Fph3 8p 9ph 9ph

where p and g are the density and viscosity, respectively, of the lubricant, t is time, and U is the sum of the surface velocities. The pressure distribution is typically subjected to zero-pressure inlet and Reynolds outlet boundary conditions. The lubricant film thickness h is given by the following:

where h0 is the reference film thickness, g0 is the undeflected geometric gap between the two surfaces, and d is the composite elastic deformation of both surfaces. The geometric gap is calculated to be:

2Req where Req = (1/RA + 1/RB)-1 is the equivalent radius of curvature as defined by Hertzian theory. The surface deflection, meanwhile, is governed by the elasticity equation for semi-infinite solids under applied load:

Fig. 18.16 Film thickness distribution in EHL, from [51]

Fig. 18.16 Film thickness distribution in EHL, from [51]

\-i the where v is Poisson's ratio and E = 2((1 — vA)/EA + (1 — vB)/EB)~ Young's modulus.

The lubricant viscosity, meanwhile, has been shown to increase with increasing pressure. A simplified model that describes this phenomenon, known as piezo-viscosity, is given by the Barus Equation, as follows:

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