Abstract
The Reynolds second order non-linear differential equation, which governs the pressure distribution between two non-parallel surfaces in relative motion constituting a gas slider bearing system, contains a parameter ϵ and a function h( x) describing the bearing geometry. The exact analytical solution of this non-linear two-point boundary value problem has been obtained previously only when h( x) is a linear function (the Harrison solution). The present paper gives the exact solutions of this problem when the bearing geometry is described by the concave functions h( x) = ( Ax + B) σ , with σ = 2 5 , 1 3 and 1 4 and for arbitrary values of ϵ, A, B and the endpoint pressures. The solutions are given in terms of Bessel functions and an exponential integral.
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