experimental aspects in the vibration-based condition...

Research ArticleExperimental Aspects in the Vibration-Based ConditionMonitoring of Large Hydrogenerators

Geraldo Carvalho Brito Junior12 Roberto Dalledone Machado2

Anselmo Chaves Neto2 and Mateus Feiertag Martini1

1Center for Engineering and Exact Sciences Western Parana State University (UNIOESTE) Foz do Iguacu PR Brazil2Numerical Methods for Engineering Graduate Program Federal University of Parana (UFPR) Curitiba PR Brazil

Correspondence should be addressed to Geraldo Carvalho Brito Junior gcbritojrgmailcom

Received 28 November 2016 Accepted 24 January 2017 Published 20 February 2017

Academic Editor Luis A San Andres

Copyright copy 2017 Geraldo Carvalho Brito Junior et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Based on experimental observations on a set of twenty 700MW hydrogenerators compiled from several technical reports issuedover the last three decades and collected from the reprocessing of the vibration signals recorded during the last commissioningtests this paper shows that the accurate determination of the journal bearings operating conditions may be a difficult task It showsthat the outsize bearing brackets of large hydrogenerators are subject to substantial dimensional changes caused by external agentslike the generator electromagnetic field and the bearing cooling water temperature It also shows that the shaft eccentricity of ajournal bearing of a healthy large hydrogenerator operating in steady-state condition may experience unpredictable sudden andsignificant changes without apparent reasons Some of these phenomena are reproduced in ordinary commissioning tests ormay benoticed even during normal operation while others are rarely observed or are only detected through special testsThese phenomenamodify journal bearings stiffness and damping changing the hydrogenerator dynamics creating discrepancies between theoreticalpredictions and experimental measurements and making damage detection and diagnostics difficult Therefore these phenomenamust be analyzed and considered in the application of vibration-based condition monitoring to these rotating machines

1 Introduction

Hydroelectricity plays an important role in the world Theelectrical systems of several countries have hundreds ofmedium-sized and large-sized hydrogenerators some ofwhich have been in operation almost uninterrupted overthe past 30 to 50 years Due to their individual importanceand relatively advanced age the application of vibration-based condition monitoring to large hydrogenerators (LHG)is needfulThe basis of this technique is well known a healthymachine has a kind of vibration fingerprint which changeswith the advent of damage The change of this vibrationfingerprint is used to detect and identify the damage [1]

Vibration monitoring is successfully applied to standardrotating machinery in many branches of the industry it isconsidered one of the few examples where structural healthmonitoring technology did ldquothe transition from research

to practicerdquo [2] However LHG are tailor-made machinesdesigned specifically for each power plant Due to minordifferences in assembly the fingerprints of two apparentlyidentical LHG may be very different from each other [3]Besides as it will be shown in the following the fingerprint ofa healthy LHGmayhave significant changeswithout apparentreasons

LHG are usually equipped with tilting pad journal bear-ings components that have significant influence on theirvibratory behavior The forces generated in the bearing oilfilm are nonlinear functions of the shaft displacement andvelocity If these two magnitudes are low enough theseforces may be linearized around the shaft static equilibriumposition defining the bearing stiffness and bearing dampingcoefficients [4] Bearing coefficients have been studied fora long time Nevertheless these studies have mostly beencarried out for flexible horizontal machines that operate at

HindawiInternational Journal of Rotating MachineryVolume 2017 Article ID 1805051 14 pageshttpsdoiorg10115520171805051

2 International Journal of Rotating Machinery

supercritical speeds equipped with shafts of relatively smalldiameter and bearings with a low number of pads LHG onthe contrary commonly are vertical assembly machines thatoperate at subcritical speeds equipped with rigid shafts oflarge diameters with outsize bearing brackets and using jour-nal bearings with many pads Besides bearings of horizontalmachines are loaded with the machine weight in a knowndirection As detailed by Nasselqvist et al [5] the LHGjournal bearings do not have predefined static loads As willbe demonstrated later the magnitudes and directions of thestatic loads in these bearings are variable andunknownThesefeatures result in particularities in the dynamic behavior ofLHG whose knowledge is essential for the application ofvibration-based condition monitoring techniques on thoserotating machines

The main objective of this paper is to describe severalphenomena observed in a set of twenty 700MWhydrogener-ators belonging to Itaipu Power Plant (Itaipu is a 14000MWhydroelectric power plant located in South America inthe Parana River belonging to both Brazil and Paraguaygovernmental electrical utilities holding companies) whichmay cause significant changes in the dynamic coefficients ofthe journal bearings and therefore in the dynamic behaviorof those machines These phenomena were obtained fromcompilation of several technical reports issued during thelast three decades and from the reprocessing of the vibrationsignals recorded during the last commissioning tests Some ofthese phenomena are reproduced in ordinary commissioningtests or may be noticed in normal operation while others arerarely observed or are only detected through special tests

2 Literature Review

The using of mathematical modeling to support vibration-based condition monitoring of hydrogenerators has begun inthe 1980s due to some cases of chronic dynamic problemsAt that time based on empirical knowledge bearing stiffnesswas overestimated minimizing the dynamic influences of theoil film For instance Sperber and Weber [6] show that a160MWhydrogenerator was modeled using bearing stiffnesswith two orders of magnitude higher than bracket stiffnessCertainly bearing stiffness had few influence on this LHGdynamics

During the design phase the manufacturer performedthe dynamic analysis of the 700MW hydrogenerators ofItaipu Power Plant using the bearing stiffness determinedtheoretically [7] Almost ten years later Cardinali et al [8]modeled the formerly mentioned 160MW hydrogeneratoralso using bearing coefficients determined in the sameway Inboth cases the stiffness of bearings and brackets had the sameorder of magnitude Gustavsson et al [9] proposed a methodto estimate experimentally the stiffness and damping coef-ficients of journal bearings using strain gauges to measurethe radial load acting on the bearing The bearing stiffnessestimated with this method in a 238MW hydrogeneratorshowed fluctuations in the range of 040 to 080GNmThesevalues are much lower than bracket stiffness furthermorethey are one order of magnitude lower than the bearingstiffness determined in the previous references ([7 8])

Nasselqvist et al [10] found a similar proportion between thebearing stiffness and the bracket stiffness both determinedtheoretically in a case study of resonance in a 42MWverticalhydrogenerator

The first remarkable information from the describedreferences is that the bearing stiffness is much lower or hasthe same order of magnitude of bearing bracket stiffnessConsequently bearing stiffness has major effects in thedynamic behavior of LHGTheunderstanding of this stiffnessand its influencing factors is of fundamental importance forvibration-based condition monitoring of these machines

A second important remark concerns the determina-tion of bearing operating conditions According to Tiwariet al [11] the theoretical estimation of bearing dynamiccoefficients ldquohas been a source of error in the prediction ofrotor-bearing systemsrdquo due to the difficulties of determiningbearing operating conditions accurately These difficultiesare amplified in the case of large hydrogenerators mainlydue to the vertical assembly of these machines [5] Forinstance to determine the bearing operating conditions ofItaipu hydrogenerators the manufacturer assumed that amagnetic pull of 600 kN was acting on the journal bearings[7] Nasselqvist et al [10] determined bearing stiffness using aprescribed load of 30 kN as indicated by performedmeasure-ments this is the load on the journal bearings during normaloperation Cardinali et al [8] modeled the already referred160MW hydrogenerator in two different ways The first useda nonlinear model where the LHG equation of motion wassolved simultaneously with the Reynolds equations of thejournal bearings The second way used a linear model wherethe journal bearing effects were represented by dynamiccoefficients The operating conditions of the journal bearingswere defined to achieve the highest coincidence betweenthe characteristic frequencies of both linear and nonlinearmodels which constitutes a complex process Fulei et al [12]determined the shaft static working point using numericalsimulations based on commercial software Xu et al [13]included the boundary conditions as part of the hydro-generators shaft model and used the previously calculatedvalues of the bearing forces in a database relating forces andoperating conditions According to the method proposed byGustavsson et al [9] the journal bearing operating conditionwas determined by measuring the bearing load with straingauges which is not always possible or feasible As analternative to the direct measurement of the bearing loadNasselqvist et al [14] proposed the estimation of bearing loadusing the measured shaft eccentricity together with curvesrelating these two parameters determined previously Theestimation of shaft eccentricity was improved by using fourproximity transducers in each journal bearing plane insteadof the two usual transducers This process attenuates theeffects of symmetrical deformations in the bearing housingsimilar to the process used in generator air gap monitoringHowever as will be shown later in this paper these bearingdeformations may be asymmetrical As a preliminary con-clusion it is possible to say that all the described methodsto determine the operating conditions of a journal bearinghave either considerable uncertainties or difficulties in theirimplementation

International Journal of Rotating Machinery 3

1

2

3

4

5

7

12 13

8

9

10

11

6

Figure 1 View of Itaipu Power Plant hydrogenerators

Based on experimental observations this paper showsthat the determination of bearing operating conditions inLHG may be even more difficult This paper shows that theoutsize bearing brackets of these machines are subject tosignificant dimensional changes caused by external agentslike the generator electromagnetic field or the bearing coolingwater temperature which modifies pad clearances distribu-tion significantly It also shows that the shaft eccentricity inthe journal bearing of a healthy large hydrogenerator oper-ating in steady-state condition may present unpredictablesudden and significant changes without apparent reasonsThese phenomena modify bearing stiffness and dampingchanging significantly the vibratory behavior of the largehydrogenerator and making damage detection and diagnos-tics difficult These phenomena were detected in practicallyall the observed hydrogenerators and it is very probable thatthis is a typical behavior of these machines Therefore it issuggested to verify these occurrences in similar hydrogenera-tors

3 The Large Hydrogenerators and theVibration Transducers

31 The Large Hydrogenerators All the experimental resultsand numerical simulations shown in this paper are relatedto the 700MW hydrogenerators of Itaipu Power Plant maincharacteristics of which are described as follows Figure 1displays the generator (1) and turbine (2) rotors as well asthe upper (3) and lower (4) shafts of the generator and theturbine shaft (5) The nominal rotating speeds are 909 rminfor the 10 machines that operate at 50Hz and 923 rmin forthe remaining 10 hydrogenerators which generate electricalenergy at 60Hz Figure 1 shows the main components of theupper journal bearing the shaft (3) the bearing pads (6) andthe bearing bracket (9)

X-direction

Y-direction

AccelerometerTransducers supportProximity transducer

Transducers

Transducers

Pad

Shaft

1

12

2

3

3

4

4

5

67

8

9

10

11

12

Figure 2 Vibration transducers arrangement in the turbine journalbearing

Likewise it shows the lower journal bearing componentsthe generator lower shaft (4) and the thrust block andbearing pads (7) including the thrust bearing bracket (10)Figure 1 also shows the turbine journal bearing (8) and theturbine headcover (11) Finally this figure shows the generatoroutputs to the transformers (12) and to the neutral connection(13) Table 1 presents the main data of these journal bearingsincluding the bearing global stiffness (shaft oil film bracketand foundation) and the bearing oil film direct stiffness bothdetermined at the design phase of these hydrogenerators [7]All journal bearings have flooded and pressurized design

32 The Vibration Transducers

321 Vibration Transducers Arrangement Figure 2 showsthe typical arrangement of the vibration transducers in ajournal bearing Each bearing has two 4Vmm proximitytransducers eddy current type to measure the shaft relativevibrationsThe accuracy class of these transducers (plusmn5) wascertified by a calibration before installation These transduc-ers were installed 90∘ apart from each other (119883-directionand 119884-direction) between two adjacent bearing pads placewhere the shaft surface has better finishing Despite thedifficulties of installing these transducers inside the bearingsthis arrangement has a significant advantage for vibration-based condition monitoring the proximity transducers aremonitoring the journal bearingrsquos main stiffness

Each journal bearing also has two low frequency piezo-electric accelerometers of industrial type and of high sen-sitivity (1000mVg) to measure the bearing absolute vibra-tions The accuracy class (plusmn5) of these transducers wasalso confirmed by calibration just before installation Theaccelerometers were installed in the bearing structure in thesame support of the proximity transducers The acceleration


Table 1 Main data of the generator upper journal bearing (UJB) generator lower journal bearing (LJB) and turbine journal bearing (TJB)

Symbol Description Unit UJB LJB TJB119899119901 Number of pads mdash 16 16 12119903 Journal radius mm 1100 2600 1600119877 Bearing pad radius mm 1103 2604 1633119880 = 120596119903 Journal speed ms 106 251 1551198880 Nominal pad clearance at standstill 120583m 500 950 200119888 Nominal pad clearance in operation 120583m 200 300 200119898 Bearing preload mdash 0933 0925 0994120572119877 Distance trailing edge pivot mm 140 248 250120573119877 Pad length mm 350 620 500119871 Pad width mm 400 310 500119898119901 Pad mass kg 172 290 390119896119887119894119894 Bearing direct stiffness (average) GNm 670 285 670119896119887119894 Bearing global stiffness GNm 080 125 145mdash Lubricant type Lubrax Turbina Plus 50120578 Lubricant viscosity at 40∘C Pas 0047 0047 0047120588 Lubricant density at 20∘C kgm3 873 873 873120599lub Lubricant temperature range ∘C 40ndash55 40ndash55 40ndash50

signals were integrated by charge amplifiers Hence exceptwhere it is otherwise clearly indicated in this article theabsolute vibration signals are expressed in velocity

322 Difficulties in Measuring Absolute Vibrations of LHGJournal Bearings The use of piezoelectric accelerometers tomeasure the absolute vibrations of LHG journal bearings hassome significant problems The experimental observationshave shown that sometimes for reasons still unknownwhen a healthy LHG operates at steady-state condition thesevibration signals show sudden and strong variations as ifthe journal bearing has received an impactThemaintenancerecords do not show indications of possible impacts how-ever such anomalous behavior may produce false alarmsin a monitoring system Another important problem withaccelerometers is the measurement of low frequency vibra-tions or vibrations at LHG rotating speed [15] Even in thecase of significant bearing vibrations at the rotating speedthe signal generated by an accelerometer of high sensitivityhas only a fraction of millivolts For example an accelerom-eter of 1000mVg generates a signal of 019mV when sub-mitted to a sinusoidal vibration of 20 micrometers (120583m) at923 rmin The measurement and the transmission of thislow voltage signal require special care particularly in a noisyenvironment like a power plant

There are traditional velocity transducers of high sensi-tivity (50mVmms) equipped with a signal conditioner thatextends its measuring range down to 1Hz or to 05Hz withminus3 dB Theoretically the voltage of the signal generated bythese transducers for the same bearing vibration is fifty timeshigher than that produced by the accelerometer previouslydescribed Therefore these vibration signals would be moresuitable to be handled However the datasheet of some ofthese transducers shows considerable fluctuations in theirsensitivity at the low frequency range from 0 to minus5 dB at 1Hz

4 Remarks on the Dynamics of LHG Based onExperimental Observations

This section describes several phenomena that frequentlyoccur in LHG causing changes in the shaft eccentricity in thelubricant viscosity or in the clearances of the journal bear-ings As consequence these phenomenamay have significantinfluence on the LHG dynamics

41 Remarks Based on Vibration Analysis

411 Typical Shaft and Bearing Vibrations in Normal Oper-ating Conditions Figure 3 shows the typical shaft relativeand the bearing absolute vibrations in 119883-direction and 119884-direction of the upper journal bearing of a healthy LHGin time and frequency domains The vibration signals weresampled with 2400Hz and their power spectral densitieswere estimated using Welchrsquos method with a Hann windowTable 2 shows the main descriptors of these vibrationsobtained in ten different measurements The first five mea-surements were done during a month while the remainingmeasurements were taken eight months later also over aperiod of a month Shaft vibrations occur mainly at therotating speed (1x) with small amplitudes at twice thisfrequency (2x) Bearing vibrations have components in manyfrequencies (eg 088 152 454 114 394 and 467Hz)always with significant differences between 119883-direction and119884-direction There are also components at 100 200 and400Hz originated by the magnetic forces transmitted fromthe stator core through the bearing bracket arms [16]

Considering the three journal bearings shaft relativevibrations occur mainly at 1x and 2x the rotating frequencyprobably originated by imbalances of hydraulic andmagneticorigins The uncertainties of these vibrations come fromthe shaft electrical and mechanical runout which in a first


Shaft vibration

Dir XDir Y

minus200minus150minus100minus50

050

100150200

(120583m

)

1 2 3 4 5 6 7 8 9 100(s)

(a)

Dir XDir Y

Bearing vibration


002040608

(mm

s )

1 2 3 4 5 6 7 8 9 100(s)

(b)

Dir XDir Y

0

20

40

60

80

100

(120583m

p)

10 20 30 40 50 600(Hz)

(c)

Dir XDir Y

0

002

004

006

008

(mm

sp

)

10 20 30 40 50 600(Hz)

(d)

Figure 3 Shaft relative vibrations ((a) and (c)) and bearing absolute vibrations ((b) and (d)) in119883-direction and 119884-direction in time domain((a) and (b)) and in frequency domain ((c) and (d)) measured at the UJB of a LHG operating with 617MW (011410)

Table 2 Typical shaft relative and bearing absolute vibrations in the upper journal bearing of a LHG

Date Power[MW]

Shaft relative vibration [120583m119901] Bearing absolute vibration [mmsRMS]119883-direction 119884-direction 119883-direction 119884-direction

Peak 1x 2x Peak 1x 2x RMS 1x 2x RMS 1x 2x040309 522 63 23 0 80 44 3 013 001 000 013 003 000040709 583 66 26 0 79 45 3 011 004 000 011 001 001041409 694 67 23 0 65 35 3 014 004 000 014 001 000042209 680 64 23 0 63 32 2 013 000 000 014 003 000042909 682 56 12 0 59 26 4 013 000 000 014 003 001010610 638 61 32 1 83 46 3 016 001 000 015 005 000011410 617 60 32 2 81 46 2 013 001 001 013 005 000012110 474 57 28 2 76 42 2 010 001 000 010 005 000012210 629 62 30 1 83 44 2 015 000 000 014 005 000012810 552 58 29 2 73 40 3 011 001 000 011 005 000

moment cannot be estimated with accuracy The 2x compo-nent of shaft vibration may be significant in some bearingsindicating excessive shaft eccentricity and consequent highernonlinearity Bearing vibrations show significant differencesbetween 119883-direction and 119884-direction in magnitudes and

frequency contents Sometimes there is a vibration compo-nent at the rotating frequency and sometimes there is notpossibly due to the low excitations at this frequency and thedifficulties described in Section 322 The turbine journalbearing absolute vibrations frequently have a significant


180

200

220

240SH

-UJB

-Y (m

m)

190 210170 230SH-UJB-X (mm)

185 205 225165SH-LJB-X (mm)

200 220 240180SH-TJB-X (mm)

180

200

220

240

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)G665 - t0 + 05 h

G425 - t1 + 65 h

Balan - t2 + 60 h

G665 - t0G425 - t1 + 55 h

Balan - t2 + 55 h

G425 - t1 + 70 h

Balan - t2G425 - t1

Figure 4 Shaft eccentricity in the upper lower and turbine journal bearings of a LHG at speed-no-load condition with the generator rotorbalanced (Balan) and unbalanced with ISO quality grades G425 and G665

0

486

45

544

88319601

139381642

193441677

200 220 240180SH-UJB-X (mm)

180 200 220160SH-LJB-X (mm)

210 230 250190SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)

170

190

210

230

SH-U

JB-Y

(mm

)

247minus 247+

Figure 5 Shaft eccentricity in the upper lower and turbine journal bearings of a LHGmeasured at several loads (from 0 to 763MW) over aperiod of 10 hours

component at 394Hz twice the blade passing frequencyof the turbine rotor There are also significant vibrationamplitudes in the ranges of 170ndash250Hz and 380ndash470Hzwhich are probably direct hydraulic excitations not relatedto the LHG rotating part ([15 17])

412 Changes in Shaft Eccentricity Each diagram of Figure 4shows the average values of two shaft relative vibrationsmeasured 90∘ apart in the plane of the three journal bearingsand plotted against each otherThemarks on the diagrams arerelated to the shaft center position or the shaft eccentricity inthe journal bearingThe radii of the red circles in dashed linesare equal to the nominal pad clearance in operation (119888)Thesemeasurements were taken during the balancing process of aLHG over three consecutive days when the generator rotorwas in the following conditions (a) unbalanced with ISOquality gradeG665 (b)with a calibrationweight unbalancedwith ISO quality grade G425 and (c) balanced In theseoperating conditions there was no magnetic pull and any

casual hydraulic pull in the turbine was minimum Theshaft eccentricity changes randomly and significantly alonga straight line on the planes of the three journal bearingsHowever it should also be considered that shaft collars andthrust block may have significant radial expansions duringtransient processes such as bearings warming

The diagrams of Figure 5 are similar to those shownin Figure 4 but there the LHG is operating in steady-statecondition at several loads from 0 to 763MW over a periodof 10 hours Now there is a magnetic pull in the generator anda hydraulic pull in the turbine both of unknown magnitudesand directions as will be shown in Section 435 The shafteccentricity varies along a horizontal line in the upperjournal bearing For the other two journal bearings the shafteccentricity varies randomly around two distant attractorsFinally the diagrams of Figure 6 show the long-term changesin shaft eccentricities measured in the conditions describedin Table 2 In summary this section has shown that thejournal bearings operating conditions vary randomly and


4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)

Figure 6 Shaft eccentricity in the upper lower and turbine journal bearings of a LHG measured at several loads (from 474 to 694MW)during several months

UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)

Figure 7 Shaft relative vibrations at the upper (UJB-119883119884) lower (LJB-119883119884) and turbine (TJB-119883119884) journal bearings of a LHG operatingwith 247MW

significantly during operation due to the similar changes inthe shaft eccentricities As these variations change the LHGdynamics shaft eccentricities must be measured and theireffects shall be considered in the monitoring process

413 Sudden Changes on Shaft Eccentricity Figure 7 showsthe shaft relative vibrations on119883-direction and119884-direction atthe upper (resp UJB-119883 and UJB-119884) lower (LJB-119883LJB-119884)and turbine (TJB-119883TJB-119884) journal bearings when a LHGwas operating with 247MW In this condition shaft vibra-tions occur mainly at a quarter of the rotating speed due tothe well-known partial load vortices in the turbine ([17 18])As indicated by the red-dashed rectangles in the shaft vibra-tions at119883-direction of the lower journal bearing (LJB-119883) andin both shaft vibrations at turbine journal bearing (TJB 119883119884)the shaft eccentricity changes abruptly at 119905 asymp 12 seconds

These changes were represented also in Figure 5 (see◼ 247minus and + 247+) and they may cause sudden changes in

bearings stiffness as well as in the LHG dynamics A possibleexplanation to these changes it that the hydrogenerator wassuddenly moved from an attractor to another by action of thelarge vortices forces in the turbine rotor

414 Changes in Shaft and Bearing Vibrations with theGenerator Load Figures 8 and 9 show respectively shaftrelative vibrations and bearing absolute vibrations measuredin the upper journal bearing of a LHG at seven differentgenerator loads over a period of ten hours Both diagramsshow the vibration displacements in this specific case oncethe journal bearing acceleration signals were integratedtwice On both diagrams each signal has a vertical scale of100 micrometers per division At speed-no-load condition(0MW) shaft vibration has stochastic characteristics whilebearing vibration has its lowest value For 100 and 255MWboth shaft and bearing vibrations increase under the influ-ence of the familiar partial load vortices giving origin to


2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv

755MW-Y700MW-X610MW-Y

500MW-Y255MW-X100MW-Y0MW-Y

Figure 8 Shaft relative vibrations at several generator loads (0 to755MW from bottom to top)

2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv



Figure 9 Bearing absolute vibrations at several generator loads (0to 755MW from bottom to top)

high amplitude vibrations at approximately a quarter of therotating speed ([17 18])

At the beginning of the operating range (500MW)shaft and bearing vibrations occur mainly at rotating speed(923 rmin) nevertheless sometimes natural frequenciesare excited in the range of 45 to 55Hz From 610 to 755MW(full wicket gates opening) vibrations occur predominantlyat rotating speed shaft vibrations displacements are lowerthan 100 micrometers peak-to-peak (120583mpp) while bearingvibrations are lower than one-third of this value By this wayit can be concluded that the operating load changes the LHGvibration fingerprint significantly and it must be consideredin the vibration monitoring activities

415 Sudden Changes on Natural Frequencies Figure 10shows the shaft relative vibration at the turbine journal

bearing of a LHG operating at 530MW in time (a) and fre-quency (b) domains Shaft vibration reached high amplitudes(400 120583mpp) with beating between two possible natural fre-quencies 486 and 525Hz Further examinations indicatedthat the shaft vibrations were in phase at the upper and lowergenerator bearings while both these vibrations were in phaseopposition related to the shaft vibration in the turbine journalbearing

The natural frequencies disappeared for about ten sec-onds and then another excitation occurred as shown inFigure 11 In this case the generator load was 540MW theshaft vibration amplitude reached 550120583mpp and the naturalfrequencies were 550 and 576Hz This sudden increasein the natural frequencies implies a substantial and abruptchange in the bearings stiffness what can be explained bysudden changes in the shaft eccentricity like the one shownin Figure 7

42 Remarks Based on Temperature Analysis Thermal effectschange journal bearing dynamics coefficients ([19 20])modifying the dynamic behavior of the rotating machineThis section describes some phenomena observed in LHGjournal bearings

421 Influence of the Cooling Water Temperature Figure 12shows the generator load the cooling water temperature thelubricant temperature and the temperatures of two pads 90∘apart from each other of the lower journal bearing of a LHGThese parameters were measured during 5000 operatinghours with a sampling interval of 30 minutes Measurementsduring three short time stoppages were disregarded Overthis period of almost 7 months the generator load fluctuatedfrom 358 to 727MW as demanded by the electrical systemThe temperature of cooling water taken from the turbinespiral case varied in the range of 20 to 30∘C mainly due tothe natural seasonal variation of the river water temperatureThe bearing losses of nearly 900 kW are removed by eightwater-oil heat exchangers equally distributed in the lubricantchamber As the cooling water flow is kept constant lubricantviscosity and pad clearancesmay have had significant changesin this period The lubricant temperature varied from 46 to50∘C due to the influence of cooling water temperature (thecorrelation factor between these two magnitudes is +098)and also under the guidance of the generator load

The temperatures of the two pads showed a distinctbehaviorWhile the temperature of pad 5 followed the coolingwater temperature with a correlation factor of +083 thetemperature of pad 1 had an opposite behavior with a corre-lation factor of minus088 Figure 12 also shows that the generatorload influences both pads temperatures This behavior maybe explained by changes in the axial hydraulic pull and in theshaft eccentricity in addition to bearing dimensional seasonalchanges caused by coolingwater temperature [3]This remarkindicates that the oil film temperature may vary significantlyfrom one pad to another in an almost unpredictable wayHowever in vibration monitoring these temperatures maybe estimated using other bearingmeasured temperatures likethe lubricant and the pads temperatures


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)

Figure 10 Shaft vibration at the TJB of a LHG with 530MW in time (a) and frequency (b) domains (spectrum main peaks are100120583mpp15Hz 130 120583mpp486Hz and 105 120583mpp525Hz)

2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)

Figure 11 Shaft vibration at the TJB of a LHG with 540MW in time (a) and frequency (b) domains (spectrum main peaks are90 120583mpp15Hz 205 120583mpp550Hz and 155 120583mpp576Hz)

422 Dimensional Changes in the Bearing Housing Figure 13shows the pads temperatures of the upper journal bearingwhen the generator was operating with 0MW just afterstart and one hour and 40 minutes later as well as after tenhours practically in steady-state condition with 763MWThe distribution of the pads temperatures indicates thatpads clearances have an elliptical distribution when thegenerator is loaded This elliptical form is attributed mainlyto the electromagnetic field induced by the generator outputswhich makes the bracket arms nearby warmer than thosethat are distant causing differential thermal expansions inthe bearing structure This symptom also can be seen in thedynamic measurement of the oil film thicknesses and padsclearances shown in Section 433

43 Remarks Based on the Bearings Special CommissioningTests In the middle of the 1980s the manufacturer carriedout special commissioning tests in the bearings of one of thefirst LHG that got into operation The tests were performedduring several months and hundreds of measurements weretaken measured data were recorded in magnetic tapes orin the mass memory of a special computer Unfortunatelyonly five of these measurements are still available in a printedreport [21] and their main results are described in thefollowing

These tests used proximity and pressure transducersinstalled in the upper shaft collar and in thrust block tomeasure oil film thickness and pressure Special slip ringswere used to collect the signals from the LHG rotating partThese tests also used additional temperature transducers to

measure the pads and the lubricant temperatures in a moredetailed way The tests report [21] does not mention theaccuracy class of these transducers however due to thecomplexity and the high costs involved in these tests thesetransducers must be of good quality at least plusmn5 for theproximity and pressure transducers as well as plusmn1∘C for thetemperature transducers

431 Temperature Distribution on Bearing Pads Twoopposed pads of each generator journal bearing receivedadditional transducers to measure the temperatures at theoil film leading edge (L Edge) and trailing edge (T Edge)besides the pad temperature at the pivot region Table 3shows these temperatures in the pads of the upper journalbearing in several operating conditions [21] As expectedthe temperatures of the pad surface and the oil film arehigher at the trailing edge as this region has the lower filmthickness higher shear rates and viscous dissipation [20]These temperatures vary significantly from an operatingcondition to another as well as from a pad to anotherBased on this table the maximum increase in the oil filmtemperature may be estimated in about 7∘C indicating thepossibility of using an adequate average viscosity for eachpad in the case of vibration monitoring applications

432 Distribution of theOil FilmThickness in a Pad Figure 14shows the oil film thickness measured over a pad of the upperjournal bearing with the LHG in two different operatingconditions at speed-no-load condition on the left and atnominal load on the right side [21] In both conditions the oil


7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)

Figure 12 Generator load (a) cooling water temperature (b) lubricant temperature (c) and temperatures of two pads 90∘ apart from eachother (d) of a LHG lower journal bearing

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW

0MW (just after start)40998400

Figure 13 Temperatures of upper journal bearing pads at 0MWandat 763MW

film thickness was measured dynamically Thus it containserrors due to the shaft and pad vibrations Measurementsshow that the pad clearances 280120583m at speed-no-loadcondition and 300 120583m at nominal load are much larger than

the nominal value of the clearance in operation (119888 = 200120583msee Table 1) They also show that oil film thickness changesfrom a condition to another probably due to pad thermaldeformation

433 Changes of Oil Film Thickness due to Bearing HousingDeformation The pads temperatures shown in Figure 13indicated that the pad clearances have an elliptical distri-bution To confirm this hypothesis a structural simulationof the complete upper journal bearing bracket was madeusing commercial software based on the Finite VolumeMethod (FVM) for solving differential equations in three-dimensional geometries The geometry of the upper journalbearing bracket was modeled in a simplified way for bettersolver processing To attain more accurate results the meshgenerator was set to obtain curved and regular elementsmaximum face size of which was fixed to 015m Thegenerated mesh had 1787 k nodes and 1062 k elements with amesh quality between good and very goodThe temperaturesmeasured at tens of points of the bearing brackets atsteady-state condition were extrapolated to create a cloudof points over all the sixteen bracket arms Communicationbetween this cloud and the defined boundary conditionswas given by a software component that manages this typeof imported data and the relative angle between the cloud


Table 3 Temperatures in the pads of upper journal bearing of a LHG

Operating condition Pad number 4 Pad number 12L Edge T Edge L Edge T Edge

[rmin] [MW] [∘C] [∘C] [∘C] [∘C]785 0 353 378 359 395923 0 433 484 452 515923 600 448 481 471 537923 700 470 497 492 560923 700lowast 552 586 573 646lowastIn the last measurement with 700MW a reduction of 10 in the bearing cooling capacity was created artificially by adequately reducing the water flow in theheat exchangers

0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)

Figure 14 Measured distributions of the oil film thickness on pad number 4 of the UJB of a LHG (a) at speed-no-load condition (b) atnominal load condition (700MW)

points and the coordinate system used in the geometry beforethe solution These data were set as input for boundaryconditions for the simulation of thermal expansion whichcombined with crimped supports at the ends and at the basesof the arms induce specific stresses and strains along thestructure which were evaluated in the observation of thesolution The shaft was considered isothermal [22] and itstemperature was estimated with basis on the lubricant andbearing pads temperatures The results of this simulation areshown in Figure 15 where the elliptical distribution of thepads clearances is clear

Figure 16 shows four pad clearances distributions in theupper journal bearingThe blue circle shows the nominal padclearances in operation referred to as clearance condition AThe green closed curve designates the clearances measuredwhen the generator load was 0MW in the bearing specialcommissioning tests [21] mentioned as clearance conditionBThe orange curve with crossed marks shows the clearancesobtained with the described FVM simulation denoted asclearance condition C Finally the red outer curve defines theclearances measured at nominal load condition [21] referredto as condition D Figure 16 shows a similarity betweenthe simulated (condition C) and measured (condition D)clearance distributions This figure indicates that bearing

clearances are much larger than the nominal values whatwill cause significant reductions in the bearing stiffness[23] Additionally it confirms the diagnostic of the symp-tom described in Section 422 that clearance distributionbecomes elliptical when the generator is loaded

434 Changes of Clearances due to Axial Hydraulic Loadand Thrust Block Expansion The thrust bearing bracket(component number (10) in Figure 1) bears both theweight ofthe LHG rotating part and the turbine hydraulic load whichdepends on the generator power water head and clearancesof the turbine labyrinth seals The weight of the rotating partis already applied on the thrust bearing bracket during theadjustment of the lower journal bearing clearances Howeverthe additional axial hydraulic load may create significantreductions in the bearing clearances

Using analytical methods the Finite Element Method(FEM) and the results of tests in a 1 10 scale modelthe manufacturer determined that this effect may cause asignificant reduction in lower journal bearing clearance [24]Besides this effect the thrust block temperature is higherthan the temperature of the ring support of the lower journalbearing pads This originates a thermal radial differentialexpansion that reduces the bearing radial clearance This


Type total deformationUnit mmTime 119052016 1703

47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min

K Static structuraltotal deformation

424 120583m

424 120583

Y

Xm

300 120583m

300 120583m

Figure 15 Elliptical deformation of the upper journal bearing bracket due to eddy currents created by the electromagnetic field of thegenerator outputs

200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y

Figure 16 UJB pads clearances (120583m) (a) nominal (condition A blue) (b) measured at 0MW (condition B green) (c) simulated at 700MW(condition C crossed orange) and (d) measured at 700MW (condition D red)

clearance reduction is not constant and depends on the gen-erator power on the cooling water temperature and on theefficiency of the bearing heat exchangersThe combination ofboth effects was verified in the bearings special commission-ing tests [21] At speed-no-load condition the thrust blockradial expansionmeasured by three different transducers wasabout 90120583m while at the generator nominal load it was270120583m This indicates a reduction of approximately 180 120583min the radial clearance of the lower journal bearing [21] withcorresponding significant increasing in the bearing stiffness

Such effect will be partially balanced by the decreasing of thelubricant viscosity with the increasing of its temperature

435 Changes in the Bearing Radial Static Load Journalbearings of LHG are subject to radial static loads like themagnetic static load originated by misalignment betweengenerator stator and rotor as well as the hydraulic static loadcreated by uneven distribution of the water flow in the wicketgates The misalignment between the three journal bearingsmay also contribute to this load Table 4 shows the radial loads


Table 4 Static loads in a LHG journal bearings

Operating condition Upper journal bearing Lower journal bearing[rmin] [MW] Static load [kN] Directed to pad Static load [kN] Directed to pad785 0 31 13 21 7923 0 61 8 91 14923 600 248 15 295 7923 700 274 10 294 15923 700 316 16 355 9

in the upper and lower journal bearings of a LHG measuredduring the bearing special commissioning tests [21]There arerandom and significant changes in both amplitude (from 20to 360 kN) and direction (over 180∘ or eight pads) of the radialloads what may change bearing stiffness and LHG dynamicsin a significant way

5 Concluding Remarks

Established on experimental evidences collected in a set oftwenty large hydrogenerators functioning in healthy condi-tions this paper has shown that the operating and boundaryconditions of the journal bearings of these machines maypresent frequent significant and unpredictable variationsSeveral of these variations are originated by external agentslike the generator electromagnetic field the bearings coolingwater temperature and the turbine axial hydraulic pull Vari-ations in the operating and boundary conditions naturallymake the accurate determination of bearing stiffness andbearing damping coefficients unfeasible even using refinedbearing models This paper has also shown that as thesebearing coefficients vary with time the vibratory behaviorof a healthy large hydrogenerator also may have frequentsignificant and unpredictable variations making damagedetection and damage diagnostics difficult Finally this paperhas shown that the real clearances of these journal bearingsmay be much larger than the nominal values making the realbearing stiffness coefficients much lower than calculated inthe design of these machines As consequence the criticalspeeds and the natural frequencies at the nominal operatingspeed are lower than theoretically predicted while the realvibration levels may be higher than calculated

The phenomena described in this paper were identifiedin the journal bearings of several of the observed largehydrogenerators The vertical assembly of these machinesthe large diameters of their journal bearings and theiroversized brackets certainly emphasized these phenomenaProbably these and other similar phenomena are typicalof this type of machine They possibly are also present inmedium-sized hydrogenerators and in other turbomachinerywith lesser intensity Therefore it is important to stimulatethe electrical utilities to identify and classify systematicallythese phenomena with a proper characterization of journalbearing operating and boundary conditions using suitable

and calibrated transducers installed properly It is also impor-tant to stimulate discussions about this subject involvingresearchers and users of these rotating machines This willhelp in the detailed understanding of the dynamic behavior ofthese journal bearings and in their influencing mechanismsin the hydrogenerators dynamics This will also help toexplain the differences between the predicted and the realdynamic behaviors of these rotating machines many timesattributed only to the refinement level of the models usedto determine the journal bearing dynamic coefficients andthe machine dynamic response Otherwise the vibrationmonitoring systems based on conventional alarm rules willcontinue issuingmany cases of false alarms (false positive andfalse negative) diminishing the confidence of users in theireffectiveness

Nomenclature

FEM Finite Element MethodFVM Finite Volume MethodISO International Standard OrganizationLHG Large hydrogeneratorLJB Lower journal bearingRMS Root mean squareTJB Turbine journal bearingUJB Upper journal bearing119883 Longitudinal coordinate [m]119884 Transversal coordinate [m]1x Once the rotating frequency2x Twice the rotating frequency

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful to Itaipu Binacional to the ItaipuTechnological Park and to the Center for Advanced Stud-ies on Safety of Dams for the encouragement in thisresearch Roberto Dalledone Machado gratefully acknowl-edges the financial support provided by the Brazilian gov-ernment agency CNPq (Conselho Nacional de Desenvolvi-mento Cientıfico e Tecnologico) under the research grants3122412015-1


References

[1] R B RandallVibration-BasedConditionMonitoring IndustrialAerospace and Automotive Applications John Wiley amp SonsNew York NY USA 2011

[2] C R Farrar and K Worden ldquoAn introduction to structuralhealth monitoringrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol365 no 1851 2007

[3] G C Brito Jr ldquoApplication of simplified statistical modelsin hydro generating units health monitoringrdquo in DamagePrognosis for Aerospace Civil and Mechanical Systems pp 451ndash470 John Wiley amp Sons Hoboken NJ USA 2005

[4] A Z Szeri Fluid Film Lubrication Theory and Design Cam-bridge University Press Cambridge UK 1998

[5] M Nasselqvist R Gustavsson and J-O Aidanpaa ldquoExper-imental and numerical simulation of unbalance response invertical test rig with tilting-pad bearingsrdquo International Journalof Rotating Machinery vol 2014 Article ID 309767 10 pages2014

[6] A Sperber and H I Weber ldquoDynamic models in hydroelectricmachineryrdquo Journal of the Brazilian Society of MechanicalSciences vol 13 pp 29ndash59 1991

[7] Itaipu Itaipu Hydroelectric Project Engineering CharacteristicsTab Marketing Editorial Porto Alegre Brazil 2009

[8] R Cardinali R Nordmann and A Sperber ldquoDynamic sim-ulation of non-linear models of hydroelectric machineryrdquoMechanical Systems and Signal Processing vol 7 no 1 pp 29ndash441993

[9] R K Gustavsson M L Lundstrom and J-O AidanpaaldquoDetermination of journal bearing stiffness and damping athydropower generators using strain gaugesrdquo in Proceedings ofthe ASME Power Conference pp 933ndash940 Chicago Ill USAApril 2005

[10] M Nasselqvist R K Gustavsson and J-O Aidanpaa ldquoRes-onance problems in vertical hydropower unit after turbineupgraderdquo in Proceedings of the 24th Symposium on HydraulicMachinery and Systems Foz do Iguacu Brazil October 2008

[11] R Tiwari A W Lees and M I Friswell ldquoIdentification ofdynamic bearing parameters a reviewrdquo Shock and VibrationDigest vol 36 no 2 pp 99ndash124 2004

[12] C Fulei S Xiaohui and L Wenxiu ldquoLateral vibration ofhydroelectric generating set with different supporting conditionof thrust padrdquo Shock and Vibration vol 18 no 1-2 pp 317ndash3312011

[13] Y Xu Z Li and X Lai ldquoDynamic model for hydro-turbinegenerator units based on a databasemethod for guide bearingsrdquoShock and Vibration vol 20 no 3 pp 411ndash421 2013

[14] M Nasselqvist R Gustavsson and J-O Aidanpaa ldquoA method-ology for protective vibration monitoring of hydropower unitsbased on the mechanical propertiesrdquo Journal of DynamicSystems Measurement and Control Transactions of the ASMEvol 135 no 4 Article ID 041007 2013

[15] International Standard Organization ISO 10816-MechanicalVibration-Evaluation of Machine Vibration by Measurementson Non-Rotating Parts International Standard OrganizationGeneva Switzerland 2000

[16] G C Brito Jr ldquoDynamic behaviour of rotating electricalmachinesrsquo statorsrdquo in Proceedings of the 9th International Con-ference on Vibrations in RotatingMachinery pp 411ndash422 ExeterUK September 2008

[17] L A Vladislavlev Vibration of Hydro Units in HydroelectricPower Plants Amerind Publishing New Delhi India 1979

[18] W Youlin L Shengcai L Shuhong D Hua-Shu and QZhongdong Vibration of Hydraulic Machinery Mechanismsand Machine Science Springer Dordrecht Netherlands 2013

[19] T Dimond A Younan and P Allaire ldquoA review of tilting padbearing theoryrdquo International Journal of Rotating Machineryvol 2011 Article ID 908469 23 pages 2011

[20] G B Daniel and K L Cavalca ldquoEvaluation of the thermaleffects in tilting pad bearingrdquo International Journal of RotatingMachinery vol 2013 Article ID 725268 17 pages 2013

[21] Itaipu Special measurements in unity 14 bearings 1987[22] D Downson J D Hudson and C N March ldquoAn experimental

investigation of the thermal equilibrium of steadily loadedjournal bearingsrdquo Proceedings of the Institution of MechanicalEngineers Conference Proceedings vol 181 no 2 1966

[23] T Someya Journal-Bearing Databook Springer Berlin Ger-many 1989

[24] ItaipuMancais das Unidades Geradoras (Bearings of the Gener-ating Units) Itaipu Foz do Iguacu Brazil 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



supercritical speeds equipped with shafts of relatively smalldiameter and bearings with a low number of pads LHG onthe contrary commonly are vertical assembly machines thatoperate at subcritical speeds equipped with rigid shafts oflarge diameters with outsize bearing brackets and using jour-nal bearings with many pads Besides bearings of horizontalmachines are loaded with the machine weight in a knowndirection As detailed by Nasselqvist et al [5] the LHGjournal bearings do not have predefined static loads As willbe demonstrated later the magnitudes and directions of thestatic loads in these bearings are variable andunknownThesefeatures result in particularities in the dynamic behavior ofLHG whose knowledge is essential for the application ofvibration-based condition monitoring techniques on thoserotating machines

The main objective of this paper is to describe severalphenomena observed in a set of twenty 700MWhydrogener-ators belonging to Itaipu Power Plant (Itaipu is a 14000MWhydroelectric power plant located in South America inthe Parana River belonging to both Brazil and Paraguaygovernmental electrical utilities holding companies) whichmay cause significant changes in the dynamic coefficients ofthe journal bearings and therefore in the dynamic behaviorof those machines These phenomena were obtained fromcompilation of several technical reports issued during thelast three decades and from the reprocessing of the vibrationsignals recorded during the last commissioning tests Some ofthese phenomena are reproduced in ordinary commissioningtests or may be noticed in normal operation while others arerarely observed or are only detected through special tests

2 Literature Review

The using of mathematical modeling to support vibration-based condition monitoring of hydrogenerators has begun inthe 1980s due to some cases of chronic dynamic problemsAt that time based on empirical knowledge bearing stiffnesswas overestimated minimizing the dynamic influences of theoil film For instance Sperber and Weber [6] show that a160MWhydrogenerator was modeled using bearing stiffnesswith two orders of magnitude higher than bracket stiffnessCertainly bearing stiffness had few influence on this LHGdynamics

During the design phase the manufacturer performedthe dynamic analysis of the 700MW hydrogenerators ofItaipu Power Plant using the bearing stiffness determinedtheoretically [7] Almost ten years later Cardinali et al [8]modeled the formerly mentioned 160MW hydrogeneratoralso using bearing coefficients determined in the sameway Inboth cases the stiffness of bearings and brackets had the sameorder of magnitude Gustavsson et al [9] proposed a methodto estimate experimentally the stiffness and damping coef-ficients of journal bearings using strain gauges to measurethe radial load acting on the bearing The bearing stiffnessestimated with this method in a 238MW hydrogeneratorshowed fluctuations in the range of 040 to 080GNmThesevalues are much lower than bracket stiffness furthermorethey are one order of magnitude lower than the bearingstiffness determined in the previous references ([7 8])

Nasselqvist et al [10] found a similar proportion between thebearing stiffness and the bracket stiffness both determinedtheoretically in a case study of resonance in a 42MWverticalhydrogenerator

The first remarkable information from the describedreferences is that the bearing stiffness is much lower or hasthe same order of magnitude of bearing bracket stiffnessConsequently bearing stiffness has major effects in thedynamic behavior of LHGTheunderstanding of this stiffnessand its influencing factors is of fundamental importance forvibration-based condition monitoring of these machines

A second important remark concerns the determina-tion of bearing operating conditions According to Tiwariet al [11] the theoretical estimation of bearing dynamiccoefficients ldquohas been a source of error in the prediction ofrotor-bearing systemsrdquo due to the difficulties of determiningbearing operating conditions accurately These difficultiesare amplified in the case of large hydrogenerators mainlydue to the vertical assembly of these machines [5] Forinstance to determine the bearing operating conditions ofItaipu hydrogenerators the manufacturer assumed that amagnetic pull of 600 kN was acting on the journal bearings[7] Nasselqvist et al [10] determined bearing stiffness using aprescribed load of 30 kN as indicated by performedmeasure-ments this is the load on the journal bearings during normaloperation Cardinali et al [8] modeled the already referred160MW hydrogenerator in two different ways The first useda nonlinear model where the LHG equation of motion wassolved simultaneously with the Reynolds equations of thejournal bearings The second way used a linear model wherethe journal bearing effects were represented by dynamiccoefficients The operating conditions of the journal bearingswere defined to achieve the highest coincidence betweenthe characteristic frequencies of both linear and nonlinearmodels which constitutes a complex process Fulei et al [12]determined the shaft static working point using numericalsimulations based on commercial software Xu et al [13]included the boundary conditions as part of the hydro-generators shaft model and used the previously calculatedvalues of the bearing forces in a database relating forces andoperating conditions According to the method proposed byGustavsson et al [9] the journal bearing operating conditionwas determined by measuring the bearing load with straingauges which is not always possible or feasible As analternative to the direct measurement of the bearing loadNasselqvist et al [14] proposed the estimation of bearing loadusing the measured shaft eccentricity together with curvesrelating these two parameters determined previously Theestimation of shaft eccentricity was improved by using fourproximity transducers in each journal bearing plane insteadof the two usual transducers This process attenuates theeffects of symmetrical deformations in the bearing housingsimilar to the process used in generator air gap monitoringHowever as will be shown later in this paper these bearingdeformations may be asymmetrical As a preliminary con-clusion it is possible to say that all the described methodsto determine the operating conditions of a journal bearinghave either considerable uncertainties or difficulties in theirimplementation


1

2

3

4

5

7

12 13

8

9

10

11

6





X-direction

Y-direction


Transducers

Transducers

Pad

Shaft

1

12

2

3

3

4

4

5

67

8

9

10

11

12


















Shaft vibration

Dir XDir Y


050

100150200

(120583m

)

1 2 3 4 5 6 7 8 9 100(s)

(a)

Dir XDir Y

Bearing vibration


002040608

(mm

s )

1 2 3 4 5 6 7 8 9 100(s)

(b)

Dir XDir Y

0

20

40

60

80

100

(120583m

p)

10 20 30 40 50 600(Hz)

(c)

Dir XDir Y

0

002

004

006

008

(mm

sp

)

10 20 30 40 50 600(Hz)

(d)



Date Power[MW]






180

200

220

240SH

-UJB

-Y (m

m)

190 210170 230SH-UJB-X (mm)

185 205 225165SH-LJB-X (mm)

200 220 240180SH-TJB-X (mm)

180

200

220

240

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)G665 - t0 + 05 h

G425 - t1 + 65 h

Balan - t2 + 60 h

G665 - t0G425 - t1 + 55 h

Balan - t2 + 55 h

G425 - t1 + 70 h

Balan - t2G425 - t1


0

486

45

544

88319601

139381642

193441677

200 220 240180SH-UJB-X (mm)

180 200 220160SH-LJB-X (mm)

210 230 250190SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)

170

190

210

230

SH-U

JB-Y

(mm

)

247minus 247+







4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)


UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)








2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

2

3

4

5

7

12 13

8

9

10

11

6





X-direction

Y-direction


Transducers

Transducers

Pad

Shaft

1

12

2

3

3

4

4

5

67

8

9

10

11

12


















Shaft vibration

Dir XDir Y


050

100150200

(120583m

)

1 2 3 4 5 6 7 8 9 100(s)

(a)

Dir XDir Y

Bearing vibration


002040608

(mm

s )

1 2 3 4 5 6 7 8 9 100(s)

(b)

Dir XDir Y

0

20

40

60

80

100

(120583m

p)

10 20 30 40 50 600(Hz)

(c)

Dir XDir Y

0

002

004

006

008

(mm

sp

)

10 20 30 40 50 600(Hz)

(d)



Date Power[MW]






180

200

220

240SH

-UJB

-Y (m

m)

190 210170 230SH-UJB-X (mm)

185 205 225165SH-LJB-X (mm)

200 220 240180SH-TJB-X (mm)

180

200

220

240

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)G665 - t0 + 05 h

G425 - t1 + 65 h

Balan - t2 + 60 h

G665 - t0G425 - t1 + 55 h

Balan - t2 + 55 h

G425 - t1 + 70 h

Balan - t2G425 - t1


0

486

45

544

88319601

139381642

193441677

200 220 240180SH-UJB-X (mm)

180 200 220160SH-LJB-X (mm)

210 230 250190SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)

170

190

210

230

SH-U

JB-Y

(mm

)

247minus 247+







4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)


UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)








2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















Shaft vibration

Dir XDir Y


050

100150200

(120583m

)

1 2 3 4 5 6 7 8 9 100(s)

(a)

Dir XDir Y

Bearing vibration


002040608

(mm

s )

1 2 3 4 5 6 7 8 9 100(s)

(b)

Dir XDir Y

0

20

40

60

80

100

(120583m

p)

10 20 30 40 50 600(Hz)

(c)

Dir XDir Y

0

002

004

006

008

(mm

sp

)

10 20 30 40 50 600(Hz)

(d)



Date Power[MW]






180

200

220

240SH

-UJB

-Y (m

m)

190 210170 230SH-UJB-X (mm)

185 205 225165SH-LJB-X (mm)

200 220 240180SH-TJB-X (mm)

180

200

220

240

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)G665 - t0 + 05 h

G425 - t1 + 65 h

Balan - t2 + 60 h

G665 - t0G425 - t1 + 55 h

Balan - t2 + 55 h

G425 - t1 + 70 h

Balan - t2G425 - t1


0

486

45

544

88319601

139381642

193441677

200 220 240180SH-UJB-X (mm)

180 200 220160SH-LJB-X (mm)

210 230 250190SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)

170

190

210

230

SH-U

JB-Y

(mm

)

247minus 247+







4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)


UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)








2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










180

200

220

240SH

-UJB

-Y (m

m)

190 210170 230SH-UJB-X (mm)

185 205 225165SH-LJB-X (mm)

200 220 240180SH-TJB-X (mm)

180

200

220

240

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)G665 - t0 + 05 h

G425 - t1 + 65 h

Balan - t2 + 60 h

G665 - t0G425 - t1 + 55 h

Balan - t2 + 55 h

G425 - t1 + 70 h

Balan - t2G425 - t1


0

486

45

544

88319601

139381642

193441677

200 220 240180SH-UJB-X (mm)

180 200 220160SH-LJB-X (mm)

210 230 250190SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

150

170

190

210

SH-L

JB-Y

(mm

)

170

190

210

230

SH-U

JB-Y

(mm

)

247minus 247+







4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)


UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)








2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4316

47114

414121

422122

429128

200 220 240180SH-UJB-X (mm)

150 170 190130SH-LJB-X (mm)

220 240 260200SH-TJB-X (mm)

200

220

240

260

SH-T

JB-Y

(mm

)

130

150

170

190

SH-L

JB-Y

(mm

)

180

200

220

240SH

-UJB

-Y (m

m)


UJB-XUJB-Y

16001800200022002400

(120583m

)

5 10 15 20 25 300Time (s)

(a)

LJB-XLJB-Y

14001600180020002200

(120583m

)

5 10 15 20 25 300Time (s)

(b)

TJB-XTJB-Y

18002000220024002600

(120583m

)

5 10 15 20 25 300Time (s)

(c)








2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv




2 4 6 8 10 12 14 16 18 200Time (s)

100120583

md

iv













2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)


2 64 8 100

(s)

minus400

0

400

(a)

0 8 16 24 32 40

(Hz)

0

200

400

(b)









7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










7000 8000 9000 10000 110006000 Time (h)

200

400

600

800

Load

(MW

)

(a)

7000 8000 9000 10000 110006000Time (h)

20

25

30

35

Coo

ling

wat

er (∘

C)

(b)

7000 8000 9000 10000 110006000Time (h)

45

50

55

Lubr

ican

t (∘ C)

(c)

Pad 1Pad 5

7000 8000 9000 10000 110006000Time (h)

52

54

56

58

60

62

Pads

(∘C)

(d)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Pads number

0MW (1 h later)

30

35

40

45

50

(∘C)

763MW










0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













0

100

200

300

400

600

500

0 100 200 300Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(a)

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350Pad lenght (mm)

Oil

film

thic

knes

s (120583

m)

(b)









47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











47284 max439074052937152

3377430397

20265168871351

10132

067549033774

23642

2702

0 min


424 120583m

424 120583

Y

Xm

300 120583m

300 120583m


200

400

600

800

30

210

60

240

90

270

120

300

150

330

180 0X

Y













Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















Nomenclature


Competing Interests


Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









experimental aspects in the vibration-based condition...

Documents