A Unified Treatment of Thick and Thin Film Elastohydrodynamic Problems by Using Higher Order Element Methods

S. M. Rohde, K. P. Oh
1975 Proceedings of the Royal Society A  
A unified mathematical treatm ent of thick and thin film elastohydro dynamic lubrication problems is presented. The construction of approxi mate solutions is discussed by using Ritz-Galerkin methods with piecewise polynomial basis functions. In particular for the line contact problem, smooth Hermite and cubic spline spaces are used to obtain solutions over a wide load-speed range. Pressure 'spikes' are obtained. N o m e n c l a t u r e Hertzian half-width Breadth of slider modified Young
more » ... dified Young modulus, E ' 1 -vf 1 -tcE 1 film thickness minimum film thickness outlet film thickness of undeformed slider characteristic length (lx = b for slider; lx = a for line contact) characteristic length ( l2 = h0 for slider; l2 -R for line contact pressure characteristic pressure ( p= h%/(ju,0uh) for slider; p iet = E ' for equivalent radius of contacting surfaces, = 1 radii of cylinders, i -1,2 surface velocities in x direction (i =1,2) load per unit width coordinate in the direction of flow coordinate perpendicular to the direction of flow viscosity pressure exponent viscosity, fi = /<0eap viscosity a t p = 0 Poisson ratio otE' [ 315 ]
doi:10.1098/rspa.1975.0068 fatcat:33i2mvc2irbyplah4x6kmfdibe