Considering Surface Roughness O-Ring Lubricating-Oil Static Seal Leakage Prediction via Optimized Circular Plate Gap Model

Zhengquan Wu^1*Guo-hai Zhuo²

• ¹Henan Institute of Technology, Xinxiang, China
• ²Shanghai Microelectronics Equipment (Group) Co., Ltd,, shanghai, China

Abstract: O-ring seals are critical to ensuring the reliability of mechanical systems under harsh operating conditions. However, the classical parallel plate leakage model often neglects the effects of surface roughness and radial pressure distribution, leading to insufficient prediction accuracy. To address this limitation, this study proposes an optimized circular plate gap leakage model for O-rings by extending the classical parallel plate leakage theory. A leakage rate correction factor μ1 is introduced to quantify the effect of surface roughness, establishing an equivalent relationship between the micro-scale rough interface and the ideal smooth surface. The leakage rates of rough surfaces with different roughness levels under various differential pressures were theoretically calculated. At a differential pressure of 0.4 MPa, the leakage rate reaches 0.67×10−12 m3/s when Ra=3.2 μm, which is 1.8 times that of the case with Ra=0.8 μm. Experimental validation was carried out under the conditions of differential pressures of 0.3 MPa and 0.6 MPa, as well as surface roughness Ra values of 0.8 μm, 1.6 μm and 3.2 μm. The results show that: (1) At the same surface roughness, the cumulative leakage volume increases with the increase of differential pressure; when Ra=1.6 μm, the cumulative leakage volume at 0.6 MPa is approximately 1.5 times that at 0.3 MPa; (2) At the same differential pressure, a larger Ra results in a higher cumulative leakage volume; at 0.3 MPa, the cumulative leakage volume at Ra=3.2 μm is about 1.7 times that at Ra=0.8 μm. Overall, the leakage rate increases almost linearly with the increase of both differential pressure and surface roughness. The relative error between the theoretical and experimental values is within 15%, which confirms the reliability of the proposed model. Despite this satisfactory verification, uncertainties in the model primarily stem from unaccounted factors, including high temperature, long-term O-ring aging, extreme high pressure, and idealized model assumptions. Consequently, the model is only valid under conditions of room temperature, low pressure, and short-term service. Nevertheless, this work provides a robust analytical framework for O-ring leakage prediction and sealing performance optimization in engineering applications.