Modeling Gas Leakage and Contact Pressure in Oil-Free Compressor Piston Rings

Piston rings in oil-free reciprocating compressors must provide effective sealing with minimal leakage and friction under fully dry-running conditions. This paper presents a unified, engineering-oriented analytical framework for predicting gas leakage, contact pressure, and wear in non-lubricated piston-ring packs. Gas leakage is modeled through three dominant paths: (a) ring–cylinder micro-clearance, (b) ring–groove clearance, and (c) the piston-ring end gap. Micro-scale clearance flows are described using Navier–Stokes-based relations, while end-gap leakage is treated as compressible throttling flow following the classical formulation of Eweis (1935). The flow model determines the inter-ring pressure distribution and the applied gas load acting on each ring. These pressures are then used as boundary conditions for an independent contact-mechanics analysis based on Greenwood–Tripp asperity theory, Bhushan’s deformation-based micro-gap model, and Wang’s mean-effective-pressure approach. Results show that, for typical industrial ring-pack geometries, the first ring sustains approximately 30–72% of the total pressure differential, while end-gap flow accounts for up to about 90% of total leakage in new rings. Wear predictions evaluated against PV limits for filled PTFE and filled PEEK demonstrate strong sensitivity to contact pressure and piston speed. The proposed framework provides a practical basis for piston-ring material selection, geometry optimization, wear-based ring-count determination, and long-term sealing performance assessment in oil-free reciprocating compressors.