gearbox super-synchronous lateral...
TRANSCRIPT
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
technical selection and design verificationof flexible and rigid couplings, load gearsand auxiliary equipment, with particularfocus on the train rotorbehaviour, torsional and lateral.
GEARBOX SUPER
Mr. Gaspare MaragioglioEngineering ManagerShaft Line Integration
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
technical selection and design verificationof flexible and rigid couplings, load gearsand auxiliary equipment, with particularfocus on the train rotorbehaviour, torsional and lateral.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
BOX SUPER
Mr. Gaspare MaragioglioEngineering ManagerShaft Line Integration
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
bringing the overall gear shaft vibration
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
bringing the overall gear shaft vibration
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
synchronous bearing stiffness and damping
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
synchronous bearing stiffness and damping
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
earbox vibration on NDE pinion bearing increases18MW @ 100% speed (reached
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
earbox vibration on NDE pinion bearing increases18MW @ 100% speed (reached
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
between the observed
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
between the observed
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
, 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
Pinion shaftNDE side
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
and the pinion shaft overhung lateral naturalcase the analytical calculation
in the original design
overhung mode shape
fixed profile journal bearings, offset halves type,have been designed and installed on the
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
trains were driven by a project gas turbine and one by aThe power to drive the compressor
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
and the pinion shaft overhung lateral naturalcase the analytical calculation also
in the original design,
fixed profile journal bearings, offset halves type,have been designed and installed on the
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
trains were driven by a project gas turbine and one by aThe power to drive the compressor
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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:
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Trend and Waterfall HSS NDE “Y”
vibration became prevalent at a specific combination ofspeed and load, and showed a full repeatability in the load
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
vibration became prevalent at a specific combination ofspeed and load, and showed a full repeatability in the load
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
vibration became prevalent at a specific combination ofspeed and load, and showed a full repeatability in the load
- 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.
Trend and Waterfall HSS NDE “Y”
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Trend and Waterfall HSS NDE “Y”
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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)
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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)
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhung
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
The excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one or
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
In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhung
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
The excitation speeds can be defined as those speeds atwhich the super synchronous vibration is activated by one or
harmonics that occur within thecompressor operating speed range. These excitation speeds
lateral naturalharmonics,
nevitably the exact calculation of the excitation speedsacquisition system
In other words, at the mentioned excitation speeds, theharmonics 9X, 10X and 11X excite the pinion shaft overhung
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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;
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
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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:
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 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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
that the excitation source isthe vibration response
shows a relationship
excitation forces originated into thedifficult to be
linear
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 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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
(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)
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
per node are considered (axial constrain)are obtained in the state space of the linearized system.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
per node are considered (axial constrain)are obtained in the state space of the linearized system.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
per node are considered (axial constrain)are obtained in the state space of the linearized system.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
mechanical deformation
Pinion shaftNDE side
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Tangential forces to shaft (stable/unstable condition)
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
mechanical deformation
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.
Tangential forces to shaft (stable/unstable condition)
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
mechanical deformation
effectivedamping determined by the bearings cross coupling stiffness
Theaforementioned coefficients represent the tangential forces
ematic sketch
(1)
Tangential forces to shaft (stable/unstable condition)
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
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
synchronous coefficients
pinion shaft 4th lateralthe 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 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
Pinion shaftNDE side
synchronous vibration5µm p-p @ 970 Hz
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
synchronous coefficients
lateralthe presence of the excitation force,
Unfortunately, due to the uncertainties on the excitationfunction, and therefore due to the difficulties to define its
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
carried out, to identify the most
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
carried out, to identify the most
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
mentioned corrective action, the expected
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
the pinion shaft designrelates to the shaft
drilling a bore onshaft drawing details in
shaft model details in Figure 22).
– NDE bored
beam model
mentioned corrective action, the expected
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
designshaft
drilling a bore on theshaft drawing details in
mentioned corrective action, the expected
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
The Campbell diagram in Figure 24 is determined usingbearing coefficients evaluated atfrequency. Next step into the pinion shaft lateral study isdamped eigenvalue calculationbearing coefficients.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
The Campbell diagram in Figure 24 is determined usingbearing coefficients evaluated atfrequency. Next step into the pinion shaft lateral study isdamped eigenvalue calculationbearing coefficients.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Figure 26 – 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
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 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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
The Figures 25÷28 show the mode shape, frequency andLogDec of each lateral mode identified with the symbols
(*), (**) 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.
Pinion shaftNDE side
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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 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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
The aforementionedrated power, corresponding toabsorbed powerrealistic condition for a comparison with the test vibrationoutcomes.
Figure 27 –
Figure 28 - Modified pinion
Figure 29 - Modified pinion
Pinion shaftDE side
Pinion shaftDE side
Pinion shaftDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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 shaftNDE side
Pinion shaNDE side
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Figure 30 - Modified pinion
Figure 31 - Modified pinion
Figure 32 - Modified pinion
At partial loadobserved a general reduction ofgeneral increase of
Pinion shaftDE side
Pinion shaftDE side
Pinion shaftDE side
Modified pinion – Mode Shape
Modified pinion – Mode Shape
Modified pinion – Mode Shape
At partial load (reduced transmitted power)a general reduction of
general increase of their modal damping
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
Mode Shape (°°)@5
Mode Shape (*)@5,
Mode Shape (**)@5
(reduced transmitted power)a general reduction of the modes frequenc
their modal damping.
Pinion shaftNDE side
Pinion shaftNDE side
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Figure 35 – Modified pinion
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
using an explorative rotating force acting on the gear mesh,with a frequency of 10X speed harmonic.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
using an explorative rotating force acting on the gear mesh,with a frequency of 10X speed harmonic.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
using an explorative rotating force acting on the gear mesh,with a frequency of 10X speed harmonic.
This additional analysis has the aim to define the shaftation at the bearing center line starting from the
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
using an explorative rotating force acting on the gear mesh,with a frequency of 10X speed harmonic.
This additional analysis has the aim to define the shaftation at the bearing center line starting from the
string test.
response on NDE probe location.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
using an explorative rotating force acting on the gear mesh,
This additional analysis has the aim to define the shaftation at the bearing center line starting from the
response on NDE probe location.
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
include the damping effects, usingng coefficients;
be collected in a Campbellthe expected excitation harmonics,
se natural frequencies
the analysis shall determine the dampedf the critical natural frequency of
, 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;
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
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
include the damping effects, usingthe
be collected in a Campbellthe expected excitation harmonics, in
se natural frequencies shall
the analysis shall determine the dampedf the critical natural frequency of
, 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;
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
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
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
Figure 3
Figure 40 - Case “F”
Figure 41 - Case “F” pinion 4
Pinion shaftDE side
Pinion shaftDE side
Pinion shaftDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
39 - Case “E” pinion 4
Case “F” pinion 4th mode
Case “F” pinion 4th
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
pinion 4th mode shape
mode shape/Logdec
th mode shape/Logdec
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
shape/Logdec
/Logdec (original design
/Logdec (mod. D
Pinion shaftNDE
Pinion shaftNDE
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
original design)
Design)
Pinion shaftNDE side
Pinion shaftNDE side
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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.
Copyright© 2015 by Turbomachinery Laboratory, Texas A&M Engineering Experiment Station
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,
Chemical and Gas Industry Services”, FifthEdition, American Petroleum Institute,Washington, DC.
API671
API684
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“Tutorial on Rotor Dynamics: Lateral Critical,Unbalance Response, Train Torsional and RotorBalancing”, Second Edition American PetroleumInstitute, Washington, DC.
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