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Hydraulic Film lubrication. [ PMICHEL ]
From the author’s Engineering Collection, included in the ETSII4 module (ETI4 on the CL Library)

This program calculates the required flow Q and front edge thickness (b1) on a film lubrication inclined pad with a perpendicular load F and moving at a uniform speed U0. The geometric data required may be either the slope angle (beta) or the thickness of the oil film at the lower end (b2).

tan(beta) = (b1-b2)/L

The formula for the radial force is a non-explicit equation on b1, the thickness of the front edge of the fluid film. This can be resolved with a root-finder routine like SLV, also included in the module.

The expression is given below, where mu is the fluid viscosity:

Fr = [2 mu U0 L / (b1-b2)] [ 2 Ln (b1/b2) – 3 (b1-b2)/(b1+b2) ]

And the flow required:

Q = U0 b1b2 / (b1+b2)


Calculate Q and b1 for a Michell pad moving at 15 m/s and bearing a perpendicular load of 200,000. The geometric parameters of the pad are 0.2 m deep x 0.4 m long, and the tapper slop is 0.0573 deg. The fluid viscosity is mu = 0.01 N/s m^2

The solutions are shown below:

b1=99,327E-6 m
b2=59,327E-6 m
L=0,4000 m
SLOPE<)=0,0001 rad

mu=0,0100 N/s m^2
U0=15,0000 m/s
F=1.000.000,000 N
FR=823,0323 N
Q=0,0006 m^3/s
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