Luis San Andrés Mast-Childs Professor Fellow ASME Texas A&M University

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 ConsortiumLuis San AndrsMast-Childs ProfessorFellow ASMETexas A&M UniversityKeun RyuResearch AssistantTexas A&M University Tae Ho KimSenior Research ScientistKorea Institute of Science and TechnologyASME TURBO EXPO 2010, Glasgow, Scotland, UKASME paper GT2010-22983Thermal Management and Rotordynamic Performance of a Hot Rotor-Gas Foil Bearings System Part 2: Predictions vs. Test DataJ. Eng. Gas Turbines Power (In-Press)

Gas Foil Bearings IssuesEndurance: performance at start up & shut down (lift off speed)Little test data for rotordynamic force coefficients & operation with limit cycles (sub harmonic motions)Thermal management for high temperature applications (gas turbines, turbochargers)Predictive models lack validation for GFB operation at HIGH TEMPERATURE

To develop a detailed, physics-based computational model of gas-lubricated foil journal bearings including thermal effects to predict bearing performance.

The result of this work shall include a fully tested and experimentally verified design tool for predicting gas foil journal bearing torque, load, gas film thickness, pressure, flow field, temperature distribution, thermal deformation, foil deflections, stiffness, damping, and any other important parameters.Main ObjectiveAgreement NASA NNH06ZEA001N-SSRW2

*Benchmark TEHD computational model for prediction of GFB performance at high temperatures and quantify effectiveness of thermal management Perform physical analysis, derive equations, implement numerical solution, and construct GUI for User ready use Compare GFB predictions to published test data (TAMU mainly)

Objective & tasksASME GT2010-22981ASME GT2009-59919

Why thermal effects are important? isothermal flow models are adequate in most applications but those with hot rotors such as in turbochargers and gas turbines. Models couple the gas film pressure generation and thermal energy transport to the underspring (bumps) structure with thermal conduction and convection paths.

Gas bearings (when airborne) are nearly friction free, hence the show small (drag) power loss and temperature raise. With hot rotors the lubricant in the bearings must also cool components. But gases have small thermal capacity and conductivity, and hence, get hot! Rises in temperature change material properties (solids and gas), and most importantly, change bearing clearances!

Overview GFB TEHD modelsLe Lez et al. (2007): THD model predicts larger load capacity because of increase in gas viscosity but forgets thermo-mechanical deformations Peng and Khonsari (2006): Noted importance of side cooling flow with incorrect THD modelFeng and Kaneko (2008), San Andrs and Kim (2009), Kim (2010): TEHD models predict temperatures agreeing with test data (Radil and Zeszotek, 2006) for room temperature & without cooling flowFew models incorporate thermo-mechanical deformations needed to ensure proper thermal management od the foil bearingsBut little is known from test bearings and operating conditions!Many assumptions to match test data.Need independent data base

Our GFB TEHD modelASME GT2009-59919Excel GUI + executable licensed by TAMU

*Gas film pressure generationXYX=RSide view of GFB with hollow shaft

*THD modelGFB with cooling flows (inner and/or outer)Outer flow streamBearing housing zxRSoz=0z=LTConvection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energy

*Heat flow paths in rotor - GFB system Heat flows & thermal resistances in a GFB & hollow shaft

Heat conducted into bearing

Cooling gas streamscarry away heat

Top foil thickness, Bump foil thickness, Bump height, Gas Constant, Viscosity, 1.73Conductivity, Density, Test Foil BearingsElastic Modulus 214 GPa,Poisson ratio=0.29

(Gen II) Uncoated top foilRead ASME GT2010-22981For test procedure and measurements. Complete bearing geometry and operating conditions DISCLOSED

*Typical predictions: P & T fieldsNo cooling: Shaft temp. rise=79 C Reduction of ~ 50 C!

*Top foilBump layerHollow shaftBearing housingExternal fluiddRSiRSoRFiRFoRBiRBoTCiTTBoTBiTFoTSoTSiTFiTfRadial directionTCoWith forced cooling, GFB will operate 50C cooler. Outer cooling stream is most effective in removing heatPredictions radial temperatureNatural convection on exposed surfaces of bearing OD and shaft IDMean temperature

DE FBRotor speed : 30 krpmw/o & w cooling flow

PeakTemp_full (4)

0000

7966.83932

7966.83932

59.401153265147.770884045725.060795793820.1772127113

58.587723972144.154489462120.838090603416.3136720453

58.57597750144.104100748520.778482312816.2603820013

0000

57.850684599141.761007202617.674918233513.526926851

57.731795897841.675188783317.63860617513.4991376406

0000

100C0L

87.8C100L

61.3C200L

55.3C300L

Radial location

Temperature rise [C]

PeakTemp_full (3)

0000

34.340.366.879

34.340.366.879

20.643925115725.238583676447.770884045759.4011532651

13.950779359818.635106744544.154489462158.5877239721

13.865134814718.549344457544.104100748558.575977501

0000

10.513214087515.050530112741.761007202657.8506845991

10.491607988515.019611224941.675188783357.7317958978

0000

55.3C300L

61.3C200L

87.8C100L

100C0L

Radial location


PeakTemp_full (2)

0000

10.85400744087.16641141148.30224368725.0369159586

11.04511494647.29259121578.44842008915.1255995825

11.56255971957.63420416948.847762415.3678806651

11.37691710567.51162352078.08871401694.9072403237

11.3746346137.51011497968.07949646374.9016528781

0000

11.23378403687.41711566167.65027572834.6412658768

11.21070771217.40188384757.63456194374.6317366181

0000

NoCool_Max

NoCool_Mean

100Cool_Max

100Cool_Mean

Radial location


Sheet4

Rotor speed = 20 krpmDispNoCool_MaxNoCool_Mean100Cool_Max100Cool_MeanNoCool_MaxNoCool_Mean100Cool_Max100Cool_Mean

Static load = 222 N1212121210000

Without coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/min2.631.854007440828.166411411429.302243687226.036915958610.85400744087.16641141148.30224368725.0369159586

Peak temp.Peak temp.Peak temp.4.432.045114946428.292591215729.448420089126.125599582511.04511494647.29259121578.44842008915.1255995825

2195.882820030999.56939980162157.222724865759.50518314512149.34711642655.77310996374.832.562559719528.634204169429.8477624126.367880665111.56255971957.63420416948.847762415.3678806651

100.112945484798.686366811198.651693400959.885709075742.624461636342.253374116956.855075882239.474140376139.10418496725.232.376917105628.511623520729.088714016925.907240323711.37691710567.51162352078.08871401694.9072403237

98.507208328797.39131015052121215.4532.37463461328.510114979629.079496463725.901652878111.3746346137.51011497968.07949646374.9016528781

Mean Temp. and thermal energyMean Temp. and thermal energyMean Temp. and thermal energy6212121210000

2168.70590465871.05452232822131.867161215732.55193024012128.318743402529.97780889836.432.233784036828.417115661628.650275728325.641265876811.23378403687.41711566167.65027572834.6412658768

71.40079985170.224121067670.19552203432.666094804331.970531051831.955571259330.257159794129.682503539929.6702959557.932.210707712128.401883847528.634561943725.631736618111.21070771217.40188384757.63456194374.6317366181

70.103985783469.397017506421212.655787689516.1807620811216.434615746613.23672927979212121210000

9.108600265530.95175393444.8990826943

MEEAN TEMPMEEAN TEMPMEEAN TEMPMEEAN TEMP

Peak tempMean tempDisp55.3C300L61.3C200L87.8C100L100C0L55.3C300L61.3C200L87.8C100L100C0L

Without coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWithout coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/min1212121210000

1Cooling flow2121212121212.655.361.387.810034.340.366.879

2.6Shaft (inner)95.882820030957.222724865749.34711642668.70590465831.867161215728.3187434025Without coolingShaft growth1.30E-058.2607560803um4.455.361.387.810034.340.366.879

4.4Shaft (outer)99.569399801659.505183145155.773109963771.054522328232.551930240129.9778088983Bearing growth1.30E-058.238834778um4.841.643925115746.238583676468.770884045780.401153265120.643925115725.238583676447.770884045759.4011532651

4.8Film flow100.112945484759.885709075756.855075882271.40079985132.666094804330.2571597941With outer cooling = 170 lit/minShaft growth1.30E-051.894413228um5.234.950779359839.635106744565.154489462179.587723972113.950779359818.635106744544.154489462158.5877239721

5.2Top foil (inner)98.686366811142.624461636339.474140376170.224121067631.970531051829.6825035399Bearing growth0.00E+000um5.4534.865134814739.549344457565.104100748579.57597750113.865134814718.549344457544.104100748558.575977501

5.45Top foil (outer)98.651693400942.253374116939.104184967270.19552203431.955571259329.670295955With inner and outer cooling = 170 lit/minShaft growth1.30E-051.3770586694um6212121210000

6Cooling flow212121212121Bearing growth0.00E+000um6.431.513214087536.050530112762.761007202678.850684599110.513214087515.050530112741.761007202657.8506845991

6.4Bearing (inner)98.507208328770.10398578347.931.491607988536.019611224962.675188783378.731795897810.491607988515.019611224941.675188783357.7317958978

7.9Bearing (outer)97.391310150569.39701750649212121210000

9cooling flow2121

MEEAN TEMPMEEAN TEMPMEEAN TEMPMEEAN TEMP

Rotor speed = 20 krpmDisp55.3C150L61.3C125L87.8C50L100C0L55.3C150L61.3C125L87.8C50L100C0L

Static load =89 N1323221210000

Without coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/min2.6647187.8100323966.879

Peak temp.Peak temp.Peak temp.4.4647187.8100323966.879

2169.173692269371.69127024852145.857123629947.35464875452139.51028107443.59192655324.852.177212711357.060795793868.770884045780.401153265120.177212711325.060795793847.770884045759.4011532651

72.073839395370.856313448270.827607447847.598859332631.605862199431.254364166944.263812966428.19409822527.84420548685.248.313672045352.838090603465.154489462179.587723972116.313672045320.838090603444.154489462158.5877239721

70.734891777370.01886501142121215.4548.260382001352.778482312865.104100748579.57597750116.260382001320.778482312844.104100748558.575977501

Mean Temp. and thermal energyMean Temp. and thermal energyMean Temp. and thermal energy6323221210000

2153.153514584954.83386830052133.200498830733.93552257172129.185847070130.99089903886.445.52692685149.674918233562.761007202678.850684599113.52692685117.674918233541.761007202657.8506845991

55.089216629754.023961188453.998846149734.055388525133.312461599933.296129876931.288022772730.67964944230.66638408177.945.499137640649.63860617562.675188783378.731795897813.499137640617.63860617541.675188783357.7317958978

53.93744417253.463254198721212.850693438217.6685443264217.000134032814.33306858979323221210000

6.517171796827.18816582963.2861563592

Updated model_112808Full heat path model

Peak tempMean tempPeak tempMean tempPeak tempMean temp

Without coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/minWithout coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/minWithout coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/minWithout coolingWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/minWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/minWith outer cooling = 170 lit/minWith inner and outer cooling = 170 lit/minWith outer cooling = 350 lit/minWith inner and outer cooling = 350 lit/min

1Cooling flow21212121212121212121212121212121212121212121212121212121

2.6Shaft (inner)66.12450958262.637098927148.992540018143.317747128235.206517793153.0635412847.323955215736.976709433630.844860703726.491779558366.297506910443.317747128235.206517793150.517490748430.844860703726.491779558338.287021651632.573142327.008177250424.6301340997

4.4Shaft (outer)69.166893359665.444375621855.554846206844.822449336340.803317967155.225328362949.09878805840.722141124331.508616120128.655324368269.351567279644.822449336340.803317967152.507630235131.508616120128.655324368239.45256669637.132512314327.4132792626.0602787555

4.8Film flow69.634577970565.880765765256.603358225145.070921843141.735253539955.55764644349.374689526341.320576744731.618235664829.015596944969.820812403445.070921843141.735253539952.813409118331.618235664829.015596944939.647521276237.897900123227.48101776426.3003649596

5.2Top foil (inner)69.195793038165.205510109356.049026134342.739153573939.696000473355.245678193848.941036207240.996087082530.529174706128.160334875569.383670726842.847623405639.80514304152.528604219130.637624926428.269464463636.687815165535.208841061226.452232681125.4572294577

5.45Top foil (outer)69.185574734165.189943517656.036617188542.688537375939.652107835155.238416161148.931040071840.988832643830.505533472528.141927511369.373412277742.799172322939.763431967352.521914533330.616256094228.253340336836.624157119235.151205701126.430107528125.4391624082

6Cooling flow21212121212121212121212121212121212121212121212121212121

6.4Bearing (inner)68.678109166554.877838374568.530169587251.972437322233.282514069232.124569726325.268739545324.4897120942

7.9Bearing (outer)67.991654504854.390071070667.845840647651.526496123433.105652742731.96439162725.207255718824.4394556421

9cooling flow212121212121212121212121

8.18135369547.319341362115.44741091462.73772811438.92731683578.20709103622.73772811438.92731683571.67079399795.9016369357

7.685999273210.97221398837.855285096924.43146211418.43293480027.65740667124.43146211418.432934800225.455832213320.8118689842

Diff film temp.Same film temp-8.0337941917-8.1674988487-8.0067581844-7.776366049-7.6994658017-8.2338598902-7.776366049-7.6994658017-7.6464005287-7.5981336864

33.7143.25170538542.315800977439.967732489637.319577768736.668512333943.351410110437.319577768736.668512333936.310633852736.0571413606

20.5249.629.088.3841911586.883645464214.5257700812.57481128498.39148354187.71844752582.57481128498.39148354181.57035007045.5467202258

21.3365.6144.287.876391655310.31873297297.386774335422.955985609517.315786767.20132597222.955985609517.3157867623.888632951919.5261365832

3.39788308753.09010423744.26E-013.48E-01

updated4.47850856784.111221734623.462745268219.177970963

Without coolingShaft growth1.30E-055.6014094848um5.6014094848um35.117550220229.543211719728.969046532228.66423332428.4590076742

Bearing growth1.30E-055.6841383481um5.6841383481um18.957328384.01241482523.26177623042.02E+014.01E+003.26E+001.54E+003.21E+003.39E+001.75E+00

With outer cooling = 170 lit/minShaft growth1.30E-051.7198687916um1.0496130751um34.225328362910.50861612017.65532436825.75E+011.36E+011.13E+011.12E+011.19E+01

Bearing growth1.30E-050.7437685844um0.762583728um8.80E+000.00E+000.00E+001.49E+001.22E+00

With inner and outer cooling = 170 lit/minShaft growth1.30E-051.1109302818um0.7162215998um11.707028846877.703080583759.773409320781.853733895467.3880522561

Bearing growth1.30E-050.6080344689um0.5855146737um21.97888940838.715407482928.9670684625.478430393219.4902095299

315.3

25.268739545324.4897120942

25.207255718824.4394556421

Load (22)

45.21327.69663.966

45.21327.69663.966

45.34327.83564.093

45.47928.00264.201

45.63128.19764.313

45.80928.42164.448

46.01728.67264.613

46.25328.95164.809

46.51829.25665.035

46.80929.58765.288

47.12829.94465.568

47.47330.32765.875

47.84530.73866.211

48.24731.17866.575

48.67831.64866.969

49.14132.1567.394

49.63832.68767.851

50.16933.25968.343

50.73733.86968.869

51.34334.51969.433

51.98935.21170.034

52.67535.94570.674

53.40336.72371.353

54.17137.54472.071

54.98138.40972.826

55.82939.31573.619

56.71340.2674.444

57.6341.2475.3

58.57442.24976.181

59.53843.28177.08

60.51744.32877.992

61.49945.38178.907

62.47746.4379.817

63.43947.46280.711

64.37448.46681.58

65.27149.4382.411

66.11750.34183.195

66.951.18683.92

67.61151.95484.576

68.23852.63485.152

68.77253.21585.641

69.20353.68786.033

69.52654.04586.323

69.73354.2886.504

69.82154.38986.572

69.78654.36986.525

69.62954.21886.361

69.34953.93886.082

68.94953.53285.69

68.43353.00385.188

67.80752.35984.582

67.0851.60783.88

66.2650.75983.09

65.3649.82682.223

64.39248.82481.292

63.37347.76880.309

62.31646.67579.29

61.23845.56278.249

60.15844.45477.202

59.1143.39476.173

58.15242.45775.207

57.38441.75674.382

56.97141.4973.818

56.94941.59673.664

57.08941.76173.78

57.21141.90673.879

57.31742.03573.963

57.4142.1574.034

57.49242.25474.095

57.56542.34874.147

57.6342.43374.192

57.68842.51274.231

57.74142.58474.264

57.78942.65274.293

57.83342.71474.319

57.87442.77474.341

57.91242.8374.361

57.94542.88274.375

57.94542.88274.375

= 0.30

Rotor speed: 20 krpmStatic load: 89 N

= 0.65

= 0.80

Mixing parameter () increases

T= 21 C

Predictions - 40 krpm-20um_0.6_20

Circumferential angle [deg]

Temperature [ C]

Chart1 (4)

5.6014094848

5.6841383481

1.0496130751

0.762583728

0.7162215998

0.5855146737

Thermal expansion [m]

PeakTemp_full

212121

66.297506910438.287021651632.5731423

69.351567279639.45256669637.1325123143

69.820812403439.647521276237.8979001232

69.383670726836.687815165535.2088410612

69.373412277736.624157119235.1512057011

212121

68.530169587233.282514069232.1245697263

67.845840647633.105652742731.964391627

212121

Radial location

Temperature [C]

PeakTemp1

212121

66.12450958243.317747128235.2065177931

69.166893359644.822449336340.8033179671

69.634577970545.070921843141.7352535399

69.195793038142.739153573939.6960004733

69.185574734142.688537375939.6521078351

212121

68.67810916656.46.4

67.99165450487.97.9

2199

Radial location

Temperature [C]

Load (38)

65.88164.0287169168123.31121.0674132517

65.88161.326123.31117.7

65.88158.84123.31114.07

65.88156.603123.31110.53

48.64344.97191.30284.206

46.61343.13286.60579.606

45.07141.73582.85476.029

Test data (Mid-plane)

40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)

Predictions(Mid-plane)

40,000 rpm

20,000 rpm

Outer cooling flow

Inner and outer cooling flows

Cooling flow rate increases

Laminar flow

Turbulent flow

ReD = 2300

No cooling flow

Withoutercooling

Withinneroutercooling

Cooling flow rate [lit/min]

Peak temperature [ C]

Load (37)

7455.18251.75943.67233.80831.243

7759.05755.82448.16638.60735.872

8269.63565.88156.60345.07141.735

9080.43775.77764.6650.90346.968

9691.79786.18172.81256.4452.31

101103.7496.71680.85561.75557.608

Inner (170 lit/min) and outer (170 lit/min) cooling flows

Outer cooling flow (170 lit/min)

Without cooling flow

Test data(Without cooling flow)

Inner (350 lit/min) and outer (350 lit/min) cooling flows

Outer cooling flow (350 lit/min)

Test data

WithoutCooling

Withoutercooling


Static load [N]


Load (36)

0.00872950.00847430.008442358.88456.12855.507

0.00900470.00873050.008696232.09432.71232.911

0.00958150.0093210.009295321.98122.2322.317

0.010230.009990.009970516.02716.76916.895

0.0109260.0106690.01067312.44313.17613.331

0.0116380.0114370.01147410.12910.70310.808

(b) Outer cooling flow (350 lit/min)

(a) Without cooling flow

(c) Inner (350 lit/min) and outer (350 lit/min) cooling flows

WithoutCooling

Withoutercooling


Static load [N]

Drag torque [N-m]

Journal attitude angle [deg]

Load (35)

17.32917.30217.3041.96391.96821.9616

12.88512.53312.4717.27.53597.5982

9.19668.66848.598112.81413.37713.457

7.20656.66046.577917.42318.07218.173

5.9655.42885.347421.6522.35322.469

5.19614.62524.528425.52726.26326.402

c= 20 m




WithoutCooling

Withoutercooling


Static load [N]

Minimum film thickness [m]

Journal eccentricity [m]

Load (32)

69.63569.635128.41128.41

65.88164.0287169168123.31121.0674132517

65.88161.326123.31117.7

65.88158.84123.31114.07

65.88156.603123.31110.53

48.64344.97191.30284.206

46.61343.13286.60579.606

45.07141.73582.85476.029


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)


40,000 rpm

20,000 rpm

Outer cooling flow

Inner and outer cooling flows

Cooling flow rate increases

Laminar flow

Turbulent flow

ReD = 2300

No cooling flow

Withoutercooling


Cooling flow rate [lit/min]


PeakTemp (4)

212121

53.0635412830.844860703726.4917795583

55.225328362931.508616120128.6553243682

55.55764644331.618235664829.0155969449

55.245678193830.529174706128.1603348755

55.238416161130.505533472528.1419275113

212121

54.87783837456.46.4

54.39007107067.97.9

2199

Radial location

Temperature [C]

PeakTemp (3)

2111

53.063541282.62.6

55.22532836294.44.4

55.5576464434.84.8

55.24567819385.25.2

55.23841616115.455.45

2166

54.87783837456.46.4

54.39007107067.97.9

2199

Radial location

Temperature [C]

Chart1

5.6014094848

5.6841383481

1.7198687916

0.7437685844

1.1109302818

0.6080344689


PeakTemp (2)

212121

66.12450958262.637098927148.9925400181

69.166893359665.444375621855.5548462068

69.634577970565.880765765256.6033582251

69.195793038165.205510109356.0490261343

69.185574734165.189943517656.0366171885

212121

68.67810916656.46.4

67.99165450487.97.9

2199

Radial location

Temperature [C]

Sheet1

20krpm170LTM170LTM350LTM350LTM170LTM170LTM350LTM350LTM

Peak temp [degC]Minfilm [um]Test dataTest data

W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/innerNSide edgeMid-planeSide edgeEdge-avgNSide edgeMid-planeSide edgeEdge-avg

955.18251.75943.67233.80831.243917.18917.18417.17717.18217.18920964746464409114137108111

4459.05755.82448.16638.60735.8724412.27612.24612.1311.94111.8814467776666.544114136107110.5

8969.63565.88156.60345.07141.735897.89457.72127.57597.37897.3151897182717189119141111115

13380.43775.77764.6650.90346.9681335.37245.28535.11584.89134.821913377907777133126149118122

17891.79786.18172.81256.4452.311783.82213.75933.60993.38563.361117882968282178134160127130.5

222103.7496.71680.85561.75557.6082222.84122.78522.65422.512.4566222861018686222149176141145

Peak press [P/Pa]Minfilm-mid [um]

W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/inner

91.10651.10471.10041.09431.0923918.00917.98417.92617.86417.849

441.36561.3641.36321.3641.36424415.24615.19515.05214.83414.76620krpm

891.70691.71091.71111.71151.71168913.07812.96612.75512.46612.372Static load 89 N

1332.02262.02332.02572.02842.02913311.65411.54811.28810.93210.817Peak temp [degC]

1782.33212.33352.33662.33522.340517810.56310.44410.1559.78739.6493outercoolingInnerOutercooling

2222.62712.62912.63322.63522.63652229.6979.56049.22748.78888.6312069.63569.635

2065.88164.0287169168

Eccen [um]350 lpmMinfilm-edge [um]350 lpm6065.88161.326

W/OcoolingW/outerW/outer/innerW/outerW/OcoolingW/outerW/outer/innerW/outer11065.88158.84

91.96391.96791.97431.96821.9616917.32917.32217.30717.30217.30417065.88156.603

447.27.22717.34027.53597.59824412.88512.8512.72812.53312.47123048.64344.971

8912.81412.95213.13113.37713.457899.19669.0488.88668.66848.598129046.61343.132

13317.42317.51717.75218.07218.1731337.20657.12026.92376.66046.577935045.07141.735

17821.6521.75622.01422.35322.4691785.9655.88315.68525.42885.347440krpm

22225.52725.64325.92326.26326.4022225.19615.10824.89614.62524.5284Static load 89 N

Peak temp [degC]

Attitude [deg]Torq [N-m]outercoolingInnerOutercooling

W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/inner0128.41128.41

958.88458.63257.78156.12855.50798.73E-038.69E-038.59E-038.47E-038.44E-0320123.31121.0674132517

4432.09432.16932.01532.71232.911449.00E-038.96E-038.86E-038.73E-038.70E-0360123.31117.7

8921.98121.80921.98222.2322.317899.58E-039.52E-039.43E-039.32E-039.30E-03110123.31114.07

13316.02716.1516.416.76916.8951331.02E-021.02E-021.01E-029.99E-039.97E-03170123.31110.53

17812.44312.56112.8413.17613.3311781.09E-021.09E-021.08E-021.07E-021.07E-0223091.30284.206

22210.12910.22410.45610.70310.8082221.16E-021.16E-021.15E-021.14E-021.15E-0229086.60579.606

35082.85476.029

40krpm170LTM170LTM350LTM350LTM170LTM170LTM350LTM350LTM

Peak temp [degC]Minfilm [um]


99

4444

8989

133133

178155.45103.0195.0121786.41935.69545.6218

222169.81112.65103.912225.26724.69014.5959

Peak press [P/Pa]Minfilm-mid [um]


99

4444

8989

133133

1782.31032.29822.29617814.22713.24713.067

2222.59072.5882.587922213.62312.53512.341

Eccen [um]350 lpmMinfilm-edge [um]350 lpm

W/OcoolingW/outerW/outer/innerW/outerW/OcoolingW/outerW/outer/innerW/outer

99

4444

8989

133133

17815.43116.01216.1161788.63087.84857.7403

22218.9619.6619.7922227.78747.01296.8827

Attitude [deg]Torq [N-m]


99

4444

8989

133133

17811.52213.24513.4471782.13E-022.01E-021.99E-02

2229.779411.32511.7062222.17E-022.06E-022.04E-02

Load1-test

26.25965.35316224410.0209260.01695111.522113.24513.4470.0212810.0200540.019904

18.87729.59449215420.0203940.0170419.779411.32511.7060.0217320.0205710.020414

14.82118.08433215740.0201110.01746

12.30114.83343536530.0201620.017994

9.522712.18104744070.0204370.018771

8.392210.37674908260.0208540.019711

THD

Isothermal

THD

Isothermal

LPM

350LPM

700LPM

0LPM

350LPM

700LPM

Static load [N]


Drag torque [N-m]

Load-test

1.8314536570.8409515.57216.57815.43116.01216.1168.63087.84857.7403

5.43435254654.224612.65513.99818.9619.6619.7927.78747.01296.8827

10.27844865978.42499.351911.445

14.615059170612.2747.13829.7296

18.781859599116.0135.54488.5452

22.650456243519.6514.44987.7094

THD

Isothermal

THD

Isothermal

c= 20 m

0LPM

350LPM

700LPM

0LPM

350LPM

700LPM

Static load [N]



Load (34)

0.00872950.00868840.008591458.88458.63257.781

0.00900470.00896060.008857732.09432.16932.015

0.00958150.00952430.009428921.98121.80921.982

0.010230.0101840.01008816.02716.1516.4

0.0109260.0108840.01078812.44312.56112.84

0.0116380.0115970.01150710.12910.22410.456




WithoutCooling

Withoutercooling


Static load [N]

Drag torque [N-m]


Load (33)

17.32917.32217.3071.96391.96791.9743

12.88512.8512.7287.27.22717.3402

9.19669.0488.886612.81412.95213.131

7.20657.12026.923717.42317.51717.752

5.9655.88315.685221.6521.75622.014

5.19615.10824.896125.52725.64325.923

c= 20 m




WithoutCooling

Withoutercooling


Static load [N]



Load (31)

7455.18251.75943.672111

7759.05755.82448.166

8269.63565.88156.603

9080.43775.77764.66

9691.79786.18172.812

101103.7496.71680.855


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)





Test data

Test data

WithoutCooling

Withoutercooling


Static load [N]


Load (30)

745521

776024

827027

908030

969232.5

101104222


40,000 rpm

Test data (Edge)

20,000 rpm

Predictions(Edge)



Static load [N]


Load (29)

0.11950.20990.3706

0.47790.83961.482

1.0751.8893.336

1.9123.3585.93

2.9875.2479.265

4.3027.55613.34

5.85510.2818.16

7.64713.4323.72

9.6781730.02

11.9520.9937.06

Solid shaft

tS = 13 mm

tS = 5 mm

Shaft wall thickness decreases


Rotor speed [krpm]

Centrifugal growth [m]

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

700000.6097560976700000.85365853660.744speedsolidts=13ts=5

891371.00E+041.00E+011.20E-071.20E-012.10E-072.10E-013.71E-073.71E-01

themal gradient deg C/mmMid-planeTemperauture Deg CSide edgeTemperauture Deg C1332.00E+042.00E+014.78E-074.78E-018.40E-078.40E-011.48E-061.48E+00Solid shaftRadial growthWall thickness: 10 mmRadial growthWall thickness: 2 mmRadial growth

3000050000700003000050000700003000050000700001781693.00E+043.00E+011.08E-061.08E+001.89E-061.89E+003.34E-063.34E+002.00E+014.83E-074.83E-012.00E+011.05E-061.05E+002.00E+011.71E-061.71E+00

440.2439024390.42682926830.609756097644639012159831112224.00E+044.00E+011.91E-061.91E+003.36E-063.36E+005.93E-065.93E+004.00E+011.93E-061.93E+004.00E+014.22E-064.22E+004.00E+016.85E-066.85E+00



7.00E+047.00E+015.86E-065.86E+001.03E-051.03E+011.82E-051.82E+011.00E+021.21E-051.21E+011.00E+022.64E-052.64E+011.00E+024.28E-054.28E+01

Solid journalMax1808.00E+048.00E+017.65E-067.65E+001.34E-051.34E+012.37E-052.37E+01

20umN3040503040509.00E+049.00E+019.68E-069.68E+001.70E-051.70E+013.00E-053.00E+01

20-2091.00E+051.00E+021.20E-051.20E+012.10E-052.10E+013.71E-053.71E+01

0.644

898811715988117157

133

Axial temp. at 37 node number178114145183114145183

30K 89N22220 krpm

63.39783.177106.3940189N9N44N89N133N178N222N

63.39783.177106.3940.0132Solid journalMax180XT (=0.65)T (=0.3)T (=0.8)XPTPTPTPTPTPT

70.93994.777121.4050.026320umN304050304050045.21327.69663.9660146.452146.2148.161151.242155.308160.112

73.799.969128.7050.039420-2094.61545.21327.69663.9664.6151.01146.4521.00546.21.00648.1611.00851.2421.00955.3081.0160.112

75.243103.026133.1230.05250.65449.23145.34327.83564.0939.2311.00846.5741.00246.2581.00748.2731.01251.41.01555.491.01760.308

76.294105.108136.1440.065689961311879413117613.84645.47928.00264.20113.8461.00746.731.00146.3491.0148.4151.01851.5821.02255.6951.02560.522

77.058106.616138.3260.078713318.46245.63128.19764.31318.4621.00846.8831.00146.4641.01448.581.02451.7851.0355.9181.03460.755

77.616107.714139.9120.091817812315920612115920223.07745.80928.42164.44823.0771.00647.0231.00346.61.01948.771.03152.011.03956.1621.04361.008

78.012108.489141.030.104922227.69246.01728.67264.61327.6921.00647.171.00546.761.02548.9861.0452.261.04856.4311.05361.285

78.273108.998141.7590.1171032.30846.25328.95164.80932.3081.00547.331.00846.9451.03249.2281.04952.5371.05956.7261.06561.588

78.426109.29142.170.13111Solid journalMax18036.92346.51829.25665.03536.9231.00647.4991.01247.1521.0449.4941.05952.8391.07157.0491.07761.921

78.275109.008141.7840.1441220umN30405030405041.53846.80929.58765.28841.5381.00647.6771.01747.381.04949.7851.07153.1681.08457.4011.09162.287

78.012108.5141.0590.1571320-20946.15447.12829.94465.56846.1541.00747.8611.02347.6271.0650.11.08353.5261.09857.7871.10762.689

77.616107.724139.9420.17140.74450.76947.47330.32765.87550.7691.00848.0511.0347.8941.07150.4391.09753.9141.11358.2081.12463.132

77.056106.624138.3550.183158915114755.38547.84530.73866.21155.3851.0148.2481.03848.1791.08350.8041.11254.3341.1358.671.14263.622

76.289105.116136.1720.196161336048.24731.17866.575601.01148.4511.04648.4811.09651.1941.12854.7891.14959.1761.16364.165

75.237103.032133.1520.2091717817924217623764.61548.67831.64866.96964.6151.01348.6591.05548.81.1151.6121.14655.2831.1759.7311.18664.768

73.69299.974128.7360.22218170 lit85 lit22269.23149.14132.1567.39469.2311.01548.8731.06449.1361.12552.0571.16555.8191.19360.3421.21265.439

70.93194.785121.4440.23519max73.84649.63832.68767.85173.8461.01849.0931.07449.4881.14152.5331.18656.3991.21861.0141.24166.185

63.3983.185106.4410.24820Load2020Solid journalMax18078.46250.16933.25968.34378.4621.0249.3161.08549.8561.15853.0391.20957.0281.24661.7521.27367.017

63.3983.185106.4410.2612120-209212119umN203040502030405020-edge40-edge83.07750.73733.86968.86983.0771.02349.5451.09650.241.17653.5781.23357.7081.27662.5641.30967.943

0.6544242520-209609614823055831251905312487.69251.34334.51969.43387.6921.02649.7771.10750.6381.19654.151.2658.4441.3163.4551.34968.973

8927290.6544619514823060881281865512292.30851.98935.21170.03492.3081.02950.0131.1251.0511.21754.7571.28959.2371.34764.4311.39370.117

1333032897111314221770981361926012396.92352.67535.94570.67496.9231.03250.2511.13251.4791.23955.3981.3260.0921.38765.4971.44271.381

17832.535.4133821131512108011014820269130101.53853.40336.72371.353101.5381.03550.4931.14551.921.26256.0751.35461.0081.43166.6561.49672.774

222178941261652209212416221481141106.15454.17137.54472.071106.1541.03850.7361.15952.3741.28756.7881.38961.9871.47867.9111.55574.299

22210714018023310413817722895155110.76954.98138.40972.826110.7691.04250.9811.17252.8391.31357.5341.42763.0281.52969.2611.61975.957

115.38555.82939.31573.619115.3851.04551.2271.18653.3161.33958.3131.46764.1281.58370.7031.68877.742

12056.71340.2674.4441201.04851.4741.20153.8011.36759.1211.50965.2831.64172.231.76279.646

124.61557.6341.2475.3124.6151.05151.7211.21554.2951.39659.9561.55366.4871.70173.8321.83981.653

222 NTHDAdiabatic129.23158.57442.24976.181129.2311.05451.9681.22954.7931.42560.8131.59867.7321.76375.4951.91983.743

20107128133.84659.53843.28177.08133.8461.05752.2141.24455.2961.45461.6871.64369.0061.82677.2022.00185.891

30140157138.46260.51744.32877.992138.4621.0652.4581.25855.7991.48362.571.68970.2991.8978.9342.08388.067

40180197143.07761.49945.38178.907143.0771.06352.7011.27156.3011.51263.4561.73471.5951.95380.6682.16490.24

50233256147.69262.47746.4379.817147.6921.06652.9411.28556.7981.54164.3371.77972.882.01482.382.24292.377

152.30863.43947.46280.711152.3081.06853.1781.29757.2871.56865.2031.82174.1372.07384.0462.31794.447

156.92364.37448.46681.58156.9231.07153.4121.3157.7641.59466.0461.86275.3512.12885.6432.38696.418

161.53865.27149.4382.411161.5381.07353.6411.32158.2271.61866.8561.89876.5052.17887.1462.44898.262

20krpm30krpm40krpm50krpm166.15466.11750.34183.195166.1541.07453.8671.33158.6721.6467.6221.93177.5832.22288.5352.50299.952

89133891338913389133170.76966.951.18683.92170.7691.07654.0871.3459.0941.65968.3371.9678.5692.25989.792.547101.464

160.30869.37785.65193.974123.254129.954183.102187.618175.38567.61151.95484.576175.3851.07754.3031.34759.4911.67668.991.98379.452.28890.8922.582102.778

260.30869.37785.6519693.974102123.254119129.954126183.102154187.61816218068.23852.63485.1521801.07854.5121.35359.8591.68869.574280.2142.3191.8252.607103.875

364.20475.13990.94102.168129.362139.621189.318197.386184.61568.77253.21585.641184.6151.07954.7161.35860.1941.69770.082.01280.8482.32292.5772.62104.742

466.14477.11493.727105.271132.374143.094191.162199.841189.23169.20353.68786.033189.2311.07954.9131.36160.4941.70270.5012.01781.3442.32693.1362.621105.365

567.32178.18595.374106.958133.993144.862191.793200.697193.84669.52654.04586.323193.8461.07955.1031.36260.7551.70370.8332.01581.6952.3293.4952.61105.738

668.12678.9296.473108.082135.008145.994192.059201.156198.46269.73354.2886.504198.4621.07955.2861.36160.9761.69971.0692.00681.8942.30493.6472.588105.853

768.70979.46497.252108.893135.697146.79192.184201.465203.07769.82154.38986.572203.0771.07855.4631.35861.1541.69171.2061.9981.9392.27993.5912.553105.709

869.13179.86297.806109.477136.168147.347192.227201.657207.69269.78654.36986.525207.6921.07755.6311.35361.2881.67971.2431.96781.8272.24593.3252.507105.306

969.42580.14198.183109.878136.474147.711192.208201.744212.30869.62954.21886.361212.3081.07655.7931.34661.3771.66271.1781.93781.5622.20192.8542.45104.65

1069.61180.31998.413110.125136.648147.921192.154201.756216.92369.34953.93886.082216.9231.07455.9471.33761.4191.6471.0121.90181.1442.14992.1822.382103.749

1169.70180.40998.517112110.24119136.707141147.999149192.066181201.702193221.53868.94953.53285.69221.5381.07256.0931.32661.4161.61470.7471.85880.5812.08991.322.304102.615

1269.60980.31498.405110.116136.61147.887192.012201.631226.15468.43353.00385.188226.1541.0756.2331.31361.3671.58470.3871.8179.882.02190.282.218101.264

1369.4280.13198.164109.857136.402147.645191.957201.525230.76967.80752.35984.582230.7691.06756.3651.29861.2751.55169.9371.75679.051.94689.0762.12399.717

1469.12279.84797.776109.445136.062147.247191.867201.344235.38567.0851.60783.88235.3851.06456.491.28161.141.51369.4021.69878.1051.86687.7272.02297.997

1568.69579.44297.21108.848135.553146.655191.708201.04824066.2650.75983.092401.06156.6081.26360.9651.47368.7921.63577.0581.78186.2571.91596.135

1668.10878.89196.418108.022134.82145.818191.448200.613244.61565.3649.82682.223244.6151.05756.721.24360.7531.4368.1131.5775.9281.69384.6911.80494.168

1767.29678.14795.303106.879133.753144.634191.013199.985249.23164.39248.82481.292249.2311.05456.8261.22160.5071.38567.3781.50274.7331.60383.0581.69292.136

1866.11377.06293.637105.167132.068142.796190.156198.894253.84663.37347.76880.309253.8461.0556.9261.19960.2321.33866.5981.43373.4931.51181.3891.5890.076

1964.16575.0790.828102.034128.976139.238188.038196.136258.46262.31646.67579.29258.4621.04557.0221.17559.9321.2965.7851.36372.2281.4279.7111.46988.026

2060.26969.30985.5399293.84598122.858111129.571118181.798136186.343143263.07761.23845.56278.249263.0771.04157.1131.15159.6141.24264.9511.29470.9591.33178.0531.36186.028

2160.26969.30985.53993.845122.858129.571181.798186.343267.69260.15844.45477.202267.6921.03657.21.12759.2821.19464.1121.22569.7111.24576.461.25884.147

272.30859.1143.39476.173272.3081.03257.2851.10258.9431.14763.2861.1668.5281.16475.0021.16482.488

2717796102119126154162276.92358.15242.45775.207276.9231.02757.3671.07858.6071.10162.5091.167.4841.09373.791.08581.194

118290112119141149181193281.53857.38441.75674.382281.5381.02257.4481.05458.2911.05961.8411.04866.6841.03772.9531.02780.437

2071779298111118136143286.15456.97141.4973.818286.1541.01857.531.03258.0241.02461.3671.01266.3081.00172.693180.26

290.76956.94941.59673.664290.7691.01357.6141.01357.8541.00161.263166.316172.797180.36

295.38557.08941.76173.78295.3851.00957.703157.889161.415166.443172.898180.44

30057.21141.90673.8793001.00557.804158.069161.558166.553172.982180.505

304.61557.31742.03573.963304.6151.00257.928158.239161.687166.648173.053180.558

309.23157.4142.1574.034309.231158.086158.398161.802166.732173.114180.603

313.84657.49242.25474.095313.846158.265158.547161.907166.806173.167180.641

318.46257.56542.34874.147318.462158.441158.687162.002166.872173.213180.673

323.07757.6342.43374.192323.077158.615158.82162.09166.932173.254180.701

327.69257.68842.51274.231327.692158.786158.945162.17166.986173.291180.725

332.30857.74142.58474.264332.308158.954159.064162.245167.036173.324180.746

336.92357.78942.65274.293336.923159.12159.178162.316167.082173.354180.765

341.53857.83342.71474.319341.538159.284159.286162.381167.124173.382180.782

346.15457.87442.77474.341346.154159.446159.39162.444167.164173.407180.798

350.76957.91242.8374.361350.769159.606159.49162.503167.202173.431180.812

355.38557.94542.88274.375355.385159.758159.583162.557167.236173.452180.824

36057.94542.88274.375360159.758159.583162.557167.236173.452180.824

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Sheet2

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Load (15)

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Load (28)

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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

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Load (27)

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Load (26)

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]


Drag torque [N-m]

AxialT133 (4)

1.8314536570.8409515.57216.578

5.43435254654.224612.65513.998

10.27844865978.42499.351911.445

14.615059170612.2747.13829.7296

18.781859599116.0135.54488.5452

22.650456243519.6514.44987.7094

THD

Isothermal

THD

Isothermal

c= 20 m

Static load [N]



Load (25)

1.8314536570.8409515.57216.578

5.43435254654.224612.65513.998

10.27844865978.42499.351911.445

14.615059170612.2747.13829.7296

18.781859599116.0135.54488.5452

22.650456243519.6514.44987.7094

THD

Isothermal

THD

Isothermal

c' = 17 m

Static load [N]



Load (24)

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



Temperature [ C]

Load (16)

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 (18)

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



Dimensionless pressure, p/pa

Load (17)

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



Dimensionless pressure, p/pa

Load (10)

7710212669.37793.974129.954

9011914975.139102.168139.621

779811877.114105.271143.094

78.185106.958144.862

78.92108.082145.994

79.464108.893146.79

79.862109.477147.347

80.141109.878147.711

80.319110.125147.921

80.409110.24147.999

80.314110.116147.887

80.131109.857147.645

79.847109.445147.247

79.442108.848146.655

78.891108.022145.818

78.147106.879144.634

77.062105.167142.796

75.07102.034139.238

69.30993.845129.571

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]

Load (13)

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]


AxialT133 (3)

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 (12)

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


Rotor speed [krpm]

Centrifugal growth [m]

Load (11)

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 (9)

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]

AxialT133

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]


thermal

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]


Chart1 (2)

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]

Chart1 (5)

107128

140157

180197

233256

Test data - Mid-plane

222 N

THD solution

Adiabatic wall


Rotor speed [krpm]


Chart2

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]


Chart2 (2)

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]


Sheet3

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]

Chart1 (8)

0.55250.510.765

76.37570.5105.75

166.725153.9230.85

Inconel X750

Inconel 718

AISI 304 (Stainless steel)

Temperature [ C]


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

978.197106146cp10

Documents

Luis San Andrés Mast-Childs Professor Fellow ASME Texas A&M University