Modelling of the Behaviour of Dynamical Gas Seals: Calculation with a Finite Element Method Implicitly Assuring the Continuity of Flow

Abstract

The objective of this paper is to present a model of the behaviour of dynamical seals and the corresponding numerical results. These seals are used in the mechanism to realize partial sealing when the relative rotating speeds are too high for usual solutions. The studied seals mainly include two discs: one is attached to the shaft and the other to the body, the last one being pushed and the first being attached by springs. During operation, a gaseous film is created between the discs, preventing any contact. The control of the film thickness allows the leakage flow to be controlled. For the behaviour of such mechanisms, an analytical formulation of the problem is firstly presented. Then a geometrical and kinematical model having one degree of freedom is proposed to model the mechanism having two discs in relative rotation, one of which is spirally grooved. A dynamical model associated with the motion of the disc attached to the body has been developed and the mechanics of thin viscous films is used to study the behaviour of the gaseous film at the interface. Utilization of the finite element method in the mechanics of thin viscous films is introduced and a description of the elements used is presented. The influence of the groove's angle and the groove's depth is shown through numerical results concerning leakage mass flow through the mechanism and the loading capacity of the fluid film, as well as the coefficients of stiffness and damping associated with the dynamical model.