Transcript Document

Analysis of the Coupled
Journal and Thrust Bearing
August 21 2004
Hakwoon Kim
PREM, Department of Mechanical Engineering
Hanyang University, Seoul, Korea
Contents
1.
2.
Motivation
Reynolds Equation
- Reynolds equation
- Boundary condition
- Load capacity and friction torque
- Finite element method for a coupled journal and thrust bearing
3.
Perturbation
- Physical perturbation
4.
Analysis Result
- Coupled analysis vs separate analysis of FDB of a 3.5 " HDD
- Reynolds BC vs half-Sommerfeld BC of FDB of a 3.5 " HDD
- FDB of a 1" Micro Driver with the effect of recirculation channel
- Result and discussion
5.
Future Work
-2-
Motivation
Journal
bearings
Plain
areas
Plain
areas
Thrust
bearings
Journal
bearings
Thrust
bearings
Plain
areas
< Structure of a 3.5" FDB spindle motor >
< Structure of a 1" FDB spindle motor >
• FDB of HDDs is composed of several sections, which are grooved or plain
journal or thrust bearings.
• Sometimes, they are connected through recirculation channel.
• One section affects the others in terms of pressure and flow of lubricant
-3-
Reynolds equation

Reynolds equation for journal bearing

R
 h3 p    h3 p  V h h

  
 

 12 R  z  12 z  2  t

h
C1
Journal
p  pa at z   L / 2
y
R
Sleeve
e
C2
r1
V
p  pa at z  L / 2
Line of Centers
p0, z   p2 , z 
z
- filmthickness : h  c  e cos 
F
x
L/2
2 
0
-L/2
< Journal bearing geometry >
-4-
Reynolds equation

Reynolds equation for thrust bearing
1   h3 p  
 r
 
r r  12 r  r
 h3 p  V h h

 

 12 r  2 r t
h  h ( r , )
V
Thrust
r
p  pa at r  ri
z

Thrust Pad
p  pa at r  ro
pr ,0  pr ,2 

ri
- filmthickness : h  c
ro
< Thrust bearing geometry >
-5-
r
Boundary condition
y
r1


Journal C1
Sleeve
e
C2
p
p
p
2



R

*

z
Line of Centers
F
< Full Sommerfeld BC >
< Half Sommerfeld BC >
< Reynolds BC >
x

The solution for a full 360 degree journal bearing leads to skew-symmetric pressure distribution.
 The pressures in the divergent film are all lower than ambient pressure.

The negative pressure can be neglected with the fact that the saturation pressure is similar to
ambient pressure
 But it violates the continuity of mass flow and pressure gradient at the outlet end of the pressure
curve.


p
p

p
,
 0 at    *
The better boundary condition is Reynolds BC, where
a

* can be determined numerically by the iterative method.
-6-
Load capacity and friction torque

Use the finite element method to solve Reynolds equation and to
determine the pressure distribution

Load capacity, friction torque and attitude angle of journal bearing
Fx   p cos  dA
Fy   p sin  dA
 Fy
F  tan 1 
 Fx
W  Fx2  Fy2



T f  R    xy dA

where,  xy
h p
R


2 x
h
Load capacity, friction torque of thrust bearing
Wz 
 p dA
 h p
r  2
 r drd
T f   

h 
 2 r
-7-
Finite element method for
a coupled journal and thrust bearing





Calculate the finite element
matrix for journal and thrust
bearing appropriately
Assemble the element matrix to
global matrix
Apply the BC at the external
boundaries
At the internal boundaries,
pressure and mass continuity is
automatically conserved
In case of Reynolds BC, the
global finite element equation
is iteratively solved until
Reynolds BC is satisfied
-8-
a
Part 1
Part 2
b
Part 3
a
External ambient pressure
p  pa
Interface
p part _ i  p part _ j
Periodic boundary
p  0  p  2
on a
on b
Perturbation

In the case of coupled journal and thrust bearing, the boundary value
problem can not be defined because the perturbed pressure
px , py , px , py , ... on the interface between the journal and the thrust
bearing is not defined

Physical perturbation has to be used for this case

Dynamic coefficients are calculated by comparing the change of
bearing reaction forces and moments with respect to the change of
translational and angular displacements and velocities in each
direction
-9-
Perturbation
3.1 Perturbation for journal bearing
 Step
 Step
 Step
h
2 : Calculate the initial load and moment with
respect to the new coordinate system
3 : Calculate the loads and moments
considering perturbed displacements and
velocities, i.e.
ex , ey ,  x ,  y , ex , ey , x , y ,
 Step
ey

1 : Set the coordinate system considering
attitude angle calculated by initial static
analysis
4 : Calculate the dynamic characteristics
from following equation
K
load
load
, C
displacem ent
velocity
- 10 -
c1
c2
F0
Y
ex
e x
Fy 2
Fx 2
K xx  
Fx1
X
Fy 2  Fy1
Fx 2  Fx1
, K yx  
ex
ex
< Geometrical description of physical
perturbation by ex >
Perturbation
3.2 Perturbation for thrust bearing
Z
 Step
1 : Set the coordinate system
 Step
2 : Calculate the initial load and moment with
respect to the fixed coordinate system
 Step
3 : Calculate the loads and moments
considering perturbed displacements and
velocities, i.e.
ez ,  x ,  y , ez , x , y ,
 Step
4 : Calculate the dynamic characteristics
K
load
load
, C
displacem ent
velocity
- 11 -
Fz2
e z
Thrust
h0
Fz1
Thrust pad
K zz  
Fz 2  Fz1
ez
< Geometrical description of physical
perturbation by ez >
h
Perturbation

Merits of physical perturbation
– It is not necessary to consider boundary values of perturbation
equations
– It can handle any case of hydrodynamic bearing including the coupled
journal and thrust bearing
– The radial-and-axial coupled stiffness and damping can be observed

Demerits of physical perturbation
– This method is dependent on the amount of perturbation, i.e.,
perturbed displacement and velocity
– It needs fine mesh for a good estimate
– It takes longer computational time than mathematical perturbation
method
- 12 -
Analysis result
4.1 Coupled analysis vs. separate analysis of FDB of a 3.5 " HDD
(1)
(2)
(3)
(6)
(4)
(5)
(7)
(9)
(8)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Plain region in journal
Upper journal bearing
Plain region in journal
Lower journal bearing
Plain region in journal
Upper thrust bearing
Plain region in journal
Lower thrust bearing
Plain region in thrust
( Plain 1 )
( Plain 3 )
( Plain 5 )
( Plain 7 )
( Plain 9 )
- 13 -
Analysis result

Specification of analysis model
Bearing Width [mm]
Upper Journal
Lower Journal
2.6
(Top:1.4, Bottom:1.2)
2.4
(Top:1.2, Bottom:1.2)
Upper Thrust
Lower Thrust
-
ID and OD of Thrust [mm]
-
Groove Pattern
Herringbone
Herringbone
Groove depth [m]
6.0
10.0
Groove Angle [deg]
20.0
20.0
Clearance [m]
2.5
9.0
Radius of Journal [mm]
2.0
-
Number of groove
6
12
0.3333
0.3333
Groove to Groove
and Ridge Ratio :
 Wg 


 Wg  WR 
ID : 5.0, OD : 6.8
Width of Plain Area [mm]
Upper Plain of Journal (Plain 1) : 0.4 ( Depth : 0.1 )
Center Plain of Journal (Plain 3) : 2.2 ( Depth : 0.1 )
Lower Plain of Journal (Plain 5) : 0.4 ( Depth : 0.1 )
Viscosity(25 deg C) [Pas]
0.016
Rotating Speed [rpm]
7200
- 14 -
Inner Plain : 0.5
( Depth : 0.03 )
Outer Plain : 0.2
( Depth : 0.03 )
ID : 4.0, OD : 6.8
Inner Plain : 0.5
( Depth : 0.03 )
Outer Plain : 0.2
( Depth : 0.03 )
Analysis result

Analysis model and result of pressure distribution
< Pressure distribution>
< Mesh for finite element method >



Number of node = 6121 [EA]
Number of element = 5508 [EA]
Element type : 4-node quadrilateral element
- 15 -
Analysis result

Result comparison between coupled analysis and separate analysis
• Pressure distribution



Eccentricity ratio = 0.1
Max pressure in upper journal = 3.344 [MPas]
Max pressure in lower journal = 3.314 [MPas]
< Coupled analysis of journal bearing >



Eccentricity ratio = 0.1
Max pressure in upper journal = 3.124 [MPas]
Max pressure in lower journal = 2.934 [MPas]
< Separate analysis of journal bearing >
- 16 -
Analysis result


Clearance = 9.0 [㎛]
Max pressure in upper journal = 509.1 [KPas]
< Coupled analysis of upper thrust bearing >
- 17 -


Clearance = 9.0 [㎛]
Max pressure in upper journal = 110.2 [KPas]
< Separate analysis of upper thrust bearing >
Analysis result



Clearance of lower thrust = 9.0 [㎛]
Clearance of center plain = 500 [㎛]
Max pressure in upper journal = 529.8 [KPas]
< Coupled analysis of lower thrust bearing >
- 18 -


Clearance = 9.0 [㎛]
Max pressure in upper journal = 125.3 [KPas]
< Separate analysis of lower thrust bearing >
Analysis result
• Static characteristics
Part
Coupled analysis
Separate analysis
Load capacity [N]
Friction torque [Nm]
Load capacity [N]
Friction torque [Nm]
Plain 1
1.06776e-005
2.42556e-006
-
-
Upper journal
3.04791e+000
5.31127e-004
3.00549e+000
5.30798e-004
Plain 3
2.19960e-003
1.33409e-005
-
-
Lower journal
2.60350e+000
4.89889e-004
2.51866e+000
4.89858e-004
Plain 5
7.16112e-004
2.42565e-006
-
-
Upper thrust
-1.18044e+001
1.99011e-004
5.42952e-001
1.98735e-004
Plain 7
4.27706e-005
1.41458e-005
-
-
Lower thrust
1.47111e+001
2.33986e-004
1.05478e+000
2.33815e-004
Plain 9
2.94034e+000
1.91859e-007
-
-
- 19 -
Analysis result
• Dynamic characteristics

Stiffness coefficient comparison
Coupled analysis
Separate analysis
Total system
Upper journal
Lower journal
Thrust part
Upper journal
Lower journal
Upper thrust
Lower thrust part
Kxx
1.5508e+007
8.3079e+006
7.2027e+006
0.0000e+000
8.3142e+006
7.2140e+006
0.0000e+000
0.0000e+000
Kyy
1.5295e+007
8.1344e+006
7.1635e+006
0.0000e+000
8.1451e+006
7.1677e+006
0.0000e+000
0.0000e+000
Kzz
5.9278e+005
0.0000e+000
0.0000e+000
5.9278e+005
0.0000e+000
0.0000e+000
1.5332e+005
4.3561e+005

Damping coefficient comparison
Coupled analysis
Separate analysis
Total system
Upper journal
Lower journal
Thrust part
Upper journal
Lower journal
Upper thrust
Lower thrust part
Cxx
3.9199e+004
2.1447e+004
1.7725e+004
0.0000e+000
2.1015e+004
1.7671e+004
0.0000e+000
0.0000e+000
Cyy
3.9184e+004
2.1402e+004
1.7755e+004
0.0000e+000
2.0922e+004
1.7701e+004
0.0000e+000
0.0000e+000
Czz
2.1473e+005
0.0000e+000
0.0000e+000
2.1473e+005
0.0000e+000
0.0000e+000
1.3796e+002
5.9448e+003
- 20 -
Analysis result
4.2. Reynolds BC vs half-Sommerfeld BC of FDB of a 3.5 " HDD
(1)
(2)
(3)
(6)
(4)
(5)
(7)
(9)
(8)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Plain region in journal
Upper journal bearing
Plain region in journal
Lower journal bearing
Plain region in journal
Upper thrust bearing
Plain region in journal
Lower thrust bearing
Plain region in thrust
( Plain 1 )
( Plain 3 )
( Plain 5 )
( Plain 7 )
( Plain 9 )
- 21 -
Analysis result

Specification of analysis model
Bearing Width [mm]
Upper Journal
Lower Journal
2.4
(Top:1.2, Bottom:1.2)
2.4
(Top:1.2, Bottom:1.2)
Upper Thrust
Lower Thrust
-
ID and OD of Thrust [mm]
-
Groove Pattern
Herringbone
Spiral
Groove depth [m]
6.0
10.0
Groove Angle [deg]
20.0
20.0
Clearance [m]
2.5
9.0
Radius of Journal [mm]
2.0
-
Number of groove
6
12
0.3333
0.3333
Groove to Groove
and Ridge Ratio :
 Wg 


 Wg  WR 
ID : 4.0, OD : 7.2
Width of Plain Area [mm]
Upper Plain of Journal (Plain 1) : 0.4 ( Depth : 0.1 )
Center Plain of Journal (Plain 3) : 2.2 ( Depth : 0.1 )
Lower Plain of Journal (Plain 5) : 0.4 ( Depth : 0.1 )
Viscosity(25 deg C) [Pas]
0.016
Rotating Speed [rpm]
7200
- 22 -
-
ID : 4.0, OD : 7.2
-
Analysis result
< Mesh for finite element method >



- 23 -
Number of node = 6121 [EA]
Number of element = 5508 [EA]
Element type : 4-node quadrilateral element
Analysis result

Result comparison between using half Sommerfeld BC and Reynolds BC
• Pressure distribution


Max pressure in FDB = 2.984 [MPas]
< Analysis result using half Sommerfeld BC >
- 24 -
Max pressure in FDB = 3.036 [MPas]
< Analysis result using Reynolds BC >
Analysis result



Eccentricity ratio = 0.1
Max pressure in upper journal = 2.984 [MPas]
Max pressure in lower journal = 2.971 [MPas]
< Analysis result using half Sommerfeld BC >
- 25 -



Eccentricity ratio = 0.1
Max pressure in upper journal = 3.036 [MPas]
Max pressure in lower journal = 3.105 [MPas]
< Analysis result using Reynolds BC >
Analysis result


Clearance of lower thrust = 9.0 [㎛]
Max pressure in upper journal = 39.467 [KPas]
< Analysis result using half Sommerfeld BC >
- 26 -


Clearance = 9.0 [㎛]
Max pressure in upper journal = 212.350 [KPas]
< Analysis result using Reynolds BC >
Analysis result



Clearance of lower thrust = 9.0 [㎛]
Clearance of center plain = 500 [㎛]
Max pressure in upper journal = 38.969 [KPas]
< Analysis result using half Sommerfeld BC >
- 27 -



Clearance = 9.0 [㎛]
Clearance of center plain = 500 [㎛]
Max pressure in upper journal = 213.540 [KPas]
< Analysis result using Reynolds BC >
Analysis result
• Static characteristics
Part
Half Sommerfeld boundary condition
Reynolds boundary condition
Load capacity [N]
Friction torque [Nm]
Load capacity [N]
Friction torque [Nm]
Plain 1
1.03087e-005
2.42556e-006
9.29389e-006
2.42556e-006
Upper journal
2.65314e+000
4.90212e-004
2.62102e+000
4.90341e-004
Plain 3
2.17523e-003
1.33409e-005
2.17079e-003
1.33409e-005
Lower journal
2.60357e+000
4.89889e-004
2.60358e+000
4.89889e-004
Plain 5
7.70566e-004
2.42565e-006
7.68795e-004
2.42565e-006
Upper thrust
- 1.31307e-001
2.62797e-004
- 2.91657e+000
2.55022e-004
Plain 7
0.00000e+000
1.41458e-005
3.06280e-004
1.41459e-005
Lower thrust
1.31140e-001
2.64862e-004
2.93510e+000
2.72671e-004
Plain 9
4.87674e-001
6.06371e-007
2.67233e+000
6.06371e-007
- 28 -
Analysis result
• Dynamic characteristics

Stiffness coefficient comparison
Half Sommerfeld boundary condition
Reynolds boundary condition
Total system
Upper journal
Lower journal
Thrust part
Total system
Upper journal
Lower journal
Thrust part
Kxx
1.4582e+007
7.3819e+006
7.2028e+006
0.0000e+000
1.4627e+007
7.4270e+006
7.2032e+006
0.0000e+000
Kyy
1.4501e+007
7.3406e+006
7.1633e+006
0.0000e+000
1.4546e+007
7.3860e+006
7.1631e+006
0.0000e+000
Kzz
2.2979e+006
0.0000e+000
0.0000e+000
2.2979e+006
2.5775e+006
0.0000e+000
0.0000e+000
2.5775e+006

Damping coefficient comparison
Half Sommerfeld boundary condition
Reynolds boundary condition
Total system
Upper journal
Lower journal
Thrust part
Total system
Upper journal
Lower journal
Thrust part
Cxx
3.5855e+004
1.8100e+004
1.7728e+004
0.0000e+000
3.5468e+004
1.7712e+004
1.7729e+004
0.0000e+000
Cyy
3.5909e+004
1.8128e+004
1.7754e+004
0.0000e+000
3.5517e+004
1.7737e+004
1.7753e+004
0.0000e+000
Czz
2.0680e+005
0.0000e+000
0.0000e+000
2.0679e+005
1.0397e+004
0.0000e+000
0.0000e+000
- 29 -
1.0397e+004
Analysis result
4.3. FDB of a 1" Micro Driver with the effect of recirculation channel
(1)
(8)
(2)
(3)
(4)
(5)
(9)
(1)
(2)
(3)
(4)
Plain region in journal
Upper journal bearing
Plain region in journal
Lower journal bearing
( Plain 1 )
(5)
(8)
(9)
Plain region in journal
Thrust bearing
Lower plain
( Plain 5 )
( Plain 3 )
( Plain 9 )
- 3 recirculation channels between upper thrust
bearing and lower plain thrust bearing
- 30 -
Analysis result

Specification of analysis model
Bearing Width [mm]
Upper Journal
Lower Journal
1.76
(Top:0.96, Bottom:0.8)
1.6
(Top:0.8, Bottom:0.8)
Thrust
Lower Plain
-
ID and OD of Thrust [mm]
-
ID : 4.6, OD : 6.0
ID : 0, OD : 1.25
Groove Pattern
Herringbone
Spiral
Plain
Groove depth [m]
5.0
15.0
0
Groove Angle [deg]
21.0
20.0
Clearance [m]
4.0
15.0
Radius of Journal [mm]
1.25
Number of groove
16
20
0.41667
0.5
Width of Plain Area [mm]
Upper Plain of Journal (Plain 1) : 0.1 ( Depth : 0.1 )
Center Plain of Journal (Plain 3) : 1.0 ( Depth : 0.1 )
Lower Plain of Journal (Plain 5) : 0.1 ( Depth : 0.1 )
Inner Plain : 1.05
( Depth : 0 )
Viscosity(25 deg C) [Pas]
0.016
Rotating Speed [rpm]
4200
Groove to Groove
and Ridge Ratio :
 Wg 


 Wg  WR 
500
-
- 31 -
-
Analysis result

Analysis model and result of pressure distribution
< Pressure distribution in FDB>
< Mesh for finite element method >



Number of node = 11041 [EA]
Number of element = 10000 [EA]
Element type : 4-node quadrilateral element
- 32 -
Analysis result

Result comparison between FDB with recirculation channel and FDB
without recirculation channel
• Pressure distribution



Eccentricity ratio = 0.1
Max pressure in upper journal = 302.960 [KPas]
Max pressure in lower journal = 297.770 [KPas]
< Journal bearing without recirculation channel>
- 33 -



Eccentricity ratio = 0.1
Max pressure in upper journal = 292.080 [KPas]
Max pressure in lower journal = 269.470 [KPas]
< Journal bearing with recirculation channel>
Analysis result



Clearance = 15.0 [㎛]
Max pressure in thrust = 208.64 [KPas]

< Thrust bearing without recirculation channel>
Clearance = 15.0 [㎛]
Max pressure in thrust = 209.03 [KPas]
< Thrust bearing with recirculation channel>
- 34 -
Analysis result



Clearance = 500.0 [㎛]
Max pressure in lower plain = 56.634 [KPas]

< Lower plain bearing without recirculation channel>
- 35 -
Clearance = 500.0 [㎛]
Max pressure in lower plain = 19.636 [KPas]
< Lower plain bearing with recirculation channel>
Analysis result



Clearance = 500.0 [㎛]
Max pressure in lower plain = 56.634 [KPas]

< Lower plain bearing without recirculation channel>
- 36 -
Clearance = 500.0 [㎛]
Max pressure in lower plain = 19.636 [KPas]
< Lower plain bearing with recirculation channel>
Analysis result
• Static characteristics
Part
Without recirculation channel
With recirculation channel
Load capacity [N]
Friction torque [Nm]
Load capacity [N]
Friction torque [Nm]
Lower thrust
3.36126e-001
4.95959e-005
3.37344e-001
4.95973e-005
Plain 1
2.68073e-006
2.84081e-008
3.05376e-006
2.84082e-008
Upper journal
1.82473e-001
3.12260e-005
1.82550e-001
3.12290e-005
Plain 3
9.45037e-006
2.84078e-007
9.45092e-006
2.84078e-007
Lower journal
1.48531e-001
2.83763e-005
1.48531e-001
2.83763e-005
Plain 5
5.13616e-008
2.84076e-008
6.72910e-008
2.84076e-008
Lower plain
1.13197e-001
5.39740e-008
9.59665e-002
5.39740e-008
- 37 -
Analysis result
• Dynamic characteristics

Stiffness coefficient comparison
Without recirculation channel
With recirculation channel
Total system
Upper journal
Lower journal
Thrust part
Total system
Upper journal
Lower journal
Thrust part
Kxx
4.9937e+005
2.6482e+005
2.3455e+005
0.0000e+000
5.0575e+005
2.7123e+005
2.3453e+005
0.0000e+000
Kyy
5.0945e+005
2.7686e+005
2.3259e+005
0.0000e+000
5.0132e+005
2.6875e+005
2.3258e+005
0.0000e+000
Kzz
6.3276e+004
0.0000e+000
0.0000e+000
6.3276e+004
8.1083e+004
0.0000e+000
0.0000e+000
8.1083e+004

Damping coefficient comparison
Without recirculation channel
With recirculation channel
Total system
Upper journal
Lower journal
Thrust part
Total system
Upper journal
Lower journal
Thrust part
Cxx
2.6797e+003
1.4937e+003
1.1860e+003
0.0000e+000
2.7101e+003
1.5241e+003
1.1859e+003
0.0000e+000
Cyy
2.6909e+003
1.4998e+003
1.1910e+003
0.0000e+000
2.7219e+003
1.5309e+003
1.1910e+003
0.0000e+000
Czz
1.8438e+005
0.0000e+000
0.0000e+000
1.8438e+005
1.0664e+003
0.0000e+000
0.0000e+000
1.0664e+003
- 38 -
Result and discussion

Coupled analysis vs. separate analysis
– High pressure of the journal bearing is transmitted to the thrust bearing,
which results in high pressure distribution in the thrust bearing in the
coupled analysis.
– It changes the load capacity and flying height of thrust bearing.

Half-Sommerfeld vs. Reynolds BC
– Half-Sommerfeld BC overestimates the cavitation area, which
underestimates the pressure, load capacity of the thrust bearing.
– Reynolds BC describes the cavitation, load capacity of bearing
realistically.

Micro Drive with recirculation channels
– Recirculation channel allows the flow between the upper and lower
thrust bearing, and it maintain the same pressure level between them
– It decreases the pressure distribution of lower thrust bearing, which
results in the small load capacity of lower thrust bearing
- 39 -
Future work

Get a feedback and verify the static and dynamic result
from HYBAP v3.0 using various model
- 40 -