Synergistic Optimization of Compliant Foil Seals: Variable-Thickness Design and Surface Micro-Textures

As an advanced non-contact dynamic sealing technology, compliant foil seals offer notable advantages, including a simple structure, light weight, ease of installation, and strong self-adaptability. However, in most designs, the foil stiffness is uniform, resulting in a substantial increase in gas leakage under high inlet pressures. Considering the distinct pressure conditions in compliant foil seals, a variable foil thickness model (VTM) along the axial direction is designed to match the pressure gradient from the inlet to the outlet. By aligning the foil thickness variation with the pressure gradient, the foil deformation is more uniformly distributed axially, thereby maintaining low leakage under high-pressure differentials. In this study, the gas film thickness equation and the Reynolds equation for the compliant foil seal are established and solved using the finite difference method combined with a point-wise iterative approach. First, the static characteristics of a traditional uniform-stiffness compliant foil seal under different rotational speeds and inlet pressures are analyzed. The results indicate that leakage increases substantially under high inlet pressure. The performance of the VTM under different operating conditions—including rotational speed and inlet pressure—is investigated. The results show that an appropriately designed VTM can maintain very low leakage under high-parameter conditions, albeit with some sacrifice in gas film pressure and an increase in viscous friction. Furthermore, surface micro-textures are integrated with the VTM. The study finds that the two approaches exhibit complementary effects: micro-textures enhance the dynamic pressure effect of VTM, while the variable-thickness design maintains extremely low leakage. The combined model demonstrates excellent performance across different speeds and inlet pressures. For instance, at a rotational speed of 30,000 r/min, the gas leakage is reduced by 50.04%, and the maximum gas film pressure is increased by 70%.