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
Temperature rise [C]
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
Temperature rise [C]
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
Withinneroutercooling
Static load [N]
Peak temperature [ C]
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
Withinneroutercooling
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
(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
Withinneroutercooling
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
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]
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
Thermal expansion [m]
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]
W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/inner
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]
W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/inner
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]
W/OcoolingW/outerW/outer/innerW/OcoolingW/outerW/outer/inner
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]
Journal attitude angle [deg]
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]
Journal eccentricity [m]
Minimum film thickness [m]
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
(b) Outer cooling flow (170 lit/min)
(a) Without cooling flow
(c) Inner (170 lit/min) and outer (170 lit/min) cooling flows
WithoutCooling
Withoutercooling
Withinneroutercooling
Static load [N]
Drag torque [N-m]
Journal attitude angle [deg]
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
(b) Outer cooling flow (170 lit/min)
(a) Without cooling flow
(c) Inner (170 lit/min) and outer (170 lit/min) cooling flows
WithoutCooling
Withoutercooling
Withinneroutercooling
Static load [N]
Minimum film thickness [m]
Journal eccentricity [m]
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
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
(c) Inner (170 lit/min) and outer (170 lit/min) cooling flows
(b) Outer cooling flow (170 lit/min)
(a) Without cooling flow
Test data
Test data
WithoutCooling
Withoutercooling
Withinneroutercooling
Static load [N]
Peak temperature [ C]
Load (30)
745521
776024
827027
908030
969232.5
101104222
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
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
Predictions - 50 krpm-20um_0.6_20
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
890.2439024390.54878048780.79268292688978109142741001295.00E+045.00E+012.99E-062.99E+005.25E-065.25E+009.27E-069.27E+006.00E+014.35E-064.35E+006.00E+019.49E-069.49E+006.00E+011.54E-051.54E+01
1330.18292682930.54878048780.853658536613391127164881191506.00E+046.00E+014.30E-064.30E+007.56E-067.56E+001.33E-051.33E+018.00E+017.73E-067.73E+008.00E+011.69E-051.69E+018.00E+012.74E-052.74E+01
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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NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Minimum gas film thickness between top foil and journal.
Minimum gas film thickness between top foil and journal.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Tae Ho Kim:With consideration of foil material degradation
Tae Ho Kim:Without foil material degradation
Update Curve Fit
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Kxx
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1
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Page &P
Cxx
Cxy
Cyx
Cyy
Cxx fit
Cxy fit
Cyx fit
Cyy fit
Load (20)
11111111
&A
Page &P
Mxx
Mxy
Myx
Myy
Mxx fit
Mxy fit
Myx fit
Myy fit
Load (27)
11111111
NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Tae Ho Kim:With consideration of foil material degradation
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Update Curve Fit
&A
Page &P
Kxx
Kxy
Kyx
Kyy
Kxx fit
Kxy fit
Kyx fit
Kyy fit
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
&A
Page &P
Cxx
Cxy
Cyx
Cyy
Cxx fit
Cxy fit
Cyx fit
Cyy fit
Load (21)
11111111
&A
Page &P
Mxx
Mxy
Myx
Myy
Mxx fit
Mxy fit
Myx fit
Myy fit
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
NOTE to USER: WFR and Keq make sense only for frequency INDEPENDENT force coefficients - GIVEN Here only as a reference
Journal eccentricity along X-direction.
Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
Journal eccentricity along Y-direction. Used only if VARY ECCENTRICITY= FIND BEARING LOAD Option is active.
External load along X-direction. See typical notation.
Used only if VERY LOAD=FIND Eccentricity Option is active.
After execution, check that output reaction force balances load, i.e.Load-X + FX =0
External load along Y-direction. See typical notation.
Used only if VARY LOAD= FIND ECCENTRICITY Option is active. After execution, check that output reaction force balances load, i.e.Load-Y + FY =0
Table of speeds (RPM)rotor or journal speed if Synchronous analysis option selected.orrotor whirl speed if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
Table of impedance coefficients (real part): Rij = Kij + w^w Mijw( frequency in rad/s)
Rotor or journal speed in rpm if Synchronous analysis option selected with varying loads.orBearing load (Load-X) in N if Synchronous analysis option selected with varying speeds.orRotor whirl speed in Hz if Asynchronous analysis option selected. In this case CONSTANT SHAFT RPM for all cases.
e_structure, rotor displacement due to lateral force along X-direction at null rotor speed. = radial clearance + max. bump deflection
e_structure > ex, ey always.
Journal eccentricity along X-direction, resulting from applied load
Journal eccentricity along Y-direction, resulting from applied load
Journal eccentricity = sqrt (ex^2+ey^2).
Dimensionless journal eccentricity resulting from applied load
Jounal attitude angle in deg.See FIGURE in TYPICAL NOTATION
Minimum gas film thickness between top foil and journal.
Bearing reaction force along X-direction
Bearing reaction force along Y-direction
Bearing reaction force = Sqrt (Fx^2 + Fy^2)
Bearing Specific load= Bearing load (or Force)/Rotor diameter/Axial length
Maximum gas film pressure
Bearing torque induced by gas film drag force
= Bearing torque times rotor speed (rad/s)
Equivalent stiffness (Keq) and whirl frequency ratio (WFR) make sense only for synchronous excitation.
Disregard results if asynchronous calculations
Whril Frequency Ratio
Minimum gas film thickness between top foil and journal.
Minimum gas film thickness between top foil and journal.
Tae Ho Kim:With consideration of foil material degradation
Structural foil stiffness coefficient (Kstructure)Concept: K = -dFx/dx, change in lateral force due to change in displacement at null rotor speed.Kstructure > Kxx, Kyy always.
Table of stiffness coefficients (Kxx, Kxy, Kyx, Kyy)Concept: Kij = -dFi/dXj, change in lateral force (i) due to change in displacement (j).
Table of damping coefficients (Cxx, Cxy, Cyx, Cyy)Concept: Cij = -dFi/dVj, change in lateral force (i) due to change in velocity (j).
THD
Isothermal
THD
Isothermal
Static load [N]
Journal attitude angle [deg]
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]
Journal eccentricity [m]
Minimum film thickness [m]
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]
Journal eccentricity [m]
Minimum film thickness [m]
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
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
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
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Temperature [ C]
Load (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
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (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
Static load increases
44 N
89 N
133 N
178 N
222 N
Predictions - 40 krpm-20um_0.6_20
Circumferential angle [deg]
Dimensionless pressure, p/pa
Load (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
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
AxialT133 (3)
741021371685583125190
771061361686088128186
821121411817098136192
9011914919380110148202
9612616020592124162214
101134176217104138177228
30,000 rpm
40,000 rpm
50,000 rpm
20,000 rpm
Test data (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
Load (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
Predictions - 40 krpm-20um_0.6_20
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 (Mid-plane)
Predictions(Mid-plane)
Test data - 30 krpm
Test data - 40 krpm
Test data - 50 krpm
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Predictions - 50 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
thermal
13712574551245311164
136128776012255110.566.5
14113682701236011571
14914890801306912277
160162969214181130.582
1761771011041559514586
Test data (Mid-plane)
40,000 rpm
Test data (Edge)
20,000 rpm
Predictions(Edge)
Predictions(Mid-plane)
Test data - 40 krpm
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
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
Predictions - 40 krpm-20um_0.6_20
Rotor speed [krpm]
Peak temperature [ C]
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
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
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
Predictions - 30 krpm-20um_0.6_20
Predictions - 40 krpm-20um_0.6_20
Static load [N]
Peak temperature [ C]
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]
Thermal expansion [m]
Chart1 (6)
0.2439024390.42682926830.6097560976
0.2439024390.54878048780.7926829268
0.18292682930.54878048780.8536585366
30,000 rpm
50,000 rpm
70,000 rpm
Static load [N]
Axial Thermal gradient [ C/mm]
Chart1 (9)
918878746359
1271191091009083
164150142129121111
Mid-plane
133 N
89 N
44 N
Side edge
Rotor speed [rpm]
Peak temperature [ C]
Sheet3 (2)
74100129
78109142
74100129
30,000 rpm
50,000 rpm
70,000 rpm
Temperature [C]
Chart1 (3)
1830207
217215
164207
Temperature [C]
http://www.hightempmetals.com/techdata/hitempInconelX750data.php
InconelX750
Modulus of Elasticity
CMPa x 10(6)
26.7213.7
260197.9
538172.4
732144.8
816127.6
Thermal Conductivity
CW/m-K
14916.9
31620.5
53826.5
64928.7
76031.4
87135.3
Inconel 718AISI4140 steel test shaftAISI 304 stainless steel bearing housing
http://www.espimetals.com/tech/inconel718.pdfTheraml expansion coefficientTheraml expansion coefficient
R0.025m211Gpahttp://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4140&prop=all&Page_Title=AISI%204140http://www.goodfellow.com/csp/active/STATIC/A/Stainless_Steel_-_AISI_304.HTML
alph1.30E-05Kavg
conductivity11.4W/m.K
CRgThermal Properties18
26.70.552516.3
26076.375
538166.725Properties
732229.775TreatmentR0.025m
816257.07512.320-100moreoil hardened, tempered 600Calph1.20E-05K
42.7100more
473150-200moreCRg
Inconel x75026.70.765
http://www.hightempmetals.com/techdata/hitempInconelX750data.php260105.75
R0.025m538230.85
alph1.20E-05Kat 20 deg C732318.15
816355.95
CRg
26.70.51
26070.5
538153.9
732212.1
816237.3
Centrifugal growth
http://www.hightempmetals.com/techdata/hitempInconel718data.php
Inconel 718
http://www.espimetals.com/tech/inconel718.pdf
R0.025m208Gpa
rpmsolid0.5 Ro0.75Ro
0000
1.00E+040.1210.2590.432
2.00E+040.4831.0371.729
3.00E+041.0872.3333.891
4.00E+041.9324.1486.917
5.00E+043.0196.48110.809
6.00E+044.3489.33315.564
7.00E+045.91812.70321.185
8.00E+047.72916.59227.67
9.00E+049.78220.99935.02
1.00E+0512.07725.92543.234
http://www.hightempmetals.com/techdata/hitempInconelX750data.php
http://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4140&prop=all&Page_Title=AISI%204140
12.3
42.7
473
http://www.goodfellow.com/csp/active/STATIC/A/Stainless_Steel_-_AISI_304.HTML
10678.197146
11190.684142
123109.38144
137127.15151
152144.91162
168161.68175
c=20 m
c=25 m
c=32 m
Static load [N]
Peak temperature [ C]
99.55678.197
112.3690.684
136.63109.38
161.32127.15
187.72144.91
215.11161.68
Adiabatic
Heat transfer convection
Static load [N]
Peak temperature [ C]
2552
2855
3359
4268
6691
Peak temperature
Inlet mixing temperature
Mixing ratio,
Temperature [ C]
50000 rpm
Peal temp
Static loadadiabaticheat coeffCalculation of specific heat
999.55678.197Specific heat
44112.3690.684
89136.63109.38
133161.32127.15Prandtl No.
178187.72144.91
222215.11161.68
Dimensionless spesific heat
adiabaticRotor speed5000065.4498469498m/s
Static loadc=32umc=25umc=20umrho1.169kg/m3
978.197106146cp10
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