A theoretical model for calculating the leakage rate of contact mechanical seals based on the fractal theory of the porous media, which can consider the real seal contact interface and objectively reflect the flow of the interfacial fluid from a microscopic perspective, is established. In order to obtain the microstructural parameters of the porous media included in the leakage model, such as the fractal dimension and the maximum pore diameter, the real seal contact interface obtained from experiments is reconstructed, a contact model between the dynamic and static rings is proposed, and then the calculation methods for the interface characteristic parameters are provided. Numerical simulation results show that as the contact pressure increases from 0.05 to 0.5 MPa, the interface porosity and the maximum pore diameter decreases gradually. Furthermore, the fractal dimension of the pore area increases and the leakage rate of the interface decreases from 0.48 to 0.33 mL/h. The proposed method provides a novel way of calculating the leakage rate of contact mechanical seals.

In this research, a model is proposed using piecewise fractal theory that considers abrasive and adhesive wear. The model demonstrated improved wear computation accuracy of a contact mechanical seal end face. The validity of the model was established by comparing the simulation results with experimental data and the conventional MB and Archard models. The loading effect and surface morphology parameters involved in wear were also investigated. Results show that severe wear occurs with increasing load ratio, large fractal dimensions, and a higher scale coefficient of the surface morphology. The findings offer a novel method for precisely calculating and projecting the amount of wear of a contact mechanical seal and predicting its wear behavior.

The fluid flow in the small pore throat is a nonlinear flow, and the microscopic force between the fluid and the wall cannot be ignored. However, the previously established theories about the leakage between sealing interfaces have not considered the influence of microscopic forces. Based on contact mechanics and percolation theory, the void characteristics of the sealing interface were clarified, and the influence of microscopic force on fluid flow in porous medium was analyzed. Combined with the capillary force, the concept of a critical void radius between the mechanical seal interfaces is proposed. The fluid flow resistance model and leakage rate calculation equation of the sealing interface considering the van der Waals force are established, and the leakage judgment criterion of the sealing interface is provided. Through numerical calculation and experiments, the effect of microscopic force is verified in terms of the fluid flow law and macroscopic leakage rate. The results show that van der Waals forces have an important influence on the fluid flow between the sealing interfaces. As the microchannel size decreases, the van der Waals forces between solid and liquid increase, and the influence of these van der Waals forces on the fluid flow between the sealing interfaces cannot be ignored. The calculation model of the sealing interface leakage rate proposed in this paper shows little difference with the results of the Persson model, and is in good agreement with the experimental results; the maximum relative error is 8.7%, the minimum relative error is only 3.8%.

The size and change of leakage channel within the mechanical seal interface are investigated to calculate and predict the leakage rate of mechanical seal. Based on the percolation theory, the computing method of the leakage channel within the mechanical seal interface is analyzed; the critical size and change of leakage channel and leakage rate are obtained. The results show that during the period of normal wear, the magnification of the leakage channel increases exponentially with load and time, the height of leakage channel follows a polynomial decline with load and decays exponentially with time. According to the load-dependence or time-dependence of magnification and height, the size of the leakage channel and the leakage rate of the mechanical seal could be calculated and predicted, which is helpful for the optimum design and safe operation of the mechanical seal.

The fluid leakage channel found in contact mechanical seals belongs to the microchannel category. Thus, upon further inspection, the influence of surface wettability and other factors neglected in previous studies becomes obvious. The porous leakage model of contact mechanical seals considering the surface wettability presented in this paper was based on the Cassie model and slip theory. The variations of the microchannel slip length and the velocity under various wettability conditions were studied and the relationship between the slip length and the apparent contact angle was established. Moreover, using porous media theory, the theoretical model of the leakage rate in contact mechanical seals considers the surface wettability depending on various parameters. The observed parameters included the surface contact angle, sealing medium pressure, viscosity coefficient, fractal dimension, and maximum pore diameter. The simulation results obtained using the proposed model have shown that the leakage rate increases with the increase of the apparent contact angle. Particularly when the contact pressure is small, the influence of the surface wettability is more significant. Furthermore, the leakage rate results obtained via the proposed model were compared to those of existing models. The comparison confirmed that the proposed model is applicable and that the necessity of considering wettability significantly affects the leakage rate calculation accuracy. The proposed model lays a foundation for further improving the calculation accuracy, making it easier for both the researchers and practitioners to suppress the leakage in contact mechanical seals.