Application of fluid-structure interaction technique for the
TEHD lubrication problems of the bidirectional thrust
bearings
Liming Zhai1, 2, Zhengwei Wang1, 2, *, Yongyao Luo1, 2, Zhongjie Li1, 2, Xin Liu1, 2
ISROMAC 2016
International
Symposium on
Transport
Phenomena and
Dynamics of
Rotating Machinery
Abstract
Thrust bearing lubrication involves fluid-thermal-structural interactions between the oil film, the pad and
the runner collar. This study used the FSI technique to investigate the lubrication characteristics of a
bidirectional thrust bearing for several typical operating conditions to analyze the influences of the operating
conditions and the thrust load on the lubrication characteristics. The results show only a very small part of
heat is dissipated through the pad and collar, while most of the heat is carried away into the fresh oil by the
film flow. The heat out of the inner radius surface, trailing surface and outer radius surface account for almost
80 percent of the total heat transferred into the pad. The heat transfer coefficients on the pad surfaces are
quite uneven with the largest on the leading surface and the least on the trailing surface. The eddies in the
space between the adjacent two pads result to the larger heat transfer coefficients on the leading surface
and less on the trailing surface.
Keywords
Bidirectional thrust bearing — TEHD — FSI — Heat transfer
Hawaii, Honolulu
April 10-15, 2016
1
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, China
Department of Thermal Engineering, Tsinghua University, Beijing, China
*Corresponding author: [email protected]
2
INTRODUCTION
The thrust bearings are one of the most crucial components
in large hydropower units which greatly affects units’ safe
and stable operation. A thrust bearing includes a thrust
collar, a mirror plate and several pads. The rotor load is
transferred to each pad through the thrust collar and the
mirror plate, and then to the base. A very narrow clearance
between the mirror plate and each pad is filled with the
lubricating oil during operation.
The lubrication of large thrust bearings is the
thermal-elastic-hydrodynamic (TEHD) problem. During
operation, high pressure is formed in the oil film
between the mirror plate and the pad which support the
thrust load. In addition, the oil film is heated by viscous
friction which leads to the temperature gradient in the
pad and collar (or mirror plate). Thus, the high pressure
in the film will result in mechanical deformation on the
pad and collar, while temperature gradient in the pad
and collar will cause the thermal deformation. In turn,
the total deformation will change the oil film thickness
and affect the pressure and temperature distribution in
the film. Luo et al. [1] theoretically and experimentally
analyzed the applications and operating conditions of
thrust bearings with different centrally supporting
structures and various operating conditions. Huang et al.
[2] [3] and Wu et al. [4] conducted experiments on a
bidirectional thrust bearing in a test rig and verified 3D
TEHD numerical results. They solved the Reynolds
equation, the energy equation, the film thickness
equation for the film with assumpted inlet temperatures
and then the heat conduction equation and the elastic
equilibrium equation for the pad with assumpted heat
transfer coefficients on the pad surfaces. The results
showed that the pressure center is almost at the pad
angular center rather than off the angular center in a
bidirectional thrust bearing. Wang et al. [5] used a CFD
model to do a 3D HD analysis of a bidirectional thrust
bearing to analyze the effects of the pad inclination angle
and the rotor speed on the lubrication. However, only the
HD model was used in the analysis. Recently, TEHD
calculations using FSI procedures which combine
computational fluid dynamics (CFD) and finite element
method (FEM) models have become more and more
popular for analyzing journal bearings [6] [7] and thrust
bearings [8] [9]. Wodtke et al. [10] used the FSI technique
to analyze the hydrodynamic lubrication bearing in journal
bearings and thrust bearings.. The oil film and the flow
surrounding the bearing pads were modeled with
inclusion of the viscosity shearing heat generation without
assuming temperatures at the film inlet and the heat
convection coefficients at the pad free surfaces which
were evaluated in the calculations and differed in different
locations in the FSI model. The temperatures,
displacements, heat fluxes and forces were exchanged at
the FSI interfaces between the oil flow and the pad.
Pajaczkowski et al. [11] used the FSI approach in
transient simulations of hydrodynamic tilting pad thrust
bearings with a ring-disc support system. The static oil
pocket and the inlet and outlet chambers were all
modeled. The results showed that the minimum oil film
thickness
almost
immediately
stabilizes,
while
stabilization of the deformations requires much more time.
This study applied the FSI technique to analyze the
lubrication of a bidirectional thrust bearing in a pump
storage unit. A 3D TEHD model was used for the thrust
bearing without the thermal and pressure boundary
condition assumptions for the pad and film. The basic
lubrication characteristics like oil film pressure,
temperature and thickness, the heat transfer coefficient
on the pad surfaces were analyzed first. Then the
mechanism of the heat dissipation and the wall heat
transfer coefficients on the pads are further discussed.
 20+T0 
 =0
3
 20+T 
3
(4)
Where μ0 is the dynamic viscosity of the oil at T 0, and T is
the absolute temperature. Since the lubrication oil is assumed
to be incompressible, the density-temperature and densitypressure effects were ignored in this study.
1.2 Solid region equations:
1. GOVERNING EQUATIONS
The numerical model of the thrust bearing consisted of
the fluid region (the oil film and the surrounding oil) and
the solid region (the pad and the runner collar). This
study coupled the computational hydrodynamics (CFD)
model for the fluid domain and finite elements analysis
(FEA) model for the solid domain to analyze the thermalelastic-hydrodynamic lubrication of the thrust bearing.
1.1 Fluid region equations:
The transient three-dimensional turbulent Navier-Stokes
equations were solved for the oil film flow including the
effects of the inertial force and body force terms. The
computational fluid dynamics method was used to solve the
momentum, continuity and energy conservation equations
with a temperature-dependent viscosity. The lubricant was
treated as a single-phase, incompressible, Newtonian fluid.
The Reynolds averaged continuity equation is



 U j   0
t x j
(1)
The Reynolds averaged momentum equations are
Ui


 UiU j 
t
x j
p



 ij   ui u j  SM
xi x j


(2)
 T

  u jh 
 

 x j

 
Ui  ij   ui u j   SE

x j 


0 u   C  0  u 


0 T   C tu  C t   T 
 K   K ut   u  F 
   


 0  K t   T  Q


(5)
where [M] is the element mass matrix, [C] is the element
structural damping matrix, [K] is the element stiffness matrix,
{u} is the displacement vector, {F} is the sum of the element
nodal force and element pressure vectors, Ct is the element
specific heat matrix, Kt is the element thermal conductivity
matrix, {T} is the temperature vector, {Q} is the sum of the
element heat generation load and element convection surface
heat flow vectors, [Kut] is the element thermoelastic stiffness
matrix.
The coupled solution method was used to solve the
fluid-thermal-solid interaction problem using existing
computational fluid dynamics and computational solid
mechanics methods with relatively little memory use.
The data exchange method for the thermal elastichydro-dynamic
interactions
must
satisfy
the
conservation of pressure, displacement, thermal flux,
and temperature at the interaction interface:
 f





 htot p 
 
 U jhtot 
t
t x j

 M 

  0
1.3 Fluid-thermal-solid interaction equation
The total Reynolds averaged energy equation is


x j
The thermoelastic finite element matrix equations are
detrived by applying the variational principle to the stress
equation of motion and the heat flow conservation equation
coupled by the thermoelastic constitutive equations as:
(3)
The dynamic viscosity of the lubricating oil decreases as
the oil temperature increases, especially at low oil
temperatures. The relationship between the viscosity and
the temperature is generally expressed as:
 n f   s  ns
d f  ds
q f  qs
(6)
T f  Ts
Where subscript f denotes the fluid and s denotes
the solid.
The commercial multi-physics software ANSYSTM
was used as the simulation platform with the MFX
feature for the TEHD lubrication simulation. The
algorithm iteratively solved the fluid domain (the oil film
model and surrounding oil) by CFX and solved the solid
domain model (the pad and runner collar) by
Mechanical APDL with the process shown in Fig. 1(a).
ANSYS interpolates between the two domains with all
the quantities (temperature, force, displacement, and
heat fluxes) exchanged during the solution process at
the matching surfaces. The oil pressure and heat
fluxes generated in the oil film were transmitted from
fluid flow model and then applied to the solids as
boundary condition. In turn, the temperatures and
thermal-elastic deformations of the pad and runner
were obtained from the solid model and used to modify
the oil film geometry. The mapping from one mesh to
the other was performed as presented in Fig. 1(b).
Thus, each mesh could be adjusted to the model
requirements usually with a fine mesh for the fluid
domain and a coarse mesh for the solid domain. The
two meshes only need to be geometrically
complementary in areas connected internally.
(a) Multi-physics process
the outlet of one being the inlet to the next. In this way,
the model gives a continuous result for a bearing
consisting of several pads with flow and energy transport
from a pad outlet to the next inlet just as in a real bearing.
A grid independence check gave a fluid domain with
about 167,000 8-nodel elements. The gap between the
pad and the collar was divided into 15 layers.
Table 1. Bearing dimensions and operating
conditions
Item
Value
Pad outer radius R1/mm
1335
Pad inner radius R2/mm
775
Pad angle θ/deg
31
Pad width, B/mm
560
Pad thickness H1/mm
203
Babbitt layer, H2/mm
3
Number of pads n
10
Total thrust load F/t
260
Rotational speed ω/r·min–1
500
Radial pivot position Or/mm
1065
Circumferential pivot eccentricity Oc/%
50
Collar outer radius R3/mm
1335
Collar inner radius R4/mm
775
Collar thickness H2/mm
660
Inlet flow rate Q/(L﹒s-1)
2.5
Oil supply temperature T/ ºC
25
(b) Conservative interpolation
Table 2. Material properties
Figure 1. Multi physics analysis
2. NUMERICAL MODEL
Material
Steel
Babbitt
Lubricant
ρ/(k·m-3)
7850
7420
890
E/Pa
2.10×1011
5.30×1010
-The technical and operational data for the bidirectional
thrust bearing are presented in Table 1. The bearing
v
0.33
0.33
-consisted of a runner collar and ten pads with flooded
-1
-1
50
38
0.145
lubrication in which all the pads were immersed in the λ/(W·m ·K )
oil contained in the bearing housing as shown in Fig. 2.
α/ K-1
1.20×10-5
2.20×10-5
3.8×10-4
To simplify the computations, the thrust load was
-1
-1
465
251
2000
assumed to be evenly distributed on each pad. The C/(J·Kg ·K )
rotational symmetry system was then used to simplify
μ40/(Pa·s)
--2.848×10-2
the model to a single sector. Figure 3 shows the
geometrical model of the single sector used for the Where ρ, E, v, λ, α, C, μ40 is the density, young's modulus, poisson's
numerical simulations, which consisted of one pad and ratio, thermal conductivity, thermal expansivity, specific heat and
one adjacent angular sector of the runner collar and the
oil flow (Fig. 3). The space between the pads was dynamic viscosity.
divided into one part adjacent to the upstream (leading)
edge and the other part adjacent to the downstream
(trailing) edge. A rotational periodic boundary condition
was used between these two parts to simulate the
entire bearing, which is a sequence of several pads with
Figure 2. Tilting pad in the bidirectional thrust bearing
The bearing was lubricated with Esso 32 oil which
was assumed to be incompressible, single-phase liquid
with a temperature-dependent viscosity. Fresh oil was
supplied to the bearing housing by the inlet boundary
condition with a constant flow rate at the given inlet
temperature. An opening boundary condition was
applied at the housing outlet to allow the oil to flow in or
out. A rotational boundary condition was applied at the
collar sliding. The fluid walls in contact with the pad and
the collar were set as fluid-solid interfaces. In addition,
the wall connecting to the FSI interface wall was set as
unspecified motion to allow the pad and collar to move
freely.
shaft axis. Machined geometrical features in the sliding
surface, chamfers and hydrostatic jacking recess were
omitted to simplify the computations. The top surface of
the collar was fixed except for its axial motion so that it
could move upwards or downwards due to the pressure
in the oil film and the external load on the collar.
Symmetric boundary conditions were used for the two
angular sides of the collar to ensure that the two sides
had the same deformation. The temperatures were
coupled along the angular direction in the collar
because the high rotational speed gives almost the
same temperatures in the angular direction. Equivalent
pressures were applied on the collar top surface to
simulate the thrust load. The pad and the collar were
also both supported by damper elements to improve the
numerical stability. Fluid-solid interaction surfaces were
imposed at all the external pad surfaces and the collar
sliding walls. The inner and outer cylindrical surfaces of
the collar are set as convention heat transfer boundary
with assumpted heat transfer coefficients and ambient
temperatures.
A uniform thickness oil film was initialized with a given
thickness between the pad and collar which could move
to a positions of static equilibrium. Too thin initial film will
lead to negative grids in the film and stop the
computation process, while too thick initial film will cost
too much time to reach the convergence. In this study,
500 μm is used as the initial thickness after some
attempts. To accelerate the process to the equilibrium, 20
iterative steps in one time step with the convergence
criteria of 1×10-4 and 5 iterative steps in one external
coupling step between the fluid and solid domain with the
convergence criteria of 1×10-2 are used.
3. Verification of the model
Since the thrust bearing in this study is a prototype,
there are no enough and abundant measurement data
collected during the operation. Only temperature was
monitored at the center of the cross-section 20 mm below
the pad sliding surface in real operation. Four typical
operation states including turbine mode with 300 MW,
turbine mode with 180 MW, turbine mode with no load
and the pump mode were computed. The corresponding
thrust load of the four modes are 260t, 310t, 330t and
150t, respectively. The numerical temperatures are
compared with the measured results as listed in Table 3.
The maximum error between the numerical and
measured results is only 2.06% which this numerical
(b) Fluid domain (oil film and surrounding oil)
model is acceptable to some extent. In addition, the
Figure 3. Numerical model of the thrust bearing
temperatures in different operation condition are almost
the same with that of the pump mode slightly higher than
The solid domain including the pad and collar was
those of the turbine modes.
meshed into 3,900 elements with mid-side nodes. The
pad and collar were made of steel with a Babbitt alloy
coating for the pad. The pad was supported on a disk
Table 3. Verification of the temperatures
which allow for tilting in both the angular and radial
directions. The disk was modeled as a 3D spar
element link180 with the option of compression-only.
Numerical Measured
Error
The disk was then locked against rotation around the
(a) Solid model (pad and collar)
(ºC)
(ºC)
(%)
Turbine, 300MW
58.17
56
2.06
Turbine, 180MW
59.07
57
1.84
Turbine, no load
59.42
58
2.06
Pump
56.05
58
0.09
4. RESULTS AND DISCUSSIONS
4.1 Oil film pressure
surface with maximum deformation of 176.34 μm near
the intersection of the trailing edge and outer radius.
The collar is slightly lifted up at the trailing edge and
significantly pushed down at the leading edge with
almost the same deformation in the angular direction.
The deformation of the pad and collar has the same
order of magnitude with the film thickness which will
greatly change the geometry of the film. The oil film
thickness distribution is shown in Fig. 6. The thickness
decreases gradually with rotational direction to form a
wedge shaped oil film produced a large thrust to support
the rotating part. The thinnest part is located near the
trailing edge with the value of only 142 μm.
Figure 4(a) and (b) show the pressure distributions n
the pad and collar sliding surfaces. The collar rotates from
the right side (leading edge) to the left side (trailing edge).
The two pressure distributions are quite similar. The
pressure has no pressure gradient through the film
thickness. In addition, the collar sliding surface is larger
than the pad. The pressure on the collar is very small
outside the pad region which means that the pressure in
the film is much higher than in the oil tank. Since the
support on the pad is located at the pad center for both
rotational directional, the high pressure is concentrated
almost at the center of the pad sliding surface rather than
close to the trailing edge for the directional thrust bearing
with eccentrically support. In addition, there are no
negative pressure region in the film which suppressed the
oil cavitation. Because the type of tilting pads is used in the
bearing, which makes pads tilt freely in both angular and
radial directions and then results in a thinner and thinner
film in the rotational direction.
(a) On the pad sliding surface
(b) On the collar sliding surface
Figure 5. Deformation of the film
(a) On the pad sliding surface
Figure 6. Oil film thickness（unit: μm）
4.3 Temperature
Figure 7(a) and (b) show the temperature distributions
on the pad and collar sliding surfaces. Unlike the
pressure, the temperature contours on the pad are quite
different from those on the collar. The temperature on the
pad near the trailing edge is much higher than the
4.2 TEHD deformation
leading edge due to the viscous friction in the oil film,
while the temperatures on the collar are almost the same
Figure 5(a) and (b) show the axial TEHD
in the angular direction, which means that the
deformation on the pad and collar sliding surfaces.
temperature gradient in the film is very large in the
The thermal deformation makes the pad form a convex
thickness direction with significant thermal conduction
(b) On the collar sliding surface
Figure 4. Pressure distribution in the oil film
across the field. The computation results give the as adiabatic boundaries to calculate the bearing
highest temperature on the pad as 68.35 ºC at the lubrication using the method iteratively solving the
trailing edge with the lowest as 50.36 ºC at the leading Reynolds and energy equations.
edge. Since the fresh oil is only 25 ºC, the temperature
at the leading edge is the result of mixing of the fresh oil
and hot oil from the trailing edge of the upstream pad.
The highest temperature on the collar is 61.85 ºC which
is higher than at the leading edge and lower than at the
trailing edge of the pad, because the collar continually
sweeps over the high and low temperature zone on the
pad so its temperatures are the mixture of the two
temperatures.
Figure 8. Heat flux through the pad
Table 4. Heat dissipation in the film
(c) On the pad sliding surface
Symbol
Heat（KW）
Proportion（%）
Ploss
109.04
100.00
Qpad
-1.16
1.06
Qcollar
-2.45
2.25
Qflow
-105.43
96.69
Where Ploss, Qpad, Qcollar, Qflow are the Frictional power loss per pad,
heat through the pad sliding surface, heat through the collar sliding
(d) On the collar sliding surface
Figure 5. Deformation of the film
4.4 Heat dissipation in the bearing
Viscous friction torque will act on the collar sliding
surface which causes friction power loss and lots of
heat in the film. There are three main dissipation
pathway for the heat generation in the film: through the
pad sliding surface, through the collar sliding surface
and carried to the spaces between the adjacent pads by
the film flow. Figure 8 shows the heat flux distribution on
the pad sliding surface where negative values mean the
heat transfers out of the film and into the pad. The heat
flux densities near the trailing edge and outer radius
edge are significantly larger than other zones on the
pad sliding surface with the maximum heat flux up to
60KW/m2. Integrate the heat flux on the pad and collar
sliding surfaces and get the quantities of the heat
through the two surfaces listed in Tab. 4. The heat
dissipations through the pad and collar sliding surfaces
only account for 1.06% and 2.25% percent of the friction
power loss in the film, and the remaining 96.69% of the
heat is carried into the space between the two adjacent
pads by the film flow and then transferred into the fresh
oil. Only a very small part of heat is dissipated through
the pad and collar. Therefore, it is reasonable to
assume the interfaces between the film and pad/collar
surface and heat carried away to the space by the film flow
As discussed before, one heat dissipation way is
through the pad where the heat first transfers into the pad
sliding surface, then out of the pad free surfaces and
finally dissipated by the surrounding fresh oil. All the
surfaces of the pad are marked in the Fig.9. Figure 10
shows the wall heat flux density on the pad free surfaces
where positive values mean the heat transfers out of the
pad and into the surrounding fresh oil. The heat flux
densities on the inner radius surface, outer radius surface
and trailing surface are larger than on the bottom surface
and leading surface. The heat quantities on all the
surfaces are listed in the Tab.5. The heat balance error of
the pad is only 1.97% which means almost all the heat
transferred into the pad flows out of the pad free
surfaces. The heat out of the inner radius surface, trailing
surface and outer radius surface account for almost 80
percent of the total heat with 34.10%, 28.14% and
19.16%, respectively. The heat out of the bottom surface
is the least with the proportion of only 7.15%.
surface are the largest, those on the outer radius
surface are less, those on the trailing surface, inner
radius surface and the bottom surface are almost the
same and the least. The largest coefficients of the
three parts are almost 4:2:1. It is interesting that the
heat transfer coefficients on the leading surface are
the largest while the heat dissipation through it is the
least.
Figure 9. Names of the pad surfaces
(a) On the pad sliding surface
Figure 10. Heat flux through the pad free surfaces
Table 5. Heat flux in the pad
Symbol
Heat（KW）
Proportion（%）
Qps
1.16
100.00
(b) On the collar sliding surface
Figure 11. Wall heat transfer coefficients on the pad
surfaces
Qpl
-0.08
7.15
Qpt
-0.33
28.14
Qpi
-0.22
19.16
Table 6. Range of the heat transfer coefficients on
Qpo
-0.39
34.10
the pad surfaces
Qpb
-0.16
13.42
ζ
-0.02
1.97
Where Qps, Qpl, Qpt, Qpi, Qpo, Qpb and ζ are the heat flux
through the sliding surface, through the leading surface,
through the trailing surface, through the inner radius
surface, through the outer radius surface, Through the
Item
Min (W·m2·K-1)
Max (W·m2·K-1)
Hs
4635
13583
Hl
511
7418
Ht
463
1843
Hir
362
1759
Hor
730
3997
Hb
294
1963
bottom surface and the heat balance error in the pad
4.5 Heat transfer coefficients on the
pad
Figure 11 shows quite uneven distribution of the
heat transfer coefficients on the sliding surface and
the free surface of the pad. Table 6 lists the range of
heat transfer coefficients on each surfaces of the
pad. The coefficients on the sliding surface are
significantly larger than the free surfaces. The free
surfaces have the same order of magnitude of the
transfer coefficients where those on the leading
Where Hs, Hl, Ht, Hir, Hor and Hb are the heat transfer coefficients on
the sliding surface, the leading surface, the trailing surface, the
inner radius surface, the outer radius surface and the bottom
surface.
Figure 12 shows the velocity distribution on the
angular sections of the space between the adjacent
two pads. Due to the rotating effects of the collar, there
exists eddies in the space with larger velocities close
to the leading surface which enhance the heat
transfer capability of the surface. Thus, the heat
transfer coefficients on the leading surface of the pad
are larger than the trailing surface.
ACKNOWLEDGEMENTS
The authors thank the National Natural Science
Foundation of China (Grant No. 51439002，Grant No.
51409148), and the Specialized Research Fund for the
Doctoral Program of Higher Education of China (Grant
No. 20120002110011, No. 20130002110072), the
State Key Laboratory of Hydroscience and
Engineering (Grant No. 2014-KY-05) for their financial
support.
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Figure 12. Velocity distribution between the two adjacent
pads
5. CONCLUSIONS
This study suggested the FSI technique to
analyze the TEHD lubrication characteristics of a
bidirectional thrust bearing in a pump storage unit.
This technique uses a full model of the thrust bearing
including not only the pad and collar but also the film
and the flow in the oil housing without thermal and
pressure boundary condition assumptions for the pad
and film, which enables a lubrication analysis with the
boundary conditions moved away from the lubricating
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transfer coefficient on the pad surfaces can be
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Only a very small part of heat is dissipated
through the pad and collar, while most of the heat is
carried away into the fresh oil by the film flow.
Therefore, it is reasonable to assume the interfaces
between the film and pad/collar as adiabatic
boundaries to calculate the bearing lubrication using
the method iteratively solving the Reynolds and
energy equations.
The heat out of the inner radius surface, trailing
surface and outer radius surface account for almost
80 percent of the total heat transferred into the pad.
The remaining heat flows out of the bottom surface
and the leading surface.
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are quite uneven. The free surfaces have the same
order of magnitude of the transfer coefficients with
the largest on the leading surface and the least on
the trailing surface. The eddies in the space between
the adjacent two pads result in the larger heat
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