ASME Turbo Expo 2009: Power for Land, Sea, and Air

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



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


44 N

133 N

222 N


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


44 N

89 N

133 N

178 N

222 N




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


44 N

89 N

133 N

178 N

222 N



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


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



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


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 - 30 krpm

Test data - 40 krpm

Test data - 50 krpm




Static load [N]


Load (13)

13712574551245311164

136128776012255110.566.5

14113682701236011571

14914890801306912277

160162969214181130.582

1761771011041559514586


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)


Test data - 40 krpm


Static load [N]


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









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






































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








































Test data - Mid-plane

222 N

THD solution

Adiabatic wall


Rotor speed [krpm]


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


Static load [N]


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



Static load [N]


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



Static load [N]


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




Static load [N]


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




Static load [N]


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




Static load [N]


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




Static load [N]


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




Static load [N]


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


Static load [N]


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





Static load [N]


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]


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]


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]


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]


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]


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


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)


Test data - 40 krpm


Static load [N]


Load (24)

741021371685583125190

771061361686088128186

821121411817098136192

9011914919380110148202

9612616020592124162214

101134176217104138177228

30,000 rpm

40,000 rpm

50,000 rpm

20,000 rpm



Test data - 30 krpm

Test data - 40 krpm

Test data - 50 krpm




Static load [N]


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


44 N

133 N

222 N



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


44 N

133 N

222 N


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


44 N

89 N

133 N

178 N

222 N




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


44 N

89 N

133 N

178 N

222 N



Temperature [ C]

Load (19)

0.4831

1.932

4.348

7.729

12.08

Solid shaft

tS = 10 mm

tS = 2 mm



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



Rotor speed [krpm]


Load (18)

8792000-44560093390097450008752100-36220048330010027000

9037000-176100726700100700009277100-7409342888010247000

9465000160800425200104800001017600030090036151010637000

9893000420900163000108100001079300065758017911011072000

10320000623700-6547011060000113980008773201332011416000

10710000784600-24970011260000119840001005200-8609611679000


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


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 - 30 krpm

Test data - 40 krpm

Test data - 50 krpm




Static load [N]


Load (13)

13712574551245311164

136128776012255110.566.5

14113682701236011571

14914890801306912277

160162969214181130.582

1761771011041559514586


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)


Test data - 40 krpm


Static load [N]


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

ASME Turbo Expo 2009: Power for Land, Sea, and Air

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Transcript of ASME Turbo Expo 2009: Power for Land, Sea, and Air