Analysis of the Coupled Journal and Thrust Bearing

1
Analysis of the CoupledJournal and Thrust Bearing

• August 21 2004
• Hakwoon Kim
• PREM, Department of Mechanical Engineering
• Hanyang University, Seoul, Korea

2
Contents

• Motivation
• Reynolds Equation
• - Reynolds equation
• - Boundary condition
• - Load capacity and friction torque
• - Finite element method for a coupled journal and
  thrust bearing
• Perturbation
• - Physical perturbation
• 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
• Future Work

3
Motivation
lt Structure of a 3.5" FDB spindle motor gt
lt Structure of a 1" FDB spindle motor gt

• 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

4
Reynolds equation

• Reynolds equation for journal bearing

- filmthickness
lt Journal bearing geometry gt
5
Reynolds equation

• Reynolds equation for thrust bearing

- filmthickness
lt Thrust bearing geometry gt
6
Boundary condition

• 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.
• The better boundary condition is Reynolds BC,
  where
• ? can be determined numerically by the iterative
  method.

7
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
• Load capacity, friction torque of thrust bearing

8
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

9
Perturbation

• In the case of coupled journal and thrust
  bearing, the boundary value problem can not be
  defined because the perturbed pressure
  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

10
Perturbation

• 3.1 Perturbation for journal bearing

• Step 1 Set the coordinate system considering
• attitude angle calculated by initial static
  analysis
• Step 2 Calculate the initial load and moment
  with
• respect to the new coordinate system
• Step 3 Calculate the loads and moments
• considering perturbed displacements and
• velocities, i.e.
• Step 4 Calculate the dynamic characteristics
• from following equation

lt Geometrical description of physical
perturbation by ?ex gt
11
Perturbation

• 3.2 Perturbation for thrust bearing

• 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.
• Step 4 Calculate the dynamic characteristics

lt Geometrical description of physical
perturbation by ?ez gt
12
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

13
Analysis result

• 4.1 Coupled analysis vs. separate analysis of
  FDB of a 3.5 " HDD

(1) Plain region in journal ( Plain 1 )
(2) Upper journal bearing
(3) Plain region in journal ( Plain 3 )
(4) Lower journal bearing
(5) Plain region in journal ( Plain 5 )
(6) Upper thrust bearing
(7) Plain region in journal ( Plain 7 )
(8) Lower thrust bearing
(9) Plain region in thrust ( Plain 9 )
14
Analysis result

• Specification of analysis model

Upper Journal Lower Journal Upper Thrust Lower Thrust
Bearing Width mm Bearing Width mm 2.6 (Top1.4, Bottom1.2) 2.4 (Top1.2, Bottom1.2) - -
ID and OD of Thrust mm ID and OD of Thrust mm - - ID 5.0, OD 6.8 ID 4.0, OD 6.8
Groove Pattern Groove Pattern Herringbone Herringbone Herringbone Herringbone
Groove depth ?m Groove depth ?m 6.0 6.0 10.0 10.0
Groove Angle deg Groove Angle deg 20.0 20.0 20.0 20.0
Clearance ?m Clearance ?m 2.5 2.5 9.0 9.0
Radius of Journal mm Radius of Journal mm 2.0 2.0 - -
Number of groove Number of groove 6 6 12 12
Groove to Groove and Ridge Ratio 0.3333 0.3333 0.3333 0.3333
Width of Plain Area mm 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 ) 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 ) Inner Plain 0.5 ( Depth 0.03 ) Outer Plain 0.2 ( Depth 0.03 ) Inner Plain 0.5 ( Depth 0.03 ) Outer Plain 0.2 ( Depth 0.03 )
Viscosity(25 deg C) Pas Viscosity(25 deg C) Pas 0.016 0.016 0.016 0.016
Rotating Speed rpm Rotating Speed rpm 7200 7200 7200 7200
15
Analysis result

• Analysis model and result of pressure distribution

• Number of node 6121 EA
• Number of element 5508 EA
• Element type 4-node quadrilateral element

16
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

• Eccentricity ratio 0.1
• Max pressure in upper journal 3.124 MPas
• Max pressure in lower journal 2.934 MPas

lt Coupled analysis of journal bearing gt
lt Separate analysis of journal bearing gt
17
Analysis result

• Clearance 9.0 ?
• Max pressure in upper journal 509.1 KPas

• Clearance 9.0 ?
• Max pressure in upper journal 110.2 KPas

lt Coupled analysis of upper thrust bearing gt
lt Separate analysis of upper thrust bearing gt
18
Analysis result

• Clearance of lower thrust 9.0 ?
• Clearance of center plain 500 ?
• Max pressure in upper journal 529.8 KPas

• Clearance 9.0 ?
• Max pressure in upper journal 125.3 KPas

lt Coupled analysis of lower thrust bearing gt
lt Separate analysis of lower thrust bearing gt
19
Analysis result
Static characteristics
Part Coupled analysis Coupled analysis Separate analysis Separate analysis
Part Load capacity N Friction torque Nm Load capacity N Friction torque Nm
Plain 1 1.06776e-005 2.42556e-006 - -
Upper journal 3.04791e000 5.31127e-004 3.00549e000 5.30798e-004
Plain 3 2.19960e-003 1.33409e-005 - -
Lower journal 2.60350e000 4.89889e-004 2.51866e000 4.89858e-004
Plain 5 7.16112e-004 2.42565e-006 - -
Upper thrust -1.18044e001 1.99011e-004 5.42952e-001 1.98735e-004
Plain 7 4.27706e-005 1.41458e-005 - -
Lower thrust 1.47111e001 2.33986e-004 1.05478e000 2.33815e-004
Plain 9 2.94034e000 1.91859e-007 - -
20
Analysis result
Dynamic characteristics

• Stiffness coefficient comparison

Coupled analysis Coupled analysis Coupled analysis Coupled analysis Separate analysis Separate analysis Separate analysis Separate analysis
Total system Upper journal Lower journal Thrust part Upper journal Lower journal Upper thrust Lower thrust part
Kxx 1.5508e007 8.3079e006 7.2027e006 0.0000e000 8.3142e006 7.2140e006 0.0000e000 0.0000e000
Kyy 1.5295e007 8.1344e006 7.1635e006 0.0000e000 8.1451e006 7.1677e006 0.0000e000 0.0000e000
Kzz 5.9278e005 0.0000e000 0.0000e000 5.9278e005 0.0000e000 0.0000e000 1.5332e005 4.3561e005

• Damping coefficient comparison

Coupled analysis Coupled analysis Coupled analysis Coupled analysis Separate analysis Separate analysis Separate analysis Separate analysis
Total system Upper journal Lower journal Thrust part Upper journal Lower journal Upper thrust Lower thrust part
Cxx 3.9199e004 2.1447e004 1.7725e004 0.0000e000 2.1015e004 1.7671e004 0.0000e000 0.0000e000
Cyy 3.9184e004 2.1402e004 1.7755e004 0.0000e000 2.0922e004 1.7701e004 0.0000e000 0.0000e000
Czz 2.1473e005 0.0000e000 0.0000e000 2.1473e005 0.0000e000 0.0000e000 1.3796e002 5.9448e003
21
Analysis result

• 4.2. Reynolds BC vs half-Sommerfeld BC of FDB of
  a 3.5 " HDD

(1) Plain region in journal ( Plain 1 )
(2) Upper journal bearing
(3) Plain region in journal ( Plain 3 )
(4) Lower journal bearing
(5) Plain region in journal ( Plain 5 )
(6) Upper thrust bearing
(7) Plain region in journal ( Plain 7 )
(8) Lower thrust bearing
(9) Plain region in thrust ( Plain 9 )
22
Analysis result

• Specification of analysis model

Upper Journal Lower Journal Upper Thrust Lower Thrust
Bearing Width mm Bearing Width mm 2.4 (Top1.2, Bottom1.2) 2.4 (Top1.2, Bottom1.2) - -
ID and OD of Thrust mm ID and OD of Thrust mm - - ID 4.0, OD 7.2 ID 4.0, OD 7.2
Groove Pattern Groove Pattern Herringbone Herringbone Spiral Spiral
Groove depth ?m Groove depth ?m 6.0 6.0 10.0 10.0
Groove Angle deg Groove Angle deg 20.0 20.0 20.0 20.0
Clearance ?m Clearance ?m 2.5 2.5 9.0 9.0
Radius of Journal mm Radius of Journal mm 2.0 2.0 - -
Number of groove Number of groove 6 6 12 12
Groove to Groove and Ridge Ratio 0.3333 0.3333 0.3333 0.3333
Width of Plain Area mm 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 ) 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 Viscosity(25 deg C) Pas 0.016 0.016 0.016 0.016
Rotating Speed rpm Rotating Speed rpm 7200 7200 7200 7200
23
Analysis result

• Number of node 6121 EA
• Number of element 5508 EA
• Element type 4-node quadrilateral element

24
Analysis result

• Result comparison between using half Sommerfeld
  BC and Reynolds BC

Pressure distribution

• Max pressure in FDB 2.984 MPas

• Max pressure in FDB 3.036 MPas

lt Analysis result using half Sommerfeld BC gt
lt Analysis result using Reynolds BC gt
25
Analysis result

• Eccentricity ratio 0.1
• Max pressure in upper journal 2.984 MPas
• Max pressure in lower journal 2.971 MPas

• Eccentricity ratio 0.1
• Max pressure in upper journal 3.036 MPas
• Max pressure in lower journal 3.105 MPas

lt Analysis result using half Sommerfeld BC gt
lt Analysis result using Reynolds BC gt
26
Analysis result

• Clearance of lower thrust 9.0 ?
• Max pressure in upper journal 39.467 KPas

• Clearance 9.0 ?
• Max pressure in upper journal 212.350 KPas

lt Analysis result using half Sommerfeld BC gt
lt Analysis result using Reynolds BC gt
27
Analysis result

• Clearance of lower thrust 9.0 ?
• Clearance of center plain 500 ?
• Max pressure in upper journal 38.969 KPas

• Clearance 9.0 ?
• Clearance of center plain 500 ?
• Max pressure in upper journal 213.540 KPas

lt Analysis result using half Sommerfeld BC gt
lt Analysis result using Reynolds BC gt
28
Analysis result
Static characteristics
Part Half Sommerfeld boundary condition Half Sommerfeld boundary condition Reynolds boundary condition Reynolds boundary condition
Part 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 2.65314e000 4.90212e-004 2.62102e000 4.90341e-004
Plain 3 2.17523e-003 1.33409e-005 2.17079e-003 1.33409e-005
Lower journal 2.60357e000 4.89889e-004 2.60358e000 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 - 2.91657e000 2.55022e-004
Plain 7 0.00000e000 1.41458e-005 3.06280e-004 1.41459e-005
Lower thrust 1.31140e-001 2.64862e-004 2.93510e000 2.72671e-004
Plain 9 4.87674e-001 6.06371e-007 2.67233e000 6.06371e-007
29
Analysis result
Dynamic characteristics

• Stiffness coefficient comparison

Half Sommerfeld boundary condition Half Sommerfeld boundary condition Half Sommerfeld boundary condition Half Sommerfeld boundary condition Reynolds boundary condition Reynolds boundary condition Reynolds boundary condition Reynolds boundary condition
Total system Upper journal Lower journal Thrust part Total system Upper journal Lower journal Thrust part
Kxx 1.4582e007 7.3819e006 7.2028e006 0.0000e000 1.4627e007 7.4270e006 7.2032e006 0.0000e000
Kyy 1.4501e007 7.3406e006 7.1633e006 0.0000e000 1.4546e007 7.3860e006 7.1631e006 0.0000e000
Kzz 2.2979e006 0.0000e000 0.0000e000 2.2979e006 2.5775e006 0.0000e000 0.0000e000 2.5775e006

• Damping coefficient comparison

Half Sommerfeld boundary condition Half Sommerfeld boundary condition Half Sommerfeld boundary condition Half Sommerfeld boundary condition Reynolds boundary condition Reynolds boundary condition Reynolds boundary condition Reynolds boundary condition
Total system Upper journal Lower journal Thrust part Total system Upper journal Lower journal Thrust part
Cxx 3.5855e004 1.8100e004 1.7728e004 0.0000e000 3.5468e004 1.7712e004 1.7729e004 0.0000e000
Cyy 3.5909e004 1.8128e004 1.7754e004 0.0000e000 3.5517e004 1.7737e004 1.7753e004 0.0000e000
Czz 2.0680e005 0.0000e000 0.0000e000 2.0679e005 1.0397e004 0.0000e000 0.0000e000 1.0397e004
30
Analysis result

• 4.3. FDB of a 1" Micro Driver with the effect of
  recirculation channel

(1) Plain region in journal ( Plain 1 )
(2) Upper journal bearing
(3) Plain region in journal ( Plain 3 )
(4) Lower journal bearing
(5) Plain region in journal ( Plain 5 )
(8) Thrust bearing
(9) Lower plain ( Plain 9 )
- 3 recirculation channels between upper thrust
bearing and lower plain thrust bearing
31
Analysis result

• Specification of analysis model

Upper Journal Lower Journal Thrust Lower Plain
Bearing Width mm Bearing Width mm 1.76 (Top0.96, Bottom0.8) 1.6 (Top0.8, Bottom0.8) - -
ID and OD of Thrust mm ID and OD of Thrust mm - - ID 4.6, OD 6.0 ID 0, OD 1.25
Groove Pattern Groove Pattern Herringbone Herringbone Spiral Plain
Groove depth ?m Groove depth ?m 5.0 5.0 15.0 0
Groove Angle deg Groove Angle deg 21.0 21.0 20.0
Clearance ?m Clearance ?m 4.0 4.0 15.0 500
Radius of Journal mm Radius of Journal mm 1.25 1.25 - -
Number of groove Number of groove 16 16 20
Groove to Groove and Ridge Ratio 0.41667 0.41667 0.5
Width of Plain Area mm 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 ) 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 Viscosity(25 deg C) Pas 0.016 0.016 0.016 0.016
Rotating Speed rpm Rotating Speed rpm 4200 4200 4200 4200
32
Analysis result

• Analysis model and result of pressure
  distribution

• Number of node 11041 EA
• Number of element 10000 EA
• Element type 4-node quadrilateral element

33
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

• Eccentricity ratio 0.1
• Max pressure in upper journal 292.080 KPas
• Max pressure in lower journal 269.470 KPas

lt Journal bearing without recirculation channelgt
lt Journal bearing with recirculation channelgt
34
Analysis result

• Clearance 15.0 ?
• Max pressure in thrust 208.64 KPas

• Clearance 15.0 ?
• Max pressure in thrust 209.03 KPas

lt Thrust bearing without recirculation channelgt
lt Thrust bearing with recirculation channelgt
35
Analysis result

• Clearance 500.0 ?
• Max pressure in lower plain 56.634 KPas

• Clearance 500.0 ?
• Max pressure in lower plain 19.636 KPas

lt Lower plain bearing without recirculation
channelgt
lt Lower plain bearing with recirculation channelgt
36
Analysis result

• Clearance 500.0 ?
• Max pressure in lower plain 56.634 KPas

• Clearance 500.0 ?
• Max pressure in lower plain 19.636 KPas

lt Lower plain bearing without recirculation
channelgt
lt Lower plain bearing with recirculation channelgt
37
Analysis result
Static characteristics
Part Without recirculation channel Without recirculation channel With recirculation channel With recirculation channel
Part 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
38
Analysis result
Dynamic characteristics

• Stiffness coefficient comparison

Without recirculation channel Without recirculation channel Without recirculation channel Without recirculation channel With recirculation channel With recirculation channel With recirculation channel With recirculation channel
Total system Upper journal Lower journal Thrust part Total system Upper journal Lower journal Thrust part
Kxx 4.9937e005 2.6482e005 2.3455e005 0.0000e000 5.0575e005 2.7123e005 2.3453e005 0.0000e000
Kyy 5.0945e005 2.7686e005 2.3259e005 0.0000e000 5.0132e005 2.6875e005 2.3258e005 0.0000e000
Kzz 6.3276e004 0.0000e000 0.0000e000 6.3276e004 8.1083e004 0.0000e000 0.0000e000 8.1083e004

• Damping coefficient comparison

Without recirculation channel Without recirculation channel Without recirculation channel Without recirculation channel With recirculation channel With recirculation channel With recirculation channel With recirculation channel
Total system Upper journal Lower journal Thrust part Total system Upper journal Lower journal Thrust part
Cxx 2.6797e003 1.4937e003 1.1860e003 0.0000e000 2.7101e003 1.5241e003 1.1859e003 0.0000e000
Cyy 2.6909e003 1.4998e003 1.1910e003 0.0000e000 2.7219e003 1.5309e003 1.1910e003 0.0000e000
Czz 1.8438e005 0.0000e000 0.0000e000 1.8438e005 1.0664e003 0.0000e000 0.0000e000 1.0664e003
39
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

40
Future work

• Get a feedback and verify the static and dynamic
  result from HYBAP v3.0 using various model