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

[nanunath]

Hi...:)

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

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

Plz help me as to how I can account the "Reynolds condition" :
p(0) = 0
p([tex]\theta[/tex]₂) = 0
[tex]\partial[/tex]p/[tex]\partial[/tex][tex]\theta[/tex]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...

 

[Navin A S]

The Reynolds equation can be solved using the finite difference method. To account for the Reynolds condition, you need to set up the boundary conditions. The boundary conditions state that p(0) = 0, p(θ2) = 0 and ∂p/∂θ2 = 0. So, at the boundaries (i.e. at x=0 and x=θ2), you have to set the values of p accordingly.As for which discretization scheme is better, it depends on your application and the accuracy you require. The i-(1/2), (i + (1/2)) and (j -(1/2)), (j + (1/2)) scheme is more accurate than the i+1, i-1 and j+1, j-1 scheme. However, the i+1, i-1 and j+1, j-1 scheme is simpler and easier to implement.