Some Consideration concerning the Mathematical Modeling of the Cavitations in Hydrodynamic Lubrication

In this paper, we present some numerical results related to the properties of the cavitations flow thin lubricant film which occurs between two contact surfaces of an axial-symmetrical tribological system (called radial seal surfaces). First, in the frame of Reynolds’ model assumptions we get the homogenized equation generalized for the case when moving contact surfaces (rotor) has roughness properties and an arbitrary oscillatory motion around the parallel position with the other contact surface. Starting from the homogenized equation, we study the dynamics of free boundary of the domains where the cavitations flow occurs. The first our objective is study the flow of a viscous Newtonian incompressible fluid film which occurs between two non-parallel surfaces, denoted S2 (the rotor) and S1 (the stator), which define a tribological system with axial symmetry, known as radial faces seals. The non-parallel character of the two seals is induced by the action of external perturbations (the most frequent being those of the vibration type). Due to these perturbations we shall have a supplementary movement of the rotor, similar to the movement of a rigid body to a fixed point. The second our objective is the study of the non-parallelism of the two contact surfaces which induces the drastically modifications in the pressure field on the stator surface and consequently, the breakages of the lubricant film can appear on different zones of this. 2000 Mathematics Subject Classification: 76D08, 35Q30, 76A20, 80M40.