Design of a MEMS Bearing
James N. Streeter
MANE 6960 Final Project
Professor Ernesto Gutierrez-Miravete
Rensselaer Polytechnic Institute
Hartford, Connecticut
December 10th, 2007
Table of Contents
Table of Contents
Abstract
Introduction
Solid Surfaces
Mechanical Contact
Friction
Wear
Lubrication
Conclusions
Works Cited
2
3
4-9
10
11-19
20-21
22
23-39
40
41
Abstract
The tribological design of a MEMS bearing is evaluated. The bearing and rotating mass
are produced by the EFAB process, which consists of selective pattern deposition.
Multiple layers of structural and sacrificial material are deposited and planarized to build
a 3-dimensional device. The sacrificial material is then removed to yield separate parts.
First the surface characteristics are evaluated using traditional statistical methods for
analysis. Mechanical contact is simulated for a number of configurations. The different
designs attempt to remove material from the journal area. The friction of the system is
assessed. Wear, mainly the result of adhesion, is discussed. Finally, lubrication is
considered due to the shear imposed on the air as a result of the shaft rotation.
Introduction
The bearing and shaft are constructed as an assembly by EFAB technology. EFAB was
invented by the University of Southern California (USC) under a Defense Advanced
Research Project (DARPA) contract during the mid ‘90s.
EFAB devices are fabricated by a multi-layer additive/subtractive plating and
planarization process. Each layer consist of a sacrificial material deposited in the
negative image of the final desired shape. The structural metal is then deposited in its
final geometry. Each layer is then planarized before the next layer is constructed.
Photomasks are used to define each layer of the device, which can achieve sub micron
resolution.
The following material properties have been tabulated for Valloy-120
Property
Units
Value
Ultimate Tensile Strength
MPa
1100
Yield Strength
MPa
900
Hardness, Rc
40
Elastic Modulus
GPa
180
Density
g/cm3
8.9
Figure 1: First Structural Layer
A photomask is constructed for the first layer of the device. Valloy-120 is deposited in
the voids left by the photomask pattern. Subsequently, the structural material is
planarized to achieve the desired layer thickness. Figure 1 shows the first layer of the
device after planarization has been performed. The red circle in the center is the .1mm
diameter shaft, which is being constructed as a separate component. The yellow square
will become the housing for the device and serve as the bearing support cage.
Figure 2: Completed first layer
Sacrificial copper material is deposited in the voids of the structural metal. The
sacrificial layer is planarized to obtain the proscribed layer thickness. Figure 2 shows the
device after the first layer of structural material (red and yellow) and sacrificial material
(green) have been deposited and lapped to the correct thickness. There is a small .01mm
radial gap between the shaft and bearing cage which has been filled. The six .08mm
diameter green circles near the shaft are etch release holes to remove material near the
bearing thrust surface. The remaining .1mm diameter green holes are also used to release
the etch, which dissolves the sacrificial material. These holes will extend through the
entire device.
Figure 3: Completed Bearing Thrust Surface
Each end of the .1mm diameter shaft is .074mm long and supports the radial loads
generated by the eccentric rotating mass. The axial loads are supported by the bearing
thrust surface. It is .625mm in diameter and .068mm thick. The area of the thrust surface
is .2653 mm2. It contains 6 .08mm diameter etch release holes on a .35mm diameter bolt
circle. Figure 3 shows the layer containing the bearing thrust surface.
Figure 4: Completed Device before Etch
All the layers of structural material have been deposited and planarized. Sacrificial
material encapsulated the rotating mass and fills the voids in the desired geometry. Once
the sacrificial material has been removed by the etchant, the bearing cage and rotating
mass will be free to move independently.
Figure 5: Completed Device
Figure 6: Cross-Section of Completed Device
A chemical etching process has been used to remove the sacrificial copper material from
the voids in the device. The rotating mass is now free to move independently of the
bearing cage. Figure 5 shows the completed device.
Figure 6 shows a cross section of the device. The two .1mm diameter shafts appear on
the top and bottom. There is .006mm clearance between the thrust surface and the
rotating element. In addition, there is .036 mm clearance between the edges of the
rotating element and the bearing cage. When the rotating element deflects elastically due
to axial loads, the aforementioned axial clearance prevents the edges of the rotating
element from contacting the bearing cage.
Solid Surfaces
The roughness of the surfaces in the MEMS device is based on the two processes:
planarization and plating in the photomask. Because EFAB is a proprietary process of
MicroFabrica, little has been published to help characterize the surface roughness. The
value of Ra was found to be .15. Figure 7 shows a plot of a Gaussian surface having
average roughness of .15.
Surface Roughness
0.6
Surface Height (1E-6m)
0.4
0.2
0
0
1000
2000
3000
4000
5000
6000
-0.2
-0.4
-0.6
Horizontal Distance (1E-6m )
Figure 7: Profilometric Trace with Ra=.15
The nominal clearance between the shaft and micro-bearing is .01E-3m. Maximum and
minimum surface peaks have a height of .5E-6 m. Therefore the radial clearance must be
reduced by 99E-6 due to the loading for asperity contact to occur.
Mechanical Contact
Hertzian Contact
1 1   12 1   22


E*
E1
E2
1
 1  .32 1  .32 
  98.9 E 9 Pa
E*  

180
E
9
180
E
9


1 1
1
 
R R1 R2
1
1
1


R

  .3E  3m
 .05 E  3 .06 E  3 
1/ 3
 3WR 
a

 4E * 
1/ 3
 3(.002)(.3E  3) 
  1.66 E  6m
a  
 4(98.9 E 9) 
6WE *2
P0  3 2
 R
6(.002)(98.9 E9) 2
P0 
 348E 6 Pa
 3 (.3E  3) 2
1  2
3
 a 2 

r2
r2
 2 1  (1  2 )3 / 2   P0 (1  2 )1 / 2
a
a
 r 


1  2  a 2 
r2
r2
 2 1  (1  2 )3 / 2   2P0 (1  2 )1 / 2
    P0
3  r 
a
a

 r  P0
r 2 1/ 2
 z   P0 (1  2 )
a
(1  2 ) P0
 MAX 
3
(1  2(.3))348 E 6
 MAX 
 46.4 E 6 Pa
3
 MAX  .31P0
 MAX  .31(348E6)  108E6Pa
( P0 )Y  1.60Y
( P0 )Y  1.60(900 E 6)  1.44E9Pa
Figure 8: Von Mises Stress in Journal Bearing
Stresses were computed for the journal bearing by applying a radial load of .2E-3 N to
half the bearing surface. A mesh consisting of 48252 elements was used within
COSMOSXpress to compute the results.
The maximum stress 0f .252E6 Pa occurs directly in the center of the bearing. Regions
with nearly equal stress appear on both sides of the center bearing surface. Immediately
below the surface, the stress is roughly half its value above. Near the top edges of the
bearing, light blue to blue colors indicate that the stress has decreased by almost an order
of magnitude.
Figure 9: Von Mises Stress in 4-Lobe Channel
A distributed radial load of .002N was applied to the bottom bearing face to simulate the
stresses due to the offset mass. FEA calculations were performed, with a mesh consisting
of 50517 elements, by COSMOSXpress.
The maximum stress of .635E6 Pa occurs at the center of the bearing face. Stress
gradually reduces towards the outer edges of the bearing face. The sides of the channels
have roughly half the maximum stress, with a slightly higher concentration appearing
near the bottom of the channel.
Figure 10: Von Mises Stresses in 4-Lobe Nozzle Bearing
The grid used for the FEA solution consisted of 49552 elements. A .002 N radial load
was used to calculate the effect of the eccentric rotating mass.
The stress at the bottom edge of the nozzle is nearly half of its value in the channel
configuration. In addition, the stress is decrease in the radial direction of the nozzle.
These two factors seem to indicate that a nozzle design may produce a stronger bearing
structure.
Figure 11: Von Mises Stresses in 4-Lobe Diffuser Bearing
COSMOSXpress was used to perform the finite element simulation. A radial load of
.002N was applied to the bottom bearing face to deduce the effects of loading. The mesh
consisted of 50338 elements.
The four lobe diffuser has the highest maximum stress of the four lobe configurations.
As in the channel design, stresses increase in the radial direction along the diffuser
surface. The value of stress at the bottom edge of the diffuser is very similar to the four
lobe channel. The four lobe diffuser has the worst structural characteristics of the four
configurations.
Figure 12: Von Mises Stresses in 6-Lobe Channel Bearing
The FEA solution for the six lobe channel bearing was computed by COSMOSXpress
using a 50101 element mesh. A radial load of .002N was applied to the bottom lobe
bearing face.
The maximum stress occurs in the center of the bearing face and slightly decreases
towards the edge of the bearing face. At the edge of the bearing face there is an increase
in stress, where the radius lies. Along the edge of the channel, stress gradually increases
to almost two-thirds of the maximum stress.
Figure 13: Von Mises Stresses in 6-Lobe Nozzle Bearing
A grid consisting of 50463 elements was used to compute the finite element solution. As
before, a radial load of .002N was applied to the bearing face.
Unlike in the four lobe nozzle design, stress seems to increase in the radial direction
along the edge of the nozzle. The stress at the root of the nozzle is approximately half of
the maximum value. This could be an effect of the decrease in nozzle angle from thirty
to twenty degrees.
Figure 14: Von Mises Stresses in 6-Lobe Diffuser Bearing
COSMOSXpress was utilized to perform the finite element analysis. A load of .002 N
was applied normal to the bearing face to simulate the effect of the eccentric rotating
mass. The mesh consisted of 50269 elements.
The six lobe diffuser bearing exhibits the highest maximum stress of any of the designs.
As before, the maximum stress occurs in the center of the bearing face. A stress
concentration can be seen at the root of the diffuser.
Table 1
Design
Journal
4-Lobe Channel
4-Lobe Nozzle
4-Lobe Diffuser
6-Lobe Channel
6-Lobe Nozzle
6-Lobe Diffuser
Von Mises Stress (Pa)
.252E6
.635E6
.618E6
.665E6
1.28E6
1.20E6
1.58E6
Displacement (m)
.116E-6
.353E-6
.348E-6
.362E-6
.460E-6
.444E-6
.529E-6
Table 1 tabulates the finite element results. The journal bearing performs the best of all
the designs. The maximum stress in the four lobe designs is on average two and a half
times the journal bearing maximum stress. Furthermore, the six lobe journal bearings
have an average maximum stress nearly double the four lobe designs. This maximum
stress is 5 times the stress in the journal bearing. All of these stresses are almost three
orders of magnitude less than the yield strength.
The maximum displacement in the four lobe designs is triple the displacement in the
journal bearing. The six lobe designs have maximum displacement of four times the
journal bearing, but only one third more than the four lobe configurations. All of the
displacements are more than one order of magnitude less than the nominal bearing
clearance.
The Hertzian analysis showed a maximum tensile stress of 46.4E6 Pa, and a maximum
shear stress of 108E6 Pa. The stresses computed with COSMOSXpress are two to three
orders of magnitude less. This very large disparity can be attributed to the fact that actual
contact only occurs at a very small area. When surface roughness is accounted for, the
real contact area is even less than the Hertzian contact area.
Friction
Wang studied the microstructure and tribological properties of electrodeposited Nickel
Cobalt alloys. An AISI-1045 steel substrate was plated with 50E-6m of nickel cobalt.
The percentage of nickel in the alloy was controlled by altering the concentration of Co2+
ions with a fixed concentration of Ni2+ ions.
Wang plotted the percent weight of cobalt in the alloy as a function of Vickers microHardness. Using ASTM E-140 the Rockwell C Hardness, 40, of Valloy-120 is converted
to Vickers micro-Hardness. For Nickel and high-nickel alloys, the following equation is
used to convert Rockwell C Hardness to Vickers Hardness. An R2 value of .9995 is
noted.
( HV 1.5,10,30)1  6.24553E  3  1.08014E  4( HRC )  4.32021E  7( HRC )^ 2
( HV 1.5,10,30)  1 /( 6.24553E  3  1.08014 E  4(40)  4.32021E  7(40)^ 2)
( HV 1.5,10,30)  382
Figure 15: Cobalt Content and Grain Size vs. Hardness
The calculated Vickers Hardness is 382. Based on Figure 15, this hardness value reveals
that the alloy is composed of either 30% Cobalt and 70% Nickel or 67 % Cobalt and 33%
Nickel.
Wang reported that a gradual decrease in metallurgical grain size will be achieved if
Cobalt component increases from 7% to 49%. The size of the grains decreases to the sub
micron range. The phase structure of these alloys is face-centered cubic. If the alloy
contains 30% Cobalt it will exhibit face-centered cubic structure with relatively small
grain size.
If Cobalt content is between 49 and 81%, a drastic change occurs. The grains become
less compact, and 3E-6 to 6E-6m crystallites are seen to form. With composition above
66% Cobalt, the phase structure began to include hexagonal close packed regions. If the
alloy contains 67% Cobalt it will exhibit a mixed face-centered cubic and hexagonal
close packed structure.
Figure 16: Cobalt Content and Sliding Time vs. Friction Coefficient
Wang assessed the plating’s friction and wear using a reciprocating ball on disk
tribometer. A 4E-3m ball with 62 Rockwell C Hardness of AISI-52100 steel was used in
the experiments. The tests utilized a load of 3N and a sliding speed of 55E-3m/s. The
friction coefficient for an alloy containing 30% Cobalt is approximately .7; whereas, for
an alloy containing 67% Cobalt, the friction coefficient is .6.
Results for the friction coefficient as a function of sliding time were also tabulated. For a
Nickel rich alloy the initial coefficient of friction jumps from .16 to .7 in the first 10
seconds. The friction coefficient then oscillates from .6 to .8. For a Cobalt rich alloy, the
friction coefficient starts at .16 and then drops slightly for the first ten seconds. The
friction coefficient then steadily increases to reach a much smaller amplitude oscillating
value. This value is between .24 and .29.
Wear
Wang reports that the wear rate of Nickel rich alloys follows Archard’s Law. Wear is
mainly due to adhesion between the plating and steel ball in his tests. With 35% Cobalt
content, the wear rate is reported as 15E-5 mm3/Nm. The wear of plating with Cobalt
content less than 49% is proportional to the inverse of hardness.
Figure 17: Cobalt Content vs. Wear Rate
Greater than half Cobalt content showed a marked decrease in wear rate, even though the
hardness decreased. The wear rate with 67% Cobalt is listed as 7E-5 mm3/Nm, half the
value with 305% Cobalt. It is thought that the formation of hexagonal close-packed
structure is responsible for this improvement. Cobalt rich alloys were found to have only
slightly adhesive wear and an increase in density was noted in the wear region.
It seems that the crystalline metallurgical composition plays an important role in the wear
rate of Nickel Cobalt alloys. Hexagonal close-packed structures exhibit lower
coefficients of friction; and, therefore, the wear rate is lower as well. Face-centered cubic
structures have double to an order of magnitude higher wear rates. If Valloy-120
contains 70% Cobalt, it will have superior wear resistance than if it contained 30%
Cobalt.
Lubrication
Bearings are typically characterized by their bearing number,  , and dimensionless load,
Wr
. The bearing number is calculated using the lubricating fluid viscosity 0 ,
dbPa
rotational speed  , radius r , pressure Pa , and clearance c . The non-dimensional load is
computed with the applied load Wr , bearing width b , bearing depth d , and pressure Pa .
A calculation of these parameters for the MEMS bearing appears below.
W  .002N
N  4000rpm  419rad / s
b  .1E  3m
d  .068E  3m
r  .05E  3m
c  .01E  3m
Pa  101E 3Pa
0  1.7984E  5Pa * s
60r 2

Pa c 2
6(1.7894 E  5)(419)(.05E  3)2

 1.11E  5
(101E3)(.01E3)2
W
Load nondim ensional  r
dbPa
Wr
.002

 2.9
dbPa (.068 E  3)(.1E  3)(101E 3)
The MEMS bearing has a very small bearing number for a rather large non-dimensional
load.
The following pages show the lubrication achieved due to shaft rotation, with the bearing
offset to simulate the applied load. In each case, the minimum clearance is maintained at
.03E-5m, and the pressure is set to zero on the shaft. COMSOL was used to perform the
incompressible fluid flow simulation. The effect of shaft offset is evaluated for each of
the seven configurations, and the pressure differential is calculated.
Figure 18: Journal Bearing with .07E-5m 0 Offset
PMAX  1.514Pa
PMIN  1.512 Pa
P  PMAX  PMIN  1.514  1.512  3.026Pa
COMSOL was used to calculate the incompressible flow solution for the journal bearing.
Offsetting the bearing simulates the load that the bearing must carry, and results in a
.03E-5m clearance between the bearing and shaft. Mesh independence was achieved
with 235 elements.
The largest pressure appears on the lower right side of the bearing, where the fluid is
flowing to. On the lower left side, the air is flowing away as indicated by the negative
pressure. An area of recirculation occurs on the top half of the bearing as evidenced by
the small velocity vectors pointing opposite to the direction of shaft rotation.
Figure 19: Journal Bearing with .07E-5m 30 Offset
PMAX  1.688Pa
PMIN  1.335Pa
P  PMAX  PMIN  1.688  1.335  3.023Pa
The incompressible fluid flow problem was solved with COMSOL by a mesh containing
245 elements. The shaft is offset at a 30 degree angle for comparison with the six-lobe
designs. The clearance was maintained at .03E-5m.
Offsetting the bearing relocates the high pressure region to the bottom of the shaft. The
low pressure area has migrated upward, but it is still in the lower right. A region of
recirculation forms in the top left to halfway in the lower right clearance area. The
pressure difference is nearly identical to the 0 degree offset configuration.
Figure 20: Journal Bearing with .07E-5m 45 Offset
PMAX  1.784Pa
PMIN  1.239Pa
P  PMAX  PMIN  1.784  1.239  3.023Pa
The bearing is now offset at a 45 degree angle for comparison with the four lobed
designs. The COMSOL simulation converged with a 231 element mesh.
The pressure difference is identical to the 30 degree configuration; and, therefore, nearly
identical to the 0 degree model. The high pressure region has migrated to center to
bottom left. The low pressure region occurs between the bottom and top left.
Recirculation of the lubricating air is visible from the top left to lower right.
Figure 21: 4-Lobe Channel Bearing with .07E-5m 0 Offset
PMAX  1.247Pa
PMIN  1.246Pa
P  PMAX  PMIN  1.247  1.246  2.493Pa
Each channel of the four lobe bearing is .042E-3m wide by .042E-3m long. The
simulation achieved mesh independence with 2393 elements. Clearance is kept at .03E5m for comparison with the standard journal bearing configuration.
Each channel in the four lobed bearing shows the formation of eddies. The formation of
these vortices may account for the lower pressure differential achieved by this bearing
configuration. A high pressure region is formed in the lower right channel, while a low
pressure region appears in the lower left channel.
Figure 22: 4-Lobe Bearing with .07E-5m 45 Offset
PMAX  .928Pa
PMIN  .512Pa
P  PMAX  PMIN  .928  .512  1.440Pa
The bearing is offset by .07E-5m at a 45 degree angle. The COMSOL model converged
with a grid containing 2395 elements. The 45 degree offset is used to gauge the
lubrication when the shaft rotates directly over one of the channels.
The high pressure region forms in the lower left channel to bottom center of the bearing.
A low pressure region is visible in the left center to upper left channel. Regions of
recirculation are present in all of the channels. The pressure difference is over 1 Pascal
less than the same bearing with no angular offset.
Figure 23: 4-Lobe Nozzle Bearing with .07E-5m 0 Offset
PMAX  1.286Pa
PMIN  1.287 Pa
P  PMAX  PMIN  1.286  1.287  2.573Pa
In the four lobe design nozzle has an inlet width of .042E-3m, a length of .040E-3m, and
an angle of 30. Having a nozzle shape should be advantageous from a structural
standpoint, as there is more area to support the shaft. The CFD results were generated
with a mesh containing 1913 elements.
Eddies occur in each of the nozzle sections. The pressure difference achieved due to
rotation of the shaft is marginally greater than the channel configuration. The highest
pressure forms in the lower right nozzle. The low pressure region occurs in the lower left
nozzle.
Figure 24: 4-Lobe Nozzle Bearing with .07E-5m 45 Offset
PMAX  .968Pa
PMIN  .540Pa
P  PMAX  PMIN  .968  .540  1.508Pa
The bearing is offset at a 45 degree angle to determine the lubricity when the shaft is
directly above one of the nozzles. The CFD model converged with 1924 elements.
The high pressure region has now migrated from the lower right nozzle to the bottom of
the bearing. The low pressure area occurs at the left center. Once again, the pressure
differential is greater than the channel design. Recirculation occurs within each of the
nozzles. Thus, from both a structural and fluids standpoint, the nozzle configuration is
superior to the channel.
Figure 25: 4-Lobe Diffuser Bearing with .07E-5m 0 Offset
PMAX  1.214Pa
PMIN  1.213Pa
P  PMAX  PMIN  1.214  1.213  2.427 Pa
In the 4 lobe design, each diffuser has an inlet width of .042E-3m, a length of .040E-3m,
and an angle of 30. COMSOL simulation achieved grid independence with a mesh
consisting of 2634 elements.
Eddies form in each of the diffuser sections. High pressure fills the lower right diffuser
and flows toward the low pressure region in the lower left diffuser. The pressure
difference due to rotation of the shaft is the lowest of the three configurations.
Figure 26: 4-Lobe Diffuser Bearing with .07E-5m 45 Offset
PMAX  .891Pa
PMIN  .485Pa
P  PMAX  PMIN  .891  .485  1.376Pa
The bearing is offset at a 45 degree angle with .03E-5m clearance to determine the effect
of the shaft rotating directly above one of the diffuser sections. CFD results converged
with a grid consisting of 2640 elements.
The high pressure region has migrated towards the bottom of the bearing. A low pressure
region can be seen at the left center. Vortices develop in each of the diffuser sections.
The pressure difference is more than one Pascal less than the zero degree offset model.
In addition, the diffuser produces the least pressure differential of the three
configurations.
Figure 27: 6-Lobe Bearing with .07E-5m 0 Offset
PMAX  1.391Pa
PMIN  1.394Pa
P  PMAX  PMIN  1.391  1.394  2.785Pa
The six lobe bearing designs attempt to lower the contact area from the four lobe
configurations. Each channel has a width of .032E-3m and a length of .041E-3m.
COMSOL was used to perform incompressible fluid flow calculations, and the simulation
was independent with a mesh containing 3101 elements.
One again, eddies are formed within each of the channel sections. Due to the rotation of
the shaft, high pressure fills the lower right channel. Air flows towards the low pressure
region in the lower left channel. The pressure differential is notably less than the journal
bearing configuration and approximately .3 Pascals greater than the four lobe
configuration.
Figure 28: 6-Lobe Bearing with .07E-5m 30 Offset
PMAX  1.019Pa
PMIN  .739Pa
P  PMAX  PMIN  1.019  .739  1.758Pa
When the bearing is offset at a 30 degree angle, the shaft rotates directly above the lower
left channel. CFD simulation used 3104 grid elements for convergence.
A region with nearly zero pressure is present in the channel supporting the shaft. The
low pressure region has moved towards the central left channel. High pressure in the
lower right channel has now moved closer to the bottom of the shaft. Vortices are
formed in each of the channels. The pressure difference is greater than the four lobe
channel configuration with 45 degree offset.
Figure 29: 6-Lobe Nozzle Bearing with .07E-5m 0 Offset
PMAX  1.415Pa
PMIN  1.418Pa
P  PMAX  PMIN  1.415  1.418  2.833Pa
In the six lobe configuration, each nozzle has an inlet width of .032E-3m, a length of
.042E-3m, and a taper angle of 20. The taper angle is 10 degrees less than the four lobe
design, and the inlet width is .010E-3m less. Offest is maintained at .07E-5m, resulting
in .03E-5m clearance. The fluid flow simulation converged with a mesh containing 3023
elements.
Eddies are formed in each of the six nozzles. A high pressure area occurs in the lower
right nozzle, which causes the air to flow towards the low pressure region in the lower
left nozzle. The pressure differential is slightly greater than the six lobe channel
configuration.
Figure 30: 6-Lobe Nozzle Bearing with .07E-5m 30 Offset
PMAX  1.034Pa
PMIN  .754Pa
P  PMAX  PMIN  1.034  .754  1.788Pa
With the bearing offset .07E-5m with a 30 degree angle, the lubrication is evaluated.
COMSOL incompressible fluid flow simulation achieved grid independence with 3001
elements.
The high pressure area has migrated towards the bottom of the shaft. Rotation forces the
fluid to flow towards a low pressure area near the left center nozzle. Eddies are formed
near the inlet of each of the six nozzles. The pressure differential is nearly .3 Pascals
greater than the four lobe nozzle design with 45 degree offset.
Figure 31: 6-Lobe Diffuser Bearing with .07E-5m 0 Offset
PMAX  1.312Pa
PMIN  1.312Pa
P  PMAX  PMIN  1.312  1.312  2.624Pa
The final configuration to be evaluated contains 6 diffusers. Each diffuser section has an
inlet width of .040E-3m, a length of .032E-3m, and an angle of 40. The CFD results
were converged from a mesh containing 3974 elements.
The pressure differential obtained with six diffuser sections is the least of the six lobe
designs; however, it is still greater than any of the four lobe configurations. As before,
low pressure in the lower right diffuser transports the lubricating air to the low pressure
region in the lower tight diffuser. Vortices are formed within each of the diffuser
sections.
Figure 32: 6-Lobe Diffuser Bearing with .07E-5m 30 Offset
PMAX  .965Pa
PMIN  .701Pa
P  PMAX  PMIN  .965  .701  1.666Pa
The six lobe diffuser design is evaluated with the shaft directly above the lower left
diffuser. COMSOL was used to perform the fluid flow simulation. Mesh independence
occurred with the initial grid, which contained 3954 elements.
The six lobe diffuser is the worst of the six lobe configurations from both a fluid and
structural perspective. However, it produces a greater pressure differential with thirty
degrees offset than any of the four lobe designs with 45 degree offset. The high pressure
region moves out of the lower right diffuser towards the bottom of the bearing. Low
pressure occurs slightly below the middle left of the bearing, moving into the left center
diffuser. Directly below the minimum clearance area with the shaft on the lower left, a
near zero pressure region occurs. Eddies form in each of the diffusers.
Table 2
Bearing
Journal Bearing
4-Lobe Channel
4-Lobe Nozzle
4-Lobe Diffuser
6-Lobe Channel
6-Lobe Nozzle
6-Lobe Diffuser
P0 ( P0 / PJOURNAL0 )
3.026 (1.00)
2.493 (.824)
2.573 (.850)
2.427 (.802)
2.785 (.920)
2.833 (.936)
2.624 (.867)
P30 / 45 ( P30 / 45 / PJOURNAL30 / 45 )
3.023
(1.00)
1.440
(.476)
1.508
(.499)
1.376
(.455)
1.758
(.582)
1.788
(.591)
1.666
(.551)
Table 2 compares the pressure differential achieved by each of the seven configurations.
The number in parentheses is normalized pressure with respect to the standard journal
configuration. All of the lobe designs produce a lower pressure differential than the
standard configuration.
The nozzle designs consistently produce the largest pressure differential among the lobe
configurations regardless of offset. In addition, all the six lobe configurations exceed the
results of the four lobe design. When the shaft is directly above the channel, nozzle or
diffuser, the highest pressure differential is still more than forty percent less than the
journal bearing.
The best of the lobe designs contains six nozzle sections. It produces within 7% of the
pressure differential of the journal bearing with zero degrees offset. However, with 45
degrees offset, less than 60% of the reference change is created.
Conclusions
Based on the simulated Gaussian surface roughness, the clearance will need to be reduced
by 99E-6m for contact to occur between peak asperities on the shaft and bearing surfaces.
Asperity contact may be prevented by a pressure differential created due to rotation.
Based on a Hertzian contact analysis, the area of each lobe in the four and six lobe design
should be sufficient to support the rotating element. The Hertzian contact stresses are
several orders of magnitude higher than those created by applying a distributed load to
the bearing surface. However, all the stresses are lower than the yield strength of Valloy120.
Friction and wear are strongly influenced by the microstructure of the Nickel Cobalt
alloy. It was found that the structure changed from face-centered cubic to hexagonal
close packed, when Cobalt varied from the minor to major constituent. This change
resulted in friction and wear that could be half to a full order of magnitude less.
From both structural and lubricity standpoints, the journal bearing was best. The nozzle
configuration seemed to be the second best. In a four-lobe configuration, it ameliorated a
stress concentration at the root. In the six lobe configuration, the pressure differential at
standard offset was within 7% of the journal bearing.