Effect of Optimized Slip and Texture Zone …
437
Here, h represents the fluid film thickness value:
h = c(1 + ε cos θ ) + h
(4)
Equation (3) is non-dimensionalized by defining the following dimensionless
parameters:
θ =
x
R
Z =
z
L
H =
h
c r
B =
b
c r
P n =
(P − P c )
P a
α =
6μU
R P a
R
C r
2
The non-dimensionalized form of Eq. (3) is:
∂
∂θ
H
3
1 +
3B
[H + B]
∂ P n
∂θ
+
∂
∂ Z
H
3
1 +
3B
[H + B]
∂ P n
∂ Z
=
∂
∂θ
α
H
1 +
B
[H + B]
(5)
To consider the effect of cavitation in bearing, the above equation is further
modified by the use of Elrod [19] cavitation algorithm.
∂
∂θ
H
3
1 +
3B
[H + B]
βg
∂φ
∂θ
+
R
L z
2 ∂
∂ Z
H
3
1 +
3B
[H + B]
βg
∂φ
∂ Z
=
∂
∂θ
α
φ H
1 +
B
[H + B]
(6)
where g and ∅ represent the cavitation index and fractional film content. The boundary
condition used for the solution of Eq. (6) is shown as below.
g(θ, Z ) = 0 φ < 1
g(θ, Z ) = 1 φ ≥ 1
The non-dimensional pressure in form of switch function and fractional film
content is defined as:
P n =
(gβ(φ − 1) − P c )
P a
(7)