of the elastoplastic deformation regime. The contact pressures evaluated by the present model were compared with those predicted by the Hertz theory without considering the surface roughness and the reported model (G-T model), including the roughness effect, but only operating in the elastic regime. The area of non-zero contact pressure is enlarged if surface roughness is considered in the microcontact behavior. The maximum contact pressure is lowered by the presence of surface roughness if the contact load is fixed. Under a normal load, both the average contact pressure and the contact area are increased by raising the plasticity index for the surface of the same surface roughness.
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