On a problem of the theory of lubrication governed by a variational inequality

Abstract

The hydrodynamic lubrication of a complete journal bearing of finite width is studied using the theory of variational inequalities: we deal mainly with existence, uniqueness and regularity of the solution.

The MINPACK-2 test problem collection

“…In the formulation of Cimatti [9], all functions in K were required to be periodic in the first argument with period 27r; in our formulation we have neglected the periodicity conditions.…”

Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization

“…We consider the variational inequality arising from the Reynolds lubrication equation; see for instance [2,9,10,15,16] for details. The control u has the meaning of the height of the gap between two rotating surfaces, and the state y corresponds to the pressure in the lubricant, which fills the gap.…”

“…One instance is the elastohydrodynamic lubrication problem in a journal bearing, where e(z) = µ −1 z 3 , f (u) = −c ∂u ∂x2 , with µ the constant viscosity coefficient and c a constant relative velocity; see for instance [2,10,15,16]. The coefficient depends on the distributed height function u between two rotating surfaces, and y represents the pressure in the lubricant which fills the gap between the surfaces.…”

On some singular perturbation problems in the theory of lubrication

“…The behaviour of a lubricant within the clearance between two bodies in relative motion can be studied, over a wide range of conditions, through the solution of a boundary problem (see for instance [3], [4]) which can be given also a variational form ( [1], [4], [6]). Some of the boundary conditions are obviously suggested by the physical circumstances; others are still in dispute (see for instance [2]).…”