explain me distribution of pressure in detail
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Answer:
3.2.3.2.1 Numerical analysis
The pressure distribution at the slot ports was modeled by the dimensionless Reynolds equation as
(3.2.7)Hs2∂∂Xs(∂P2∂Xs)+Hs∂∂Ys(∂P2∂Ys)=4Λ∂P∂τ
and, similarly, the pressure distribution at the journal port was modeled by the dimensionless Reynolds equation as
(3.2.8)∂∂θ(H3∂P2∂θ)+∂∂ζ(H3∂P2∂ζ)=2Λ∂(PH)∂θ+4Λ∂(PH)∂τ
where P is the pressure distribution, Hs is the slot clearance, H is the clearance between rotor and bearing, Λ is the bearing number, and τ is dimensionless time. Furthermore, H is given by the following equation:
(3.2.9)H=1+XG2+YG2cos[θ+(π−tan−1(YGXG))]
where XG and YG represent rotor geometric center displacement in the X and Y directions, respectively.
The Reynolds equation is a nonlinear partial differential equation, and so a direct numerical method is used for its solution. Eqs. (3.2.7) and (3.2.8) are discretized using the central-difference scheme in the Xs,Ys, θ, and ζ directions, and the implicit-backward-difference scheme in time τ. The pressure distribution was iteratively calculated using the Successive Over-Relaxation (SOR) method. Using the obtained pressure distribution, the load capacity is given by the following equations:
(3.2.10)Fx=2∫0L/2∫02π−Pcosθdθdζ
(3.2.11)Fy=2∫0L/2∫02π−Psinθdθdζ
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