Considering surface roughness O-ring lubricating-oil static seal leakage prediction via optimized circular plate gap model

Introduction 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. This study addresses this limitation by extending the classical parallel plate leakage theory to develop an optimized circular plate gap leakage model for O-rings. Methods A leakage rate correction factor μ 1 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 are theoretically calculated. Experimental validation is carried out under 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. Results At a differential pressure of 0.4 MPa, the leakage rate reaches 0.67 × 10 −12 m 3 /s when Ra = 3.2μm , which is 1.8 times that of the case with Ra = 0.8μm. Experimental results show that: (1) At the same surface roughness, the cumulative leakage volume increases with the increase of differential pressure; when Ra = 1.6μm, 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 = 3.2μm is about 1.7 times that at Ra = 0.8μm. Overall, the leakage rate increases almost linearly with the increase of both differential pressure and surface roughness. The relative error between theoretical and experimental values is within 15%. Discussion The relative error within 15% confirms the reliability of the proposed model. However, 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.