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An analytical approach of the thermoelastohydrodynamic behaviour of mechanical face seals operating in mixed lubrication

Abstract This article presents a semianalytical analysis of mechanical face seals. The model takes an account of thermal effects and face distortions that are the principal determinants of the performance of mechanical seals. Since the fluid film thickness observed during the operation of mechanical face seals is generally a fraction of a micrometre, asperity contact is also considered. A closed-form solution for the elastic rough surfaces’ contact is obtained by assuming a simplified distribution for asperity height. It has been shown in a previous article that the behaviour of a non-contacting seal is a function of just two dimensionless parameters: the sealing number Se, which depends on the operating and design parameters of the seal, and the coning number Co, which is the ratio between elastic and thermal distortions. When contact involving asperities is considered, the number of dimensionless parameters rises to six. The behaviour of the seal is, in addition, a function of the ratio of the asperity height to the thermal distortion magnitude, the ratio of the elastic properties of the asperities to the sealed fluid pressure, the ratio between dry and viscous frictions, as well as the balance ratio. Nevertheless, this model allows one to determine in a simple and rapid way the performance of a mechanical seal: temperature of the faces, film thickness, leakage, dissipated power, proportion of contact, etc. The model is applied to several examples in order to illustrate the behaviour of a mechanical seal.