1. 33rd Turbomachinery Research Consortium Meeting
A FE Model for Static Load in Tilting Pad Journal Bearing with Pad Flexibility
TRC-B&C
Luis San Andrés
Mast-Childs Professor
Yingkun Li
Graduate Research Assistant
May 2013
Year III
TRC Project 32513/15196B
Computational Model for Tilting Pad Journal Bearings

2. Past TRC work 2010-12 TRC-B&C-01-2013
Pivot flexibility reduces the force coefficients in heavily loaded tilting pad journal bearings (TPJBs).
W, static load Y X
Housing
Pad
Pivot
Fluid film
Journal
W , Journal speed
d, Pad tilt angle x h
TRC-B&C
Developed XLTPJB®, benchmarked by test data, to predict K-C-M coefficients of TPJBs. Code accounts for thermal energy transport and the (nonlinear) effects of pivot flexibility. 2

3. 2013 funded by TRC (2 years) Kd = P + C∆T
$ 40,984
Objective: Enhance TPJB code to accurately predict pad surface deformations
Pad surface elastic & thermal deformations change bearing & pad clearances
Hydrodynamic pressure P
Kd = P + C∆T
Hot oil flow
K, Pad stiffness matrix
P, Fluid film pressure vector
C, Mechanical-thermal stiffness matrix
d, Pad displacement vector
Pivot constraint 3

4. Proposed work
$ 40,984
Build a 3-D FE ANSYS® model to obtain pad stiffness matrix. Reduce model with active DOFs.
Implement oil feed arrangements (LEG, spray bar blockers etc.) in the FE model
Construct new Excel GUI and Fortran code for XLTRC2
Digest test data and continue to update predictions using enhanced code. 4

5. Pad elastic deformation
TRC funded
$ 40,984
Under moderate to heavy loads, pivot and pad flexibility affect the static and dynamic forced response of TPJBs. XLTPJB© includes pivot flexibility and delivers improved predictions but does not account for pad flexibility.
Pad elastic deformation
Pressure field
Research objective:
Extend TPJB© code with effects of pad flexibility.

6. Tasks completed
Built FE structural models and extracted reduced stiffness matrices from ANSYS®
Included pad flexibility into XLTPJB© code for static force case
Compared predictions from the TPJB code against test data
Composed a guide for pad FE analysis with ANSYS®

7. FE pad model with ANSYS®5 6 7 8 1 2 3 4
FE pad model with ANSYS®
Circumferential direction, θ
Axial direction, z
Radial
direction, r
8-noded, isoparametric element
FE Model built in ANSYS®
Cylindrical coordinate (r,θ,z)
Degrees of freedom (DOFs)
of each node: ur, uθ, uz
NO ROTATIONS
Assemble over whole domain
K, stiffness matrix
u, Displacement load vector
Q, Load vector
S, Vector of surface tractions

8. Pad reduced stiffness matrix
z=0
z=L/2
z=-L/2
Boundary conditions: Desbordes’s model [1]
Loads: pressure field acting on pad upper surface
Pressure field
Reduce K matrix to active DOFs
Constraints along two lines:
ur=0
Constraints at a point (pivot):
ur=uθ=uz=0
K, Reduced stiffness matrix
up, Displacements load vector
f, Loads vector
[1] Desbordes. H., Fillon, M., Frene, J. and Chan, C., 1995, ASME J. Tribol, 117, 380

9. System of linear equations
Cholesky decomposition
K is symmetric positive definite, then Cholesky decomposition is applicable:
L: lower triangular matrix
System of linear equations
Back substitution
L is calculated prior to running XLTPJB®. Savings in processing time!

10. Fluid film thickness in a padY
Cp : Pad radial clearance
CB= Cp-rp Bearing assembled clearance
Rd= Rp+t : Pad radius and thickness
rp : Pad dimensional preload
dp : Pad tilt angle
xpiv, hpiv : Pivot radial and transverse deflections
up: Pad upper surface deformation
Pad Center OP
Fluid Film Ω RB
Bearing Center OB WY X WX θP RJ η θ θL
ξpiv h δp
Unloaded Pad up
ηpiv
Loaded Pad ξ
Pivot ΘP

11. Predictions for a four-pad TPJB
(Tschoepe) Four pad, Rocker-back tilting pad bearing (LOP)
Specific load, W/LD
0 MPa MPa (421 psi)
Journal speed, W
6.8krpm-13.2krpm X Y
Pad 3
Pad 2
Pad 4 W
Pivot offset=0.57
Journal
Fluid film
QP =72o
Pad 1
Number of pads, Npad 4
Configuration
LOP
Rotor diameter, D
mm (4 inch)
Pad axial length, L
60.33 mm (2.4 inch)
Pad arc angle, QP
72o
Pivot offset
57%
Preload,
0.589(pad1)
0.457(pad2)
0.559(pad3)
0.460(pad4)
Pad clearance, CP
112 µm (4.4mil)
Pad inertia, IP
1.81kg.cm2 (0.618lb.in2)
Oil inlet temperature
~43.3 oC (110 oF)
Lubricant type
ISO VG32
Supply viscosity, m0
0.023 Pa.s
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

12. Light load Film thickness and pad deformation: Film thickness
Rotor speed W =6.8 krpm
Specific load W/LD=726kPa
Film thickness and pad deformation: X Y q
Pad 2 W
Pad 1
Pad 3
Pad 1
Pad 2
Pad 4
Pad 3
Film thickness
Pad 4
Pad deformation
Pad 4
Pad 3
Pad 1
Pad 2
Deformation of loaded pad (#1) is very small compared to film thickness.
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

13. Large load Film thickness and pad deformation: Film thickness
Rotor speed W =6.8 krpm
Specific load W/LD=2.9MPa
Film thickness and pad deformation: X Y q
Pad 2 W
Pad 1
Pad 3
Pad 1
Pad 2
Pad 4
Pad 3
Pad 4
Film thickness
Pad deformation
Pad 4
Pad 3
Pad 1
Pad 2
Deformation of loaded pad (#1) is 30% of the minimum film thickness
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

14. Journal eccentricity vs. static loadX Y q
Pad 2 W
Pad 1
Max. 421 psi
-eY
-eX
: test data
: prediction for rigid pad
: prediction for flexible pad
Rotor speed W =6.8 krpm
Journal eccentricity agrees well with test data. Pad flexibility affects little the journal eccentricity.
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

15. Light load Pad temperatures
Rotor speed W =6.8 krpm
Specific load W/LD=726kPa
Pad temperatures X Y q
Pad 2 W
Pad 1
Pad 1
Pad 2
Pad 4
Pad 3
Oil Inlet temperature
: test data
: prediction for rigid pad
: prediction for flexible pad
Loaded pad
Predictions agree well with temperature in loaded pad
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

16. Large load Pad temperatures Predictions underestimate the temperature
Rotor speed W =6.8 krpm
Specific load W/LD=2.9MPa
Pad temperatures X Y q
Pad 2 W
Pad 1
Pad 1
Pad 2
Pad 4
Pad 3
Oil Inlet temperature
: test data
: prediction for rigid pad
: prediction for flexible pad
Loaded pad
Rotor speed W =6.8 krpm
Specific load W/LD=2.9MPa
Predictions underestimate the temperature
Tschoepe, D.P., 2012, Master Thesis, Texas A&M University.

17. Predictions for a five-pad TPJB
Five pad, Rocker-back tilting pad bearing (LBP)
Specific load, W/LD
1MPa-2.5MPa (363 psi)
Journal speed, W
500rpm-3krpm
Number of pads, Npad 5
Configuration
LBP
Rotor diameter, D
500mm (19.7 inch)
Pad axial length, L
350mm (13.7 inch)
Pad arc angle, QP
56o
Pivot offset
60%
Preload,
0.23
Bearing clearance, CB
300µm (11.81mil)
Pad inertia, IP
0.438kg. m2 (1496.7lb.in2)
Oil inlet temperature
~50oC (122 oF)
Lubricant type
ISO VG32
Oil supply viscosity, m0
Pa.s X Y
Pad 3
Pad 2
Pad 4 W
=0.23, CB=300 mm, Pivot offset=0.6
Journal
Fluid film
QP =56o
Pad 5
Pad 1
Hagemann, T., Kukla, S., and Schwarze, H., 2013, ASME GT

18. Film thickness Film thickness Pad deformation Rotor speed W =3krpm
Specific load W/LD=2.5MPa X Y q
Pad 3
Pad 2
Pad 4 W
Pad 5
Pad 1
Pad 1
Pad 2
Pad 4
Pad 3
Pad 5
Film thickness
Pad deformation
Pad 5
Pad 4
Pad 2
Pad 3
Pad 1
: test data
: prediction
Predicted film thickness correlates poorly with measurements
Hagemann, T., Kukla, S., and Schwarze, H., 2013, ASME GT

19. Film pressures
Rotor speed W =3krpm
Specific load W/LD=2.5MPa X Y q
Pad 3
Pad 2
Pad 4 W
Pad 5
Pad 1
Pad 1
Pad 2
Pad 4
Pad 3
Pad 5
: test data
: prediction for rigid pad
: prediction for flexible pad
Predicted film pressure < test data. ~20bar difference on loaded pads (#1 & #2).
Oil jacking ports located in pads #1 & #2.
Notes: flow in bearing is turbulent & test data shows much larger pad deformations (mechanical and thermal)
Hagemann, T., Kukla, S., and Schwarze, H., 2013, ASME GT

20. Conclusions
Selected examples for comparison do not show pad flexibility affects TPJB static load performance.
Considerable discrepancies exist between predictions and measurements for large size TPJBs.
FE pad model is too stiff leading to underestimation of the pad surface elastic deformation.
XLTPJB® models laminar flow bearings. Large size TPJBs operate in both the laminar & turbulent flow regions.

21. 2013 Continuation Proposal to TRC
Enhanced Computational Model for Tilting Pad Journal Bearing with Pad Flexibility
May 2013
Luis San Andrés
Mast-Childs Professor
Yingkun Li
Graduate Research Assistant
Year IV

22. Proposed work
Year IV
Enable model for operation with laminar/transition & turbulent flow conditions.
Validate the constructed pad FE structural surface deformation model with comparisons to test data.
Include pad flexibility on the prediction of frequency reduced TPJB dynamic force coefficients.
Construct the FE model that relates pad elastic deformation to thermally induced stresses.
Compare predictions from code to test data.

23. TRC Budget
Year IV
Year III
Support for graduate student (20 h/week) x $ 2,050 x 12 months
$ 24,600
Fringe benefits (0.6%) and medical insurance ($185/month)
$ 2,368
Travel to (US) technical conference
$ 1,200
Tuition & fees three semesters ($362/credit hour)
$ 8,686
Other (Mathcad® and portable data storage HD) $
Total Cost:
$ 37,073
XLTPJB® will continue to assist TRC members in modeling accurately TPJBs for specialized applications. The model and GUI reduce the burden on the unseasoned user by minimizing the specification of empirical parameters and guessing the correct boundary conditions for a proper analysis with thermal effects. 23