Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the [Formula: see text]-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the [Formula: see text]-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

Due to the complexity of sealing surface topography, it is difficult to take the surface topography into consideration when building a leakage rate model theoretically. Therefore, a theoretical model for estimating the leakage rate of metal-to-metal seals based on the fractal theory of porous medium, which can objectively reflect the influence of sealing surface topography from a microscopic perspective, is proposed in the present work. In the approach, fractal parameters are adopted to characterize the sealing surface. The sealing interface is supposed to be a porous medium space and the intrinsic parameters are obtained through rigorous theoretical derivation. The results show that the topography parameters of the sealing surface have a significant effect on the intrinsic parameters of the pore space and lead to a significant influence on the leakage rate of metal-to-metal seals. Specifically, the smoother the sealing surface, the lower the leakage rate of the metal-to-metal seal. Moreover, the leakage rate decreases with an increase in the contact pressure, and, if the fluid pressure difference is too large, the sealing performance will be seriously reduced. The proposed model provides a novel way to calculate the leakage rate of metal-to-metal seals.

A contact model for rough surfaces based on the fractal theory is proposed in the present work. Firstly, the deformation of the material is divided into four stages: elastic deformation, the first elastoplastic deformation, the second elastoplastic deformation, and full plastic deformation. And the variation of material hardness is considered when analyzing the contact characteristics of a single asperity within the first and second elastoplastic deformation stages. Secondly, the size distribution function of contact spots at different frequency levels is derived. And the expressions of asperity critical frequency levels are rederived. Lastly, the feasibility and credibility of the proposed model are verified by comparison with other contact models and experimental data. The results show that when the variation of the material hardness is considered, the contact area of a single asperity in the first elastoplastic deformation stage becomes larger, while the contact area of a single asperity in the second elastoplastic deformation stage becomes smaller. Moreover, the critical asperity frequency levels of the rough surface are not constant, but the variables are related to the total real contact area of the rough surface and decrease as the real contact area increases. The proposed model is a modification and improvement of the existing fractal contact models, which can lead to a more accurate relationship between the contact load and the total real contact area of the rough surface.