# Tribology:Numerical solution of finite Journal Bearing-Reynolds condition.

1. May 5, 2010

### nanunath

Hi...:)

I need help as to how to solve the Reynolds equation:
$$\partial$$h/$$\partial$$t - $$\partial$$((h3/12n)*$$\partial$$p/$$\partial$$x) - $$\partial$$((h3/12n)*$$\partial$$p/$$\partial$$z) + $$\partial$$(U0*h*.5)/$$\partial$$x + $$\partial$$(W0*h*.5)/$$\partial$$z = 0
For a finite journal bearing assuming $$\partial$$h/$$\partial$$t = 0
And W0 = 0
The eqn becomes :

- $$\partial$$((h3/12n)*$$\partial$$p/$$\partial$$x) - $$\partial$$((h3/12n)*$$\partial$$p/$$\partial$$z) + $$\partial$$(U0*h*.5)/$$\partial$$x = 0

Plz help me as to how I can account the "Reynolds condition" :
p(0) = 0
p($$\theta$$2) = 0
$$\partial$$p/$$\partial$$$$\theta$$2 = 0
in the numerical soultion.

Also which discretization scheme would be better?
(i-(1/2)), (i + (1/2)) and (j -(1/2)), (j + (1/2))
or
i+1, i-1 and j+1, j-1

{PS: i in X direction , j in Z direction, and h varies only in X direction}

Plz help....

Last edited: May 5, 2010