1. – An Alternative Cavitation Analysis University of Arkansas
2007 STLE/ASME International Joint Tribology Conference
Rolling Stream Trails
– An Alternative Cavitation Analysis
Coda H. Pan
Global Technology
Tae Ho Kim
Texas A&M University
Joseph J. Rencis
University of Arkansas
IJTC
October

2. Eccentric rotating shaft
INTRODUCTION
Fluid film bearings generate hydrodynamic pressures in the region of local converging film thickness due to an eccentric rotating shaft
Cavitation zone
Bearing
Eccentric rotating shaft Z Ω
Fluid film
At fluid film trailing edge, low film pressure close to ambient pressure causes cavitations (film rupture).

3. Previous works Fluid film cavitations
Gumbel(1914): Half-Sommerfeld solution (No sub-ambient pressure due to rupture)
Swift (1932) and Stieber(1933): Reynolds boundary condition (Pressure gradient is zero at the boundary of the void)
Floberg (1957): Fluid transport streamers associated to the tensile strength of the fluid.
Olsson (1965): A trans-rupture continuity equation to determine the speed of a moving rupture point
Dowson (1974): Visual observations of the ruptured film in the steady-state operation
Elrod (1981): Universal cavitation algorithm. Two dimensional rupture model in the bearing film. Most comprehensive model to date.

4. Simplified Film pressure field
Reynolds boundary condition (dP/dx = 0, P=0)
Half-Sommerfeld (P=0)
Centerline pressures for Gumbel and Reynolds boundary conditions.
Reynolds boundary may not satisfy flow continuity in the cavitation zone except at its onset.

5. Fluid film cavitation Time varying rupture boundary
Adhered film flowing parallel to the shear surface velocity
Time increases
Half-Sommerfeld
Steady-state
Transient film model

6. Width fraction of streamer in rupture front: 0< γ <1
Objective
Elrod cavitation algorithm is most popular but does not treat the Olsson equation which considers the morphology model (partial film separation) for the ruptured region.
Full film
New cavitation model
Emphasizing coexistence of ligament and ventilated cavitation regions side by side in rupture front.
Speed increases
Full film
Void
Film extending A A
Width fraction of streamer in rupture front: 0< γ <1 B B
Dowson (1974)

7. Fluid film flow velocity profiles
A-A
Coexistence of ligament and ventilated cavitation regions side by side in rupture front.
Wetting terminated
Wet void in rupture front
Gumbel rupture
Wetting trace
Width fraction of streamer in rupture front: 0≤ γ <1 ωR
Ventilated cavitation regions
Streamer in rupture front
ωR/2 ωR
ligament regions
B-B

8. Schematic of journal bearings
L/D < 2
Long bearing,
i.e. dp/dz ~ 0
Where
D = Diameter
L = Length
P = Film pressure
Z= axial coordinate
One-dimensional analysis is useful for long journal bearings

9. Governing equation (filled fluid film)
1D Reynolds equation
Dimensionless form
where
where

10. General solutions Generalized Gumbel solution with
Swift-Stieber Steady state boundary condition:
is determined iteratively.
- Existence of a steady state rupture location,

11. Trans-rupture continuity (Olsson)
Rupture point speed
Formation point speed
No supply groove

12. Rupture point speed vs rupture point angle
Time increases
With a fixed formation point angle of – 90°, the uncavitated region is 292° (= 90°+ 202 °)

13. Phase Chart
With a fixed formation point angle of – 155°, the uncavitated region is eliminated.
Wet initial void
Dry initial void (γ = 0)
Solution approach from Gumbel to Swift-Stieber boundary.
Wet initial void increases the uncavitated region when compared to that with dry initial void.

14. Rupture boundary speedγ= γ= γ= γ= γ=
Time increases
Initial rupture point speed increases as the wet void portion (γ) increases. Final rupture point speed decreases to zero.

15. Time for arrival at the rupture locationγ= γ= γ= γ= γ=
Time for arrival at the current rupture boundary location increases as the wet void portion (γ) increases.

16. Formation boundary speedγ= γ= γ= γ= γ=
Time increases
Initial formation point speed increases as the wet void portion (γ) increases. Final formation point speed decreases to zero.

17. Formation point angle γ= γ= γ= γ= γ=
Formation point angle has different inverse-trajectories with different wet void portion (γ), as rupture point angle increases. Initial and final angles are identical.

18. Fully filled film thickness
No cavitation with fully filled fluid film

19. Swift-Stieber pressure and film thickness
In cavitated region, pressure is zero until the film is reformed.
Pressure gradient is zero at film rupture front.

20. Snapshots of pressure and film thickness fields.
Dry initial void (γ=0)
Pressure field
Snapshots of pressure and film thickness fields.
As time increase, Solutions move from Gumbel boundary to Swift-Stieber boundary
Time increases
Time increases
Film thickness field
Time increases

21. Snapshots of pressure and film thickness fields.
Wet initial void (γ=1)
Pressure field
Snapshots of pressure and film thickness fields.
With wet initial void, positive pressure and uncavitated film region increases.
Time increases
Time increases
Film thickness field
Time increases
Time increases

22. Swift-Stieber pressure profile
Present study with two component rupture front conditions predicts different pressure from full Sommerfeld pressure

23. Conclusions
Modeled film rupture front with two (wet and dry initial voids) boundary conditions.
=> Verified by experimentally observation.
Wet and dry initial voids show different pressure and film thickness behaviors.
Pressure profile is different from that obtained using Elrod Cavitation Algorithm
Alternative cavitation model.
Demonstrate viability of Rolling Stream Trail cavitation analysis.