Leakage rate estimation of mechanical seals based on fractal contact surface analysis and experimental validation

Purpose The purpose of this paper is to develop a reliable method for estimating the leakage rate of solid contact surfaces, particularly in sealing devices. By integrating fractal geometry with contact mechanics, this research aims to provide a more accurate and scalable approach to characterizing surface roughness and predicting leakage behavior. This method helps engineers optimize seal design, enhance equipment efficiency and extend the service life of mechanical systems. Ultimately, it contributes to improving the safety, reliability and environmental protection of industrial equipment by minimizing fluid or gas leakage. Design/methodology/approach The methodology proposed in this study involves three main steps: capturing images of the solid contact surface to extract characteristic parameters, forming a Fractal Index-Roughness Space; solving the basic contact equations to determine the critical leakage line under specific contact area ratios; and analyzing strain energy to estimate the theoretical leakage rate at a given leakage channel height. This approach combines fractal surface characterization with contact mechanics principles to provide a robust estimation of leakage, useful for the design and analysis of sealing devices in practical engineering applications. Findings This project is funded by the Youth Science and Technology Fund of China National Machinery Industry Corporation (Project No. QNJJ-PY-2024–28). Originality/value The originality of this study lies in the integration of self-affine fractal analysis with traditional contact mechanics to estimate the leakage rate of solid contact surfaces. Unlike conventional roughness parameters, which only capture surface characteristics at specific scales, the proposed method provides a comprehensive, scale-independent approach. By using fractal surface characterization and strain energy analysis, this research offers a more accurate estimation of leakage behavior, which is crucial for improving sealing efficiency and the longevity of mechanical systems. The findings have significant value for the design and optimization of sealing devices in industrial applications.