asme turbo expo 2009: power for land, sea, and air
DESCRIPTION
ASME Turbo Expo 2009: Power for Land, Sea, and Air. Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data. Luis San Andrés Tae Ho Kim Mast-Childs Professor Research Associate. Texas A&M University. ASME GT2009-59919. - PowerPoint PPT PresentationTRANSCRIPT
-
This material is based upon work supported by NASA Research Announcement NNH06ZEA001N-SSRW2, Fundamental Aeronautics: Subsonic Rotary Wing Project 2 # 32525/39600/ME and the Turbomachinery Research ConsortiumASME Turbo Expo 2009: Power for Land, Sea, and AirThermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test DataTexas A&M UniversityLuis San Andrs Tae Ho KimMast-Childs Professor Research AssociateASME GT2009-59919Accepted for J. Eng. Gas Turbines Power (In-Press)
-
Gas Foil Bearings Bump typeSeries of corrugated foil structures (bumps) assembled within a bearing sleeve. Integrate a hydrodynamic gas film in series with one or more structural layers. PROVEN TECHNOLOGY!!Applications: Aircraft ACMs, micro gas turbines, turbo expanders, turbo compressors, Damping from dry-friction and operation with limit cyclesTolerant to misalignment and debris, also high temperatureNeed coatings to reduce friction at start-up & shutdownOften need cooling flow for thermal management of rotor-GFB system
-
Gas Foil Bearings (+/-)Increased reliability: large load capacity (< 100 psi)No lubricant supply system, i.e. reduce weight High & low temperature capability (up to 1,200 F) No scheduled maintenance with increased life Less load capacity than rolling or oil bearingsThermal management (cooling) issuesLittle test data for rotordynamic force coefficientsPredictive models lack validation. Difficulties in accessing full test data geometry and operating conditions
-
Overview GFB computational modelsSalehi et al. (2001): Couette flow approximation to estimate bearing temperatures.Heshmat (1983), Carpino and Talmage (2003, 2006), Kim and San Andrs (2005, 2007), Lee, et al. (2006), Le Lez, et al. (2008): Predict static/dynamic performance of bump-type GFBs with isothermal flow model and simple to complex foil modelsLe Lez et al. (2007): Nonlinear elastic bump model. THD model predicts larger load capacity than isothermal flow model.Peng and Khonsari (2006): Thermal management of GFB from cooling gas stream underneath top foil.Feng and Kaneko (2008), San Andrs and Kim (2009): FE top foil & support structure model. Predicted bearing temperatures in agreement with test data (Radil and Zeszotek, 2006), obtained at room temperature (~21C) without cooling flow.Thermohydrodynamic (THD) model predictions:
-
Overview Rotordynamic measurementsDellaCorte and Valco (2000): Review open literature and estate Rule of Thumb to estimate load capacity of GFBs. Salehi et al. (2001) : Measure temperatures in foil bearing operating with axial cooling stream flow.San Andrs et al. (2006, 2008): Large imbalances cause subsync. whirl motions due to FB structure hardening.Ruscitto et al (1978): Load capacity tests on simple GFB. Full test data & bearing geometryHeshmat (1994): Demonstrates maximum speed of 132 krpm, i.e. 4.61 106 DN. Ultimate specific load (~100 psig). Most designs operate at 10 psig or below. Radil and Zeszotek (2006): Measure temperatures in foil bearing operating with changes in load and rotor speed.
-
Foil Bearing Research at TAMUTest Gas Foil Bearing (Bump-Type)Generation II. Diameter: 38.1 mm25 corrugated bumps (0.38 mm of height)Reference: DellaCorte (2000)Rule of Thumb2003-2009: Funded by NSF, Capstone Turbines, NASA GRC, Turbomachinery Research Consortium
-
THD modelGFB with cooling flows (inner and outer)Outer flow streamBearing housing zxRSoz=0z=LT
-
THD model governing equationsConvection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energyXYX=RSide view of GFB with hollow shaft
-
Configuration of control volume for integration of flow equations ( = Pf or Tf)Subscripts E,W,N,S for east, west, north, and south nodes; and subscripts e,w,n,s for east, west, north, and south faces of control volumeNumerical solution of Reynolds and thermal energy transport equations implement exact advection control volume model (Faria and San Andrs, 2000)Numerical solution procedure
-
Heat flux paths in rotor - GFB system Simple representation in terms of thermal resistances within a GFB supporting a hot hollow shaft
Heat conducted into the bearing
Cooling gas streamcarries away heat Heat flow model
-
Equivalent heat transfer coefficients: Heat transfer from film flow to outer bearing cartridgeWithout outer cooling flow stream
-
Thermal energy mixing processAt gap in between trailing and leading edge of top foil. : empirical thermal mixing coefficient enforced. Top foil detachment doest not allow for gas film pressure to fall below ambient pressure. No ingress of fresh gas
-
Width of arrow denotes intensity of energy transportBalance of thermal energy transportExample only
-
Top foil thickness, Bump foil thickness, Bump height, Gas Constant, Viscosity, 1.73Conductivity, Density, GFB model: Generation I GFB with single top foil and bump strip layerModel Validation: geometry & operating conditionsGas viscosity, density & conductivity, foil material props., and clearance change with temperature Ref. [7, 21]: Radil and Zeszotek, 2004Dykas and Howard, 2004
-
Predicted peak film temperatureStatic load (vertical:180)
Comparison to test data (Radil and Zeszotek, 2004)Peak film temperature grows as static load increases and as rotor speed increases. Peak film temperatures higher than ambient temperature, even for small load of 9 N. TSupply=21 CW/LD= 16 psi= 1.1 barTshaft=Tbearing =Tambient = 21 C
Load (24)
741021371685583125190
771061361686088128186
821121411817098136192
9011914919380110148202
9612616020592124162214
101134176217104138177228
30,000 rpm
40,000 rpm
50,000 rpm
20,000 rpm
Test data (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (23)
111
1.0051.0081.01
1.0021.0121.017
1.0011.0181.025
1.0011.0241.034
1.0031.0311.043
1.0051.041.053
1.0081.0491.065
1.0121.0591.077
1.0171.0711.091
1.0231.0831.107
1.031.0971.124
1.0381.1121.142
1.0461.1281.163
1.0551.1461.186
1.0641.1651.212
1.0741.1861.241
1.0851.2091.273
1.0961.2331.309
1.1071.261.349
1.121.2891.393
1.1321.321.442
1.1451.3541.496
1.1591.3891.555
1.1721.4271.619
1.1861.4671.688
1.2011.5091.762
1.2151.5531.839
1.2291.5981.919
1.2441.6432.001
1.2581.6892.083
1.2711.7342.164
1.2851.7792.242
1.2971.8212.317
1.311.8622.386
1.3211.8982.448
1.3311.9312.502
1.341.962.547
1.3471.9832.582
1.35322.607
1.3582.0122.62
1.3612.0172.621
1.3622.0152.61
1.3612.0062.588
1.3581.992.553
1.3531.9672.507
1.3461.9372.45
1.3371.9012.382
1.3261.8582.304
1.3131.812.218
1.2981.7562.123
1.2811.6982.022
1.2631.6351.915
1.2431.571.804
1.2211.5021.692
1.1991.4331.58
1.1751.3631.469
1.1511.2941.361
1.1271.2251.258
1.1021.161.164
1.0781.11.085
1.0541.0481.027
1.0321.0121
1.01311
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
Static load increases
44 N
133 N
222 N
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (22)
46.251.24260.112
46.251.24260.112
46.25851.460.308
46.34951.58260.522
46.46451.78560.755
46.652.0161.008
46.7652.2661.285
46.94552.53761.588
47.15252.83961.921
47.3853.16862.287
47.62753.52662.689
47.89453.91463.132
48.17954.33463.622
48.48154.78964.165
48.855.28364.768
49.13655.81965.439
49.48856.39966.185
49.85657.02867.017
50.2457.70867.943
50.63858.44468.973
51.05159.23770.117
51.47960.09271.381
51.9261.00872.774
52.37461.98774.299
52.83963.02875.957
53.31664.12877.742
53.80165.28379.646
54.29566.48781.653
54.79367.73283.743
55.29669.00685.891
55.79970.29988.067
56.30171.59590.24
56.79872.8892.377
57.28774.13794.447
57.76475.35196.418
58.22776.50598.262
58.67277.58399.952
59.09478.569101.464
59.49179.45102.778
59.85980.214103.875
60.19480.848104.742
60.49481.344105.365
60.75581.695105.738
60.97681.894105.853
61.15481.939105.709
61.28881.827105.306
61.37781.562104.65
61.41981.144103.749
61.41680.581102.615
61.36779.88101.264
61.27579.0599.717
61.1478.10597.997
60.96577.05896.135
60.75375.92894.168
60.50774.73392.136
60.23273.49390.076
59.93272.22888.026
59.61470.95986.028
59.28269.71184.147
58.94368.52882.488
58.60767.48481.194
58.29166.68480.437
58.02466.30880.26
57.85466.31680.36
57.88966.44380.44
58.06966.55380.505
58.23966.64880.558
58.39866.73280.603
58.54766.80680.641
58.68766.87280.673
58.8266.93280.701
58.94566.98680.725
59.06467.03680.746
59.17867.08280.765
59.28667.12480.782
59.3967.16480.798
59.4967.20280.812
59.58367.23680.824
59.58367.23680.824
Static load increases
44 N
133 N
222 N
Circumferential angle [deg]
Temperature [ C]
Load (21)
111111
1.0111.0051.0061.0081.0091.01
1.0081.0021.0071.0121.0151.017
1.0071.0011.011.0181.0221.025
1.0081.0011.0141.0241.031.034
1.0061.0031.0191.0311.0391.043
1.0061.0051.0251.041.0481.053
1.0051.0081.0321.0491.0591.065
1.0061.0121.041.0591.0711.077
1.0061.0171.0491.0711.0841.091
1.0071.0231.061.0831.0981.107
1.0081.031.0711.0971.1131.124
1.011.0381.0831.1121.131.142
1.0111.0461.0961.1281.1491.163
1.0131.0551.111.1461.171.186
1.0151.0641.1251.1651.1931.212
1.0181.0741.1411.1861.2181.241
1.021.0851.1581.2091.2461.273
1.0231.0961.1761.2331.2761.309
1.0261.1071.1961.261.311.349
1.0291.121.2171.2891.3471.393
1.0321.1321.2391.321.3871.442
1.0351.1451.2621.3541.4311.496
1.0381.1591.2871.3891.4781.555
1.0421.1721.3131.4271.5291.619
1.0451.1861.3391.4671.5831.688
1.0481.2011.3671.5091.6411.762
1.0511.2151.3961.5531.7011.839
1.0541.2291.4251.5981.7631.919
1.0571.2441.4541.6431.8262.001
1.061.2581.4831.6891.892.083
1.0631.2711.5121.7341.9532.164
1.0661.2851.5411.7792.0142.242
1.0681.2971.5681.8212.0732.317
1.0711.311.5941.8622.1282.386
1.0731.3211.6181.8982.1782.448
1.0741.3311.641.9312.2222.502
1.0761.341.6591.962.2592.547
1.0771.3471.6761.9832.2882.582
1.0781.3531.68822.312.607
1.0791.3581.6972.0122.3222.62
1.0791.3611.7022.0172.3262.621
1.0791.3621.7032.0152.322.61
1.0791.3611.6992.0062.3042.588
1.0781.3581.6911.992.2792.553
1.0771.3531.6791.9672.2452.507
1.0761.3461.6621.9372.2012.45
1.0741.3371.641.9012.1492.382
1.0721.3261.6141.8582.0892.304
1.071.3131.5841.812.0212.218
1.0671.2981.5511.7561.9462.123
1.0641.2811.5131.6981.8662.022
1.0611.2631.4731.6351.7811.915
1.0571.2431.431.571.6931.804
1.0541.2211.3851.5021.6031.692
1.051.1991.3381.4331.5111.58
1.0451.1751.291.3631.421.469
1.0411.1511.2421.2941.3311.361
1.0361.1271.1941.2251.2451.258
1.0321.1021.1471.161.1641.164
1.0271.0781.1011.11.0931.085
1.0221.0541.0591.0481.0371.027
1.0181.0321.0241.0121.0011
1.0131.0131.001111
1.00911111
1.00511111
1.00211111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
9 N
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (20)
46.45246.248.16151.24255.30860.112
46.45246.248.16151.24255.30860.112
46.57446.25848.27351.455.4960.308
46.7346.34948.41551.58255.69560.522
46.88346.46448.5851.78555.91860.755
47.02346.648.7752.0156.16261.008
47.1746.7648.98652.2656.43161.285
47.3346.94549.22852.53756.72661.588
47.49947.15249.49452.83957.04961.921
47.67747.3849.78553.16857.40162.287
47.86147.62750.153.52657.78762.689
48.05147.89450.43953.91458.20863.132
48.24848.17950.80454.33458.6763.622
48.45148.48151.19454.78959.17664.165
48.65948.851.61255.28359.73164.768
48.87349.13652.05755.81960.34265.439
49.09349.48852.53356.39961.01466.185
49.31649.85653.03957.02861.75267.017
49.54550.2453.57857.70862.56467.943
49.77750.63854.1558.44463.45568.973
50.01351.05154.75759.23764.43170.117
50.25151.47955.39860.09265.49771.381
50.49351.9256.07561.00866.65672.774
50.73652.37456.78861.98767.91174.299
50.98152.83957.53463.02869.26175.957
51.22753.31658.31364.12870.70377.742
51.47453.80159.12165.28372.2379.646
51.72154.29559.95666.48773.83281.653
51.96854.79360.81367.73275.49583.743
52.21455.29661.68769.00677.20285.891
52.45855.79962.5770.29978.93488.067
52.70156.30163.45671.59580.66890.24
52.94156.79864.33772.8882.3892.377
53.17857.28765.20374.13784.04694.447
53.41257.76466.04675.35185.64396.418
53.64158.22766.85676.50587.14698.262
53.86758.67267.62277.58388.53599.952
54.08759.09468.33778.56989.79101.464
54.30359.49168.9979.4590.892102.778
54.51259.85969.57480.21491.825103.875
54.71660.19470.0880.84892.577104.742
54.91360.49470.50181.34493.136105.365
55.10360.75570.83381.69593.495105.738
55.28660.97671.06981.89493.647105.853
55.46361.15471.20681.93993.591105.709
55.63161.28871.24381.82793.325105.306
55.79361.37771.17881.56292.854104.65
55.94761.41971.01281.14492.182103.749
56.09361.41670.74780.58191.32102.615
56.23361.36770.38779.8890.28101.264
56.36561.27569.93779.0589.07699.717
56.4961.1469.40278.10587.72797.997
56.60860.96568.79277.05886.25796.135
56.7260.75368.11375.92884.69194.168
56.82660.50767.37874.73383.05892.136
56.92660.23266.59873.49381.38990.076
57.02259.93265.78572.22879.71188.026
57.11359.61464.95170.95978.05386.028
57.259.28264.11269.71176.4684.147
57.28558.94363.28668.52875.00282.488
57.36758.60762.50967.48473.7981.194
57.44858.29161.84166.68472.95380.437
57.5358.02461.36766.30872.69380.26
57.61457.85461.26366.31672.79780.36
57.70357.88961.41566.44372.89880.44
57.80458.06961.55866.55372.98280.505
57.92858.23961.68766.64873.05380.558
58.08658.39861.80266.73273.11480.603
58.26558.54761.90766.80673.16780.641
58.44158.68762.00266.87273.21380.673
58.61558.8262.0966.93273.25480.701
58.78658.94562.1766.98673.29180.725
58.95459.06462.24567.03673.32480.746
59.1259.17862.31667.08273.35480.765
59.28459.28662.38167.12473.38280.782
59.44659.3962.44467.16473.40780.798
59.60659.4962.50367.20273.43180.812
59.75859.58362.55767.23673.45280.824
59.75859.58362.55767.23673.45280.824
9 N
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Temperature [ C]
Load (19)
0.4831
1.932
4.348
7.729
12.08
Solid shaft
tS = 10 mm
tS = 2 mm
Shaft wall thickness decreases
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Centrifugal growth [ C]
Load (16)
0.48311.0541.712
1.9324.2176.846
4.3489.48815.4
7.72916.8727.39
12.0826.3542.79
Solid shaft
tS = 10 mm
tS = 2 mm
Shaft wall thickness decreases
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Centrifugal growth [m]
Load (18)
8792000-44560093390097450008752100-36220048330010027000
9037000-176100726700100700009277100-7409342888010247000
9465000160800425200104800001017600030090036151010637000
9893000420900163000108100001079300065758017911011072000
10320000623700-6547011060000113980008773201332011416000
10710000784600-24970011260000119840001005200-8609611679000
Solid lines: THDDash lines: Isothermal
KXX
THD
KYY
KXY
KYX
Isothermal
Static load [N]
Stiffness coefficient [MN/m]
Load (17)
742.3-193.1235.1529.8622.88-173.95244.72546
659.9-136.5227.4478.7565.24-157.39218.65498.52
538.7-74.91215.9409.4509.03-124.49197.16427.97
435.5-32.93200.1349.3430.7-79.451188.34367.62
349.9-5.784179.6295.1362.34-45.516172.35325.72
282.212.23157.2246.9315.66-26.816151.76295.17
Solid lines: THDDash lines: Isothermal
CXX
THD
CYY
CXY
CYX
Isothermal
Static load [N]
Damping coefficient [KN-s/m]
Load (15)
26.25965.35316224410.0209260.016951
18.87729.59449215420.0203940.017041
14.82118.08433215740.0201110.01746
12.30114.83343536530.0201620.017994
9.522712.18104744070.0204370.018771
8.392210.37674908260.0208540.019711
THD
Isothermal
THD
Isothermal
Static load [N]
Journal attitude angle [deg]
Drag torque [N-m]
Load (14)
0.840951.83145365716.57815.572
4.22465.434352546513.99812.655
8.424910.278448659711.4459.3519
12.27414.61505917069.72967.1382
16.01318.78185959918.54525.5448
19.65122.65045624357.70944.4498
THD
Isothermal
THD
Isothermal
c' = 17 m
Static load [N]
Journal eccentricity [m]
Minimum film thickness [m]
Load (10)
102137168831251907455
106136168881281867760
112141181981361928270
1191491931101482029080
1261602051241622149692
134176217138177228101104
30,000 rpm
40,000 rpm
50,000 rpm
20,000 rpm
Test data (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (13)
13712574551245311164
136128776012255110.566.5
14113682701236011571
14914890801306912277
160162969214181130.582
1761771011041559514586
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
AxialT133 (3)
93.974129.95410212669.37777
102.168139.62111914975.13990
105.271143.0949811877.11477
106.958144.86278.185
108.082145.99478.92
108.893146.7979.464
109.477147.34779.862
109.878147.71180.141
110.125147.92180.319
110.24147.99980.409
110.116147.88780.314
109.857147.64580.131
109.445147.24779.847
108.848146.65579.442
108.022145.81878.891
106.879144.63478.147
105.167142.79677.062
102.034139.23875.07
93.845129.57169.309
20,000 rpm
30,000 rpm
40,000 rpm
Side edge (rear)
Side edge (front)- Edges
Mid-plane
Test data
Predictions
Axial node number
Temperature [C]
Sheet2
50krpm222N30-50krpm89N30-50krpm133N40krpm1.932um
Side edgeMid-planeSide edgekrpmSide edgeMid-planeSide edgekrpmSide edgeMid-planeSide edgershaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
183217164180degTest data309611292309611292Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg41118401191411114011914111190.8307625.5816.32217.74816.5772.10E-028.88E+06-4.67E+059.55E+059.86E+06755.5-197.1240.6541.6
207215207311195015417113650154171136444.101417.58313.46716.69314.1562.06E-029.15E+06-2.02E+057.61E+051.02E+07674.9-139.3230.9491.9
21120898.19214.1510.41215.63311.6652.04E-029.62E+061.28E+054.78E+051.06E+07556.4-75.83215.8425.3
13311.92312.3628.22614.8339.97122.04E-021.01E+073.80E+052.36E+051.10E+07456.3-31.56195.4368.8
20.52.0530-50krpm30-50krpm17815.55110.5646.611114.1518.7622.07E-021.06E+075.69E+052.95E+041.13E+07375.4-2.171169.2319.9
34.54.116.4NSide edgeMid-planeSide edgeEdge-avg30umN30405020umN30405022218.9739.20525.456813.5717.91442.12E-021.10E+077.17E+05-1.29E+051.15E+07312.219.1139.7277.8
6.5209647464643097409176145
4467776666.50.844870.74417615540krpm1.932um20krpm0.5um
50krpm89N89718271718911089167155rshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyyrshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
ReaCenterFront13377907777133132133165163Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/mLoad (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
1788296828217817890.8409526.25916.31117.7816.5782.09E-028.79E+06-4.46E+059.34E+059.75E+06742.3-193.1235.1529.891.430841.57617.11217.74617.2198.82E-038.22E+065.55E+06-2.81E+055.26E+057.17E+061922.1-720.931053.31829.7
190deg41118222861018686222222444.224618.87713.26316.70613.9982.04E-029.04E+06-1.76E+057.27E+051.01E+07659.9-136.5227.4478.7446.751830.17512.08315.06512.6998.93E-031.31E+076.67E+063244.31.19E+057.80E+061510.7-497.57773.111685.2
1001091003111930um898.424914.82110.06715.67711.4452.01E-029.47E+061.61E+054.25E+051.05E+07538.7-74.91215.9409.48912.23721.17.775613.0069.10269.44E-031.31E+078.23E+063.91E+05-597518.53E+061202.8-281.5462.951494.9
21120309861028384.52095420umN30405013312.27412.3017.788414.8939.72962.02E-029.89E+064.21E+051.63E+051.08E+07435.5-32.93200.1349.313316.75515.5475.270511.6237.14471.00E-021.47E+079.47E+066.46E+05-1.28E+059.10E+061085.1-137.47278.271357.8
44901068788.50.7446820915714517816.0139.52276.101514.2258.54522.04E-021.03E+076.24E+05-6.55E+041.11E+07349.9-5.784179.6295.117820.92612.1393.678510.5475.92781.07E-021.47E+071.05E+078.24E+05-1.79E+059.58E+061053.3-38.164156.41249.8
8996112929489880.74414122219.6518.39224.840913.6477.70942.09E-021.07E+077.85E+05-2.50E+051.13E+07282.212.23157.2246.9
30krpm89N1331021199810013310789
ReaCenterFront178108126103105.5178133ex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyyex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyy
222113134109111222178mmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/mmmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg4111830um2229.00.0400008.22E+068.75E+06-3.62E+054.83E+051.00E+07622.9-174.0244.7546.09.00.0200008.22E+065.91E+06-4.71E+057.63E+057.24E+062018.9-812.1938.51969.9
74787431119409114137108111096044.00.0400001.31E+079.28E+06-7.41E+044.29E+051.02E+07565.2-157.4218.7498.544.00.0200001.31E+076.96E+06-4.34E+043.60E+058.14E+061552.9-503.4825.01790.5
2112044114136107110.50.7447220umN30405089.00.0400001.47E+071.02E+073.01E+053.62E+051.06E+07509.0-124.5197.2428.089.00.0200001.31E+078.72E+064.62E+05-9.27E+038.88E+061245.3-269.7525.71606.7
89119141111115899220-209141122133.00.0400001.47E+071.08E+076.58E+051.79E+051.11E+07430.7-79.5188.3367.6133.00.0200001.47E+071.02E+077.75E+05-1.26E+059.44E+061159.4-135.6325.81470.9
70krpm89N1331261491181221330.744141121178.00.0400001.57E+071.14E+078.77E+051.33E+041.14E+07362.3-45.5172.4325.7178.00.0200001.47E+071.13E+079.47E+05-1.82E+059.89E+061178.0-56.5210.21378.7
ReaCenterFront178134160127130.517889222.00.0400001.57E+071.20E+071.01E+06-8.61E+041.17E+07315.7-26.8151.8295.2
222149176141145222133139136FOIL Bearing static load performance parameters
190deg4111825um178150150Load-Xe_structureexeyEccentricityeccentricityAngleMinimum filmFx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR
12914212931119509146168131138.50997222200.00.0400001.57E+071.17E+079.47E+05-4.50E+041.16E+07337.2-35.0162.3309.3[N]mmmmratiodeg[m]NNNbar[bar]N-m[kW]N/m-
21120441461681281370.744989.0020.101.231.331.810.1047.1816.72-9.0-0.29.00.041.098.14E-031.70E-026.85E+060.00
891541811361458911225umN30405044.0023.536.724.207.930.4332.0310.88-44.0-0.344.00.211.398.40E-031.76E-027.57E+060.00
133162193143152.513312920-209119110FOIL Bearing static load performance parameters89.0027.0112.945.0413.890.7521.266.03-89.2-0.489.20.431.749.11E-031.91E-028.70E+060.03
Themmal gradient (Deg C/mm)1781722051541631781460.844Load-Xe_structureexeyEccentricityeccentricityAngleMinimum filmMinimum filmMinimum filmFx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR133.0030.0118.005.1018.71.015.813.27-133.98-1.3134.00.652.079.94E-032.08E-029.74E+060.00
300000.24390243922218321716317322289133133[N]mmmmratiodeg[m][m][m]NNNbar[bar]N-m[kW]N/m-178.0033.1322.474.8022.971.2412.071.78-178.7-0.8178.70.872.391.09E-022.27E-021.06E+070.00
500000.54878048782.052.051339.0018.630.761.661.830.1165.3515.3316.71915.572-9.0-0.09.00.041.181.70E-027.10E-029.58E+060.00
700000.79268292684.116.44.116.417817117144.0021.974.732.685.430.3229.5912.0115.18412.655-43.6-0.743.60.211.401.70E-027.14E-029.87E+060.00
22289.0025.399.773.1910.280.6018.088.0813.3649.3519-89.0-0.389.00.431.711.75E-027.31E-021.04E+070.00
133.0028.3914.133.7414.60.914.835.3612.1057.1382-133.08-0.9133.10.652.031.80E-027.54E-021.08E+070.00
50krpm44N50krpm133N20umN304050178.0031.4518.363.9618.781.1012.183.4710.9775.5448-178.2-0.7178.20.862.351.88E-027.86E-021.12E+070.139N : 20 - 100 krpm
ReaCenterFrontReaCenterFront20-20910790222.0034.2522.284.0822.651.3310.382.2410.0264.4498-222.1-1.0222.11.082.651.97E-028.26E-021.16E+070.28ex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyy
0.644mmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg41118190deg41118891071009.00.0200008.22E+065.91E+06-4.71E+057.63E+057.24E+062018.9-812.1938.51969.9
8390833111911912711831119133200.0032.8520.353.9820.731.2111.062.8010.4874.9532-200.1-0.3200.10.972.501.92E-028.05E-021.14E+070.229.00.0400008.22E+068.09E+06-5.19E+056.83E+058.73E+06879.9-263.9276.2742.7
21120211201781231209.00.0600008.22E+068.88E+06-4.42E+058.83E+059.32E+06572.2-143.3137.3428.6
2229.00.0800008.22E+069.37E+06-3.76E+058.79E+059.67E+06411.3-91.384.8289.0
9.00.01000008.22E+069.66E+06-3.33E+058.64E+059.90E+06315.8-64.659.7213.7
30krpm44N30krpm133N32umN304050
ReaCenterFrontReaCenterFront20-209117100FOIL Bearing static load performance parameters
0.644Speede_structureexeyEccentricityeccentricityAngleMinimum filmMinimum film (center)Minimum film (near edge)Fx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR
190deg41118190deg4111889128128[rpm]mmmmratiodeg[m][m][m]NNNbar[bar]N-m[kW]N/m-
596359311198891883111913320000.0020.101.231.331.810.1047.1816.7217.26116.81-9.0-0.29.00.041.098.14E-031.70E-026.85E+060.00
211202112017840000.0020.101.090.711.300.0733.0117.2317.85517.334-9.0-0.19.00.041.091.62E-026.80E-028.64E+060.15
22260000.0020.101.040.511.160.0626.0517.3918.02317.497-9.0-0.09.00.041.092.43E-021.53E-019.32E+060.19
70krpm44N70krpm133N80000.0020.101.000.411.10.122.2917.4718.117.583-8.99-0.29.00.041.093.24E-022.71E-019.71E+060.20
ReaCenterFrontReaCenterFront27umN304050180deg100000.0020.100.980.341.040.0619.0817.5218.14517.642-9.0-0.19.00.041.094.05E-024.24E-019.95E+060.20
20-209609921486175
190deg41118190deg411180.644999920krpm0.5um
11112111131119150164150311198980109214109182rshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
2112021120133Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
17810814019820091.430841.57617.11217.74617.2198.82E-035.55E+06-2.81E+055.26E+057.17E+061922.1-720.931053.31829.7
222440.9669928.4117.61118.80817.8251.90E-027.61E+06-4.00E+058.27E+058.78E+06876.26-233.34313.41706.46
Themmal gradient (Deg C/mm)Themmal gradient (Deg C/mm)890.8242517.44217.84619.69218.2743.07E-028.65E+06-2.35E+055.34E+059.56E+06470.46-105.18142.74379.62
300000.243902439300000.182926829325umN3040501330.770156.163918.07820.33918.8984.38E-029.28E+06-300122.53E+051.01E+07289.36-54.98590.006232.87
500000.4268292683500000.548780487820-2091171780.8279-4.146717.55321.27319.7595.75E-029.69E+061.61E+05837191.04E+07206.68-32.47373.863153.01
700000.6097560976700000.85365853660.744
89137
themal gradient deg C/mmMid-planeTemperauture Deg CSide edgeTemperauture Deg C133
300005000070000300005000070000300005000070000178169
440.2439024390.42682926830.60975609764463901215983111222
890.2439024390.54878048780.7926829268897810914274100129
1330.18292682930.54878048780.85365853661339112716488119150Solid shaftRadial growthWall thickness: 10 mmRadial growthWall thickness: 2 mmRadial growth
2.00E+014.83E-074.83E-012.00E+011.05E-061.05E+002.00E+011.71E-061.71E+00
Solid journalMax1804.00E+011.93E-061.93E+004.00E+014.22E-064.22E+004.00E+016.85E-066.85E+00
20umN3040503040506.00E+014.35E-064.35E+006.00E+019.49E-069.49E+006.00E+011.54E-051.54E+01
20-2098.00E+017.73E-067.73E+008.00E+011.69E-051.69E+018.00E+012.74E-052.74E+01
0.6441.00E+021.21E-051.21E+011.00E+022.64E-052.64E+011.00E+024.28E-054.28E+01
898811715988117157
133
Axial temp. at 37 node number178114145183114145183
30K 89N22220 krpm
63.39783.177106.394019N44N89N133N178N222N
63.39783.177106.3940.0132Solid journalMax180XPTPTPTPTPTPT
70.93994.777121.4050.026320umN3040503040500146.452146.2148.161151.242155.308160.112
73.799.969128.7050.039420-2094.6151.01146.4521.00546.21.00648.1611.00851.2421.00955.3081.0160.112
75.243103.026133.1230.05250.65449.2311.00846.5741.00246.2581.00748.2731.01251.41.01555.491.01760.308
76.294105.108136.1440.065689961311879413117613.8461.00746.731.00146.3491.0148.4151.01851.5821.02255.6951.02560.522
77.058106.616138.3260.078713318.4621.00846.8831.00146.4641.01448.581.02451.7851.0355.9181.03460.755
77.616107.714139.9120.091817812315920612115920223.0771.00647.0231.00346.61.01948.771.03152.011.03956.1621.04361.008
78.012108.489141.030.104922227.6921.00647.171.00546.761.02548.9861.0452.261.04856.4311.05361.285
78.273108.998141.7590.1171032.3081.00547.331.00846.9451.03249.2281.04952.5371.05956.7261.06561.588
78.426109.29142.170.13111Solid journalMax18036.9231.00647.4991.01247.1521.0449.4941.05952.8391.07157.0491.07761.921
78.275109.008141.7840.1441220umN30405030405041.5381.00647.6771.01747.381.04949.7851.07153.1681.08457.4011.09162.287
78.012108.5141.0590.1571320-20946.1541.00747.8611.02347.6271.0650.11.08353.5261.09857.7871.10762.689
77.616107.724139.9420.17140.74450.7691.00848.0511.0347.8941.07150.4391.09753.9141.11358.2081.12463.132
77.056106.624138.3550.183158915114755.3851.0148.2481.03848.1791.08350.8041.11254.3341.1358.671.14263.622
76.289105.116136.1720.19616133601.01148.4511.04648.4811.09651.1941.12854.7891.14959.1761.16364.165
75.237103.032133.1520.2091717817924217623764.6151.01348.6591.05548.81.1151.6121.14655.2831.1759.7311.18664.768
73.69299.974128.7360.2221822269.2311.01548.8731.06449.1361.12552.0571.16555.8191.19360.3421.21265.439
70.93194.785121.4440.2351973.8461.01849.0931.07449.4881.14152.5331.18656.3991.21861.0141.24166.185
63.3983.185106.4410.24820Solid journalMax18078.4621.0249.3161.08549.8561.15853.0391.20957.0281.24661.7521.27367.017
63.3983.185106.4410.2612119umN203040502030405020-edge40-edge83.0771.02349.5451.09650.241.17653.5781.23357.7081.27662.5641.30967.943
20-209609614823055831251905312487.6921.02649.7771.10750.6381.19654.151.2658.4441.3163.4551.34968.973
0.6544619514823060881281865512292.3081.02950.0131.1251.0511.21754.7571.28959.2371.34764.4311.39370.117
897111314221770981361926012396.9231.03250.2511.13251.4791.23955.3981.3260.0921.38765.4971.44271.381
133821131512108011014820269130101.5381.03550.4931.14551.921.26256.0751.35461.0081.43166.6561.49672.774
178941261652209212416221481141106.1541.03850.7361.15952.3741.28756.7881.38961.9871.47867.9111.55574.299
22210714018023310413817722895155110.7691.04250.9811.17252.8391.31357.5341.42763.0281.52969.2611.61975.957
115.3851.04551.2271.18653.3161.33958.3131.46764.1281.58370.7031.68877.742
1201.04851.4741.20153.8011.36759.1211.50965.2831.64172.231.76279.646
124.6151.05151.7211.21554.2951.39659.9561.55366.4871.70173.8321.83981.653
222 NTHDAdiabatic129.2311.05451.9681.22954.7931.42560.8131.59867.7321.76375.4951.91983.743
20107128133.8461.05752.2141.24455.2961.45461.6871.64369.0061.82677.2022.00185.891
30140157138.4621.0652.4581.25855.7991.48362.571.68970.2991.8978.9342.08388.067
40180197143.0771.06352.7011.27156.3011.51263.4561.73471.5951.95380.6682.16490.24
50233256147.6921.06652.9411.28556.7981.54164.3371.77972.882.01482.382.24292.377
152.3081.06853.1781.29757.2871.56865.2031.82174.1372.07384.0462.31794.447
156.9231.07153.4121.3157.7641.59466.0461.86275.3512.12885.6432.38696.418
161.5381.07353.6411.32158.2271.61866.8561.89876.5052.17887.1462.44898.262
20krpm30krpm40krpm50krpm166.1541.07453.8671.33158.6721.6467.6221.93177.5832.22288.5352.50299.952
89133891338913389133170.7691.07654.0871.3459.0941.65968.3371.9678.5692.25989.792.547101.464
160.30869.37785.65193.974123.254129.954183.102187.618175.3851.07754.3031.34759.4911.67668.991.98379.452.28890.8922.582102.778
260.30869.37785.6519693.974102123.254119129.954126183.102154187.6181621801.07854.5121.35359.8591.68869.574280.2142.3191.8252.607103.875
364.20475.13990.94102.168129.362139.621189.318197.386184.6151.07954.7161.35860.1941.69770.082.01280.8482.32292.5772.62104.742
466.14477.11493.727105.271132.374143.094191.162199.841189.2311.07954.9131.36160.4941.70270.5012.01781.3442.32693.1362.621105.365
567.32178.18595.374106.958133.993144.862191.793200.697193.8461.07955.1031.36260.7551.70370.8332.01581.6952.3293.4952.61105.738
668.12678.9296.473108.082135.008145.994192.059201.156198.4621.07955.2861.36160.9761.69971.0692.00681.8942.30493.6472.588105.853
768.70979.46497.252108.893135.697146.79192.184201.465203.0771.07855.4631.35861.1541.69171.2061.9981.9392.27993.5912.553105.709
869.13179.86297.806109.477136.168147.347192.227201.657207.6921.07755.6311.35361.2881.67971.2431.96781.8272.24593.3252.507105.306
969.42580.14198.183109.878136.474147.711192.208201.744212.3081.07655.7931.34661.3771.66271.1781.93781.5622.20192.8542.45104.65
1069.61180.31998.413110.125136.648147.921192.154201.756216.9231.07455.9471.33761.4191.6471.0121.90181.1442.14992.1822.382103.749
1169.70180.40998.517112110.24119136.707141147.999149192.066181201.702193221.5381.07256.0931.32661.4161.61470.7471.85880.5812.08991.322.304102.615
1269.60980.31498.405110.116136.61147.887192.012201.631226.1541.0756.2331.31361.3671.58470.3871.8179.882.02190.282.218101.264
1369.4280.13198.164109.857136.402147.645191.957201.525230.7691.06756.3651.29861.2751.55169.9371.75679.051.94689.0762.12399.717
1469.12279.84797.776109.445136.062147.247191.867201.344235.3851.06456.491.28161.141.51369.4021.69878.1051.86687.7272.02297.997
1568.69579.44297.21108.848135.553146.655191.708201.0482401.06156.6081.26360.9651.47368.7921.63577.0581.78186.2571.91596.135
1668.10878.89196.418108.022134.82145.818191.448200.613244.6151.05756.721.24360.7531.4368.1131.5775.9281.69384.6911.80494.168
1767.29678.14795.303106.879133.753144.634191.013199.985249.2311.05456.8261.22160.5071.38567.3781.50274.7331.60383.0581.69292.136
1866.11377.06293.637105.167132.068142.796190.156198.894253.8461.0556.9261.19960.2321.33866.5981.43373.4931.51181.3891.5890.076
1964.16575.0790.828102.034128.976139.238188.038196.136258.4621.04557.0221.17559.9321.2965.7851.36372.2281.4279.7111.46988.026
2060.26969.30985.5399293.84598122.858111129.571118181.798136186.343143263.0771.04157.1131.15159.6141.24264.9511.29470.9591.33178.0531.36186.028
2160.26969.30985.53993.845122.858129.571181.798186.343267.6921.03657.21.12759.2821.19464.1121.22569.7111.24576.461.25884.147
272.3081.03257.2851.10258.9431.14763.2861.1668.5281.16475.0021.16482.488
2717796102119126154162276.9231.02757.3671.07858.6071.10162.5091.167.4841.09373.791.08581.194
118290112119141149181193281.5381.02257.4481.05458.2911.05961.8411.04866.6841.03772.9531.02780.437
2071779298111118136143286.1541.01857.531.03258.0241.02461.3671.01266.3081.00172.693180.26
290.7691.01357.6141.01357.8541.00161.263166.316172.797180.36
295.3851.00957.703157.889161.415166.443172.898180.44
3001.00557.804158.069161.558166.553172.982180.505
304.6151.00257.928158.239161.687166.648173.053180.558
309.231158.086158.398161.802166.732173.114180.603
313.846158.265158.547161.907166.806173.167180.641
318.462158.441158.687162.002166.872173.213180.673
323.077158.615158.82162.09166.932173.254180.701
327.692158.786158.945162.17166.986173.291180.725
332.308158.954159.064162.245167.036173.324180.746
336.923159.12159.178162.316167.082173.354180.765
341.538159.284159.286162.381167.124173.382180.782
346.154159.446159.39162.444167.164173.407180.798
350.769159.606159.49162.503167.202173.431180.812
355.385159.758159.583162.557167.236173.452180.824
360159.758159.583162.557167.236173.452180.824
Update Curve Fit
Sheet2
11111111
&A
Page &P
Kxx
Kxy
Kyx
Kyy
Kxx fit
Kxy fit
Kyx fit
Kyy fit
Load (12)
11111111
&A
Page &P
Cxx
Cxy
Cyx
Cyy
Cxx fit
Cxy fit
Cyx fit
Cyy fit
Load (11)
11111111
&A
Page &P
Mxx
Mxy
Myx
Myy
Mxx fit
Mxy fit
Myx fit
Myy fit
AxialT133 (2)
11111111
NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Minimum gas film thickness between top foil and journal.
Minimum gas film thickness between top foil and journal.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Tae Ho Kim:With consideration of foil material degradation
Tae Ho Kim:Without foil material degradation
Update Curve Fit
&A
Page &P
Kxx
Kxy
Kyx
Kyy
Kxx fit
Kxy fit
Kyx fit
Kyy fit
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
&A
Page &P
Cxx
Cxy
Cyx
Cyy
Cxx fit
Cxy fit
Cyx fit
Cyy fit
Load (9)
11111111
&A
Page &P
Mxx
Mxy
Myx
Myy
Mxx fit
Mxy fit
Myx fit
Myy fit
Load (8)
11111111
NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Tae Ho Kim:With consideration of foil material degradation
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Update Curve Fit
&A
Page &P
Kxx
Kxy
Kyx
Kyy
Kxx fit
Kxy fit
Kyx fit
Kyy fit
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
&A
Page &P
Cxx
Cxy
Cyx
Cyy
Cxx fit
Cxy fit
Cyx fit
Cyy fit
AxialT133
11111111
&A
Page &P
Mxx
Mxy
Myx
Myy
Mxx fit
Mxy fit
Myx fit
Myy fit
AxialT89
107128
140157
180197
233256
NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Minimum gas film thickness between top foil and journal.
Minimum gas film thickness between top foil and journal.
Tae Ho Kim:With consideration of foil material degradation
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Test data - Mid-plane
222 N
THD solution
Adiabatic wall
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Peak temperature [ C]
Load (7)
1371257455124531141086464
1361287760122551141076766
1411368270123601191117171
1491489080130691261187777
1601629692141811341278282
176177101104155951491418686
Test data - Mid-plane
40,000 rpm
Test data - Edges
20,000 rpm
Predictions- Edges
Predictions- Mid-plane
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (6)
93.974129.954187.61810212616269.37777
102.168139.621197.38611914919375.13990
105.271143.094199.8419811814377.11477
106.958144.862200.69778.185
108.082145.994201.15678.92
108.893146.79201.46579.464
109.477147.347201.65779.862
109.878147.711201.74480.141
110.125147.921201.75680.319
110.24147.999201.70280.409
110.116147.887201.63180.314
109.857147.645201.52580.131
109.445147.247201.34479.847
108.848146.655201.04879.442
108.022145.818200.61378.891
106.879144.634199.98578.147
105.167142.796198.89477.062
102.034139.238196.13675.07
93.845129.571186.34369.309
30,000 rpm
40,000 rpm
50,000 rpm
Axial node number
Temperature [C]
Load (4)
10213712517455
106136128447760
112141136898270
1191491481339080
1261601621789692
134176177222101104
20,000 rpm
30,000 rpm
40,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (5)
1021375312574961486055
1061365512877951486160
11214160136821131427170
11914969148901131518280
12616081162961261659492
13417695177101140180107104
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (3)
93.974129.954187.61810212616269.37777
102.168139.621197.38611914919375.13990
105.271143.094199.8419811814377.11477
106.958144.862200.69778.185
108.082145.994201.15678.92
108.893146.79201.46579.464
109.477147.347201.65779.862
109.878147.711201.74480.141
110.125147.921201.75680.319
110.24147.999201.70280.409
110.116147.887201.63180.314
109.857147.645201.52580.131
109.445147.247201.34479.847
108.848146.655201.04879.442
108.022145.818200.61378.891
106.879144.634199.98578.147
105.167142.796198.89477.062
102.034139.238196.13675.07
93.845129.571186.34369.309
30,000 rpm
40,000 rpm
50,000 rpm
Axial node number
Temperature [C]
Load (2)
85.651123.254183.10296119154160.30871
90.94129.362189.31811214118164.20482
93.727132.374191.1629211113666.14471
95.374133.993191.79367.321
96.473135.008192.05968.126
97.252135.697192.18468.709
97.806136.168192.22769.131
98.183136.474192.20869.425
98.413136.648192.15469.611
98.517136.707192.06669.701
98.405136.61192.01269.609
98.164136.402191.95769.42
97.776136.062191.86769.122
97.21135.553191.70868.695
96.418134.82191.44868.108
95.303133.753191.01367.296
93.637132.068190.15666.113
90.828128.976188.03864.165
85.539122.858181.79860.269
30,000 rpm
40,000 rpm
50,000 rpm
Axial node number
Temperature [C]
Load
10213716853125124
10613616855128122
11214118160136123
11914919369148130
12616020581162141
13417621795177155
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
centri
1021371685312512474961482306055
1061361685512812277951482306160
11214118160136123821131422177170
11914919369148130901131512108280
12616020581162141961261652209492
13417621795177155101140180233107104
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
thermal
10213716899974
10613616844444477
1121411819413117682
11914919313313313390
12616020512115920296
134176217222222222101
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Chart1 (2)
10213716899974
10613616844444477
112141181941478982
11914919313313313390
12616020512117623796
134176217222222222101
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Chart1 (5)
102137168999
106136168444444
11214118188117157
119149193133133133
126160205114145183
134176217222222222
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Chart2
10213716891756099
10613616844444499
1121411818918280109
119149193133133133133
126160205178200108140
134176217222222222222
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.7_0
Static load [N]
Peak temperature [ C]
Chart2 (2)
1021371687454609791221109017560
106136168876872984412144444444
1121411811108892112898913310018280
119149193132107133129133136133133133133
126160205178178178146178150171120200108
134176217222222222222222222222222222222
30,000 rpm
40,000 rpm
50,000 rpm
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-0.8_30
Predictions - 30 krpm-0.7_20
Predictions - 30 krpm-0.7_0
Predictions - 30 krpm-25um_0.7_0
Predictions - 30 krpm-20um_0.7_0
Static load [N]
Peak temperature [ C]
Sheet3
000
0.1210.2590.432
0.4831.0371.729
1.0872.3333.891
1.9324.1486.917
3.0196.48110.809
4.3489.33315.564
5.91812.70321.185
7.72916.59227.67
9.78220.99935.02
12.07725.92543.234
Solid shaft
Ri =0.5 Ro
Ri =0.75 Ro
22
Rotor speed [rpm]
Centrifugal growth [m]
Chart1 (8)
0.55250.510.765
76.37570.5105.75
166.725153.9230.85
Inconel X750
Inconel 718
AISI 304 (Stainless steel)
Temperature [ C]
Thermal expansion [m]
Chart1 (6)
0.2439024390.42682926830.6097560976
0.2439024390.54878048780.7926829268
0.18292682930.54878048780.8536585366
30,000 rpm
50,000 rpm
70,000 rpm
Static load [N]
Axial Thermal gradient [ C/mm]
Chart1 (9)
918878746359
1271191091009083
164150142129121111
Mid-plane
133 N
89 N
44 N
Side edge
Rotor speed [rpm]
Peak temperature [ C]
Sheet3 (2)
74100129
78109142
74100129
30,000 rpm
50,000 rpm
70,000 rpm
Temperature [C]
Chart1 (3)
1830207
217215
164207
Temperature [C]
http://www.hightempmetals.com/techdata/hitempInconelX750data.php
InconelX750
Modulus of Elasticity
CMPa x 10(6)
26.7213.7
260197.9
538172.4
732144.8
816127.6
Thermal Conductivity
CW/m-K
14916.9
31620.5
53826.5
64928.7
76031.4
87135.3
Inconel 718AISI4140 steel test shaftAISI 304 stainless steel bearing housing
http://www.espimetals.com/tech/inconel718.pdfTheraml expansion coefficientTheraml expansion coefficient
R0.025m211Gpahttp://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4140&prop=all&Page_Title=AISI%204140http://www.goodfellow.com/csp/active/STATIC/A/Stainless_Steel_-_AISI_304.HTML
alph1.30E-05Kavg
conductivity11.4W/m.K
CRgThermal Properties18
26.70.552516.3
26076.375
538166.725Properties
732229.775TreatmentR0.025m
816257.07512.320-100moreoil hardened, tempered 600Calph1.20E-05K
42.7100more
473150-200moreCRg
Inconel x75026.70.765
http://www.hightempmetals.com/techdata/hitempInconelX750data.php260105.75
R0.025m538230.85
alph1.20E-05Kat 20 deg C732318.15
816355.95
CRg
26.70.51
26070.5
538153.9
732212.1
816237.3
Centrifugal growth
http://www.hightempmetals.com/techdata/hitempInconel718data.php
Inconel 718
http://www.espimetals.com/tech/inconel718.pdf
R0.025m208Gpa
rpmsolid0.5 Ro0.75Ro
0000
1.00E+040.1210.2590.432
2.00E+040.4831.0371.729
3.00E+041.0872.3333.891
4.00E+041.9324.1486.917
5.00E+043.0196.48110.809
6.00E+044.3489.33315.564
7.00E+045.91812.70321.185
8.00E+047.72916.59227.67
9.00E+049.78220.99935.02
1.00E+0512.07725.92543.234
http://www.hightempmetals.com/techdata/hitempInconelX750data.php
http://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4140&prop=all&Page_Title=AISI%204140
12.3
42.7
473
http://www.goodfellow.com/csp/active/STATIC/A/Stainless_Steel_-_AISI_304.HTML
10678.197146
11190.684142
123109.38144
137127.15151
152144.91162
168161.68175
c=20 m
c=25 m
c=32 m
Static load [N]
Peak temperature [ C]
99.55678.197
112.3690.684
136.63109.38
161.32127.15
187.72144.91
215.11161.68
Adiabatic
Heat transfer convection
Static load [N]
Peak temperature [ C]
2552
2855
3359
4268
6691
Peak temperature
Inlet mixing temperature
Mixing ratio,
Temperature [ C]
50000 rpm
Peal temp
Static loadadiabaticheat coeffCalculation of specific heat
999.55678.197Specific heat
44112.3690.684
89136.63109.38
133161.32127.15Prandtl No.
178187.72144.91
222215.11161.68
Dimensionless spesific heat
adiabaticRotor speed5000065.4498469498m/s
Static loadc=32umc=25umc=20umrho1.169kg/m3
978.197106146cp1080J/kg-degK
4490.684111142EMU1.85E-05Pa-s
89109.38123144K0.0257W/m.KFor air
133127.15137151Pr No.7.77E-01
178144.91152162Specific heat6.18E+02
222161.68168175Diml spe heat9.90E-01c/(emu*cp)1.60E-03
Nu avg4.92E+02
ReL6.50E+05
Specific heat8.05E+01492.1050786737
Mixing
Lminlet tempPeak
02552
0.22855
0.43359
0.64268
0.86691
6390121
78109142
91127164
30,000 rpm
50,000 rpm
70,000 rpm
Static load [N]
Peak temperature [ C]
MBD00553F60.unknown
MBD005545AE.unknown
MBD00553C7F.unknown
-
Mid-plane & edge film temperaturesDifference in film temperatures at mid-plane and edge (axial thermal gradient) increases as rotor speed increases. Higher film temperatures at bearing mid-plane evidence absence of axial cooling flow pathStatic load (vertical:180).
Comparison to test data (Radil and Zeszotek, 2004)TSupply=21 CTshaft=Tbearing =Tambient = 21 C
Load (25)
74641371115553125124
7766.5136110.56055128122
82711411157060136123
90771491228069148130
9682160130.59281162141
1018617614510495177155
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (24)
741021371685583125190
771061361686088128186
821121411817098136192
9011914919380110148202
9612616020592124162214
101134176217104138177228
30,000 rpm
40,000 rpm
50,000 rpm
20,000 rpm
Test data (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (23)
111
1.0051.0081.01
1.0021.0121.017
1.0011.0181.025
1.0011.0241.034
1.0031.0311.043
1.0051.041.053
1.0081.0491.065
1.0121.0591.077
1.0171.0711.091
1.0231.0831.107
1.031.0971.124
1.0381.1121.142
1.0461.1281.163
1.0551.1461.186
1.0641.1651.212
1.0741.1861.241
1.0851.2091.273
1.0961.2331.309
1.1071.261.349
1.121.2891.393
1.1321.321.442
1.1451.3541.496
1.1591.3891.555
1.1721.4271.619
1.1861.4671.688
1.2011.5091.762
1.2151.5531.839
1.2291.5981.919
1.2441.6432.001
1.2581.6892.083
1.2711.7342.164
1.2851.7792.242
1.2971.8212.317
1.311.8622.386
1.3211.8982.448
1.3311.9312.502
1.341.962.547
1.3471.9832.582
1.35322.607
1.3582.0122.62
1.3612.0172.621
1.3622.0152.61
1.3612.0062.588
1.3581.992.553
1.3531.9672.507
1.3461.9372.45
1.3371.9012.382
1.3261.8582.304
1.3131.812.218
1.2981.7562.123
1.2811.6982.022
1.2631.6351.915
1.2431.571.804
1.2211.5021.692
1.1991.4331.58
1.1751.3631.469
1.1511.2941.361
1.1271.2251.258
1.1021.161.164
1.0781.11.085
1.0541.0481.027
1.0321.0121
1.01311
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
Static load increases
44 N
133 N
222 N
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (22)
46.251.24260.112
46.251.24260.112
46.25851.460.308
46.34951.58260.522
46.46451.78560.755
46.652.0161.008
46.7652.2661.285
46.94552.53761.588
47.15252.83961.921
47.3853.16862.287
47.62753.52662.689
47.89453.91463.132
48.17954.33463.622
48.48154.78964.165
48.855.28364.768
49.13655.81965.439
49.48856.39966.185
49.85657.02867.017
50.2457.70867.943
50.63858.44468.973
51.05159.23770.117
51.47960.09271.381
51.9261.00872.774
52.37461.98774.299
52.83963.02875.957
53.31664.12877.742
53.80165.28379.646
54.29566.48781.653
54.79367.73283.743
55.29669.00685.891
55.79970.29988.067
56.30171.59590.24
56.79872.8892.377
57.28774.13794.447
57.76475.35196.418
58.22776.50598.262
58.67277.58399.952
59.09478.569101.464
59.49179.45102.778
59.85980.214103.875
60.19480.848104.742
60.49481.344105.365
60.75581.695105.738
60.97681.894105.853
61.15481.939105.709
61.28881.827105.306
61.37781.562104.65
61.41981.144103.749
61.41680.581102.615
61.36779.88101.264
61.27579.0599.717
61.1478.10597.997
60.96577.05896.135
60.75375.92894.168
60.50774.73392.136
60.23273.49390.076
59.93272.22888.026
59.61470.95986.028
59.28269.71184.147
58.94368.52882.488
58.60767.48481.194
58.29166.68480.437
58.02466.30880.26
57.85466.31680.36
57.88966.44380.44
58.06966.55380.505
58.23966.64880.558
58.39866.73280.603
58.54766.80680.641
58.68766.87280.673
58.8266.93280.701
58.94566.98680.725
59.06467.03680.746
59.17867.08280.765
59.28667.12480.782
59.3967.16480.798
59.4967.20280.812
59.58367.23680.824
59.58367.23680.824
Static load increases
44 N
133 N
222 N
Circumferential angle [deg]
Temperature [ C]
Load (21)
111111
1.0111.0051.0061.0081.0091.01
1.0081.0021.0071.0121.0151.017
1.0071.0011.011.0181.0221.025
1.0081.0011.0141.0241.031.034
1.0061.0031.0191.0311.0391.043
1.0061.0051.0251.041.0481.053
1.0051.0081.0321.0491.0591.065
1.0061.0121.041.0591.0711.077
1.0061.0171.0491.0711.0841.091
1.0071.0231.061.0831.0981.107
1.0081.031.0711.0971.1131.124
1.011.0381.0831.1121.131.142
1.0111.0461.0961.1281.1491.163
1.0131.0551.111.1461.171.186
1.0151.0641.1251.1651.1931.212
1.0181.0741.1411.1861.2181.241
1.021.0851.1581.2091.2461.273
1.0231.0961.1761.2331.2761.309
1.0261.1071.1961.261.311.349
1.0291.121.2171.2891.3471.393
1.0321.1321.2391.321.3871.442
1.0351.1451.2621.3541.4311.496
1.0381.1591.2871.3891.4781.555
1.0421.1721.3131.4271.5291.619
1.0451.1861.3391.4671.5831.688
1.0481.2011.3671.5091.6411.762
1.0511.2151.3961.5531.7011.839
1.0541.2291.4251.5981.7631.919
1.0571.2441.4541.6431.8262.001
1.061.2581.4831.6891.892.083
1.0631.2711.5121.7341.9532.164
1.0661.2851.5411.7792.0142.242
1.0681.2971.5681.8212.0732.317
1.0711.311.5941.8622.1282.386
1.0731.3211.6181.8982.1782.448
1.0741.3311.641.9312.2222.502
1.0761.341.6591.962.2592.547
1.0771.3471.6761.9832.2882.582
1.0781.3531.68822.312.607
1.0791.3581.6972.0122.3222.62
1.0791.3611.7022.0172.3262.621
1.0791.3621.7032.0152.322.61
1.0791.3611.6992.0062.3042.588
1.0781.3581.6911.992.2792.553
1.0771.3531.6791.9672.2452.507
1.0761.3461.6621.9372.2012.45
1.0741.3371.641.9012.1492.382
1.0721.3261.6141.8582.0892.304
1.071.3131.5841.812.0212.218
1.0671.2981.5511.7561.9462.123
1.0641.2811.5131.6981.8662.022
1.0611.2631.4731.6351.7811.915
1.0571.2431.431.571.6931.804
1.0541.2211.3851.5021.6031.692
1.051.1991.3381.4331.5111.58
1.0451.1751.291.3631.421.469
1.0411.1511.2421.2941.3311.361
1.0361.1271.1941.2251.2451.258
1.0321.1021.1471.161.1641.164
1.0271.0781.1011.11.0931.085
1.0221.0541.0591.0481.0371.027
1.0181.0321.0241.0121.0011
1.0131.0131.001111
1.00911111
1.00511111
1.00211111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
9 N
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (20)
46.45246.248.16151.24255.30860.112
46.45246.248.16151.24255.30860.112
46.57446.25848.27351.455.4960.308
46.7346.34948.41551.58255.69560.522
46.88346.46448.5851.78555.91860.755
47.02346.648.7752.0156.16261.008
47.1746.7648.98652.2656.43161.285
47.3346.94549.22852.53756.72661.588
47.49947.15249.49452.83957.04961.921
47.67747.3849.78553.16857.40162.287
47.86147.62750.153.52657.78762.689
48.05147.89450.43953.91458.20863.132
48.24848.17950.80454.33458.6763.622
48.45148.48151.19454.78959.17664.165
48.65948.851.61255.28359.73164.768
48.87349.13652.05755.81960.34265.439
49.09349.48852.53356.39961.01466.185
49.31649.85653.03957.02861.75267.017
49.54550.2453.57857.70862.56467.943
49.77750.63854.1558.44463.45568.973
50.01351.05154.75759.23764.43170.117
50.25151.47955.39860.09265.49771.381
50.49351.9256.07561.00866.65672.774
50.73652.37456.78861.98767.91174.299
50.98152.83957.53463.02869.26175.957
51.22753.31658.31364.12870.70377.742
51.47453.80159.12165.28372.2379.646
51.72154.29559.95666.48773.83281.653
51.96854.79360.81367.73275.49583.743
52.21455.29661.68769.00677.20285.891
52.45855.79962.5770.29978.93488.067
52.70156.30163.45671.59580.66890.24
52.94156.79864.33772.8882.3892.377
53.17857.28765.20374.13784.04694.447
53.41257.76466.04675.35185.64396.418
53.64158.22766.85676.50587.14698.262
53.86758.67267.62277.58388.53599.952
54.08759.09468.33778.56989.79101.464
54.30359.49168.9979.4590.892102.778
54.51259.85969.57480.21491.825103.875
54.71660.19470.0880.84892.577104.742
54.91360.49470.50181.34493.136105.365
55.10360.75570.83381.69593.495105.738
55.28660.97671.06981.89493.647105.853
55.46361.15471.20681.93993.591105.709
55.63161.28871.24381.82793.325105.306
55.79361.37771.17881.56292.854104.65
55.94761.41971.01281.14492.182103.749
56.09361.41670.74780.58191.32102.615
56.23361.36770.38779.8890.28101.264
56.36561.27569.93779.0589.07699.717
56.4961.1469.40278.10587.72797.997
56.60860.96568.79277.05886.25796.135
56.7260.75368.11375.92884.69194.168
56.82660.50767.37874.73383.05892.136
56.92660.23266.59873.49381.38990.076
57.02259.93265.78572.22879.71188.026
57.11359.61464.95170.95978.05386.028
57.259.28264.11269.71176.4684.147
57.28558.94363.28668.52875.00282.488
57.36758.60762.50967.48473.7981.194
57.44858.29161.84166.68472.95380.437
57.5358.02461.36766.30872.69380.26
57.61457.85461.26366.31672.79780.36
57.70357.88961.41566.44372.89880.44
57.80458.06961.55866.55372.98280.505
57.92858.23961.68766.64873.05380.558
58.08658.39861.80266.73273.11480.603
58.26558.54761.90766.80673.16780.641
58.44158.68762.00266.87273.21380.673
58.61558.8262.0966.93273.25480.701
58.78658.94562.1766.98673.29180.725
58.95459.06462.24567.03673.32480.746
59.1259.17862.31667.08273.35480.765
59.28459.28662.38167.12473.38280.782
59.44659.3962.44467.16473.40780.798
59.60659.4962.50367.20273.43180.812
59.75859.58362.55767.23673.45280.824
59.75859.58362.55767.23673.45280.824
9 N
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Temperature [ C]
Load (19)
0.4831
1.932
4.348
7.729
12.08
Solid shaft
tS = 10 mm
tS = 2 mm
Shaft wall thickness decreases
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Centrifugal growth [ C]
Load (16)
0.48311.0541.712
1.9324.2176.846
4.3489.48815.4
7.72916.8727.39
12.0826.3542.79
Solid shaft
tS = 10 mm
tS = 2 mm
Shaft wall thickness decreases
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Centrifugal growth [m]
Load (18)
8792000-44560093390097450008752100-36220048330010027000
9037000-176100726700100700009277100-7409342888010247000
9465000160800425200104800001017600030090036151010637000
9893000420900163000108100001079300065758017911011072000
10320000623700-6547011060000113980008773201332011416000
10710000784600-24970011260000119840001005200-8609611679000
Solid lines: THDDash lines: Isothermal
KXX
THD
KYY
KXY
KYX
Isothermal
Static load [N]
Stiffness coefficient [MN/m]
Load (17)
742.3-193.1235.1529.8622.88-173.95244.72546
659.9-136.5227.4478.7565.24-157.39218.65498.52
538.7-74.91215.9409.4509.03-124.49197.16427.97
435.5-32.93200.1349.3430.7-79.451188.34367.62
349.9-5.784179.6295.1362.34-45.516172.35325.72
282.212.23157.2246.9315.66-26.816151.76295.17
Solid lines: THDDash lines: Isothermal
CXX
THD
CYY
CXY
CYX
Isothermal
Static load [N]
Damping coefficient [KN-s/m]
Load (15)
26.25965.35316224410.0209260.016951
18.87729.59449215420.0203940.017041
14.82118.08433215740.0201110.01746
12.30114.83343536530.0201620.017994
9.522712.18104744070.0204370.018771
8.392210.37674908260.0208540.019711
THD
Isothermal
THD
Isothermal
Static load [N]
Journal attitude angle [deg]
Drag torque [N-m]
Load (14)
0.840951.83145365716.57815.572
4.22465.434352546513.99812.655
8.424910.278448659711.4459.3519
12.27414.61505917069.72967.1382
16.01318.78185959918.54525.5448
19.65122.65045624357.70944.4498
THD
Isothermal
THD
Isothermal
c' = 17 m
Static load [N]
Journal eccentricity [m]
Minimum film thickness [m]
Load (10)
102137168831251907455
106136168881281867760
112141181981361928270
1191491931101482029080
1261602051241622149692
134176217138177228101104
30,000 rpm
40,000 rpm
50,000 rpm
20,000 rpm
Test data (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (13)
13712574551245311164
136128776012255110.566.5
14113682701236011571
14914890801306912277
160162969214181130.582
1761771011041559514586
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
AxialT133 (3)
93.974129.95410212669.37777
102.168139.62111914975.13990
105.271143.0949811877.11477
106.958144.86278.185
108.082145.99478.92
108.893146.7979.464
109.477147.34779.862
109.878147.71180.141
110.125147.92180.319
110.24147.99980.409
110.116147.88780.314
109.857147.64580.131
109.445147.24779.847
108.848146.65579.442
108.022145.81878.891
106.879144.63478.147
105.167142.79677.062
102.034139.23875.07
93.845129.57169.309
20,000 rpm
30,000 rpm
40,000 rpm
Side edge (rear)
Side edge (front)- Edges
Mid-plane
Test data
Predictions
Axial node number
Temperature [C]
Sheet2
50krpm222N30-50krpm89N30-50krpm133N40krpm1.932um
Side edgeMid-planeSide edgekrpmSide edgeMid-planeSide edgekrpmSide edgeMid-planeSide edgershaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
183217164180degTest data309611292309611292Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg41118401191411114011914111190.8307625.5816.32217.74816.5772.10E-028.88E+06-4.67E+059.55E+059.86E+06755.5-197.1240.6541.6
207215207311195015417113650154171136444.101417.58313.46716.69314.1562.06E-029.15E+06-2.02E+057.61E+051.02E+07674.9-139.3230.9491.9
21120898.19214.1510.41215.63311.6652.04E-029.62E+061.28E+054.78E+051.06E+07556.4-75.83215.8425.3
13311.92312.3628.22614.8339.97122.04E-021.01E+073.80E+052.36E+051.10E+07456.3-31.56195.4368.8
20.52.0530-50krpm30-50krpm17815.55110.5646.611114.1518.7622.07E-021.06E+075.69E+052.95E+041.13E+07375.4-2.171169.2319.9
34.54.116.4NSide edgeMid-planeSide edgeEdge-avg30umN30405020umN30405022218.9739.20525.456813.5717.91442.12E-021.10E+077.17E+05-1.29E+051.15E+07312.219.1139.7277.8
6.5209647464643097409176145
4467776666.50.844870.74417615540krpm1.932um20krpm0.5um
50krpm89N89718271718911089167155rshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyyrshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
ReaCenterFront13377907777133132133165163Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/mLoad (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
1788296828217817890.8409526.25916.31117.7816.5782.09E-028.79E+06-4.46E+059.34E+059.75E+06742.3-193.1235.1529.891.430841.57617.11217.74617.2198.82E-038.22E+065.55E+06-2.81E+055.26E+057.17E+061922.1-720.931053.31829.7
190deg41118222861018686222222444.224618.87713.26316.70613.9982.04E-029.04E+06-1.76E+057.27E+051.01E+07659.9-136.5227.4478.7446.751830.17512.08315.06512.6998.93E-031.31E+076.67E+063244.31.19E+057.80E+061510.7-497.57773.111685.2
1001091003111930um898.424914.82110.06715.67711.4452.01E-029.47E+061.61E+054.25E+051.05E+07538.7-74.91215.9409.48912.23721.17.775613.0069.10269.44E-031.31E+078.23E+063.91E+05-597518.53E+061202.8-281.5462.951494.9
21120309861028384.52095420umN30405013312.27412.3017.788414.8939.72962.02E-029.89E+064.21E+051.63E+051.08E+07435.5-32.93200.1349.313316.75515.5475.270511.6237.14471.00E-021.47E+079.47E+066.46E+05-1.28E+059.10E+061085.1-137.47278.271357.8
44901068788.50.7446820915714517816.0139.52276.101514.2258.54522.04E-021.03E+076.24E+05-6.55E+041.11E+07349.9-5.784179.6295.117820.92612.1393.678510.5475.92781.07E-021.47E+071.05E+078.24E+05-1.79E+059.58E+061053.3-38.164156.41249.8
8996112929489880.74414122219.6518.39224.840913.6477.70942.09E-021.07E+077.85E+05-2.50E+051.13E+07282.212.23157.2246.9
30krpm89N1331021199810013310789
ReaCenterFront178108126103105.5178133ex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyyex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyy
222113134109111222178mmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/mmmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg4111830um2229.00.0400008.22E+068.75E+06-3.62E+054.83E+051.00E+07622.9-174.0244.7546.09.00.0200008.22E+065.91E+06-4.71E+057.63E+057.24E+062018.9-812.1938.51969.9
74787431119409114137108111096044.00.0400001.31E+079.28E+06-7.41E+044.29E+051.02E+07565.2-157.4218.7498.544.00.0200001.31E+076.96E+06-4.34E+043.60E+058.14E+061552.9-503.4825.01790.5
2112044114136107110.50.7447220umN30405089.00.0400001.47E+071.02E+073.01E+053.62E+051.06E+07509.0-124.5197.2428.089.00.0200001.31E+078.72E+064.62E+05-9.27E+038.88E+061245.3-269.7525.71606.7
89119141111115899220-209141122133.00.0400001.47E+071.08E+076.58E+051.79E+051.11E+07430.7-79.5188.3367.6133.00.0200001.47E+071.02E+077.75E+05-1.26E+059.44E+061159.4-135.6325.81470.9
70krpm89N1331261491181221330.744141121178.00.0400001.57E+071.14E+078.77E+051.33E+041.14E+07362.3-45.5172.4325.7178.00.0200001.47E+071.13E+079.47E+05-1.82E+059.89E+061178.0-56.5210.21378.7
ReaCenterFront178134160127130.517889222.00.0400001.57E+071.20E+071.01E+06-8.61E+041.17E+07315.7-26.8151.8295.2
222149176141145222133139136FOIL Bearing static load performance parameters
190deg4111825um178150150Load-Xe_structureexeyEccentricityeccentricityAngleMinimum filmFx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR
12914212931119509146168131138.50997222200.00.0400001.57E+071.17E+079.47E+05-4.50E+041.16E+07337.2-35.0162.3309.3[N]mmmmratiodeg[m]NNNbar[bar]N-m[kW]N/m-
21120441461681281370.744989.0020.101.231.331.810.1047.1816.72-9.0-0.29.00.041.098.14E-031.70E-026.85E+060.00
891541811361458911225umN30405044.0023.536.724.207.930.4332.0310.88-44.0-0.344.00.211.398.40E-031.76E-027.57E+060.00
133162193143152.513312920-209119110FOIL Bearing static load performance parameters89.0027.0112.945.0413.890.7521.266.03-89.2-0.489.20.431.749.11E-031.91E-028.70E+060.03
Themmal gradient (Deg C/mm)1781722051541631781460.844Load-Xe_structureexeyEccentricityeccentricityAngleMinimum filmMinimum filmMinimum filmFx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR133.0030.0118.005.1018.71.015.813.27-133.98-1.3134.00.652.079.94E-032.08E-029.74E+060.00
300000.24390243922218321716317322289133133[N]mmmmratiodeg[m][m][m]NNNbar[bar]N-m[kW]N/m-178.0033.1322.474.8022.971.2412.071.78-178.7-0.8178.70.872.391.09E-022.27E-021.06E+070.00
500000.54878048782.052.051339.0018.630.761.661.830.1165.3515.3316.71915.572-9.0-0.09.00.041.181.70E-027.10E-029.58E+060.00
700000.79268292684.116.44.116.417817117144.0021.974.732.685.430.3229.5912.0115.18412.655-43.6-0.743.60.211.401.70E-027.14E-029.87E+060.00
22289.0025.399.773.1910.280.6018.088.0813.3649.3519-89.0-0.389.00.431.711.75E-027.31E-021.04E+070.00
133.0028.3914.133.7414.60.914.835.3612.1057.1382-133.08-0.9133.10.652.031.80E-027.54E-021.08E+070.00
50krpm44N50krpm133N20umN304050178.0031.4518.363.9618.781.1012.183.4710.9775.5448-178.2-0.7178.20.862.351.88E-027.86E-021.12E+070.139N : 20 - 100 krpm
ReaCenterFrontReaCenterFront20-20910790222.0034.2522.284.0822.651.3310.382.2410.0264.4498-222.1-1.0222.11.082.651.97E-028.26E-021.16E+070.28ex_inputey_inputLoad-XLoad-YSpeedKstructureKxxKxyKyxKyyCxxCxyCyxCyy
0.644mmNNrpmN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
190deg41118190deg41118891071009.00.0200008.22E+065.91E+06-4.71E+057.63E+057.24E+062018.9-812.1938.51969.9
8390833111911912711831119133200.0032.8520.353.9820.731.2111.062.8010.4874.9532-200.1-0.3200.10.972.501.92E-028.05E-021.14E+070.229.00.0400008.22E+068.09E+06-5.19E+056.83E+058.73E+06879.9-263.9276.2742.7
21120211201781231209.00.0600008.22E+068.88E+06-4.42E+058.83E+059.32E+06572.2-143.3137.3428.6
2229.00.0800008.22E+069.37E+06-3.76E+058.79E+059.67E+06411.3-91.384.8289.0
9.00.01000008.22E+069.66E+06-3.33E+058.64E+059.90E+06315.8-64.659.7213.7
30krpm44N30krpm133N32umN304050
ReaCenterFrontReaCenterFront20-209117100FOIL Bearing static load performance parameters
0.644Speede_structureexeyEccentricityeccentricityAngleMinimum filmMinimum film (center)Minimum film (near edge)Fx ReactionFy ReactionForceSpecific loadMax pressureTorquePower LossKeqWFR
190deg41118190deg4111889128128[rpm]mmmmratiodeg[m][m][m]NNNbar[bar]N-m[kW]N/m-
596359311198891883111913320000.0020.101.231.331.810.1047.1816.7217.26116.81-9.0-0.29.00.041.098.14E-031.70E-026.85E+060.00
211202112017840000.0020.101.090.711.300.0733.0117.2317.85517.334-9.0-0.19.00.041.091.62E-026.80E-028.64E+060.15
22260000.0020.101.040.511.160.0626.0517.3918.02317.497-9.0-0.09.00.041.092.43E-021.53E-019.32E+060.19
70krpm44N70krpm133N80000.0020.101.000.411.10.122.2917.4718.117.583-8.99-0.29.00.041.093.24E-022.71E-019.71E+060.20
ReaCenterFrontReaCenterFront27umN304050180deg100000.0020.100.980.341.040.0619.0817.5218.14517.642-9.0-0.19.00.041.094.05E-024.24E-019.95E+060.20
20-209609921486175
190deg41118190deg411180.644999920krpm0.5um
11112111131119150164150311198980109214109182rshaftKstructureKxxKxyKyxKyyCxxCxyCyxCyy
2112021120133Load (N)eccenanglehminhminchminneartorN/m[N/m]N/mN/mN/m[N-s/m]N-s/mN-s/mN-s/m
17810814019820091.430841.57617.11217.74617.2198.82E-035.55E+06-2.81E+055.26E+057.17E+061922.1-720.931053.31829.7
222440.9669928.4117.61118.80817.8251.90E-027.61E+06-4.00E+058.27E+058.78E+06876.26-233.34313.41706.46
Themmal gradient (Deg C/mm)Themmal gradient (Deg C/mm)890.8242517.44217.84619.69218.2743.07E-028.65E+06-2.35E+055.34E+059.56E+06470.46-105.18142.74379.62
300000.243902439300000.182926829325umN3040501330.770156.163918.07820.33918.8984.38E-029.28E+06-300122.53E+051.01E+07289.36-54.98590.006232.87
500000.4268292683500000.548780487820-2091171780.8279-4.146717.55321.27319.7595.75E-029.69E+061.61E+05837191.04E+07206.68-32.47373.863153.01
700000.6097560976700000.85365853660.744
89137
themal gradient deg C/mmMid-planeTemperauture Deg CSide edgeTemperauture Deg C133
300005000070000300005000070000300005000070000178169
440.2439024390.42682926830.60975609764463901215983111222
890.2439024390.54878048780.7926829268897810914274100129
1330.18292682930.54878048780.85365853661339112716488119150Solid shaftRadial growthWall thickness: 10 mmRadial growthWall thickness: 2 mmRadial growth
2.00E+014.83E-074.83E-012.00E+011.05E-061.05E+002.00E+011.71E-061.71E+00
Solid journalMax1804.00E+011.93E-061.93E+004.00E+014.22E-064.22E+004.00E+016.85E-066.85E+00
20umN3040503040506.00E+014.35E-064.35E+006.00E+019.49E-069.49E+006.00E+011.54E-051.54E+01
20-2098.00E+017.73E-067.73E+008.00E+011.69E-051.69E+018.00E+012.74E-052.74E+01
0.6441.00E+021.21E-051.21E+011.00E+022.64E-052.64E+011.00E+024.28E-054.28E+01
898811715988117157
133
Axial temp. at 37 node number178114145183114145183
30K 89N22220 krpm
63.39783.177106.394019N44N89N133N178N222N
63.39783.177106.3940.0132Solid journalMax180XPTPTPTPTPTPT
70.93994.777121.4050.026320umN3040503040500146.452146.2148.161151.242155.308160.112
73.799.969128.7050.039420-2094.6151.01146.4521.00546.21.00648.1611.00851.2421.00955.3081.0160.112
75.243103.026133.1230.05250.65449.2311.00846.5741.00246.2581.00748.2731.01251.41.01555.491.01760.308
76.294105.108136.1440.065689961311879413117613.8461.00746.731.00146.3491.0148.4151.01851.5821.02255.6951.02560.522
77.058106.616138.32