1. SEMINAR (ME6692)
2015-16
Experimental And Numerical Studies
of
Cavitation Effects in
a
Tapered Land Thrust Bearing
(Copyright by ASME JANUARY 2015)
Authors : Presented By:
Yin Song Harveer Kumar
Xieo ren ME160095ME
Chun-wei Gu MACHINE DESIGN
Xue-song Li M.Tech (Ist Year)

2. Presentation Outline
 Objectives
 Cavitation and its effects
 Thrust bearing
 Experimental method
 Numerical Methods
 Results
 Conclusions

3. Objectives
 To make clear understanding of bubbly flow ,cavitation
and its effects
To provide better solution to eliminate the problem of cavitation

4. Cavitation
 Rapid formation and collapse of a vapour bubbles within a liquid
main cause of cavitation
Cavitation Process

5. Effects of Cavitation
 Generation of pressure waves
 Flow separation due to disturbance generation
 Smaller bubbles may be more detrimental to the
hydraulic machine body
EffectBubble
Formation
Zoom

6. Thrust Bearing
Definition:
A thrust bearing is a particular type of rotary rolling element
bearing.
Like other bearings they permit rotation between parts
Support the axial thrust of both horizontal as well as vertical shafts

7. Tapered Land Thrust Bearing
 Optimize only for one speed and load combination
 Taper for oil wedge formation is machined into the
bearing surface
 Alignment is critical to operation
 Practical load limit is 150 to 225psi
Simple Taper Compound Taper

8. Types of Thrust Bearing
Tilting pad type ( Michell type)
The surfaces are at an angle to each other
One surface is usually stationary while the other moves
Undergoes hydrodynamic lubrication, therefore formation
of a wedge of lubricant under pressure
The amount of pressure build up depends on the
speed of motion and viscosity
The pressure takes on axial loads

9. Tilted Pad Thrust Bearing

10. Experimental Method
Drive System:
 Drive is powered by 37kW Motor
 Rated speed 3000rpm
 Gearbox with increasing ratio 3.36
Diagrammatic view of test rig

11. Tested Thrust Bearing:
 Outer radius 90mm and inner radius 45mm
 Consist 4 tapered land without oil feed groves
 Bearing is made up of organic glass
 Collar and Backing disc made up of steel
Lubricant used ISO VG46 oil at 38℃
configuration
of the
tested bearing

12. Measuring System
Techno scope camera Kulite pressure sensor
(Accuracy 0.0075Mpa)
fig. 1
fig. 3
fig. 2

13. Numerical Methods
 Navior Stokes Equation (Conservation of momentum)
(01)
 Momentum equation in cylindrical coordinate
Momentum in r-direction
(02)

14.  Momentum in θ-direction
 Momentum in z-direction
(03)
(04)

15. Reynolds's Equation with centrifugal effects
Assumptions
 The fluid is assumed to be Newtonian, with direct proportionality
between shear stress and shearing velocity
 Inertia and body force terms are assumed to be negligible compared
to the viscous terms
 Variation of pressure across the film is assumed to be negligibly
small i.e dP/dz = 0
 Flow is laminar
 Curvature effects are negligible

16. Navier-Stokes equations for a sectorial configuration portrayed in Figure
(05a)
(05b)
figure

17. Now u=us +up , v ≡ vp where s refers to shear induced flow
p refers to pressure induced flow
up  us , v ≡ vp  us
So eq. (05) can be written as
(06a)
(06b)
Since us =U(y/h),the value of us at any particular film height (y/h) be the
same regardless of angular position θ, so we have
𝜕𝑈𝑠
𝜕𝜃
≈ 0

18. So we left with centrifugal term only
with boundary conditions
u= rω v=0 at y=0
u= rωB v=0 at y=h
By integrating and applying the boundary conditions we get u and v
in terms of pressure gradient.
(07a)
(07b)

19. From continuity equation we have
Integrating w.r.t y and assuming that there is no motion of the surface
then
(08)
Above u = u(y, θ) ,v = v(y, r) and since h = h(θ, r) by using Leibnitz’s rule
equation (08) can be written as
(09)

20. Evaluation of integral of eq. (07a & 07b) and eq. (09) we got the final
Reynolds’s equation in terms pressure distribution with centrifugal
terms
(10)
“ The Reynolds equation is solved with the finite-difference method,
by using the Gauss–Seidel method with over relaxation”
Using boundary conditions (gauge pressure)
p(θ = θo) = 0
p(θ = θ2) = 0

21. 3-D Navier Strokes Equation
Why 3-D NSE
 It fully describe the laminar flow property of the lubricants
without assumptions
 The realistic geometry of bearing can be easily simulated
 Easily incorporated with navier stokes solver with without
major modification to governing equations
The 3-D NSE
(11a)
(11b)

22. Rayleigh-Plesset Equation
The Rayleigh–Plesset equation describes the growth of a gas
bubble in a liquid
The R-P equation is given by
(12)
where R is the bubble radius, p is the surrounding pressure
ρ1 is the liquid density and pB pressure in the bubble
The variation with bubble radius is neglected and pB is treated as a constant
Neglecting the second order term in eq.(12)
(13)

23. If the bubbles grow from an initial average radius Rb, the cavitation
source term can be derived as with multiply by density (ρ) gives ṁ
(14)
Where N represent the number of bubbles per unit volume and ρg is
the bubble gas density
The liquid volume fraction equation can the be given by
(15)

24. Results (Flow visualization)
Flow visualization at different rotational speeds

25. Results (Pressure measurement)
Solution from Reynolds equation
And experimental
Solution from Reynolds equation
3-D NSE and experimental

26. When the circumferential angle is
smaller than 30 deg or larger than 70
deg, the measured oil–film pressure
falls to or below the atmosphere,
implicating presence of cavitation
Tapered area, i.e., 0 deg–60 deg, the 3D NSE
with R–P cavitation model has predicted
presence of cavitation, which agrees with
the experimental results, and the predicted
pressure profiles are much better than those
by the Reynolds equation.

27. In the radial direction, the gas
volume fraction at the inner end
is nearly zero in both the
cavitating region and non
cavitating region
3D NSE solution at 3400 rpm

28. Solution at Low Speed Conditions
Experimental 3-D NSE Solution
By analyzing the above figures it can be concluded that results deviate from
experiment visualization since almost no bubble are visible
?

29. Parametric Studies Results
Variations of load with speed for different
minimum film thicknesses
Effect of cavitation is more
significant at higher film
thickness

30. Variations of load with speed at different oil
supply pressures (ho = 240μm)
At higher supply, pressure
shift the load speed curve
upward

31. Contours of gas volume fraction at different speeds
(ho = 240μm)
 Cavitation area expands
prominently along both radial
and circumferential directions
with the increasing speed
 Enlarge cavitation area
depresses the higher pressure
region

32. Remedies for cavitation
 Operating pressure must be greater then the static pressure of
the fluid
 Oil Film thickness should be minimum
 Rotating part must have good surface finish
 Rotational speed should be optimum to increase the load capacity

33. Conclusions
 The observed cavitation area start from the interface between
adjacent pad
 In the rotational direction, the cavitation area starts from the
beginning of the tapered area, which agrees with the observed
phenomenon
The load capacity decreases as the rotational speed increases
due to increase in cavitation area
 Negative effects of cavitation can be reduced at smaller
film thickness and high supply pressure

34. THANK YOU