GEARBOX SUPER-SYNCHRONOUS LATERAL...

ABSTRACTThis paper investigate

vibrationsynchronous vibrationdamages, since they are associatedthe shaftequipment

Moreover, thecan affect theoperability at site, byabove the acceptance value

The phenomenduringtransmittedexcitation of theside)

Etheoreticalwhich govern this phenomenapproach into the train rotating components modeling

technical selection and design verificationof flexible and rigid couplings, load gearsand auxiliary equipment, with particularfocus on the train rotorbehaviour, torsional and lateral.

Mr. Gaspare MaragioglioEngineering ManagerShaft Line Integration

GE Oil & GasFlorence,

ABSTRACTThis paper investigate

vibrations experiencedsynchronous vibrationdamages, since they are associatedthe shafts, thus producingequipment.

Moreover, thecan affect theoperability at site, byabove the acceptance value

The phenomenduring a complete unittransmitted loadexcitation of the pinion

).Experimental observation and

theoretical calculationwhich govern this phenomenapproach into the train rotating components modeling

Gaspare Maragioglio iscurrently the EngineeringManager of the Shaft LineIntegration Team for GEOil & Gas Nuovo Pignonein Florence, Italy. Henow responsible


GEARBOX SUPER


GE Oil & GasFlorence, Italy

This paper investigateexperienced in turbo

synchronous vibrations can be potentially causedamages, since they are associated

thus producing fatigue stress

Moreover, these non-synchronouscan affect the string testoperability at site, by bringing the overall gear shaft vibrationabove the acceptance values.

The phenomena analyzed in thecomplete unit string t

load, and it waspinion shaft overhung mode (

xperimental observation andcalculations drove the focus on the key

which govern this phenomenapproach into the train rotating components modeling

Gaspare Maragioglio iscurrently the EngineeringManager of the Shaft LineIntegration Team for GEOil & Gas Nuovo Pignonein Florence, Italy. Henow responsible


Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station

BOX SUPER


This paper investigates gear superturbo-compressor trains

can be potentially causedamages, since they are associated to alternating torque in

fatigue stresses in the rotating

synchronous vibration componentstring test execution or limit the train

bringing the overall gear shaft vibration

analyzed in the casesstring test, at partial and full

it was observed asshaft overhung mode (

xperimental observation and comparativedrove the focus on the key

which govern this phenomenon, and suggested a newapproach into the train rotating components modeling

Gaspare Maragioglio iscurrently the EngineeringManager of the Shaft LineIntegration Team for GEOil & Gas Nuovo Pignone,in Florence, Italy. He isnow responsible for

technical selection and design verificationof flexible and rigid couplings, load gearsand auxiliary equipment, with particularfocus on the train rotor-dynamicbehaviour, torsional and lateral.


BOX SUPER-SYNCHRONOUS LATERAL

Mr. Alessandro Pescioni

Shaft Line Integration

super-synchronouscompressor trains. N

can be potentially cause of gearalternating torque in

es in the rotating

vibration componentor limit the train


s studied occurredest, at partial and full

observed as a harmonicshaft overhung mode (non-drive end

comparative analysis withdrove the focus on the key factors

and suggested a newapproach into the train rotating components modeling

Manager of the Shaft Line

dynamic

the requisition taskstrain rotorresponsibility includes also support toNPI, manufacturing and test departmefor full speed full load string test.


3rd Middle East Turbomachinery Symposium (METS III)15-18 February 2015 | Doha, Qatar |

SYNCHRONOUS LATERAL

Mr. Alessandro PescioniLead Engineer

Shaft Line IntegrationGE Oil & Gas

Florence, Italy

synchronous. Non-gears’

alternating torque ines in the rotating

vibration componentsor limit the train


occurredest, at partial and full

harmonicdrive end

analysis withfactors

and suggested a newapproach into the train rotating components modeling

procedure, in order to establishverification.

validation

attention to theand the supercoefficients;

lateralfor a comparative analys

assess gearbox rotorto have super

The three aforementioned steps provide a sound method toassess

AlessandrocurrentlyEngineer inLine Integration Teamfor GE Oil & Gas NuovoPignone, in Florence,Italy. He

the requisition tasks andtrain rotor-dynamicresponsibility includes also support toNPI, manufacturing and test departmefor full speed full load string test.


Middle East Turbomachinery Symposium (METS III)18 February 2015 | Doha, Qatar |

SYNCHRONOUS LATERAL

Mr. Alessandro PescioniLead Engineer

Shaft Line IntegrationGE Oil & Gas

Florence, Italy

procedure, in order to establishverification.

The aim of the paper is, ovalidation, to provide

- Direction on the train model criteria, with specialattention to theand the super-coefficients;

- Step by step procedure to carry out the high frequenclateral rotor-dynamicfor a comparative analys

- Acceptance criteria for theassess gearbox rotorto have super-synchronous vibration

The three aforementioned steps provide a sound method toassess the gear shafts' 4th lateral mode.

Alessandro Pescioni iscurrently a DesignEngineer in the ShaftLine Integration Teamfor GE Oil & Gas NuovoPignone, in Florence,

is responsible ofand the integrated

dynamic studies.responsibility includes also support toNPI, manufacturing and test departmefor full speed full load string test.


Middle East Turbomachinery Symposium (METS III)18 February 2015 | Doha, Qatar |

SYNCHRONOUS LATERAL VIBRATION

procedure, in order to establish

The aim of the paper is, oto provide:

irection on the train model criteria, with specialattention to the gyroscopic effects of the overhu

-synchronous bearing stiffness and damping

tep by step procedure to carry out the high frequencdynamic analysis and

for a comparative analyses among the various

cceptance criteria for theassess gearbox rotor-dynamic behaviour and reduce the risk

synchronous vibration

The three aforementioned steps provide a sound method tothe gear shafts' 4th lateral mode.

Pescioni isa Design

ShaftLine Integration Teamfor GE Oil & Gas NuovoPignone, in Florence,

s responsible ofintegrated

Hisresponsibility includes also support toNPI, manufacturing and test department

execute new technology programs.Additionallysynergies and integration across GE andGlobal Research Centerstechnology edge of Oil & Gas products.


Middle East Turbomachinery Symposium (METS III)18 February 2015 | Doha, Qatar | mets.tamu.edu

VIBRATION

Mr. Mirko LibraschiSenior Engineer

Advanced TechnologyGE Oil & Gas

Florence,

procedure, in order to establish robust and reliable design tool

The aim of the paper is, on the basis of string test

irection on the train model criteria, with specialgyroscopic effects of the overhu

synchronous bearing stiffness and damping

tep by step procedure to carry out the high frequencanalysis and to have a common base

among the various

cceptance criteria for the predictionsdynamic behaviour and reduce the risk

synchronous vibration when

The three aforementioned steps provide a sound method tothe gear shafts' 4th lateral mode.

Mirko Libraschi is currentlya Senior EngineerAdvanced TechnologyOrganizationGas Nuovo Pignone, inFlorence, Italy.responsible

execute new technology programs.dditionally Mirko

synergies and integration across GE andGlobal Research Centerstechnology edge of Oil & Gas products.


Middle East Turbomachinery Symposium (METS III)mets.tamu.edu

VIBRATION

Mr. Mirko LibraschiSenior Engineer

Advanced TechnologyGE Oil & Gas

Florence, Italy

and reliable design tool

n the basis of string test

irection on the train model criteria, with specialgyroscopic effects of the overhung inertias


tep by step procedure to carry out the high frequencto have a common base

among the various cases;

predictions to effectivelydynamic behaviour and reduce the risk

when in operation

The three aforementioned steps provide a sound method to

Mirko Libraschi is currentlya Senior EngineerAdvanced TechnologyOrganization, for GE Oil &Gas Nuovo Pignone, inFlorence, Italy.responsible to define and

execute new technology programs.Mirko leads the technology

synergies and integration across GE andGlobal Research Centers, to improvetechnology edge of Oil & Gas products.


Middle East Turbomachinery Symposium (METS III)mets.tamu.edu

and reliable design tool

n the basis of string test

irection on the train model criteria, with specialinertias


tep by step procedure to carry out the high frequencyto have a common base

to effectivelydynamic behaviour and reduce the risk

in operation.

The three aforementioned steps provide a sound method to

Mirko Libraschi is currentlya Senior Engineer of theAdvanced Technology

, for GE Oil &Gas Nuovo Pignone, in

He isto define and

execute new technology programs.leads the technology

synergies and integration across GE and, to improve

technology edge of Oil & Gas products.


INTRODUCTIONA key factor to delivery first class products in the turbo-

machinery application is the capability to define theoptimum shaft line architecture for the required duty, in anintegrated system environment.

The single pieces of rotating equipment can exhibitsatisfactory rotor-dynamic behavior during the FactoryAcceptance Test (FAT), when in a standalone configuration,but this cannot always be considered representative to thereal operating conditions in the site service.

In particular for the gearboxes, the mechanical runningtest at the manufacturer’s workshop, as required by theAPI613, is able to capture only the macroscopic nonconformities and their basic rotor-dynamic behavior. In fact,being the gearbox a load dependent piece of the rotatingequipment, its dynamic behavior is heavily affected by thebalance between the internal forces (shafts weight andtransmitted torque) and the external forces applied to theshafts. At the gear manufacturer’s workshop the typicalmaximum applicable load is roughly 800kW, so for the multimegawatt machines the applied loads are nowhere nearsufficient to replicate the actual operating conditions in thejournal bearings or the tooth contact. Moreover the onlyexternal forces applied to the gearbox during the FAT are theoverhung weights of the job couplings moment simulators.

Much more significant is the contribution that the stringtest can provide in understanding the gear behavior at siteconfiguration when operating at full speed and full load.

The material presented in this paper is based on theoutcomes of a complete unit string test carried out for aMethane LNG project, here after identified as the case “C”,and their correlation with the associated rotor-dynamicanalytical studies. The intention is also to present the mostrecent experience obtained by authors in the area of gearsuper-synchronous lateral vibration, observed in turbo-compressor trains. The results will give wide and deepunderstanding of the subject.

Case “C” project overviewThe project is one of the latest Australian mega-projects

to liquefy the natural gas (LNG), which includes theextraction of the coal seam gas, the gas transmissionpipeline and a the LNG Facility composed by the trainsPropane, Ethylene and Methane (the arrangement ofMethane train is shown in Figure 1).

Case “C” string test arrangement and executionThe Methane train package was erected on a dedicated

test bench at the manufacturer plant. The installationincluded all the auxiliaries, base-frame and structures to beused in operation at site. In the previous individual tests eachof the sub-components has been validated by the FactoryAcceptance Test at the manufacturer’s works, in accordanceto the API Standards.

The purpose of the string test was to demonstrate themechanical integrity and efficiency of the integrated shaft-line and the aerodynamic stability of the compressors, in thespecified operating conditions, as well as to validate therotor-dynamic performances of the rotating equipment.

Summary of the tests:a) Full Speed, Full Load, Full Pressure complete unit test

(the compressors performance curves have beenexplored during the test run) – a torquemeter installedon load coupling measured the driver rated power;

b) Lube Oil Temperature Variation test from 50°C to60°C.

Figure 1 – Methane train arrangement

MOTIVATION FOR STUDY AND APPROACHMoved by the lessons learnt during the full speed full

load test of the case “C”, the paper collects also theexperience of the following cases, which are listed in theTable 1, in a chronological order.

In all these cases the turbo-machinery train wasequipped with an API613 speed increasing gearbox, doublehelix and horizontal offset, tilting pad journal bearings on theHSS and thrust bearing on the LSS. The gearboxes aredefined as high energy gears, due to the combination ofpitch line velocity and transmitted torque. The powertransmission was realized through the flexible couplings,diaphragm and disc types.

Table 1 - Case Studies

Train

Composition

Rated

Power

(kW)

HSS

Speed

Range

HSS

bearings

Speed

RatioPLV (m/s) L/D

Case "A" GT-GB-CC-CC 33,50010,829 rpm

70-105%TPJ 1.78 184 1.72

Case "B" GT-GB-CC 23,50010,617 rpm

70-105%TPJ 1.63 173 1.59

Case "C" GT-GB-CC-CC-CC 36,6706,068 rpm

85-105%TPJ 1.69 138 1.44

Case "D" GT-GB-CC 35,00010,981 rpm

70-105%TPJ 2.35 174 1.95

Case "E" GT-GB-CC 32,5619,281 rpm

70-105%TPJ 1.52 171 1.58

Case "F" GT-GB-CC-CC-CC 48,2005,940 rpm

85-105%TPJ 1.65 143 1.64

GT GB CCCC CC

THET

precedent tocases available in literatureeach caseidentification

The string test observations, relative to the cases“F”, are reportedand validate theof system modelling and results acceptabilityit can be noted that allusing the new proposed method, andfull load string testsvibration issuecalculation

Case “A”The g

when45÷50µm pcomponentat 1,262

CaseThe super

pinion shaft overhungwith a poor damping capability

THE STATE OF ARTThis section

precedent to the case “C”cases available in literatureeach case is:identification – corrective actions

string test observations, relative to the cases“F”, are reported as part of the conclusionand validate the new criteria proposed bof system modelling and results acceptabilityit can be noted that allusing the new proposed method, andfull load string testsvibration issues, confirmcalculations.

Case “A” - Problem statementThe gearbox vibration on NDE pinion bearing increases

when the power45÷50µm p-p @ 10component is the 7

262 Hz, as shown in

Figure 2 -

Case “A” - Phenomenon identificationThe super-synchronous

pinion shaft overhungwith a poor damping capability

STATE OF ARTprovides a summary of

the case “C” (cases “A” and “B”)cases available in literature. T

is: problem statementcorrective actions

string test observations, relative to the casesas part of the conclusionnew criteria proposed b

of system modelling and results acceptabilityit can be noted that all the three casesusing the new proposed method, andfull load string tests, successfully completed without any

confirmed the prediction of

Problem statementearbox vibration on NDE pinion bearing increasespower exceeds 18MW @ 100% speed (reached

p @ 10,830 rpm and 23MW). The main vibrationthe 7X speed harmonic, observed 17

s shown in Figure

- Case “A” vibration Waterfall HSS NDE

henomenon identificationsynchronous lateral

pinion shaft overhung lateral natural mode at 75with a poor damping capability


a summary of(cases “A” and “B”)

. The presentationproblem statement

corrective actions.

string test observations, relative to the casesas part of the conclusion in order to supportnew criteria proposed by this paper in terms

of system modelling and results acceptabilitythree cases have been analyz

using the new proposed method, and the outcomes ofsuccessfully completed without any

he prediction of

earbox vibration on NDE pinion bearing increases18MW @ 100% speed (reached

rpm and 23MW). The main vibrationspeed harmonic, observed 17

Figure 2.

Case “A” vibration Waterfall HSS NDE

henomenon identificationlateral analysis

lateral natural mode at 75with a poor damping capability, LogDec 0.24


a summary of the experience(cases “A” and “B”), as well as the

presentation format– phenomenon

string test observations, relative to the cases “D”, “E” andin order to support

y this paper in termsof system modelling and results acceptability. For reference

have been analyzthe outcomes of

successfully completed without anyhe prediction of the theoretical


rpm and 23MW). The main vibrationspeed harmonic, observed 17.5µm p

Case “A” vibration Waterfall HSS NDE

analysis confirmedlateral natural mode at 75,117 cpm,

LogDec 0.24 (see Figure

7 x


experiences, as well as the

format forphenomenon

“D”, “E” andin order to support

y this paper in terms. For reference

have been analyzedthe outcomes of the

successfully completed without anytheoretical


rpm and 23MW). The main vibration5µm p-p

confirmed the117 cpm,

Figure 3).

Case “A”

typejournal bearings were TPJ type)bysystem damping at the frequencyThe estring test, confirmed theimprovements.

Case “B”

a certain combination of speed and load on the gearboxpinion shaft,maximum continuous speed (11synchronous vibrationexcited frequencyspeed harmonicsynchronous vibrationFigure

Case “B”

between the observed

x Rev


Figure 3

Case “A” - Corrective actionsInstallation of fixed profile journal bearing

type, with pressure damjournal bearings were TPJ type)by the calculation,system damping at the frequencyThe experimental outcomes, observed during thestring test, confirmed theimprovements.

Case “B” - Problem staAn high vibration was observed during the string test at

a certain combination of speed and load on the gearboxpinion shaft, specificallymaximum continuous speed (11synchronous vibrationexcited frequencyspeed harmonicsynchronous vibrationFigure 4).

Figure

Case “B” - Phenomenon identificationThe calculation


Pinion shaftNDE side


3 - Case “A” GB HSS

orrective actionsInstallation of fixed profile journal bearing

pressure dam onjournal bearings were TPJ type)

calculation, whichsystem damping at the frequency

xperimental outcomes, observed during thestring test, confirmed theimprovements.

Problem statementigh vibration was observed during the string test at

a certain combination of speed and load on the gearboxspecifically at the no

maximum continuous speed (11synchronous vibration is activated at roughly 14MW, theexcited frequency is ~1,300Hz, corresponding to the 7speed harmonic. At lower shaftsynchronous vibration is detected at

Figure 4 - Case “B” vibration Waterfall HSS NDE

Phenomenon identificationalculations again



Case “A” GB HSS overhung mode shape

Installation of fixed profile journal bearingon gear pinion shaft

journal bearings were TPJ type); this solutionhighlighted an increase of

system damping at the frequency of interestxperimental outcomes, observed during the

string test, confirmed the expected

tementigh vibration was observed during the string test at

a certain combination of speed and load on the gearboxat the non-drive end side. At the

maximum continuous speed (11,157 rpm) the superactivated at roughly 14MW, the

300Hz, corresponding to the 7shaft rotational speed th

s detected at 8X speed harmonic

Case “B” vibration Waterfall HSS NDE

Phenomenon identificationagain confirmed

between the observed super-synchronous vibration

Pinion shaftDE


overhung mode shape

Installation of fixed profile journal bearings, offset halvesgear pinion shaft (the original

; this solution was validatedhighlighted an increase of

of interest.xperimental outcomes, observed during the full load

expected rotor-dynamic

igh vibration was observed during the string test ata certain combination of speed and load on the gearbox

drive end side. At the157 rpm) the super

activated at roughly 14MW, the300Hz, corresponding to the 7

rotational speed the superspeed harmonic

Case “B” vibration Waterfall HSS NDE

onfirmed the correlationsynchronous vibration

Pinion shaftDE side


, offset halvesoriginal

validatedhighlighted an increase of the

full loaddynamic

igh vibration was observed during the string test ata certain combination of speed and load on the gearbox

drive end side. At the157 rpm) the super-

activated at roughly 14MW, the300Hz, corresponding to the 7X

e super-speed harmonic (see

the correlationsynchronous vibration

7 x Rev

frequencyfrequencyhighlightLogDec 0.0044

Case “Special

with pressure dam,gear high speed shaft (These bearings have been optimized to increase thedamping; moreover the position of the NDE bearing wasshifted toward the NDE side by 13 mmin the section

The sload conditions, demonstratedperformance

Cases available in literatureMemmott

compressor trains, a gear pinion shaftrequired to solve the superobserved duringtrains were driven by a project gas turbine and one by ashop steam turbine.rangedthe gear design wasspeedbearings on the high

The frequency of concern wasshaftload conditionwith the shaftthree cases10,780 rpmMemmottremovingtwo pinions were modified by adding weight to the noendaforementionedexcitation

frequency and the pinion shaft overhung lateral naturalfrequency. In thishighlights a very poor system dampingLogDec 0.0044 (see

Figure 5 - Case “B”

Case “B” - Corrective actionsSpecial fixed profile journal bearings, offset halves type,

with pressure dam,gear high speed shaft (These bearings have been optimized to increase thedamping; moreover the position of the NDE bearing wasshifted toward the NDE side by 13 mmin the section with

The string test obsload conditions, demonstratedperformances obtained with the

Cases available in literatureMemmott [1]

compressor trains, a gear pinion shaftrequired to solve the superobserved duringtrains were driven by a project gas turbine and one by ashop steam turbine.ranged from 16.18the gear design wasspeed ratio rangbearings on the high

The frequency of concern wasshaft running speed (8load condition. The superwith the shaft fourththree cases the speed

780 rpm – 11,608 rpmMemmott [1] states that tremoving weight from the notwo pinions were modified by adding weight to the no

side. The modifications aimedaforementionedexcitation range with the 8


and the pinion shaft overhung lateral naturalthis case the analytical calculation

poor system dampingsee Figure 5).

Case “B” GB HSS

Corrective actionsfixed profile journal bearings, offset halves type,

with pressure dam, have been designed and installed on thegear high speed shaft (the originalThese bearings have been optimized to increase thedamping; moreover the position of the NDE bearing wasshifted toward the NDE side by 13 mm

with major shaft motion.tring test observations, at the

load conditions, demonstrateds obtained with the

Cases available in literature[1] details that in

compressor trains, a gear pinion shaftrequired to solve the super-observed during the full speedtrains were driven by a project gas turbine and one by ashop steam turbine. The power to drive the compressor

18 MW to 22.8the gear design was a double helix, single stage, with a

ratio ranging from 2.14 to 2.44, and tilting padbearings on the high speed shaft.

The frequency of concern wasunning speed (8XRev),

. The super-synchronous frequency coincidedfourth lateralspeed of gear pinion shaft608 rpm – 12,304

states that the first pinion was modified byweight from the non

two pinions were modified by adding weight to the no. The modifications aimed

lateral natural frequency out of thewith the 8X speed


and the pinion shaft overhung lateral naturalcase the analytical calculation

poor system damping in the original design

GB HSS overhung mode shape

fixed profile journal bearings, offset halves type,have been designed and installed on the

original bearing wereThese bearings have been optimized to increase thedamping; moreover the position of the NDE bearing wasshifted toward the NDE side by 13 mm to locate

major shaft motion.ervations, at the various

load conditions, demonstrated agains obtained with the corrective actions.

details that in threecompressor trains, a gear pinion shaft modification was

-synchronous vibration issuefull speed - full load string test

trains were driven by a project gas turbine and one by aThe power to drive the compressor

84 MW; in the three instances,double helix, single stage, with a

from 2.14 to 2.44, and tilting padshaft.

The frequency of concern was eightRev), and it was observed only at

synchronous frequency coincidedlateral natural frequency (

gear pinion shaft304 rpm).

he first pinion was modified byn-drive end side,

two pinions were modified by adding weight to the no. The modifications aimed

lateral natural frequency out of thespeed harmonic

Pinion shaftDE


and the pinion shaft overhung lateral naturalcase the analytical calculation

in the original design

overhung mode shape


bearing were TPJ typeThese bearings have been optimized to increase thedamping; moreover the position of the NDE bearing was

to locate the bearing

various speed andagain the improved

corrective actions.

three separate turbomodification was

synchronous vibration issuefull load string tests. Two


the three instances,double helix, single stage, with a

from 2.14 to 2.44, and tilting pad

times the pinionit was observed only at

synchronous frequency coincidednatural frequency (for these

was respectively:

he first pinion was modified byside, and the other

two pinions were modified by adding weight to the non-drive. The modifications aimed to move the

lateral natural frequency out of theharmonic.

Pinion shaftDE side


and the pinion shaft overhung lateral naturalcase the analytical calculation also

in the original design,


type).These bearings have been optimized to increase thedamping; moreover the position of the NDE bearing was

the bearing

speed andimproved

turbo-modification was

synchronous vibration issues. Two


the three instances,double helix, single stage, with a

from 2.14 to 2.44, and tilting pad

the pinionit was observed only at

synchronous frequency coincidedfor these

respectively:

he first pinion was modified byand the other

driveto move the

lateral natural frequency out of the

CASE “C”

superthe gear pinion shaft NDE side; the vibwas

bywasAt the time frame highlighted by the red circle (excited frequencyMW aexcitation mechanism is realized with theharmonic.

Thespeed and load, and showed a full repeatability in the loaddependence


CASE “C” PROBLEM STATEMENTDuring the internal FSFL

super-synchronous vibration componentthe gear pinion shaft NDE side; the vibwas also captured by the gear casing accelerometers.

Figure 6 showsby a displacementwas observed along the “X” direction, but omitted for brevityAt the time frame highlighted by the red circle (excited frequencyMW and a rotor speedexcitation mechanism is realized with theharmonic.

Figure 6 - Trend and Waterfall HSS NDE “Y”

The vibration became prevalent at a specific combination ofspeed and load, and showed a full repeatability in the loaddependence:


PROBLEM STATEMENTDuring the internal FSFL

synchronous vibration componentthe gear pinion shaft NDE side; the vib

captured by the gear casing accelerometers.

6 shows the vibration trend and spectra recordeda displacement sensor HSS NDE “Y”

along the “X” direction, but omitted for brevityAt the time frame highlighted by the red circle (excited frequency is ~955 Hz,

rotor speed ofexcitation mechanism is realized with the

Trend and Waterfall HSS NDE “Y”

vibration became prevalent at a specific combination ofspeed and load, and showed a full repeatability in the load


PROBLEM STATEMENTDuring the internal FSFL test of the

synchronous vibration componentthe gear pinion shaft NDE side; the vibration phenomenon

captured by the gear casing accelerometers.

the vibration trend and spectra recordedHSS NDE “Y”. A similar vi

along the “X” direction, but omitted for brevityAt the time frame highlighted by the red circle (

~955 Hz, with a transmitted loadof 5,170 rpm.

excitation mechanism is realized with the




the Methane trainsynchronous vibration component was observed on

ration phenomenoncaptured by the gear casing accelerometers.

the vibration trend and spectra recorded. A similar vibration

along the “X” direction, but omitted for brevityAt the time frame highlighted by the red circle (Figure

transmitted load. Consequently, the

excitation mechanism is realized with the 11X

Trend and Waterfall HSS NDE “Y” – 5,170 rpm



train, aobserved on

ration phenomenoncaptured by the gear casing accelerometers.

the vibration trend and spectra recordedbration

along the “X” direction, but omitted for brevity.igure 6), the

of 19.2Consequently, the

speed

rpm


- At the speed where this phenomenon occurred, thevibration amplitudefixed the operating speedtorquesynchronous

- The lbehaviorat the MCS, the super24With the lube oil inlet temperature at 60°Ccomponent persisted up to the full load condition.

- Variation in the lube oil flow and pressure influencedthe amplitude of the super

The5,776excitwas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,in accordance to the relevant mode shape.

At the speed where this phenomenon occurred, thevibration amplitudefixed the operating speedtorque, an increase in the amplitude of supersynchronous vibration responseThe lube oil inlet temperaturebehavior. With the lube oil inlet temperature at 50°C, andat the MCS, the super24-25 MW, andWith the lube oil inlet temperature at 60°Ccomponent persisted up to the full load condition.Variation in the lube oil flow and pressure influencedthe amplitude of the super

The Figure 7 depicts76 rpm and 23

excites the ~965 Hz. In both cases the observed frequencywas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,in accordance to the relevant mode shape.

Figure 7 - Trend and Waterfall HSS NDE “Y”

At the speed where this phenomenon occurred, thevibration amplitude increasedfixed the operating speed and increasing the transmitted

, an increase in the amplitude of supervibration response

ube oil inlet temperatureith the lube oil inlet temperature at 50°C, and

at the MCS, the super-synchronous vibration appeared at25 MW, and later disappear

With the lube oil inlet temperature at 60°Ccomponent persisted up to the full load condition.Variation in the lube oil flow and pressure influencedthe amplitude of the super-

7 depicts the superrpm and 23.9 MW. In this

the ~965 Hz. In both cases the observed frequencywas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,in accordance to the relevant mode shape.



At the speed where this phenomenon occurred, theincreased with the load

and increasing the transmitted, an increase in the amplitude of super

vibration response occurredube oil inlet temperature did affect the vibration

ith the lube oil inlet temperature at 50°C, andsynchronous vibration appeared atdisappeared at full load

With the lube oil inlet temperature at 60°Ccomponent persisted up to the full load condition.Variation in the lube oil flow and pressure influenced

-synchronous shaft vibration

super-synchronousn this case the 10X

the ~965 Hz. In both cases the observed frequencywas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,in accordance to the relevant mode shape.



At the speed where this phenomenon occurred, thewith the load. Keeping

and increasing the transmitted, an increase in the amplitude of super

occurred.affect the vibration

ith the lube oil inlet temperature at 50°C, andsynchronous vibration appeared at

at full load operationWith the lube oil inlet temperature at 60°C, the vibrationcomponent persisted up to the full load condition.Variation in the lube oil flow and pressure influenced

synchronous shaft vibration

synchronous vibrationX speed harmonic

the ~965 Hz. In both cases the observed frequencywas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,

Trend and Waterfall HSS NDE “Y” – 5,776 rpm


At the speed where this phenomenon occurred, theeeping

and increasing the transmitted, an increase in the amplitude of super-

affect the vibrationith the lube oil inlet temperature at 50°C, and

synchronous vibration appeared atoperation.

the vibration

Variation in the lube oil flow and pressure influenced littlesynchronous shaft vibration.

vibration atspeed harmonic

the ~965 Hz. In both cases the observed frequencywas recognized as the gear pinion shaft fourth lateral mode;the phenomenon mainly involved the pinion shaft NDE side,

threshold (51 µm pexceededtherefore it jeopardizvibration contributor was the component at ~950÷965Hz.The observed vibration frequency slightly varspeed and load conditionthese parametersthe journal bearing

CASE “C”

required to identify the following:---

synchronous phenomenon is well understoodTherotationalThe excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one ormore gear rotationalcompressor operating speed range. These excitation speedsare identiffrequency by the relevant shaft rotation9X, 10X and 11X.

is affected by the uncertainty due to theresolution:

In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhungmodethese three speedsrange

mesh, and this can be demonstratedvibration spectrum captured during thegearbox manufacturerduring this test there wereapplied in the string test arrangement, but the spectrumclearly showcostring test.


The overall vibration was always well within the alarmthreshold (51 µm pexceeded the string acceptance criteritherefore it jeopardizvibration contributor was the component at ~950÷965Hz.The observed vibration frequency slightly varspeed and load conditionthese parametersthe journal bearing

CASE “C” RCATo establish

required to identify the following:Excitation MechanismExcitation SourceExcitation Function

The excitation mechanismsynchronous phenomenon is well understood

he pinion shaft fourth lateral mode is excited by the gearrotational speedThe excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one ormore gear rotationalcompressor operating speed range. These excitation speedsare identified by dividing the pinion 4frequency by the relevant shaft rotation9X, 10X and 11X.

Inevitably the exact calculation of the excitation speedsis affected by the uncertainty due to theresolution:

In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhungmode, based onthese three speedsrange (5,158÷6

Most likely themesh, and this can be demonstratedvibration spectrum captured during thegearbox manufacturerduring this test there wereapplied in the string test arrangement, but the spectrumclearly shows severalcomponents were to bestring test.

Operating speed (rpm)

Speed harmonic

Observed Frequency

Excitation speed (rpm)


he overall vibration was always well within the alarmthreshold (51 µm p-p), however under

the string acceptance criteritherefore it jeopardized the pervibration contributor was the component at ~950÷965Hz.The observed vibration frequency slightly varspeed and load conditions, tthese parameters (transmitted power and speed)the journal bearings force coefficients.

establish the root causerequired to identify the following:

Excitation Mechanism = relation betweenExcitation Source = location of excitationExcitation Function = deviation that produce

excitation mechanismsynchronous phenomenon is well understood

pinion shaft fourth lateral mode is excited by the gearspeed harmonics.

The excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one ormore gear rotational speedcompressor operating speed range. These excitation speeds

ied by dividing the pinion 4frequency by the relevant shaft rotation9X, 10X and 11X.

nevitably the exact calculation of the excitation speedsis affected by the uncertainty due to the

In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhung

on the energy available into the systemthese three speeds are in the

÷6,371 rpm).

Most likely the excitation sourcemesh, and this can be demonstratedvibration spectrum captured during thegearbox manufacturer ’s workshopduring this test there were noapplied in the string test arrangement, but the spectrum

s several speed harmonics componentsmponents were to be observed

Operating speed (rpm)

Speed harmonic

Observed Frequency

Excitation speed (rpm)


he overall vibration was always well within the alarmhowever under

the string acceptance criterionthe performance test

vibration contributor was the component at ~950÷965Hz.The observed vibration frequency slightly var

s, this was due to the effects that(transmitted power and speed)

force coefficients.

the root cause of therequired to identify the following:

relation between cause= location of excitation= deviation that produce

excitation mechanism that results insynchronous phenomenon is well understood

pinion shaft fourth lateral mode is excited by the gearharmonics.

The excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one or

speed harmonics that occur within thecompressor operating speed range. These excitation speeds

ied by dividing the pinion 4frequency by the relevant shaft rotation

nevitably the exact calculation of the excitation speedsis affected by the uncertainty due to the


the energy available into the systemin the compressors

excitation source ismesh, and this can be demonstratedvibration spectrum captured during the gear

workshop (seeno external forces similar to those

applied in the string test arrangement, but the spectrumspeed harmonics components

observed later

MCS

6,371

9X

6,333


he overall vibration was always well within the alarmhowever under some condition

on of 35 µm p-formance test. The main

vibration contributor was the component at ~950÷965Hz.The observed vibration frequency slightly varied versus the

due to the effects that(transmitted power and speed) have on

the gear vibration

cause and effects= location of excitation origin;= deviation that produces the excitation;

results in the supersynchronous phenomenon is well understood.

pinion shaft fourth lateral mode is excited by the gear


harmonics that occur within thecompressor operating speed range. These excitation speeds

ied by dividing the pinion 4th lateral naturalfrequency by the relevant shaft rotation speed harmonics,

nevitably the exact calculation of the excitation speedsis affected by the uncertainty due to the acquisition system


the energy available into the systemcompressors operative speed

located at the gearmesh, and this can be demonstrated by observing the

gear FSNL test at thesee Figure 8). I

external forces similar to thoseapplied in the string test arrangement, but the spectrum

speed harmonics components. Theselater during the full load

100%

6,068

10X

5,700

950Hz


he overall vibration was always well within the alarmsome conditions it

-p, andhe main

vibration contributor was the component at ~950÷965Hz.versus the

due to the effects thathave on

vibration is

s;

the excitation;

the super-

pinion shaft fourth lateral mode is excited by the gear


harmonics that occur within thecompressor operating speed range. These excitation speeds

lateral naturalharmonics,

nevitably the exact calculation of the excitation speedsacquisition system


the energy available into the system. Alloperative speed

located at the gearobserving the

FSNL test at theIn fact,

external forces similar to thoseapplied in the string test arrangement, but the spectrum

. Thesefull load

MOS

5,158

11X

5,182

This observationlocateddependwith

Unfortunately, themeshingidentifiedand are heavily influenced by many factors- Total helix deviation;- Total profile deviation;- Tooth- Total pitch deviation;- Cumulative pitch error;

The transmission errors are due to the difference betweenthe actualwould occupy if the gear drive were perfectly conjugatedIn general the gear transmission errors areexcitationas ageared system

Ifquantified,shaftsdangerous superproposed a waymodes, providing thecritical area, wheresynchronous rotorwhereexpected.

Thelessons learntpredicase “C”carried out by the gearbox manufacturer overestimatsystem damping (LogDec predicteddue to the incorrect rotormain contributi

Figure 8 - Vibration Spectrum HSS NDE “Y” @ 5

This observationlocated within the gearbox anddepends on the transmitted torque, i

the teeth meshingUnfortunately, the

meshing, due to the transmission errors,identified. In fact,and are heavily influenced by many factors

Total helix deviation;Total profile deviation;Tooth-to tooth pitch deviation;Total pitch deviation;Cumulative pitch error;

The transmission errors are due to the difference betweenthe actual position of the output gear and the position itwould occupy if the gear drive were perfectly conjugatedn general the gear transmission errors are

excitation functiona multiple of running spe

geared system.

If the excitation functionquantified, it cannot beshafts 4th lateraldangerous super-proposed a waymodes, providing thecritical area, wheresynchronous rotorwhere no superexpected.

The aforementionedlessons learnt (seepredict the critical lateral behaviocase “C”. This iscarried out by the gearbox manufacturer overestimatsystem damping (

Dec predicteddue to the incorrect rotormain contributing error

Vibration Spectrum HSS NDE “Y” @ 5

This observation indicates that the excitation sourcethe gearbox and

transmitted torque, ithe teeth meshing mechanism

Unfortunately, the excitation forces originated into thedue to the transmission errors,

, the dynamics of the mesh are nonand are heavily influenced by many factors

Total helix deviation;Total profile deviation;

to tooth pitch deviation;Total pitch deviation;Cumulative pitch error;

The transmission errors are due to the difference betweenposition of the output gear and the position it

would occupy if the gear drive were perfectly conjugatedn general the gear transmission errors are

function for high frequencymultiple of running speed are very likely to occur

the excitation functionit cannot be removed,

mode shall-synchronous vibration

proposed a way to assess the gear shafts high frequencymodes, providing the LogDeccritical area, where it is required to carry out a supersynchronous rotor response analysis, or the confidence area,

no super-synchronous vibration components are

mentioned criteria(see cases “A” and “B”

ct the critical lateral behavio. This is because the super

carried out by the gearbox manufacturer overestimatsystem damping (the actual LogDec

Dec predicted in the original analysis)due to the incorrect rotor-bearings model

ng error arising


Vibration Spectrum HSS NDE “Y” @ 5

that the excitation sourcethe gearbox and as the vibration response

transmitted torque, it shows a relationshipmechanism.excitation forces originated into the

due to the transmission errors, arethe dynamics of the mesh are non

and are heavily influenced by many factors,

to tooth pitch deviation;


would occupy if the gear drive were perfectly conjugatedn general the gear transmission errors are

high frequency vibrationed are very likely to occur

the excitation function is not wellremoved, and therefore

be properly dampedsynchronous vibration. In the pastto assess the gear shafts high frequency

ec threshold that defines theit is required to carry out a super

response analysis, or the confidence area,synchronous vibration components are

criteria, basedcases “A” and “B” in table 1

ct the critical lateral behavior of the gearbecause the super-synchronous analysis

carried out by the gearbox manufacturer overestimatLogDec was

in the original analysis). The differencebearings model;

arising from the use of


Vibration Spectrum HSS NDE “Y” @ 5,800 rpm

that the excitation sourcethe vibration response

shows a relationship

excitation forces originated into theare difficult to

the dynamics of the mesh are non-linear, namely:


would occupy if the gear drive were perfectly conjugatedn general the gear transmission errors are the most likely

vibration. Excitationsed are very likely to occur

understood andand therefore the gear

be properly damped to avoidn the past the OEM

to assess the gear shafts high frequencythreshold that defines the

it is required to carry out a superresponse analysis, or the confidence area,synchronous vibration components are

, based on the previoustable 1), failed togear pinion shaft

synchronous analysiscarried out by the gearbox manufacturer overestimated

was smaller than theThe difference; in particular

use of synchronous


that the excitation source isthe vibration response

shows a relationship

excitation forces originated into thedifficult to be

linear


would occupy if the gear drive were perfectly conjugated.the most likely

xcitationsin a

understood andthe gearto avoidthe OEM

to assess the gear shafts high frequencythreshold that defines the

it is required to carry out a super-response analysis, or the confidence area,synchronous vibration components are

previous, failed to

pinion shaft,synchronous analysis

ed thesmaller than the

The difference wasin particular the

synchronous

bearing stiffness and dampingcases, at different bearings clearancethe

BASE LINE

as well asTimoshenko beammode synthesis analysissoftware

was tuned to match the first two freedetermined(the FEM is shown in

angle between two layers ofone of these having only mass propehaving mass and elastic


bearing stiffness and dampingcases, at different bearings clearancethe predicted LogDec

BASE LINE ANALYSISThe super-

as well as thoseTimoshenko beammode synthesis analysissoftware (the original pinion design is shown in Figure 9)

The Figurewas tuned to match the first two freedetermined bythe FEM is shown in

The tuning was made by adjusting the separation lineangle between two layers ofone of these having only mass propehaving mass and elastic

F


bearing stiffness and dampingcases, at different bearings clearance

LogDec was above 0.8)

ANALYSIS – ORIGINAL DESIGN-synchronous

those of the other cases,Timoshenko beams, with gyroscopic effectmode synthesis analysis using

original pinion design is shown in Figure 9)

Figure 9 – Original p

igure 10 shows thewas tuned to match the first two free

by a full FEM anathe FEM is shown in Figure 1

The tuning was made by adjusting the separation lineangle between two layers ofone of these having only mass propehaving mass and elastic prope

Figure 10 - Pinion shaft


bearing stiffness and damping coefficientscases, at different bearings clearances and load condition

above 0.8).

ORIGINAL DESIGNsynchronous study of pinion shaft

of the other cases, weregyroscopic effect

using a commercial rotororiginal pinion design is shown in Figure 9)

Original pinion design

he structural beamwas tuned to match the first two free-free shaft modes

a full FEM analysis using 3D solid elementsFigure 11).

The tuning was made by adjusting the separation lineangle between two layers of the same element (gear body),one of these having only mass properties and the other one

properties.

Pinion shaft beam


coefficients (for all the studiedand load condition

ORIGINAL DESIGNpinion shaft, case “C”ere carried out using

gyroscopic effects in a componenta commercial rotor-dynamics

original pinion design is shown in Figure 9)

design

structural beam modelfree shaft modes

lysis using 3D solid elements

The tuning was made by adjusting the separation linesame element (gear body),

ties and the other one

beam model


(for all the studiedand load conditions,

case “C”,carried out using

in a componentdynamics

original pinion design is shown in Figure 9).

model whichfree shaft modes as

lysis using 3D solid elements

The tuning was made by adjusting the separation linesame element (gear body),

ties and the other one

Thegearbox andsystemwhichsynchronouscouplingidentifiedFigur

Tcoefficienteffects ofalwaysobserved the impact ofdeformationtendbearingpreload (mechanical effect).

The rotoreigencomponent model synthesis

Figure 1

The modelinggearbox and thesystem and fully accounting forwhich play a fundamental role into the gearsynchronous lateral modecoupling transverse and polaridentified through a

re 12).

Figure 1

To establish a sensitivitycoefficients, theseeffects of the pad thermoalways considering theobserved the impact ofdeformation on the bearing direct stiffnesstends to increasebearing clearancepreload (mechanical effect).

The rotor-dynamic codeeigenvalues ofcomponent model synthesis

Figure 11 - Pinion shaft FEM model

ing of the flexiblethe centrifugal compressor

and fully accounting forplay a fundamental role into the gear

lateral moderansverse and polar

through an ANSYS model

Figure 12 – Coupling FEM model

a sensitivity on, these were calculated

pad thermo-mechanical deformationconsidering the pivot flexibility

observed the impact of theon the bearing direct stiffness

to increase the direct stiffness by decreasingclearance (thermal effect)

preload (mechanical effect).dynamic code

values of the rotor-bearing system,component model synthesis (CMS)


Pinion shaft FEM model

flexible couplingcentrifugal compressor was added to the

and fully accounting for the gyroscopic effectsplay a fundamental role into the gear

lateral mode frequenciesransverse and polar moment of

model of the

Coupling FEM model

on the tilting pad bearing forcecalculated with and without

mechanical deformationpivot flexibility. In Figure 13

the pad thermoon the bearing direct stiffness. T

direct stiffness by decreasing(thermal effect) and by

dynamic code calculatesbearing system,

(CMS). Four degrees of freedom


Pinion shaft FEM model

coupling betweenwas added to the

gyroscopic effectsplay a fundamental role into the gear super

definition.moment of inertia were

of the component

Coupling FEM model

pad bearing forcewith and without

mechanical deformation, butFigure 13, it can be

ad thermo-mechanical. This deformation

direct stiffness by decreasingby increasing

calculates the complexbearing system, using

our degrees of freedom


between thewas added to the

gyroscopic effects,super-

Thewere(see

pad bearing forcewith and without the

, but, it can be

mechanicalhis deformation

direct stiffness by decreasing theing the

the complexusing the

our degrees of freedom

per node are considered (axial constrain)are obtained in the state space of the linearized system.

highlights the intersection between the system lateral criticalspeeds and the aforementionedwith

and LogDecconsidering the pad thermoLogDec decreases from 0.95 (Figure

Figure

Pinion shaft



The undamped critical speed map shown inhighlights the intersection between the system lateral criticalspeeds and the aforementioned

ith and w/o the

The figuresand LogDecconsidering the pad thermoLogDec decreases from 0.95 (

igure 16).

igure 15 –HSS

w/o pad def. effect

w/ pad def. effect

Pinion shaftDE side



Figure 13 - TPJ Direct Stiffness

The undamped critical speed map shown inhighlights the intersection between the system lateral criticalspeeds and the aforementioned

the pad deformation

Figure 14 - Original pinion

s 15 and 16 depict the rotor mode shapeand LogDec for the 4th

considering the pad thermoLogDec decreases from 0.95 (

HSS mode shape w/o

def. effect

pad def. effect



TPJ Direct Stiffness

The undamped critical speed map shown inhighlights the intersection between the system lateral criticalspeeds and the aforementioned bearing

pad deformation effect.

Original pinion U

15 and 16 depict the rotor mode shapelateral dumped mode. When

considering the pad thermo-mechanical deformation, theLogDec decreases from 0.95 (see Figure

w/o thermo-mechanical deformation


per node are considered (axial constrain). The eigenvaluesare obtained in the state space of the linearized system.

TPJ Direct Stiffness

The undamped critical speed map shown in Figure 14highlights the intersection between the system lateral critical

bearing direct stiffnesseffect.

UCS

15 and 16 depict the rotor mode shapelateral dumped mode. When

mechanical deformation, thesee Figure 15) to 0.58 (

mechanical deformation

Pinion shaftNDE

w/o pad def. effect

w/ pad def. effect


he eigenvaluesare obtained in the state space of the linearized system.

Figure 14,highlights the intersection between the system lateral critical

direct stiffnesses,

15 and 16 depict the rotor mode shape thelateral dumped mode. When

mechanical deformation, the15) to 0.58 (see



w/o pad def. effect

pad def. effect

Figure

damping determined by the bearings cross coupling stiffnesscoefficients also affects the system overall LogDecaforementioned coefficients represent the tangential forcesacting to the shaft as shown onpresented in

Figure 1

Thecarried out in an iterativecalculatThese coefficientsthe complex eigenvaluesasynchronous beariThis procedure is repeatedin theAs depicted in Figure 18, creducedfourreduced coefficientthe direct terms

Pinion shaftDE

igure 16 – HSS mode shape

In addition to thedamping determined by the bearings cross coupling stiffnesscoefficients also affects the system overall LogDecaforementioned coefficients represent the tangential forcesacting to the shaft as shown onpresented in the Figure 17.

Where C

Figure 17 – Tangential forces to shaft (stable/unstable condition)

The bearings acarried out in an iterativecalculating the coefficientsThese coefficientsthe complex eigenvaluesasynchronous beari

his procedure is repeatedin the resulting 4th

As depicted in Figure 18, creduced coefficient

times respect those obtained by usingreduced coefficientthe direct terms).

Pinion shaftDE side

mode shape with

In addition to the bearing direct stiffness, thedamping determined by the bearings cross coupling stiffnesscoefficients also affects the system overall LogDecaforementioned coefficients represent the tangential forcesacting to the shaft as shown on

Figure 17.

௧

Where Cnet=Cxx+Cyy

Tangential forces to shaft (stable/unstable condition)

a-synchronous coefficients calculationcarried out in an iterative process. T

coefficients at the frequency of interestThese coefficients are then successivelythe complex eigenvalues, and thereforeasynchronous bearing coefficients at the new frequency

his procedure is repeated untilth mode frequency.

As depicted in Figure 18, considering the supercoefficients, the cross coupling terms increase

times respect those obtained by usingreduced coefficients (while no


with thermo-mechanical deformation

bearing direct stiffness, thedamping determined by the bearings cross coupling stiffnesscoefficients also affects the system overall LogDecaforementioned coefficients represent the tangential forcesacting to the shaft as shown on the sch

௧

ήఆ

yy and knet=kxy


synchronous coefficients calculationprocess. The first step consist

at the frequency of interestsuccessively used toand therefore

ng coefficients at the new frequencyuntil there is a negligible variation

mode frequency.onsidering the supercross coupling terms increase

times respect those obtained by usingwhile no significant changes



bearing direct stiffness, the effectivedamping determined by the bearings cross coupling stiffnesscoefficients also affects the system overall LogDec.aforementioned coefficients represent the tangential forces

the schematic sketch

xy-kyx.


synchronous coefficients calculationhe first step consist

at the frequency of interestused to re-defin

and therefore to obtainng coefficients at the new frequency

negligible variation

onsidering the super-synchronouscross coupling terms increase

times respect those obtained by using the synchronouschanges result in

Pinion shaftNDE



effectivedamping determined by the bearings cross coupling stiffness

Theaforementioned coefficients represent the tangential forces

ematic sketch

(1)


synchronous coefficients calculation ishe first step consists of

at the frequency of interest.define

to obtain theng coefficients at the new frequency.

negligible variation

synchronouscross coupling terms increase by

the synchronousresult in

Moreover, wstiffnessdamping termsbetween krepresent this behaviour with adefined as

The WFR valuerepresents physically the padthecapacityincrease of the WFRthethe super0.21, and this leads the tilting pad bfixed geometry bearing, with a consequent increasing oftangential forces, and therefore(WFRNeverthelessto invert the scenario, providing special fethefrequencycoefficientsdependsthe geometrysynchronous

Usingpinion shaftrespectdownBased on the collected experience,considered inadequate to provide thedampingnot be evaluated as a selfLogDec <0.1), but as a forced excited modeexcitation originated into the gear mesh



Figure 1

Moreover, while the absolute valuestiffness increasedamping termsbetween knet and Crepresent this behaviour with adefined as:

The WFR valuerepresents physically the padthe oil film, and at high frequency the pad inertia reduces itscapacity to follow theincrease of the WFRthe system LogDecthe super-synchronous coefficients, the WFR increases up to0.21, and this leads the tilting pad bfixed geometry bearing, with a consequent increasing oftangential forces, and therefore(WFR≈0.5). Nevertheless, theto invert the scenario, providing special fethe WFR; and consequently tofrequency modifyingcoefficients, like independs on thethe geometrysynchronous frequency

sing the asynchronous coefficientspinion shaft 4th

respect to the case showndown to 0.18, as shown

ased on the collected experience,considered inadequate to provide thedamping. In factnot be evaluated as a selfLogDec <0.1), but as a forced excited modeexcitation originated into the gear mesh


18 - TPJ quadrature stiffness

hile the absolute valueincrease at the specified frequency, the direct

damping terms do not increasand Cnet keeps increasing. It

represent this behaviour with a

The WFR value, linked to the system effective damping,represents physically the pad

, and at high frequency the pad inertia reduces itsto follow the shaft vibration. This explain

increase of the WFR leads to asystem LogDec. In particular, considering

synchronous coefficients, the WFR increases up to0.21, and this leads the tilting pad bfixed geometry bearing, with a consequent increasing oftangential forces, and therefore

the fixed geometry bearings can be designedto invert the scenario, providing special fe

consequently tomodifying the direct, like in the cases ”A” and “B”. Of course,

on the bearing manufacturer capability totowards improve

frequency.

synchronous coefficientsth lateral mode decrease

the case shown ito 0.18, as shown in Figure 1

ased on the collected experience,considered inadequate to provide the

n fact, the gear pinion shaft 4not be evaluated as a selfLogDec <0.1), but as a forced excited modeexcitation originated into the gear mesh


quadrature stiffness vs shaft speed

hile the absolute valuesat the specified frequency, the direct

not increase, and therefore the ratiokeeps increasing. It

represent this behaviour with a whirl frequency ratio (WFR)

∙

, linked to the system effective damping,represents physically the pad ability to adapt its position to

, and at high frequency the pad inertia reduces itsshaft vibration. This explain

leads to a corresponding decreasen particular, considering

synchronous coefficients, the WFR increases up to0.21, and this leads the tilting pad bearing to behave like afixed geometry bearing, with a consequent increasing oftangential forces, and therefore of the system instability

fixed geometry bearings can be designedto invert the scenario, providing special fe

consequently to increase the stability at highdirect stiffnesscases ”A” and “B”. Of course,

bearing manufacturer capability toimproved damping at

synchronous coefficients the LogDec of gearlateral mode decrease

in Figure 16, the LogDec reducesn Figure 19.

ased on the collected experience, theconsidered inadequate to provide the

the gear pinion shaft 4not be evaluated as a self-excited mode (LogDec <0.1), but as a forced excited modeexcitation originated into the gear mesh.


vs shaft speed

of cross couplingat the specified frequency, the direct

and therefore the ratiokeeps increasing. It is possible to

whirl frequency ratio (WFR)

∙ఆ

, linked to the system effective damping,to adapt its position to

, and at high frequency the pad inertia reduces itsshaft vibration. This explains why an

corresponding decreasen particular, considering for the case “C”

synchronous coefficients, the WFR increases up toearing to behave like a

fixed geometry bearing, with a consequent increasing ofthe system instability

fixed geometry bearings can be designedto invert the scenario, providing special features to decrease

increase the stability at highstiffness (K) and damping (

cases ”A” and “B”. Of course,bearing manufacturer capability to optimize

damping at the

the LogDec of gearlateral mode decreases even more

the LogDec reduces

the LogDec 0.18considered inadequate to provide the required

the gear pinion shaft 4th eigenvalue, shallexcited mode (critical w

LogDec <0.1), but as a forced excited mode with an


of cross couplingat the specified frequency, the direct

and therefore the ratiois possible to

whirl frequency ratio (WFR)

(2)

, linked to the system effective damping,to adapt its position to

, and at high frequency the pad inertia reduces itswhy an

corresponding decrease offor the case “C”

synchronous coefficients, the WFR increases up toearing to behave like a

fixed geometry bearing, with a consequent increasing of thethe system instability

fixed geometry bearings can be designeddecrease

increase the stability at high) and damping (C)

cases ”A” and “B”. Of course, thisoptimize

the super-

the LogDec of geareven more. With

the LogDec reduces

0.18 isrequired modaleigenvalue, shall

critical whenwith an

Figure

Finally the vibration atfrequency dependsby its amplitude, andUnfortunately, due to the uncertainties on the excitationfunction, and therefore due to the difficulties to define itsamplitude versus tsuperout only on hypotheconsidered representative ofTheenergyamplitudedamping.

ORIGINAL DESIGNThe s

designconfirming thesynchronous bearing coefficients

Unfortunately the risk of superwas

Pinion shaftDE

Figure 19 – HSS

Finally the vibration atfrequency depends

its amplitude, andUnfortunately, due to the uncertainties on the excitationfunction, and therefore due to the difficulties to define itsamplitude versus tsuper-synchronous rotor response analysis can be carriedout only on hypotheconsidered representative ofThe ultimate postulatenergy arising fromamplitude to excite this mode due to its low level ofdamping.

ORIGINAL DESIGNThe string test observations

design are consistentconfirming the validity ofsynchronous bearing coefficients

Figure 20

Unfortunately the risk of supernot captured

Pinion shaftDE side

HSS mode shape with a

Finally the vibration atfrequency depends on the presence of the excitation force,

its amplitude, and by the system modal damping.Unfortunately, due to the uncertainties on the excitationfunction, and therefore due to the difficulties to define itsamplitude versus the gear teeth geometrical deviation

synchronous rotor response analysis can be carriedout only on hypothetical basis, and so it cannot beconsidered representative of the

postulate is thatfrom the gear meshing

to excite this mode due to its low level of

ORIGINAL DESIGN - EXPERIMENTAL RESULTtring test observations

consistent with the basevalidity of the

synchronous bearing coefficients

- Base-line full Waterfall

Unfortunately the risk of supernot captured during the gearbox design stage because

Observed super


with a-synchronous coefficients

Finally the vibration at the pinion shaft 4the presence of the excitation force,the system modal damping.

Unfortunately, due to the uncertainties on the excitationfunction, and therefore due to the difficulties to define its

he gear teeth geometrical deviationsynchronous rotor response analysis can be carried

basis, and so it cannot bethe actual system

that in case thegear meshing wa

to excite this mode due to its low level of

EXPERIMENTAL RESULTtring test observations for the case “C”

with the base-line predictionthe calculations

synchronous bearing coefficients are used.

line full Waterfall – HSS NDE “Y”

Unfortunately the risk of super-synchronous vibrationthe gearbox design stage because

Observed super-synchronous vibration


synchronous coefficients

pinion shaft 4th lateralthe presence of the excitation force,the system modal damping.


he gear teeth geometrical deviations,synchronous rotor response analysis can be carried

basis, and so it cannot besystem behaviour.the “C” the external

was sufficientto excite this mode due to its low level of modal

EXPERIMENTAL RESULTSfor the case “C” original

line predictions,calculations when the

HSS NDE “Y”

synchronous vibrationthe gearbox design stage because


synchronous vibration5µm p-p @ 970 Hz


synchronous coefficients

lateralthe presence of the excitation force,


s, thesynchronous rotor response analysis can be carried

basis, and so it cannot bebehaviour.the externalsufficient in

modal

original, thus

the a-

synchronous vibrationthe gearbox design stage because

the original pinion shaft 4erroneous LogDec values, which were in the area ofconfidence (i.e. too high and overThepinion shaft vibration behaviour. The observed supersynchronous componentthe predicted frequencywith the sameFigure 19)

superpinion shaft vibration above the string acceptance criteriasome conditions this compo

MODIFIED ROTOR ANALY

corrective actions needed to reduce the amplitudesupernovelbearing system is-

-

-

available in literaturanalyzed in order to define the optimum compromise toavoid the excitation mechanism (inspeed harmonics were known), or to increase the systemmodal damping. For each of these design changessensitivity analysiseffective parameters.

A summary of-

-

--

proposed by the bearing manufacturer, none of the caseswith modified bearings was able to providebeneficial results in terms of system modal damping.

Pinion shaftside

synchronous vibration970 Hz


the original pinion shaft 4erroneous LogDec values, which were in the area ofconfidence (i.e. too high and overThe Figure 20pinion shaft vibration behaviour. The observed supersynchronous componentthe predicted frequencywith the sameFigure 19).

As described in thesuper-synchronous vibration component brought the overallpinion shaft vibration above the string acceptance criteriasome conditions this compo

MODIFIED ROTOR ANALYThe new modeling criteria

corrective actions needed to reduce the amplitudesuper-synchronous vibrationnovel proposed method of analysis; in partibearing system is

The shaft beam modeloutcomes;The coupling componentsincluding themoment of inertiThe bearingcalculatedphenomenonlateral mode analysis and LogDecperformed through an iterative cycleupdating each time the asynchronous coefficientsdependingappropriate

According toavailable in literaturanalyzed in order to define the optimum compromise toavoid the excitation mechanism (inspeed harmonics were known), or to increase the systemmodal damping. For each of these design changessensitivity analysiseffective parameters.

summary of the casesBearing substitution with fixed profile and pressure damconfiguration.Bearing span change (move the NDE bearing closethe shaft major motion area)Bearing clearances and prePinion shaft NDE, mass increase/decrease

Due to the limited number ofproposed by the bearing manufacturer, none of the caseswith modified bearings was able to providebeneficial results in terms of system modal damping.


the original pinion shaft 4erroneous LogDec values, which were in the area ofconfidence (i.e. too high and over

shows the recordedpinion shaft vibration behaviour. The observed supersynchronous component isthe predicted frequency of thewith the same forward whirl

As described in the sectionsynchronous vibration component brought the overall

pinion shaft vibration above the string acceptance criteriasome conditions this compo

MODIFIED ROTOR ANALYSISnew modeling criteria

corrective actions needed to reduce the amplitudesynchronous vibrationproposed method of analysis; in parti

bearing system is modeled as described below:haft beam model

oupling componentsthe flexible element

nt of inertia are thoseearing’s damping and stiffness coefficients

calculated at the frequency ofphenomenon (asynchronous

mode analysis and LogDecperformed through an iterative cycleupdating each time the asynchronous coefficientsdepending on the new mode frequencyappropriate convergence

According to the past experienceavailable in literature, a series of gear design changes wereanalyzed in order to define the optimum compromise toavoid the excitation mechanism (inspeed harmonics were known), or to increase the systemmodal damping. For each of these design changessensitivity analysis was carried out, to identify the mosteffective parameters.

the cases studiedBearing substitution with fixed profile and pressure damconfiguration.Bearing span change (move the NDE bearing close

ft major motion area)Bearing clearances and prePinion shaft NDE, mass increase/decrease

Due to the limited number ofproposed by the bearing manufacturer, none of the caseswith modified bearings was able to providebeneficial results in terms of system modal damping.


the original pinion shaft 4th mode analysiserroneous LogDec values, which were in the area ofconfidence (i.e. too high and overly optimistic).

recorded spectra ofpinion shaft vibration behaviour. The observed super

970 Hz, roughly 1% lower thanthe pinion shaft 4

forward whirl (see the prediction shown in

section “problem statementsynchronous vibration component brought the overall

pinion shaft vibration above the string acceptance criteriasome conditions this component exceeded 20µm p

SISnew modeling criteria were adopted

corrective actions needed to reduce the amplitudesynchronous vibrations. These criteriaproposed method of analysis; in parti

modeled as described below:haft beam model is tuned according to

oupling components are modeled separately,flexible element; the polar and t

are those defined by FEM;damping and stiffness coefficients

at the frequency of(asynchronous coefficient

mode analysis and LogDecperformed through an iterative cycleupdating each time the asynchronous coefficients

the new mode frequencyconvergence is reached;

past experiencee, a series of gear design changes were

analyzed in order to define the optimum compromise toavoid the excitation mechanism (in thespeed harmonics were known), or to increase the systemmodal damping. For each of these design changes

carried out, to identify the most

studied follows:Bearing substitution with fixed profile and pressure dam

Bearing span change (move the NDE bearing closeft major motion area).

Bearing clearances and pre-load modificationPinion shaft NDE, mass increase/decrease

Due to the limited number of theproposed by the bearing manufacturer, none of the caseswith modified bearings was able to providebeneficial results in terms of system modal damping.


mode analysis providerroneous LogDec values, which were in the area of

mistic).spectra of the original

pinion shaft vibration behaviour. The observed super970 Hz, roughly 1% lower than

pinion shaft 4th lateral modeprediction shown in

problem statementsynchronous vibration component brought the overall

pinion shaft vibration above the string acceptance criterianent exceeded 20µm p-p).

were adopted to define thecorrective actions needed to reduce the amplitude

. These criteria are part of theproposed method of analysis; in particular the rotor

modeled as described below:according to the

modeled separately,olar and transversal

defined by FEM;damping and stiffness coefficients

at the frequency of the observedcoefficients); the overhung

mode analysis and LogDec definitionperformed through an iterative cycle of calculationupdating each time the asynchronous coefficients

the new mode frequency unt

past experiences, and the casese, a series of gear design changes were

analyzed in order to define the optimum compromise tothe case “C” the active

speed harmonics were known), or to increase the systemmodal damping. For each of these design changes


Bearing substitution with fixed profile and pressure dam

Bearing span change (move the NDE bearing close

load modification.Pinion shaft NDE, mass increase/decrease.

the design solutionsproposed by the bearing manufacturer, none of the caseswith modified bearings was able to provide the sufficientbeneficial results in terms of system modal damping.


rovidederroneous LogDec values, which were in the area of

originalpinion shaft vibration behaviour. The observed super-

970 Hz, roughly 1% lower thanlateral mode,

prediction shown in

problem statement”, thesynchronous vibration component brought the overall

pinion shaft vibration above the string acceptance criteria (in.

o define theof the

part of thecular the rotor-

the FEM

modeled separately,ransversal

damping and stiffness coefficients areobservedverhung

definition areof calculation,

updating each time the asynchronous coefficients,until an

, and the casese, a series of gear design changes were

analyzed in order to define the optimum compromise tocase “C” the active

speed harmonics were known), or to increase the systemmodal damping. For each of these design changes a


Bearing substitution with fixed profile and pressure dam

Bearing span change (move the NDE bearing closer to

design solutionsproposed by the bearing manufacturer, none of the cases

sufficient

Therefore the analysis focused onmodificationmass reduction,NDE sideFigure

With thebenefits

- Reducmode, incrthe excitation mechanismspeed harmonics, eventhe excitation withharmonics

- Changelocated far awayincrease its

Therefore the analysis focused onmodification. The solutionmass reduction, andNDE side of the pinionFigure 21 and the

Figure 21 - Modified pinion

Figure 2

ith the aforementioned corrective action, the expectedbenefits are:

Reduction ofmode, increasing the associated frequency and avoidthe excitation mechanismspeed harmonics, eventhe excitation withharmonics.Change the modallocated far awayincrease its damping

Therefore the analysis focused onThe solution finally adopted

and was realizedof the pinion shaft (see

the shaft model details in Figure 22

Modified pinion

Figure 22 - Modified pinion shaft

mentioned corrective action, the expected

tion of the modal mass participaeasing the associated frequency and avoid

the excitation mechanismspeed harmonics, even if itthe excitation with the 10X or with

modal shape,located far away from a nodal point,

damping capability.


Therefore the analysis focused on the pinion shaftfinally adopted relates torealized by drilling a bore on

see the shaft drawing details inshaft model details in Figure 22

Modified pinion shaft design –

Modified pinion shaft beam model


modal mass participaeasing the associated frequency and avoid

the excitation mechanism at the observed 9X and 11Xif it was not possible to

10X or with higher order

, with the bearingnodal point,

capability.


the pinion shaft designrelates to the shaft

drilling a bore onshaft drawing details in

shaft model details in Figure 22).

– NDE bored

beam model


modal mass participation to theeasing the associated frequency and avoid

the observed 9X and 11Xwas not possible to eliminate

higher order of speed

with the bearing center linenodal point, and therefore to

Modified shaftNDE bore

ModifiedNDE bore


designshaft

drilling a bore on theshaft drawing details in


the NDEeasing the associated frequency and avoiding

the observed 9X and 11Xeliminate

speed

center lineand therefore to

Modified Pinion Shaft

Figure 23mode frequencyresultyet included

In fact, tincreasing of the overhungkCPMdiagram

The Campbell diagram in Figure 24 is determined usingbearing coefficients evaluated atfrequency. Next step into the pinion shaft lateral study isdamped eigenvalue calculationbearing coefficients.

Modified shaftNDE bore

Modified modelNDE bore


Modified Pinion ShaftAs expected t

Figure 23), highlightmode frequencyresult as the contribution ofyet included in the model.

Figure

In fact, the daincreasing of the overhungCPM, as it can be clearly observed on the Campbell

diagram depicted in

Figure(Damped analysis with



Modified Pinion Shaft – ResultsAs expected the undamped critical speed map

highlighted an increasmode frequency (white and brown

the contribution ofin the model.

igure 23 – Modified pinion

amped eigenvaluesincreasing of the overhung

it can be clearly observed on the Campbelldepicted in Figure 2

Figure 24 – Modified pinionDamped analysis with synch



esults of Analysishe undamped critical speed map

an increase of theand brown curve

the contribution of the bearings damping

Modified pinion - UCS (no damping)

eigenvalues analysis shows aincreasing of the overhung mode frequency

it can be clearly observed on the CampbellFigure 24.

Modified pinion – Campbellynchronous bearing

The Campbell diagram in Figure 24 is determined usingbearing coefficients evaluated at the synchronous speedfrequency. Next step into the pinion shaft lateral study isdamped eigenvalue calculation using the a


of Analysishe undamped critical speed map

of the pinion overhungcurves). This is a parti

bearings damping was

(no damping)

analysis shows afrequency, now above 70

it can be clearly observed on the Campbell

Campbellearing coefficients

The Campbell diagram in Figure 24 is determined usingsynchronous speed

frequency. Next step into the pinion shaft lateral study isusing the a-synchronous


he undamped critical speed map (seepinion overhung

). This is a partialwas not

furtherabove 70

it can be clearly observed on the Campbell

oefficients)

The Campbell diagram in Figure 24 is determined using thesynchronous speed

frequency. Next step into the pinion shaft lateral study is thesynchronous

The Figures 25÷28 show the mode shape, frequency andLogDec of each lateral mode identified with the symbols(°°), (*), (**) in Figure 24, using the aThe mentioned lateral modesaccording to what observed during the string test in terms offrequency andvibration

F

Respect to the original pinion shaft design (seeshape and LogDec in Figure 19), the puremodes are now shifted above 74 kcpm, with an increasedLogDec as shown in Figure

The modes marked with the symbols (°) and (°°)in the frequency range of the60 kcpm),an adeguate

Figureanalysis carried out at partial load conditionrecalculated set of

Pinion shaft

Pinion shaftDE

The Figures 25÷28 show the mode shape, frequency andLogDec of each lateral mode identified with the symbols

(*), (**) in Figure 24, using the aThe mentioned lateral modesaccording to what observed during the string test in terms offrequency andvibration was observed on the pinion shaft NDE side)

Figure 25 – Modified pinion


Respect to the original pinion shaft design (seeshape and LogDec in Figure 19), the puremodes are now shifted above 74 kcpm, with an increasedLogDec as shown in Figure

The modes marked with the symbols (°) and (°°)in the frequency range of the60 kcpm), they involvan adeguate LogDec up to 0.7 and 0.73 respectively.

Figures 29÷32 showanalysis carried out at partial load conditionrecalculated set of

Pinion shaftDE side

Pinion shaftDE side


(*), (**) in Figure 24, using the aThe mentioned lateral modesaccording to what observed during the string test in terms offrequency and shaft location (

observed on the pinion shaft NDE side)

Modified pinion –

Modified pinion –

Respect to the original pinion shaft design (seeshape and LogDec in Figure 19), the puremodes are now shifted above 74 kcpm, with an increasedLogDec as shown in Figures 27 and 28.

The modes marked with the symbols (°) and (°°)in the frequency range of the

involve the whole pinion shaftLogDec up to 0.7 and 0.73 respectively.

29÷32 show the results ofanalysis carried out at partial load conditionrecalculated set of bearings coefficients



(*), (**) in Figure 24, using the a-synchronous coefficients.The mentioned lateral modes are those of interest,according to what observed during the string test in terms of

location (the superobserved on the pinion shaft NDE side)

– Mode Shape (°)

Mode Shape (°°)

Respect to the original pinion shaft design (seeshape and LogDec in Figure 19), the puremodes are now shifted above 74 kcpm, with an increased

27 and 28.

The modes marked with the symbols (°) and (°°)in the frequency range of the previous test observation (55

whole pinion shaftLogDec up to 0.7 and 0.73 respectively.

the results of theanalysis carried out at partial load condition

bearings coefficients.





synchronous coefficients.are those of interest,

according to what observed during the string test in terms ofsuper-synchronous

observed on the pinion shaft NDE side).

(°) @ 5,700 rpm

(°°) @ 5,700 rpm

Respect to the original pinion shaft design (see the modeshape and LogDec in Figure 19), the pure shaft overhungmodes are now shifted above 74 kcpm, with an increased

The modes marked with the symbols (°) and (°°) fall nowtest observation (55

whole pinion shaft but nowLogDec up to 0.7 and 0.73 respectively.

the a-synchronousanalysis carried out at partial load condition, using a

Pinion shaft

Pinion shaft


The Figures 25÷28 show the mode shape, frequency andLogDec of each lateral mode identified with the symbols (°),

synchronous coefficients.are those of interest,

according to what observed during the string test in terms ofsynchronous

rpm

700 rpm

modeshaft overhung

modes are now shifted above 74 kcpm, with an increased

fall nowtest observation (55-

but now with

synchronous, using a

The aforementionedrated power,absorbed powerrealistic condition for a comparison with the test vibrationoutcomes.

Figure


The aforementionedrated power, corresponding toabsorbed powerrealistic condition for a comparison with the test vibrationoutcomes.

Figure 27 –



Pinion shaftDE side

Pinion shaftDE side

Pinion shaftDE side


The aforementioned partial load condition is 50% of gearcorresponding to

absorbed power at 5,700rpmrealistic condition for a comparison with the test vibration

Modified pinion

Modified pinion

Modified pinion – Mode Shape


partial load condition is 50% of gearcorresponding to the compressors nominal

700rpm, so it represents the mostrealistic condition for a comparison with the test vibration

Modified pinion – Mode Shape (*)

Modified pinion – Mode Shape (**) @ 5

Mode Shape (°) @


Pinion shaNDE side



partial load condition is 50% of gearthe compressors nominal

, so it represents the mostrealistic condition for a comparison with the test vibration

Mode Shape (*) @ 5,700 rpm

Mode Shape (**) @ 5,700 rpm

@ 5,700 rpm, 50% load

Pinion shaftside

Pinion shaftside

Pinion shaftside


partial load condition is 50% of gearthe compressors nominal

, so it represents the mostrealistic condition for a comparison with the test vibration

700 rpm

700 rpm

50% load

Figure

Figure

Figure

At partial loadobservedgeneral increase of

Pinion shaft




At partial loadobserved a general reduction ofgeneral increase of

Pinion shaftDE side

Pinion shaftDE side

Pinion shaftDE side




At partial load (reduced transmitted power)a general reduction of

general increase of their modal damping


Mode Shape (°°)@5

Mode Shape (*)@5,

Mode Shape (**)@5

(reduced transmitted power)a general reduction of the modes frequenc

their modal damping.





5,700 rpm, 50% load

,700 rpm, 50% load

5,700rpm, 50% load

(reduced transmitted power) itthe modes frequency and a

Pinion shaft

Pinion shaftside

Pinion shaft


50% load

50% load

50% load

it isy and a

MODIFIED PINION SHAF

correctivethe improvedvibration well below the acceptance criteriaoperating conditionsshaft vibration trendsμm p

As shown in Figure 35componentdemonstratingcalculated29)Consideringthe very high frequency ofcalculation


MODIFIED PINION SHAFThe new string test

corrective action (pinion shaft NDEthe improved shaft vibrationvibration well below the acceptance criteriaoperating conditionsshaft vibration trendsμm p-p.

Figure 33 –Modified pinion

Figure 34 –Modified pinion

s shown in Figure 35component is still presentdemonstratingcalculated frequency of mode (°) is29) i.e. 960.3Considering the acquisition system frequency resolution andthe very high frequency ofcalculation can be considered


MODIFIED PINION SHAFT - EXPERIMENTAL RESULTnew string test carried out

action (pinion shaft NDEshaft vibration

vibration well below the acceptance criteriaoperating conditions. The figures 33 and 34 showshaft vibration trends, with a

Modified pinion

Modified pinion

s shown in Figure 35, the super synchronous vibrationis still present at 970 Hz (10

the good correlation withfrequency of mode (°) is

Hz, so roughly 1%the acquisition system frequency resolution and

the very high frequency ofcan be considered


EXPERIMENTAL RESULTcarried out to validate

action (pinion shaft NDE modification)shaft vibration behavior, with

vibration well below the acceptance criteriaigures 33 and 34 showa maximum direct

Modified pinion – Measured vibration @

Modified pinion – Measured vibration @

the super synchronous vibrationat 970 Hz (10

good correlation withfrequency of mode (°) is 57,618 cpm (

roughly 1% less ofthe acquisition system frequency resolution and

the very high frequency of the studiedcan be considered very accurate.


EXPERIMENTAL RESULTSvalidate the adopted

modification) confirmswith the overall

vibration well below the acceptance criteria of 35 μm igures 33 and 34 show the

direct vibration of 1

vibration @ NDE

Measured vibration @ NDE

the super synchronous vibrationat 970 Hz (10X speed harmonic)

good correlation with the prediction:618 cpm (see

less of that measuredthe acquisition system frequency resolution and

studied phenomenon, thevery accurate.


adoptedconfirms

the overall shaftof 35 μm in all

the pinionvibration of 16

NDE “X”

NDE “Y”

the super synchronous vibrationspeed harmonic),

ion: thesee Figure

that measured.the acquisition system frequency resolution and

phenomenon, the

The rwhich wasand avoid the intersection withharmonics, not to remove the

Moreover, theterms of whirl direction and amplitude are perfectlyconsistent with the calculationcomponentthe modified pinion isto the increased LogDecsuper

The fresponse atlocation, based on a rotor response analysis

The results are in line withwhich was aimedand avoid the intersection withharmonics, not to remove the


Moreover, theterms of whirl direction and amplitude are perfectlyconsistent with the calculationcomponent is predominant

modified pinion isto the increased LogDecsuper-synchronous component

Figure 36 - Vibration

The figures 36 and 37 show the calculated vibrationresponse at thelocation, based on a rotor response analysis

esults are in line with theaimed to increase the system modal damping

and avoid the intersection withharmonics, not to remove the excitation function.

Modified pinion -

Moreover, the observedterms of whirl direction and amplitude are perfectlyconsistent with the calculation

predominant and themodified pinion is much lower than the original case,

to the increased LogDec, in fact thesynchronous component

Vibration response on NDE bearing location

igures 36 and 37 show the calculated vibrationthe NDE bearing centerline and

location, based on a rotor response analysis

DE


the corrective action purpose,to increase the system modal damping

and avoid the intersection with the 9Xexcitation function.

- full Waterfall –

observed vibration characteristics interms of whirl direction and amplitude are perfectlyconsistent with the calculation results: the forward whirl

and the vibration responsemuch lower than the original case,

in fact the maxsynchronous component is now 3 µm p

response on NDE bearing location

igures 36 and 37 show the calculated vibrationNDE bearing centerline and

location, based on a rotor response analysis

NDE

HSSDE side


corrective action purpose,to increase the system modal damping

and 11X speedexcitation function.

– HSS NDE “Y”

vibration characteristics interms of whirl direction and amplitude are perfectly

the forward whirlvibration response

much lower than the original case,maximum observed

3 µm p-p @ 970 Hz.

response on NDE bearing location.

igures 36 and 37 show the calculated vibrationNDE bearing centerline and NDE probe

location, based on a rotor response analysis carried out

HSSNDE side

~5820 rpm


corrective action purpose,to increase the system modal damping

speed

vibration characteristics interms of whirl direction and amplitude are perfectly

the forward whirlvibration response with

much lower than the original case, dueobserved

p @ 970 Hz.

igures 36 and 37 show the calculated vibrationprobe

carried out

using an explorative rotating force acting on the gear mesh,with a frequency of 10X speed harmonic.

vibrmeasured vibration during

The ratio betweenlocation and1.47contact probe corresponds to a vibration of roughly 2 µm pp at thethe

PROPOSED METHOD OF 4

method to study the gear rotors 4

1

1.1

1.2

1.3

22.1



This additional analysis has the aim to define the shaftvibration at the bearing center line starting from themeasured vibration during

Figure 37

he ratio betweenlocation and the

47. Thereforecontact probe corresponds to a vibration of roughly 2 µm pp at the NDE bearing sectionthe calculated ratio

PROPOSED METHOD OF 4This section collect

method to study the gear rotors 4

System Model CriteriaAs describedof the modified pinion shaft (system model proceduresteps:

1.1 The shaft beam modeloutcomessecond free

1.2 The coupling componentsincluding themoment of inertia

1.3 The bearing damping andcalculated at the frequency ofcoefficients)mechanical effects andtilting pad journal bearing

Lateral Analysis & Deliverables2.1 The lateral study

Undamped Critical Speed Map (UCS), in order todetermine the shaft lateral natural frequencysynchronous bearing stiffness



This additional analysis has the aim to define the shaftation at the bearing center line starting from the

measured vibration during the

7 - Vibration response on NDE probe location.

he ratio between the vibration response atthe one at the bearing centerline is

herefore, a vibration of 3 µm pcontact probe corresponds to a vibration of roughly 2 µm p

NDE bearing sectioncalculated ratio).

PROPOSED METHOD OF 4TH

his section collects the mainmethod to study the gear rotors 4

System Model Criteriadescribed in the paragraph

of the modified pinion shaft (system model procedure

haft beam model shall be in accordance(tune the beam model to match the first and

second free-free modes calculated by a FEM analysis)oupling components

the flexible element;moment of inertia shall be

earing damping andcalculated at the frequency ofcoefficients), shall consider the system thermomechanical effects andtilting pad journal bearing

Lateral Analysis & DeliverablesThe lateral study shallUndamped Critical Speed Map (UCS), in order todetermine the shaft lateral natural frequencysynchronous bearing stiffness




the string test.

response on NDE probe location.

vibration response atone at the bearing centerline is

a vibration of 3 µm p-p detected bycontact probe corresponds to a vibration of roughly 2 µm p

NDE bearing section (measured vibration dived by

TH MODE ANALYSISthe main steps

method to study the gear rotors 4th lateral mode

paragraph dedicated to the analysisof the modified pinion shaft (Modifiedsystem model procedure shall include the following

shall be in accordance(tune the beam model to match the first and

free modes calculated by a FEM analysis)oupling components shall be mod

flexible element; the polar and transversalshall be defined by

earing damping and the stiffness coefficientscalculated at the frequency of interest

onsider the system thermomechanical effects and the inertia effects in case oftilting pad journal bearing.

Lateral Analysis & Deliverablesshall start with the analysis of the

Undamped Critical Speed Map (UCS), in order todetermine the shaft lateral natural frequencysynchronous bearing stiffness.




string test.


vibration response at theone at the bearing centerline is 12.67 / 8

p detected by the nocontact probe corresponds to a vibration of roughly 2 µm p

measured vibration dived by

MODE ANALYSISsteps of the proposed

lateral mode.

dedicated to the analysisModified Rotor Analysis

include the following

shall be in accordance to the(tune the beam model to match the first and

free modes calculated by a FEM analysis)modeled separately,

polar and transversaldefined by a FEM analysis

stiffness coefficientsinterest (asynchronous

onsider the system thermoinertia effects in case of

start with the analysis of theUndamped Critical Speed Map (UCS), in order todetermine the shaft lateral natural frequency with


using an explorative rotating force acting on the gear mesh,



the probe67 / 8.6 =

the no-contact probe corresponds to a vibration of roughly 2 µm p-

measured vibration dived by

proposed

dedicated to the analysisAnalysis), the

include the following

the FEM(tune the beam model to match the first and

free modes calculated by a FEM analysis).eled separately,

polar and transversalanalysis.

stiffness coefficients(asynchronous

onsider the system thermo-inertia effects in case of

start with the analysis of theUndamped Critical Speed Map (UCS), in order to

with the

2.2 Then, thethe bearing synchronous dampioutcomes of this stepdiagramorder to define which of thebe deeply

2.3 Finally,eiinterestorder to definedampingtransmitted load conditionoperating pointschange the 4the bearing superand then again recalculate the natural mode in order toconverge

3 Acceptance CriteriaConsideringmeasurements results,identify the critical area- LogDec- LogDec

Acceptability ofthe proposed method, in case the analyzed gear falls in thecritical area, it is strongly suggested to further investigateany design changesinto the area of confidence

CASESThe c

tests results withoutcomes ofcalculation method.pinion shaft 4th mode shape and LogDec for each of thementioned cases.

Then, the studythe bearing synchronous dampioutcomes of this stepdiagram showingorder to define which of thebe deeply investigated.Finally, the analysis shall determine the dampedeigenvalues for each ointerest, using the asynchronous bearing coefficients, inorder to definedamping. Thetransmitted load conditionoperating pointschange the 4the bearing superand then again recalculate the natural mode in order toconverge through an

Acceptance CriteriaConsideringmeasurements results,identify the critical areaLogDec ≥ 0.38LogDec < 0.38

cceptability of thethe proposed method, in case the analyzed gear falls in thecritical area, it is strongly suggested to further investigateany design changesinto the area of confidence

CASES STUDY RESULTSThe cases “D”, “E” and “F” point out successfully string

tests results withoutcomes of thecalculation method.pinion shaft 4th mode shape and LogDec for each of thementioned cases.

Figure 38 -

f=75794.3 cpm

d=.3573 logd

N=11530 rpm

Pinion shaftDE side

study shall include the damping effects, usingthe bearing synchronous dampioutcomes of this step shall

showing the expected excitation harmonics,order to define which of the

investigated.the analysis shall determine the damped

for each of the critical natural frequency of, using the asynchronous bearing coefficients, in

order to define its frequency,. The analysis shall

transmitted load conditionoperating points (if the different load will significantlychange the 4th mode frequency,the bearing super-synchronous coefficients calculationand then again recalculate the natural mode in order to

through an iterative pro

Acceptance CriteriaConsidering the analyticalmeasurements results, the LogDec thresholdidentify the critical area is 0.3

8 => low risk of high vibration response;8 => high risk of

the specific gear design shall be based onthe proposed method, in case the analyzed gear falls in thecritical area, it is strongly suggested to further investigateany design changes which would bring the system dampinginto the area of confidence.

STUDY RESULTS - “D”, “E” AND “F”ases “D”, “E” and “F” point out successfully string

tests results with the gearbox behavior consistent with thethe performed

calculation method. The figures 38pinion shaft 4th mode shape and LogDec for each of thementioned cases.

Case “D” pinion 4

f=75794.3 cpm

d=.3573 logd

N=11530 rpm


include the damping effects, usingthe bearing synchronous damping coe

shall be collected in a Campbellthe expected excitation harmonics,

order to define which of these natural frequencies

the analysis shall determine the dampedf the critical natural frequency of

, using the asynchronous bearing coefficients, inits frequency, mode shapeanalysis shall consider

transmitted load conditions, based on t(if the different load will significantly

mode frequency, the analyst shall repeatsynchronous coefficients calculation

and then again recalculate the natural mode in order toiterative process).

tical outcomes andhe LogDec threshold0.38, and therefore:

=> low risk of high vibration response;risk of high vibration response;

specific gear design shall be based onthe proposed method, in case the analyzed gear falls in thecritical area, it is strongly suggested to further investigate

which would bring the system damping

“D”, “E” AND “F”ases “D”, “E” and “F” point out successfully string

gearbox behavior consistent with theperformed analysis with

igures 38-41 depictpinion shaft 4th mode shape and LogDec for each of the

pinion 4th mode shape


include the damping effects, usingng coefficients;

be collected in a Campbellthe expected excitation harmonics,

se natural frequencies


, using the asynchronous bearing coefficients, inmode shape and modal

consider the different, based on the compressors

(if the different load will significantlythe analyst shall repeat

synchronous coefficients calculationand then again recalculate the natural mode in order to

outcomes andhe LogDec threshold which

, and therefore:=> low risk of high vibration response;

vibration response;



ases “D”, “E” and “F” point out successfully stringgearbox behavior consistent with the

with the proposed41 depict the calculated

pinion shaft 4th mode shape and LogDec for each of the

shape/Logdec

forwardbackward

Pinion shaftNDE


include the damping effects, usingthe

be collected in a Campbellthe expected excitation harmonics, in

se natural frequencies shall


, using the asynchronous bearing coefficients, inand modal

differenthe compressors

(if the different load will significantlythe analyst shall repeat

synchronous coefficients calculationand then again recalculate the natural mode in order to

outcomes and thewhich

=> low risk of high vibration response;vibration response;



ases “D”, “E” and “F” point out successfully stringgearbox behavior consistent with the

proposedcalculated

pinion shaft 4th mode shape and LogDec for each of the

Figure

Figure

Pinion shaftside

Pinion shaft

Pinion shaft


Figure 3

Figure 40 - Case “F”

Figure 41 - Case “F” pinion 4

Pinion shaftDE side

Pinion shaftDE side

Pinion shaftDE side


39 - Case “E” pinion 4

Case “F” pinion 4th mode

Case “F” pinion 4th


pinion 4th mode shape

mode shape/Logdec

th mode shape/Logdec



shape/Logdec

/Logdec (original design

/Logdec (mod. D

Pinion shaftNDE

Pinion shaftNDE


original design)

Design)




The case “D” (Figure 38) point out a LogDec below theproposed acceptance criteria, even if really close to the areaof confidence. A further sensitivity analysis versus load at thesite operating conditions proved the goodness of originalpinion shaft design.

The case “F” original design (Figure 40) had a 4th modeLogDec well below the acceptance criteria, thus leads toadopt the same pinion modification adopted in case “C”. Themodified pinion shaft improved the LogDec up to ~0.47(compare the Figure 40 with the Figure 41).Finally the good rotor-dynamic behaviour predicted by thecalculation was confirmed by the positive results of the FSFLstring test.

CONCLUSIONThe paper details a series of experiences on super-

synchronous vibration phenomena observed on gearedsystems. The authors develop a proven and reliable methodto study and assess the gear super-synchronous behaviourduring the design stage of the mechanical component. Inaddition to the lateral rotor-dynamic analysis required byAPI613, rotor super-synchronous analyses must be carriedout to guarantee optimum gearbox behaviour duringspecific operating conditions.

A typical approach based on the separation speedmargin cannot be used, since all shaft speed harmonics (7X,8X, 9X, 10X, 11X, etc.) can excite a pinion 4th lateral mode inthe operative speed range. This is even more critical in avariable speed drive application, where each of these shaftspeed harmonics produces a wide speed range withpotential to excite the super-synchronous behaviour.

In a trouble-shooting activity, where the operating speedrange is already explored and active speed harmonics areidentified, the pinion shaft could be modified to avoid theexcitation mechanism. Nonetheless, it is much moreeffective having a method to assess the gear super-synchronous lateral behavior during the design phase.The proposed method is based on the system modaldamping, independent of the excitation source and itsmagnitude. If the system is well damped, the vibrationresponse remains within an acceptable limit, which assuresthe correct operation of the gearbox during the performancetest and the site service.

The new method of study is validated by several stringtest campaigns; in particular for case “C” at the authors’company, comprehensive tests confirm a good correlationbetween analytical outcomes and actual rotor dynamicbehavior for both original and modified pinion shaftconditions.

Also of significant interest are the string test results forother published cases in the literature, “D”, “E” and “F”, whichalso validate the analytical model calculations and confirmthe overall expectation.

ACKNOWLEDGMENTSSpecial thanks go to Hans P. Weyermann Engineering

Fellow, Rotating Equipment (ConocoPhillips Company), andPaul Bradley Technical Director (GE Allen Gears Company),for the contribution that they have provided to the writing ofthis paper.


NOMENCLATURE

FAT Factory Acceptance TestGT Gas TurbineGB GearboxHSS High Speed ShaftLSS Low Speed ShaftPLV Pitch Line VelocityL/D Length/DiameterFSFL Full Speed Full LoadFSNL Full Speed No LoadFEM Finite Element ModelNDE Not Drive EndMCS Maximum Continuous SpeedMOS Minimum Continuous SpeedRCA Root Cause AnalysisCMS Component mode synthesisWFR Whirl Frequency RatioLogDec Logarithmic Decrementahx,y Housing acceleration [m/s2]Ahx,y Complex component of housing acceleration

[m/s2]Cij Bearing damping coefficient [N.s/m]Fx,y Complex component of external forces [m/s2]Hij Dynamic impedance functions [N/m]I 1Kij Bearing stiffness [N/m]Mh Test housing mass [kg]Mij Bearing mass coefficients [kg]Ω Excitation frequency [Hz]Ω Rotor speed [cpm]x,y Bearing dynamic motions in X,Y directions [m]X,Y Complex component of bearing motions [m]UCS Undamped Critical Speed

Subscriptsi,j X and Y directionsH Test housing

REFERENCESAPI613 “Special Purpose Gear Units for Petroleum,

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API671

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