The Experimental Analysis of Vibration Monitoring in System Rotor Dynamic with Validate Results ...

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ISRNMechanicalEngineering
Volume2012,ArticleID981010,17pages
doi:10.5402/2012/981010
Research Article
The Experimental Analysis of Vibration Monitoring in System
Rotor Dynamic with Validate Results Using Simulation Data
HishamA.H.Al-Khazali1andMohamadR.Askari2
1FacultyofScience,EngineeringandComputing,SchoolofMechanicalandAutomotiveEngineering,KingstonUniversity,
LondonSW153DW,UK
2FacultyofScience,EngineeringandComputing,SchoolofAerospaceandAircraftEngineering,KingstonUniversity,
LondonSW153DW,UK
CorrespondenceshouldbeaddressedtoHishamA.H.Al-Khazali,[email protected]
Received12December2011;Accepted19January2012
AcademicEditor:D.Zhou
Copyright©2012H.A.H.Al-KhazaliandM.R.Askari.ThisisanopenaccessarticledistributedundertheCreativeCommons
AttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkis
properlycited.
There is a growing tendency today to extract information about the prognostic parameters based on system analysis through
variousdiagnostictechniquestoassessthehealthoftheplantorequipment.Vibrationmonitoringhelpsinreducingthemachine
down time. A vibration signature measured at the external surface of machine or at any other suitable place contains a good
amountofinformationtorevealtherunningconditionofthemachine.Consideringtheimportanceofvibrationmonitoringin
therotatingmachineryfaultdiagnostics,ithasbeenappliedinthispaper.Effectsofmodalparameterslikenaturalfrequency,
modeshapes,anddamping,misalignmentshavebeenstudied.Balancingisusuallyanexpensiveandlaboriousprocedureand
a balancing system would be beneficial for motor engine and power generation application. In this research, there have been
identifiedunbalanceparametersthatexistinrotatingmachineryanddevelopafinite-elementmodelofrotatingdynamicssystem
tocreateamathematicalmodelofthesystemfromthetestdataandsubsequentlyobtainingtheunbalancedparameters.Duringthis
study,therawdataobtainedfromtheexperimentalresults(SmartOfficesoftware)arecurvefittedbytheoreticaldataregenerated
from simulating it using finite element (ANSYS 12) model for comparisons. The experimental analysis used thus far is called
ModalTesting,awell-knownandwidelyusedtechniqueinresearchandindustrytoobtaintheModalandDynamicresponse
propertiesofstructures.Thetechniquehasrecentlybeenappliedtorotatingstructuresandsomeresearchpapersbeenpublished,
however, the full implementation of Modal Testing in active structures and the implications are not fully understood and are
therefore in need of much further and more in-depth investigations. The aim is to find a system identification methodology
usingtheanalytical/computationaltechniquesandupdatethemodelusingexperimentaltechniquesalreadyestablishedforpassive
structuresbuttoactiverotatingstructures,whichsubsequentlyhelptocarryouthealthmonitoringaswellasfurtherdesignand
developmentinrotatingmachinery.
1.Introduction greater power have created complex vibration problems.
Engineering judgments based on understanding of physical
Astherotatingmachinewears,foundationssettle,andparts phenomena are needed to provide the diagnosis and meth-
deform, subtle changes in the dynamic properties of the odsforcorrectingtherotatingmachineryfaults[1,2].Modes
machine begin to occur. Shafts become misaligned, parts are used as a simple and efficient means of characterizing
begin to wear, rotors become unbalanced, and clearances resonantvibration.Themajorityofstructurescanbemade
increase. All of these factors are reflected in an increase in toresonate.Thatis,undertheproperconditions,astructure
vibration energy, which as it is dissipated throughout can be made to vibrate with excessive, sustained, and
the machine, excites resonances, and puts considerable oscillatory motion. Resonant vibration is caused by an
extra dynamic loads on bearings. Increased complexities interaction between the inertial and elastic properties of
of rotating machinery and demands for higher speeds and thematerialswithinastructure.Resonantvibrationisoften
2 ISRNMechanicalEngineering
the cause of, or at least a contributing factor to, many of completemachine,whichimposescertainlimitationsonthe
the vibration related problems that occur in structures and modal testing for rotating machines. Bucher and Ewins [6]
operating machinery. To better understand any structural have discussed these issues in detail. Irretier [7] gave the
vibrationproblem,theresonancesofastructureneedtobe mathematical background to extract the modal model for
identifiedandquantified.Acommonwayofdoingthisisto rotatingstructureswhicharecharacterisedbynonsymmetric
definethestructure’smodalparameters[1–3]. and time-variant matrices, unlike the assumptions for the
Modes(orresonances)areinherentpropertiesofastruc- experimentalmodalanalysisofstationarystructures,namely,
ture. Resonances are determined by the material properties a linear, time-invariant system where reciprocity holds.
(mass, stiffness, and damping properties), and boundary Another alternative is the use of a modal model of the
conditionsofthestructure.Eachmodeisdefinedbyanatural foundation alone together with the FE model of the rotor
(modularresonant)frequency,modaldamping,andamode and the mathematical model for the bearings, Pennacchi et
shape. If either the material properties or the boundary al.[8].
conditionsofastructurechange,itsmodeswillchange.For Inthispaper,searchingforanewtechniquetointerpret
instance, if mass is added to a vertical pump, it will vibrate the results obtained from experimental data of dynamic
differently because its modes have changed. At or near the performance of machinery for condition monitoring, it is
natural frequency of a mode, the overall vibration shape clearthatadatabasecouldbecreated.Thisdatabaseconsists
(operating deflection shape) of a machine or structure will of complete mathematical model of the machine which
tendtobedominatedbythemodeshapeoftheresonance. includesboththesupportingstructuresaswellasthemoving
Rotordynamicsisthestudyofvibrationbehaviorinaxi- partsandisbasedonthestructuraldynamicscharacteristics
allysymmetricrotatingstructures.Devicessuchasengines, ofthesystem[9,10].
motors, disc drives, and turbines all develop characteristic Linear structures for the purpose of vibration analysis
inertia effects that can be analyzed to improve the design maybemodelledeitherasacontinuoussystemoradiscrete
and decrease the possibility of failure. At higher rotational one.Inthecaseofthelattermethod,themassofthesystemis
speeds,suchasinagasturbineengine,theinertiaeffectsof lumpedintoafinitenumberofmassesconnectedbysprings
therotatingpartsmustbeconsistentlyrepresentedinorder and dampers representing the stiffness and damping in the
toaccuratelypredicttherotorbehavior[2,3]. system,respectively.Thesystemisthensaidtopossessafinite
numberofdegreesoffreedom.Dampingmechanismcomes
indifferentformssuchasviscous,structural,hysteretic,and
1.1.ExistingTechniqueUsedforModelling. Therehasbeena coulomb. The viscous damping being the most common
long-standing interest in rotor dynamic modelling that has form.Theequationsofmotionofthediscretemodelconsists
evolved since the first and incorrect rotor dynamic analysis of a finite number of second-order ordinary differential
by Rankine in 1869. They need to understand the system equations coupled together, in which case they have to
response to design predictable, low maintenance, cost- be solved simultaneously [2, 9, 11]. The process becomes
effective,andoptimalsystemsthathavedrivenrotordynam- progressively more difficult as the number of degrees of
icstooftenmodellarge-ordercomplexrotorsystemmodels. freedomincreases.
The models contain more intricate geometric complexities,
bearings, seals, and attached components such as discs,
blades, fans, and couplings. Some models involve relatively 1.2.MeasurementofFrequencyResponseFunctions(FRFs). A
simple beam representations of the rotor on bearings that naturalfrequencymaybedetectedexperimentallybyexciting
are represented as stiffness and damping. These models do thestructurewithtransientoraharmonicforceeachmethod
notusuallyneedreductionsotheyarenotthetopiccovered hasadifferentapplicationdependingontheobjectiveofthe
here.Thestandardanalysisofrotorsystemsincludescritical testandthetimeavailable.Forexample,impacttestingwith
speeds,stabilityandunbalancedresponse[4]. a hammer, which is quick and easy, is ideal for studying
In recent years with continuing demands for increased a car’s exhaust system’s vibration problem and varying the
performance, many rotating industrial machines are now frequency until “resonance” is achieved. At resonance, the
being designed for operation at high speed, a trend which modeassociatedwiththenaturalfrequencymaybeobserved
has resulted in increased mechanical vibration and noise [1].Thefrequencyresponsefunction(FRF)isafundamental
problems[2].Themodalmodel(naturalfrequencies,mode measurement that isolates the inherent dynamic properties
shapes, and modal damping) of a complete machine based of a mechanical structure. Experimental modal parameters
on the in-situ experimental modal tests is one possible (frequency, damping, and mode shape) are also obtained
modelling approach. Irretier [5] gave an overview of the from a set of FRF measurements. The FRF describes the
different experimental modal analysis techniques. Such an input-outputrelationshipbetweentwopointsonastructure
experimental model is expected to avoid all uncertainties as a function of frequency. Therefore, an FRF is actually
in the mathematical modelling approach (often FE Model) defined between a single input DOF (point and direction),
and its updating. However, conducting modal tests on a andasingleoutput(DOF),althoughtheFRFwaspreviously
machine such as a TG set, which has a number of fluid defined as a ratio of the Fourier transforms of an output
bearings, is not straightforward. The dynamics of the fluid and input signal, is it actually computed differently in all
bearings during machine operation and the rotation of modern (FFT) analyzers. This is done to remove random
the shaft itself influence the dynamic behaviour of the noiseandnonlinearity(distortion)fromthe(FRF)estimates.
ISRNMechanicalEngineering 3
Rotating machines such as steam or gas turbines, turbo-
Y p
generators, internal combustion engines, motors, and disc b
drives can develop inertia effects that can be analyzed to a
improve the design and decrease the possibility of failure 4-DOF X Disc 2-DOF
[1, 12]. Current trends in rotating equipment design focus Z
Bearing
on increased speeds, which increase operational problems
causedbyvibration.Athigherrotationalspeeds,theinertia
X
effects of rotating parts must be consistently represented to 3-DOF 1-DOF
L
accuratelypredictrotorbehaviour[3,6].
Figure1:Schematicofarotoronediscsetupparameter[2,3].
2.Objective
The target of this paper is to utilize the developed solution
moduleininvestigatingassortedaspectsofthevibrationper- Accelerometer Bearings
formanceofaninductionmotorsystemforsolvingitsfailure
troubleoftheshaft.Someofthecrucialfactorstothequality
andperformanceofthemotor,suchasthevibrationampli-
tudeasresultedfromthebearingwear,dampingeffects,and
thepassingofsystemresonancecriticalspeeds,areallinves-
tigatedinthestudy.Anefficientdual-rotormodelisverified
Hammer Disc
to have excellent accuracy when comparing the calculated
frequency response function (FRF) with that from modal
testing. Present paper is to investigate the effects of design
Figure2:Experimentalsetupforthemodaltesting.
parametersonthenoiseproducedbyrotor-bearingsystems.
Mathematical model of the system from the test data
can be assembled. Transient orbit analysis in the literature
indicates that the bearing stiffness and damping dominates
the vibration amplitude remarkably. In this project, the
dampingeffectsofthestiffnessofbearingshavebeenstudied.
The research work included the development of relevant
theoretical groundwork originated from principles of rotor
dynamics. The method would be capable of solving many
oftherelatedrotatingmachineproblemssuchashigh-speed
gas-bearingspindleandelectricmotors.
Excessvibrationcancausenoiseandwearinmachinery 1st flexural mode shape, 2nd flexural mode shape, 3rd flexural mode shape
andbearing,itisimportanttoidentifyallthecriticalspeeds
Figure3:Basicmachinemodelcross-section[2,3].
within the range of operation and analyse the damping
effects, mass unbalance and other phenomena in rotating
machineryandtheireffectsinthesafeoperationofrotating
method [2]. For the vibration equation of a system, the
machinery,whichwouldbethesubjectofstudyinthispaper
mathematicalmodelcanbeexpressedasfollows[9]:
which will help to obtain the necessary results for reducing
amplitude and subsequently reducing noise happened due Mx¨+Cx˙+Kx= f, (1)
to excess vibration in bearing through the reaction forces
act in right and left bearing with increasing the speed of where M, C, and K are the mass, damping, and stiffness
rotation. It is envisaged that the approach is not limited to matrices of the system, respectively. Moreover, x and f are
the condition monitoring and predictive failure but could the displacement and external forcevectors, respectively. In
help the designers to have better understanding of rotor (1),thedisplacementvectorofthesystemcanberepresented
performanceatthesystemdesignstage. in the modal coordinate with the following mode shape
matrix:
(cid:2)N
3.Method xN×1= ηrνr =UN×NηN×1, (2)
r=1
3.1.MathematicalModel
where N is the total number of components in the modal
3.1.1. Description of Frequency Response Functions (FRFs). coordinate; ηr and νr are the components of the modal
The derivative processes of FRFs are described here. The coordinate and the mode shape vector at the rth mode,
FRF data of any structure can also be obtained through respectively; U = ν1,ν2,...,νN denotes the mode shape
experimentalmodaltestingorbymeansoftheFEsimulation matrix; η = η1,η2,...,ηNTrefers to the modal coordinate
4 ISRNMechanicalEngineering
+0.00...0.00
+0.00...0.00
+0.00...0.00
+0.00...0.00
+0.00...0.00
+0.00...0.00
−0.00...0.00
−0.00...0.00
−0.00...0.00 −0.00...0.00
−0.00...0.00 −0.00...0.00
−0.00...0.00
(a) Atstartrotation
Geometry3
29.79 Hz reference accelorometer (m/N)
(b) Afterrotation(firstmodeshape)
Figure4:Geometrydesignformodel(onediscinthemiddle),experimentaltestusingSmartOffice.
1
Elemeennttss
MatNNuumm MMaarr 1188 22001111
U
Omeg 1166::3322::0099
Y
Z X
(a) ANSYS(APDL),(3D) (b) (ANSYS)workbench,(3D).
Figure5:Finiteelementmodalrotatingmachinery(onedisc,3D).
vector. Substituting (2) into (1), the equation of spatial MultiplyingthematrixUT atbothsidesof (3)producesthe
motionstransformedintotheequationofdecoupledmotion following:
isobtained:
MUη¨+CUη˙+KUη= f. (3) (cid:2)M(cid:2)η¨+(cid:3)C,η˙+(cid:4)Kη=UTf =μ, (4)
ISRNMechanicalEngineering 5
1Nodes 1Elements
U
Mar 29 2011 Omeg Mar 29 2011
16:57:58 16:58:30
Y
Z Y
Z X
One disc, rotor on bearings One disc, rotor on bearings
(a) (b)
Figure6:Finite-elementmodel(FEM)rotatingmachineryANSYS(APDL),twodimensions(2D).
Figure7:Stationaryloadinthemiddle,onedisc(FRF)versusfrequency(Hz),firstmodeshape.Naturalfrequency29.79Hz,range(0–
500)Hz.
where(cid:2)M(cid:2),(cid:3)C,and(cid:4)Karethediagonalmass,damping,andstiff- oftheexcitingforce,componentsofthemodeshape,andthe
ness matrices, respectively; and μ is the modal force vector. modalparameters:
The equation of motion at the rth mode is represented as
follows:
(cid:2)N
x(cid:4) = η(cid:4) ν
N×1 r r
r=1
Mrη¨+Crη˙r+Krηr =μr, (5) (6)
(cid:2)N (cid:2)N ϕ f(cid:4)
where μr = νrT, f = (cid:3)NJ=1ϕjr, and fj and ϕjr the jth =r=1j=1Mr(cid:5)ωr2−ωj2r+j2iωξrωr(cid:6)νr,
componentsoftherthmodeshapevector.Byconsideringthe
harmonicexcitationactingonthesystem,thecomponentto where x = x(cid:4)eiωt is the displacement vector of the spatial
f themodalcoordinate,andthemodalforceattherthmode model and fj = f(cid:4)jeiωt is the exciting force. In addition, ωr
canbedesignatedasηr =η´eiωt andμr =μ(cid:4)reiωt,respectively. andζr standfortherthnaturalfrequencyanddampingratio
Equation (2) becomes the summation of a series consisting (called modal parameters), respectively. Considering just a
6 ISRNMechanicalEngineering
1Nodal solution 1Nodal solution
Feb 23 2011 Feb 23 2011
15:07:07 15:07:24
Y Y
ZX ZX
0 0.220712 0.441423 0.662135 0.882847
0.110356 0.331068 0.551779 0.772491 0.993203
One disc, rotor on bearings One disc, rotor on bearings
(a) Naturalfrequency29.9393Hz(2D)
Y Y
Z X Z X
(b) Naturalfrequency29.95Hz(3D)
Figure8:Finite-elementmethodsimulations,firstmodeshape,onediscwithtwobearings.
singlecomponent f(cid:4)j oftheexcitingforce,theithcomponent involves the first four natural frequencies (N = 4) that can
ofthedisplacementvectorcanberewrittenas beexpressedasfollows[2]:
ϕ ϕ ϕ ϕ
x(cid:4)i=r(cid:2)N=1(cid:2)jN=1Mr(cid:5)ωr2−ϕiωrϕ2j+rf(cid:4)2jiωξrωr(cid:6). (7) Hij = M1(cid:5)ω12−ωi1ϕ2+jϕ12iωξ1ω1(cid:6) + M2(cid:5)ω22−ωi2ϕ2+jϕ22iωξ2ω2(cid:6)
+ (cid:5) i3 j3 (cid:6) + (cid:5) i4 j4 (cid:6),
The(FRF)Hij isdefinedastheratiooftheithdisplacement M3 ω32−ω2+2iωξ3ω3 M4 ω42−ω2+2iωξ4ω4
componentx(cid:4)i tothe jthexcitingforcecomponent f(cid:4)j.Itcan (9)
alsobeshownasfollows: wherei=1,2,...,4and j =1,2,..., 4.Assumethatthefirst
termattheright-handsideof (9)wasdominantinaffecting
x(cid:4)f(cid:4)ij =Hij =r(cid:2)N=1Hij,r ttehremvsahluaedsaowfethakei(nFflRuFesn)cweohnenthωese=FRωF1s.wThheures,asthtehseecoothnedr,
(8) third,andfourthtermscanbeomitted.Thesimplifiedform
= (cid:2)N (cid:5) ϕirϕjr (cid:6), of (9)cannowbepresentedasfollows:
r=1Mr ωr2−ω2+2iωξrωr Hij,1= Mϕ2i1iϕξj1ω2. (10)
whereHij,risthepeakvalueofFRFattherthmode.Equation 1 1 1
(8) represents the relationship between the single exciting As mentioned, with two DOFs at each of two bearing sup-
force and displacement. However, the situation of multiple ports,therewereatotaloffour(DOFs)forallofthesupports
excitationsisnotconsideredinthefollowingtheory. of the whole system [10]. After this, a (4 ∗ 4) symmetric
frequencyresponsefunctionmatrixwasbuiltasfollows:
⎡ ⎤
3.1.2. The Pseudomode Shape Method. The simple system H
o(sfeea Friogtuorre-b1e)artihnagt-edsteambloisnhsmtraentets styhsetem(MiBsMsh)oowpneraabtioovne. FRFmatrix=⎢⎢⎢⎣HH1211,,rr HH22,r H ⎥⎥⎥⎦. (11)
31,r 32,r 33,r
The rotor was treated as the mother structure, while the H H H H
41,r 42,r 43,r 44,r
foundation and two bearing supports were treated as the
sub structure. Considering only the translation (DOF) sin At the first mode (r = 1), the available peak values in the
the Y and Z directions at each of the bearing supports, the (FRF) data were denoted as H , H , H , H , H ,
11,1 21,1 31,1 41,1 22,1
mode shape vectors of the bearing-foundation structure H ,H ,H ,H ,andH .Thesevaluescanthenbe
32,1 42,1 33,1 43,1 44,1
were represented with a total of four DOFs. Equation (8) utilisedtoevaluatetherelatedcomponents.
ISRNMechanicalEngineering 7
Figure9:Stationaryloadinthemiddle,(FRF)versusfrequency(Hz),onedisc,secondmodeshape.Naturalfrequency242.7Hz,range
(0–500)Hz.
1Nodal solution 1Nodal soolluuttiioonn
Feb 23 2011 Feb 23 2011
15:09:26 15:09:47
Y
Z X MX YZX MX
0 0.464236 0.928472 1.393 1.857
0.232118 0.696354 1.161 1.625 2.089
One disc, rotor on bearings One disc, rotor on bearings
(a) Secondmodeshape,naturalfrequency243.71Hz,(2D)
Y Y
Z X Z X
(b) Secondmodeshape,frequency243.68Hz,(3D)
Figure10:Finite-elementmethod,simulationsonediscwithtwobearings.
3.2. Revolve Acquisition and Analysis Investigational. The 3.2.1. Experiment Setup. Experimental modal analysis has
rotate acquisition and analysis software package is part of grown steadily in popularity since the advent of the digital
(m+pinternational’s).Itisdesignedfortroubleshootingand FFT spectrum analyser in the early 1970’s. Today’s impact
analyzing noise or vibration problems related to the speed testing (or bump testing) has become widespread as a fast
characteristicsofrotatingorreciprocatingcomponentsofa andeconomicalmeansoffindingthemodesofvibrationof
machineinoperation[10,11,13]. amachineorstructure.ThetestrotorisshowninFigure2.
8 ISRNMechanicalEngineering
2.5 Amplitude
5
ζ=0, no damping
4.5
2 ζ=0.1
4
mber kFo 3.5
u 1.5 X ζ=0.2
Mode shape n 1 fication ratio 2.352 ζ=ζ0.=30.5
pli
0.5 m 1.5 ζ=1, critical damping
A
1
0 0.5
0 50 100 150 200 250 300
0
Natural frequency (Hz)
0 0.5 1 1.5 2 2.5
ωn (ANSYS) one disc (Hz) Frequency ratior= ffn
Frequency one disc experiment (Hz)
Figure13:Amplificationratioversusr[3].
Figure11:NaturalfrequencyexperimentwithANSYS,(onedisc).
300
60
50 250
z)
H
ζo (%) 40 ntal), ( 200
ng rati 30 perime
ampi y (ex 150
D 20 nc
e
u
q
e
10 ed fr 100
ur
as
e
M
0
0 50 100 150 200 250 300 50
Natural frequency (Hz)
Damping ratio versus, natural frequency
(0–500) Hz, accelerometer fix, one disc 0
0 50 100 150 200 250 300
Figure12:Dampingratio(ζ)versusnaturalfrequency(0–500)Hz, Predicted frequency (ANSYS), (Hz)
onedisc.
Comparison between measured and predicted
natural frequency (Hz)
Basically, the rotor consisted of a shaft with a nominal Figure14:Comparisonbetweenmeasured&predictedfrequency
diameter of 10mm, with an overall length of 610mm. Two (Hz).
plainbearings,RK4RotorKitmadebyBentleyNevada(the
advancedpowersystemsenergyservicescompany),areused
toextractthenecessaryinformationfordiagnosticofrotat- inthisproject[14].Theanalyzerissuitableforaccurateand
ingmachinery,suchasturbinesandcompressor.Thetesting efficientnoiseandvibrationmeasurements,third-partydata
oftheprocesswillbeconductedontherotarymachineasthe import/export, data analysis, and reporting of the results.
project is based on rotary dynamics reach practical results The SO analyzer supports a wide range of measurement
forthepurposeofsubsequentlyappliedmachineryrotaryby front-end (USB, PCI, PX1, and VX1) which enables the
using(SmartOfficeprogram).Itisthesoftwarewhichisused applications (from two to hundreds of input channels).
ISRNMechanicalEngineering 9
600 6
Hz) 500 4 5
y (
c
n400
e
u
q
e
d fr 300 3
ure 2
as
e
M200
1
100
0 100 200 300 400 500 600 700
Predicted frequency (Hz)
Figure15:Measuredandpredictedfrequency(Hz)[9].
Then, do the experimental testing using the impact test, and performance of 2D and 3D model analyses are closest
installedfixedtwoaccelerometer(model333B32,sensitivity matcheachotherwhenincomparisonwithexperimenttest.
97.2 and 98.6 mV/g) in Y–Z direction and roving the Rotor dynamics play a crucial role in identifying critical
hammer (model 4.799.375, S.N24492) on each point for speeds and to ultimately design rotating structures that
the purpose of generating strength of the movement for tolerate extremely high vibrations. This example illustrates
the vibration body and the creation of vibration for that theapplicationofrotordynamicsanalysisproceduresusing
with creating a computer when taking readings in file that theNelson-Vaughrotormodel[11,16,17].
wasdimensionsandintroducingitwiththedatawithinthe A2Daxisymmetricrepresentationofthe3Dsolidmodel
program Smart office to look for mode shape, see Figure3. is used to perform a rotor dynamic analysis. The results of
[10,15].Configurationsoftestingontherotarymachines,all the2Daxisymmetricmodelanalysesareclosestmatchtothe
necessaryequipmentfortestwereshownwiththegeometry full3Dsolidmodelresults[16,18,19].
designwizard(seeFigure4).
4.Results
3.3.SimulationofModel. Amodelofrotorsystemonedisc
withmultidegreeoffreedom(Y andZ directions)hasbeen As it can be seen from the experimental one disc in the
used to demonstrate the above capability Figures 5 and6. middlefirstmode(Figure7)andFEsimulation(Figures8(a)
ProgramhasbeenwritteninANSYS12,Postprocessingcom- and 8(b)), the result of natural frequency and mode shape
mands (/POST26). Applying of gyroscopic effect to rotat- closestmatcheachother,asthesamewith(Figures9,10(a),
ing structure was carried by using CORIOLIS command. and 10(b)) the second mode, we see all the results closest
This command also applies the rotating damping effect. matcheachotherbetweentheexperimentalandsimulation
CMOMEGE specifies the rotational velocity of an element (ANSYS),wecanseetheresultinTable1andFigure11for
componentaboutauser-definedrotationalaxis.(OMEGA) comparison.Frequencyresponsefunction(FRF)oftherotor
specifies the rotational velocity of structure about global wasfoundusingtheimpacttestmechanismandSmartOffice
Cartesian axes. Model the bearings using a spring/damper software.Asitcanbeseenfromfiguresbelowdifferentmode
element (COMBIN 14). Another command used input file shape for the range (0–500)Hz, the experiment shows that
(SYNCHRO) which specifies whether the excitation fre- by applying a negligible excessive loading to the system the
quencyissynchronousorasynchronouswiththerotational valueofthenaturalfrequencymodeshapedoesnotchanges
velocityofastructureinaharmonicanalysis[11].Thefinite- significantlyfordifferentspeed.
element (FE) method used in ANSYS offers an attractive we find the damping ratio (ζ) for different mode shape
approachtomodelingarotordynamicsystem. by curve fitting [20], (multi degree of freedom system) in
Inthesectionsthatfollows,modelingdetailsandanalysis experimentalpart,(Table2)and(Figure12).Wedrawgraph
procedures for a rotating structure are detailed. Generally, comparisonbetweenmeasured(experimental)andprediect
a 3D model directly available from the CAD can be used natural frequency (ANSYS), (Figure14) show the slope
for the analysis Figure5; however, 3D models result in a approximatelynearbyfrom45◦.Withfurthersimulationwe
large number of nodes and element models. This paper find the relation between the reaction forces with respect
demonstrates how to extract a plane 2D model (Figure6) timecanbeseenfromFigures16(a),16(b),16(c)and16(d).
fromthe3Dmodel(Figure5),whichcanbeanalyzedusing The performance of reaction forces in the right and left
far fewer nodes and elements. The ease of use, accuracy, bearingswithdifferentspeedofrotations.
10 ISRNMechanicalEngineering
100 50
0
N) 50 0 0.002 0.004 0.006 0.008 0.01 0.012
(left bearing), (y 0 0 0.002 0.004 0.006 0.008 0.01 0.012 F(bearing), (N)y −−15000
F e
eaction force −−15000 Reaction forc −150
R −200
−150 −250
Time (s) Time(s)
(a) Reactionforce(Fy)leftbearing (b) Reactionforce(Fy)rightbearing
60 80
60
N) 40 N)
eft bearing), ( 20 ght bearing), ( 2400
F(lz 0 0 0.002 0.004 0.006 0.008 0.01 0.012 F(riz 0
Reaction force −−2400 Reaction force −−4200 0 0.002 0.004 0.006 0.008 0.01 0.012
−60 −60
Time(s) Time(s)
1000 rpm 6000 rpm 1000 rpm 6000 rpm
3000 rpm 10000 rpm 3000 rpm 10000 rpm
(c) Reactionforce(Fz)leftbearing (d) Reactionforce(Fz)rightbearing
Figure16:Relationbetweenreactionforcebearingsversustimeatdifferentspeedofrotation(onediscinthemiddle).
Table 1: Comparison between natural frequency outcomes from Table 2: Natural frequency and damping ratio (ζ) for one disc
experiment&ANSYS,(onedisc). range(0–500)Hz(experimentalpart).
Mode ωn(ANSYS) dFirsecqeuxepnecryimoennet Error% F(Hrezq)uency Dam(pζi)n%gratio ModalA[kg/s] Name
shape onedisc(Hz)
(Hz)
29.79 56.701 0.009123329–(0.01562434) Mode1
1 29.939 29.79 0.497678613 0.001488148–
242.74 7.561 Mode2
2 243.71 242.74 0.398014033 (0.002922353)
As it can be seen from the experimental (Figures 17, loadaddedinthediscgroovebyangle(135◦,315◦)degree,
18 and 19) and FE simulation, when 8 gram of excessive frequencyresponsefunctions(FRFs)oftherotorhasfound
load is added to the loading of the system, the excessive it.Withfurthersimulation,wefindtherelationbetweenthe
loading is away from the centre of the shaft by (30mm), bendingstresswithrespectoftime(Figures21(a),21(b)),the