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/7 77SNASA Techn.icalMemorar_du.m_106.!62 ........ Army ResearchLaboratory
AIAA-93-2150 _ MemorandumReport ARL - MR" 77
Vibration and Noise Analysis of a Gear
_TF.K, Choy and W. Oian
The University of Akron --Akron, Ohio _._
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......... and ............... - ........................
J.J. Zakrajsek __andEB: Qsw, ald ........ ..... = ............ ,
Lewis Research Center _Cleveland, Oh_io
Prepared for the....... 29th Joint Propulsion Co_nfer_ence and _E_xhibi!............................. ,-.,_
cosponsored by the AZAA, SAE, ASME, andASEE -'_2.
: :Monterey, California, June 28-30, 1993
N/ A ............. RESEARCHLABORATORY
https://ntrs.nasa.gov/search.jsp?R=19930018452 2020-04-09T12:59:25+00:00Z
VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM
F.K. Choy and W. Qian
Department ofMechanical Engineering
The Universityof Akron
Akron, Ohio 44325-3903
and
J.J.Zakrajsek and F.B. Oswald
National Aeronautics and Space Administration
Lewis Research Center
Cleveland,Ohio 44135-3191
Abstract
This paper presents a comprehensive procedure to
predictboth the vibrationand noisegeneratedby a gear
transmissionsystem under normal operatingconditions.
The gearbox vibrationswere obtained from both numeri-
cal simulation and experimental studiesusing a gear
noise testrig.In addition,the noise generated by the
gearbox vibrationswas recordedduringthe experimental
testing.A numerical method was used to develop linear
relationshipsbetween the gearbox vibrationand thegen-
eratednoise.The hypercoherence functionisintroduced
to correlatethe nonlinearrelationshipbetween the fun-
damenta! noisefrequency and itsharmonics. A numeri-
cal procedure was developed using both the linearand
nonlinearrelationshipsgeneratedfrom the experimental
data to predictnoiseresultingfrom the gearbox vibra-
tions.The applicationof thismethodology isdemon-
stratedby comparing the numerical and experimental
resultsfrom the gear noisetestrig.
A
Ac
B
Be
[cb]
[cJ
D
Dt
De
Nomenclature
rotor modal displacement of (X, 0x)
casingmodal displacement of (X¢, 9cx}
rotormodal displacement of (Y, 0y)
rotor modal displacement of (Yc, 0cy}
bearingdamping matrix
casingstructuredamping matrix
[#]T [Cb] [#] _
[#jT[%][#¢l
[#JIce][#elrotormodal displacement of Z
rotormodal displacementof 0t
casing modal displacement of (Ze,8¢z}
{F(t)}
{FG(t)}
{Fc(t)}
{F,(t)}
[GAI
[Gvl
[Kb]
[Kj
[K.]
[KA]
Kbx,Kby
[MI
[MjW
Wc
x rotorx-displacement
xe
Y
Yc
g
zc
externaland mass-imbalance excitations
gear force
forceactingon casingstructure
shaftbow force
rotorangular acceleration
gyroscopic
[#]z[CA][#I
[#]T [Gvl [#l
bearingstiffness
casingstructurestiffness
shaftbow stiffness
1/2{[Kbx] + [Kby]}
[#]T [Kb] [#]
[#lT IKA][#]
[#c]T [Kb] [#¢]
bearing stiffnessin x and y directions
mass matrix ofrotor
mass matrix of casingstructure
generalizeddisplacementvector ofrotor
generalizeddisplacementvector ofcasing
casingx-displacement
rotory-displacement
casingy-displacement
rotorz-displacement
casingz-displacement
frictioncoefficientbetween the gear teeth
surface
1
_c
_x
_xe
Ox,#y,O,
Ocx,Ocy,
Ocz
(d
angle of orientation
rotor orthonormal mode shape
casing orthonormal mode shape
rotor translational mode shape
rotor rotational mode shape
rotor rotational motion
casing rotational motion
criticalspeed ofrotor
criticalspeed ofcasing
Introduction
The ever increasingpower-to-weight ratiorequire-
ments of newer transmission systems often resultin
greaternoise and vibrationat both the gear mesh and
the gearbox structure.Large vibrationsingeartransmis-
sionsystems resultin higher gear tooth wear ratesand
possibletooth root crackformation which leadsto pre-
mature gear failure.In addition,excessivenoise pro-
duced by a gear transmissionin an aircraftcausescrew
fatigue,strainedcommunication, and possiblehearing
damage for crew and passengers.In order to assure a
quiet,smooth, and safeoperationofa gear transmission
system itisnecessaryto understand the dynamics ofthe
system and the noisegeneratedby the system under var-
iousoperating conditions.
A largeamount ofwork isreported inthe literature
on analyzing the localizedeffectsof gear tooth interac-
tions.In the area of experimental investigationsof
localizedgear toothinteractions,a significantamount of
work was performed over the last10 years (Akin, 1989;
Choy, 1989; Oswald, 1987; Krantz, 1992; Lewicki, 1992;
El-Bayoumy, 1989; and Rebbechi, 1991). There is muchless information available in the literature on the study
of the global dynamics of a transmission system. There
have been some studies on the vibration analysis of a
single-stage gear (August, 1982; Choy, 1988; Markl
1982; and Boyd, 1989) and on multistage gear dynamic
analysis (Choy, 1991, 1993; David, 1987; and Ozguven,
1988). The experimental study of gear system vibrations
is somewhat limited (Choy, 1991; Lira, 1989; and
Oswald, 1992). Reported research is even more limited
in the areas of noise analysis and noise prediction in gear
transmission systems. Some work on predicting and veri-
fying the noise field of a gear transmission system has
only recentlybeen reported (Seybert,1991 and Oswald,
1992).
In response to the importance ofthe applicationand
the limitedamount of work performed in the area of
gearbox noise and vibrationresearch,a program was
startedwith the main objectiveofdeveloping the meth-
odology required to predictgear transmission system
noiseand vibration.This paper describesthe globaldy-
namic model that was developed to simulate the noise
and vibrationof a multistagegear system. Resultspre-
dictedby the numerical-model axe compared to experi-
mental resultsobtained from the gear noisetestrig at
NASA Lewis Research Center.
AnalyticalProcedure for Gear System Vibration
To achieve the numerical solution,the generalized
equations of motion developed in a previous paper
(Choy, 1993) presents the numerical procedure using the
modal synthesis method. Using the undamped modes for
both the rotor-bearing-gear system and the gearbox
structure, the generalized equations of motion for the
system aretransformed intothecorrespondingmodal co-
ordinates. This procedure significantlyreduces the
degreesoffreedom of the system, and provides an esti-mate ofthe modal excitationsat the variousmodes.
The modal transformation procedure can be devel-
oped by assuming that the generalizeddisplacementscan
be represented by a linearcombination of the modal
characteristics,(Choy, 1991, 1993) as
{w}
I#=]{A}
[#y]{s}
[#yo]{B)
[#,.] {S}
[@t] {Dr}
(1)
where A, B, D, and D t are the time-dependent modal
excitationfunctions,and [_x],[_xS] [#y],[_y0],{_-],
and [_t]are the matrices containing the orthonormal
modes ofthe correspondingrotorsystem. Similarly,for
the gearbox housing structure,
using
{we}
[#_]{A,}
= [#.]{Be}
[@cy0]{Be}
[#cze]{De}
(2)
{A}
{B}
{z} = {D}[ {Z_}
!Dt}l[[Dc}
(s)
The modal equationsfor the rotorsystem (Choy, 1991,
1993) can be written-in ffiodalcoordinatesas:
if]{_,}= [_.]{_}- [_A]{Z}- [_b]{_'}
+ [_:b--KAl{Z}--[#]T[Cbl[#j{_,_}
- [J]{z}+ [_IT[KB][_,¢1{Zc}
+ [#IT{F(t)+FG(t)+L(t)}
and forthe casing
(4)
[I]{_._}= [U_]{z_}- [_1{z_}- _0 (z_}- [Ub]{_,_}
+ [#c] T [Kb] [@] {Z} + [#tIT [Cb] 1@]{Z} -t- [_¢]T {F¢(t)}
(s)
Using the appropriateinitialconditionsfor the modal
velocity{7,}and displacement {Z}, the modal accelera-
tions {Z} can be solved.The solutionprocedure can besummarised asfollows:
1. Input initialconditions to calculate modal
accelerations.
2. Use variabletime-steppingintegrationscheme to
evaluatemodal velocityand displacement at next time
step.
8.Calculatevelocityand displacement ingeneralizedcoordinates.
4. Calculate nonlineargear mesh forcesdue to rela-
tivemotion between th_ two gears.
5. Calculate bearing forcesdue to relativemotion
between the rotorand the casing.
6. Calculatemodal bearing and gear forces.
7.Repeat from step number 2.
Experimental Studies
Test resultsfrom the gear noisetestrig(Fig. l(a)) at
NASA Lewis were used inthisstudy to rei'meand vali-
date the globaldynamic model developed.Three phases
ofexperimentalstudieswere performed: (1) the determi-
nation ofstaticmodal characteristicsusingthe impulse-
response technique;(2)the transientvibration of both
rotor and the gearbox structureduring operation;and
(8)measurement ofthe noisegenerationat the gearbox
surfaces.An outlineof the experimental studiesispre-sented below:
Evaluation of Experimental Modal Characteristics
The gear transmissionsystem used in this test is
shown inFig. l(b).The gear system consistsofa p_r of
identicalparallelaxis spur gears supported by rolling
element bearings.The top and four sidesofthe gearbox
were dividedintoa gridof 116 node points.The transfer
functionsof the system were found from the impulse-
response technique by using an impact hammer. Three
accelerometers,one on the surface in the x-direction,
another in the y-direction, and the last in the
_direction,were used to obtain the responsesfrom the
impacts. Natural frequenciesand their corresponding
mode shapes excitedduring the experiment were evalu-
ated using a two-channel dynamic signalanalyzer with
PC-based modal software.The modal characteristics
found during the experiment were compared with those
generated by the numerical model for verification
purposes.
Experimental Investigationsof System Dynamics
The testrig ispowered by a 150-kW (200-hp) vari-
ablespeed electricmotor. An eddy-currentdynamometer
is used to absorb power at the opposite end. During this
test, accelerometers were placed on the top surface of the
gearbox to monitor the vibrations of the gearbox struc-
ture. In addition, two sets of noncontacting eddy-current
proximitors monitored motion of the gear shafting. The
vibration signals of the gearbox surface and the shafts
were recorded over a range of operating speeds from
3000 to 5000 rpm. A two-channel dynamic signal anal-
yzer computed the vibration frequency spectra which are
displayed in a waterfall diagram. The lateral vibration
frequency spectra of the gears were also computed. The
results of this phase of the experimental work were corn,
pared with those from the model for verification of the
numerical procedure and improvement of the modeling
of the gear transmission system.
Investigations of Gearbox Noise
Two acousticmicrophones were used in th_sexperi-
ment. Both microphones were placedover the top cover
ofthe gearbox with one inthe verticaldirectionand the
other at a 45° angle from the vertical.While rotor and
gearbox vibrationare recorded as describedin the last
section,noisewas obtained by the microphone system
at various running speeds. A correlationbetween the
gearbox vibrationsand the noiselevelwas performed in
the frequency domain using lineartransferand cross-
correlationfunctions.The nonlinear hypercoherence
function (Jong, 1986) was alsoused to generate a rela-
tionship between the noise and the vibration data in
order to develop a noise predictionalgorithm for the
globaldynamic model.
Correlation and Benchmarking of .System Dynamics By
Numerical Procedures with Experimental Results
The modal hammer excitedmany vibrationmodes of
the gearbox structure.Eight of thesemodes in the fre-
quency range 0 to 3000 Hz seem to dominate the trans-
ferfunctionspectra.These eightmodes, shown inFig. 2,
were chosen to representthe vibrationofthe system. In
orderto produce an accurateanalyticalsimulationofthe
testgearbox, a similarsetofmodes was generatedusing
a NASTRAN finiteelement model ofthe gearbox struc-
ture.Out of 25 modes in the analyticalmodel in the
0 to 3000 Hs frequency range, the eight dominant modes
(similar to those from the experimental studies) were
used to represent the gearbox dynamic characteristics.
These analytically simulated modes are shown in Fig. 3.
Table I lists the natural frequencies of the simulated
modes. The calculated natural frequencies are within
5 percent of the measured modes. The three-dimensionai
analytical mode shapes (Fig. 3) are very similar to the
experimental mode shapes (Fig. 2). The correlation ofthe results between the analytical model and the experi-
mental measurements confn'ms the accuracy of the dy-
namic representation of the test gearbox using only a
limited number of modes. In addition, this correlation of
the experimental modal characteristics with the numeri-
cal model helps to reduce the number of modes beingused in the numerical simulation to achieve an accurate
result.
A slow roll of the rotor-gear assembly revealed that
a substantial residual bow was present in the rotor as
shown by its large orbital motion given in Fig. 4. Fig-
ure 4(a) represents the orbit of the driver rotor at the
gear location and Fig. 4(b) represents the orbit of thedriven rotor. The circular orbit in the driver rotor at
slow roll represents the residual bow deformation of the
rotor.The ellipticalorbitin the drivenrotorisdue to a
combination ofthe residualbow effectsand the vertical
gear forcefrom the torque of the drivinggear.In order
to analyticallysimulate the influenceof this effect,a
residual bow of 0.05 mm (2 mil) was incorporated intothe numerical model. Figure 5 represents the frequency
spectra of the driven gear vibration generated from both
the experimental and the numerical procedures. The ex-
ceUent agreement in both results further verifies the
validity of the numerical study.
In order to predict the noise of the transmission
system during operation,the vibrationof the gearbox
must be accuratelymodeled. Figures6 and 7 presentthe
time domain vibration signal and corresponding fre-
quency spectraof the signalfor the gearbox top surface
from both experimental and numerical studies. Fig-
ure 6(b) shows the analyticallypredictedvibrationsig-
nal (acceleration)atthe top ofthe casingstructureat an
operatingspeed of3000 rpm while the corresponding ex-
perimental resultsare given in Fig. 6(a).Note that the
amplitudes and generalshapes of the two time signals
are very similar.The comparison of their frequency
contents are given by the frequency spectra in Fig. 7.
Figure 7(a) shows the frequency components of the
measured vibrationat the top of the gearbox. Note that
the major vibrationcomponents occur at the mesh fre-
quency of1250 Hz and at 3-times(3750 Hz) and 4-times
(5000 I-Is)the mesh frequency.The very largeamplitude
in the frequency components at 3750 and 5000 I-Isare
due to the excitationofthe gearbox naturalfrequencies
near the 3-timesand 4-timesmultiplesof the mesh fre-
quency. The fundamental and the 2-times mesh fre-
quency component are substantially smaller due to the
lack of any gearbox natural frequencies near 1250 and
2500 Hz. In addition, frequency components of substan-
tial magnitude are also noticed at 700 and 2900 Hz,
which are also close to the natural frequencies of the
gearbox. Figure 7(b) depicts the results from the numer-
ical simulations of the system. The numerical results
correspond closely to those from the experimental study
with the exception of the 4-times mesh frequency
4
component. The magnitude and the generaldistribution
of the frequency contentof the spectrum isvery similar
to the experimentalresults.
CorrelationofNoise and Vibration
In order to predict the noise generated in a gear
transmissionsystem, a two-phase procedure was devel-
oped to correlatethe noiseand vibrationdata obtained
during experimental studies: (1)linear correlation
through transferfunctions,and (2)nonlinearcorrelation
through hypercoherence functions.The relationships
derivedin thisstudy were used topredictgearbox noise
from the numericalsimulationofthe gearboxvibrations.
A descriptionofthe proceduresused ispresentedinthe
followingparagraphs:
CorrelationofExperimental Noise and Vibration Data
In this experiment, a new set of two identical25-
tooth gears were installedin the gearbox shown in
Fig. l(b). The vibration of the gearbox surfaceswas
monitored by accelerometers,and the noise data was
obtained by microphones, as describedin the previous
section.The frequency and power spectraof both the
vibrationand noisesignalsat 3000 rpm running speed
axe shown hx Fig.8. Note that in the vibration spec-
trum, a small frequency component existsat the mesh
frequencyof 1250 Hz with two very largecomponents at
3-timesthe mesh frequency(3750 Hz), and 4-timesmesh
frequency (5000 I-Is).In the noise spectrum, while fre-
quency components of considerable magnitudes are
observed atthe mesh frequencyof1250 Hz, and at2 and
S-times the mesh frequency (2500 and 3750 Hz), _ large
amplitude frequency component is also noticed at
400 I-Is. This 400-I_ frequency component does not coin-cide with any of the major vibration frequencies at the
top surface of the gearbox. A closer examination of the
system dynamic characteristics reveals that the 400-Hz
frequency is an excitation of one of the natural frequen-
cies of the rotor system, which has a very small ampli-
tude in the gearbox vibration spectrum. A logical
explanation is that noise is being produced at the rotor-
gear system at 400 I-Is and is not being transferred to
the vibration of the gearbox surface. This phenomenon
is further verified by the very large amplitude of the
vibration-to-noise transfer function at 400 I-Iz as given
in Fig. 9(a). A linear coherence function between the
noise and vibration signals is also given in Fig. 9(b).
From the experimental data, it can be observed that
in the frequency domain, most of the noise components,
other than the 400-Hz contributions, exist at multiples
of the mesh frequency. The nonlinear hypercoherence
function was used for the second phase of this study.
The hypercoherence function (Jong,1986) establishesa
nonlinearrelationshipbetween the basicfrequency com-
ponent and itsmultipleharmonics. Figure 10 shows the
hypercoherence functions of the noise signalsfor the
3000-rpm case.The magnitudes ofthe harmonic compo-
nents form the nonlinearrelationshipofeach component
to the fundamental gear mesh frequency.These relation-
shipsprovidea pictureofthe relativecontributionofthe
higher harmonics with i_pect to the fundamental fre-
quency. These hypercoherence functionswere used on
the numerical simulationdata to examine the accuracy
ofthe noiseprediction.
In order to predictthe noiselevelofthe transmission
system during operation,the vibrationsof the gearbox
structure were simulated using the modal synthesis
method. The transferfunctionformicrophone number 1
(verticalto the plate),asgiven inFig. 9(a), was used to
predictthe noise spectrum of the system (Fig.11(b)).
Figure 11 shows the comparison of the resultsof the
experimentalnoise (Fig.11(a))with the predictednoise
(Fig.11(b)) for the verticalmicrophone. Although all
the m_jor frequency components excitedin both cases
are very similar,one can see that the predicted noise
spectrum (Fig.11(b))has a somewhat higheramplitude
at mesh frequency (lx) and.a very small 4-timesmesh
frequency (4.x)component as in the vibrationspectrum.
Another way of examining the validityof the pre-
dicted noisesignalisthrough the nonlinearrelationships
derivedby the hypercoherencefunction.Figure 12shows
the comparison of the hypercoherence functionsfrom
both experimental and numerical solutionsfor micro-
phone number 1.Note that both the experimental and
numerical resultsshow a very small 2-timescomponent,
with a substantial amplitude at $, 4, and 5 times funda-
mental frequency. However, a 50-percent coherence is
found in the 3, 4, and 5 times components from numeri-
cal predictions (Fig. 12(b)) while only about a 25-percent coherence is seen from the experimental results
(Fig. 12(a)). This difference is possibly due to thelimitations of the numerical model in simulating various
details in the gearbox transmission system. An explana-
tion of the much higher (nearly double} coherence ampli-tudes in the numerical study is that only the major
frequency-related vibration factors axe included in the
model, which results in a predicted vibration signal con-
sisting mostly of frequency components that are closely
related to the fundamental frequency.
Conclusions and Summary
A methodology was developed using the modal syn-
thesistechnique to simulate the globaldynamics of a
gear transmission system. Good correlationhas been
obtained using resultsfrom the global dynamic model
andmeasureddynamiccharacteristicsfrom the NASA 6.
gear noise testrig.A numerical relationshipwas also
developed from the experimental data to correlatenoise
and vibrationsin the frequency domain. This relation-
ship was appliedto the vibrationsimulationsto predict
the noise generated by the gearbox. Resultsof the pre- 7.
dictednoisewere compared to the experimentallymeas-
ured data linearlyusing the frequency spectra and
nonlinearly using the hypercoherence function. Some
conclusionsofthisstudy can be summarized asfollows:
I. The dynamics of a gear transmission system
coupled with the vibrationsof the gearbox structure
during operation can be simulated within 5 percent
of the modal frequenciesusing the modal synthesis
technique.
2.Predicted vibrationsat the housing surfaceusing
the globaldynamic model are in good agreement with
measured values.
3.Both the frequenciesand magnitudes of the pre-
dicted noisecomponents are similarto those obtained
from experimentalstudy.
4. The hypercoherence function was found to be a
valuabletoolincomparing the nonlinearrelationshipsin
the predictednoiseto the corresponding nonlinearrela-
tionshipsin the measured noise.
References
1. Akin, L.S., and Townsend, D.P., _Lubricant Jet
Flow Phenomena in Spur and HelicalGears with
Modified Addendums--for Radially Directed Indi-
vidualJets,_ NASA TM-101460, 1989.
2. August, R., and Kasuba, R., _Torsional Vibrations
and Dynamic Loads in a Basic Planetary Gear
System," JournalofVibration7Acoustic_Stress_and
Reliabilityin Design, Vol. 108, No. 3, July 1986,
pp. 348-353.
3. Boyd, L.S.,and Pike,J.A.,"EpicyclicGear Dynam-
ics,"AIAA Journal, Vol. 27, No. 5, May 1989,
pp. 6O3-6O9.
4. Choy, F.K., Townsend, D.P., and Oswald, F.B.,
"Dynamic Analysis of Multimesh-Gear Helicopter
Transmissions,_ NASA TP-2789, 1988.
5. Choy, F.K., Townsend, D.P., and Oswald, F.B.,
"Experimental and Analytical Evaluation of Dy-
namic Load and Vibration of a 2240-kW Rotorcraft
Transmission," Journal of The Franklin Institut%
Vol. 326, No. 5, 1989, pp. 721-735. -
8.
9o
10.
11.
12.
13.
14.
15.
16.
Choy, F.K., Tu, Y.K., Savage, M., and Townsend,
D.P., "Vibration Signature Analysis of Multistage
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Choy, F.K., Ruan, Y.F., Zakrajsek, J.J.,
Oswald, F.B., and Coy, J.J., "Analytical and
Experimental Study ofVibrationsin a Gear Trans-
mission,r AIAA Paper 91-2019, 1991.
Choy, F.K., Ruan, Y.F., Zakrajsek, J.J.,
Oswald, F.B., "Modal Simulation of Gear Box
Vibrations with Experimental Correlation,_ to be
published in AIAA Journal of Propulsion and
Power, 1993.
David, J.W., Mitchell, L.D., and Daws, J.W.,
_Using Transfer Matrices for Parametric System
Forced Response,_ Journal ofVibration_Acoustics_
Stressand Reliabilityin Design, Vol. 109, No. 4,
Oct. 1987, pp. 356-360.
EI-Bayoumy, L.E.,Akin, L.S.,Townsend, D.P.,and
Choy, F.C., _The Role of Thermal and Lubricant
Boundary lJayersinthe TransientThermal Analysis
ofSpur Gears,_ NASA TM-I01435, 1989.
Jong, J.,and Coffin,T., _DiagnosticAssessment of
Turbomachinery by the Hyer-Coherence Method,"
Advanced Earth-to-Orbit Propulsion Technology
1986, Vol. 1, NASA CP-2436, VOL-1, pp. 45-64,1986.
Krantz, T.L., "Gear Tooth StressMeasurements of
Two Helicopter Planetary Stages,_ NASA
TM-105651, 1992.
Lewicki, D.G., Decker, H.J., and Shimski, J.T.,
_Full-Scale Transmission Testing to Evaluate
Advanced Lubricants,_ NASA TM-I05668, 1992.
Lira,T.C., Signh, R., and Zakrajsek,J.J.,_Modal
AnalysisofGear Housing and Mounts," Proceedinss
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Vol. 2,SocietyofExperimental Mechanics, Bethel,
CT, 1989, pp. 1072-1078.
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Gear System Dynamics Applied to Conventional
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CR-3626, 1982.
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the UH-60A Helicopter Transmission,_ NASA
TP-2698, 1987.
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Conditionson Geaxbox Noise,"NASA TM-105331,
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TABLE I.--COMPARISON OF EXPERIMENTAL
MEASURED AND ANALYTICAL MODELED
NATURAL FREQUENCIES
Experimental, Analytical, Difference,
Hz Hz percent
658
1049
1710
2OO0
2276
2536
2722
2962
658
1006
1762
2051
2336
1536
2752
3012
0
-4.1
3.0
2.6
2.6
0
1.1
1.7
Dynamometer-=,
_... rSoft coupling ,_Test gearbox_
Speed _-_ \ r-Torqueincreaser 7 _ \_,____
(a) Schematic of NASA gear noise rig.
(b) Test gearbox.
Figure I .--Gear noise test dg at NASA LeRC.
8
9
7" ..L j.
IIMode: 1
Frequency = 658
• /
z z
Mode: 2
Frequency = 1006
z
Mode: 3
Frequency = 1762
t
z
f
Mode: 5
Frequency = 2336
Mode: 4
Frequency = 2051
Mode: 6
Frequency = 2536
z
z
!
Mode: 7
Frequency = 2752
Mode: 8
Frequency = 3012
1x
Figure 3.--Analytica_ determined mode shapes of the gear box (0 to 3000 Hz).
z
10
.OO6
C
o
-.006
Shaft #1D
Shaft #2
I I I J0 .006 -.006 0 .006
Displacement, X-direction, In.
(a) Dflving rotor orbit. (b) Driven rotor orbit.
Rgure 4.-.-Orbital motion of rotor during slow roll.
11
,o]0.5
0
0 500 1000 1500 2000
X-direction vibration
I(a) Experimental
0
Frequency, Hz
Co)Ana_ical.
I , I
5OO 1000
I I1500 2OOO
Y-direction vibmSon
i_gum 5.--*Frequency spectra of the driving rotor vibration.
Rotationalspeed,
rpm
6O0O
5500
50OO
4500
4O00
35OO
3000
25OO
2000
I 15oo
6OO0
55O0
500O
450O
4OOO
35O0
30OO
25OO
2OO0
1500
12
20f2.5
2.0
4X
3x
r" Mesh10 1.5 - I frequency
I
-10,I | I
-2o I l i i I ._ o _ =_ '
(a) Experimental data. { (a) F_xpedmentai dat;__" 2.5 3x
20 2.0 - Mesh
10 1.5 _-- frequency 1
o 1.0-10
0.5
0 0,1 0.2 0 2000 4000 6000 8000 10 O00
Time, s Frequency, Hz
(b) Numencal simulations. (b) Numerical simulatiorm.
Figure 6.ITime vibration signal at top of gear box for operating Iqgum 7._Vibration frequency spectra at top of gear box forspeed of 3000 rprn. operating speed of 3000 rpm.
13
CL
3°E2.5
2.0
1.0
0.5
0 _ ++
(a) Frequency spectrum for vibratiorL
@,+..,
"5.E<
.15 i
r 400 I-tzf
.10
0 .. I
(b) Frequency spectrum for noise from micro-phone number 1.
2000xl 03
0 I J,, t,, l i_ I
(c) Power spectrum for vibration.
40005000i.._400 Hz_3000
i
L . .. I [ I I
0 2000 "4000 6000 8000
Frequency, Hz
(d) Power spectnJm for noise from microphonenumber 1.
Figure 8,--Frequency and power spectrum atthe operating speed of 3000 rpr_
.7O
.60
.50
+_.+o
,20
.10
I0
(a) Transfer function.
1.00
.75
o¢
8.25
I0 2000 4000 6000 8000 10000
Frequency, Hz
(b) Coherence function.
Figure 9.---Functione between noise (microphone number 1) andvibration at the obemting speed of 3000 rpn_
1.00 1 I I I I I
.75 --
¢D
02
-r
.50 --
.25
II
-- !
]
o 1
ill2 3 4 5 6
Harmonics of mesh frequency
I7
Figure 10.--Hypercoherence function for the noise signal frommicrophone number 2 at 3000 rpm.
14
.14
•12 frequency
.10 3x
.08
.06 2x
.02
r- Mesh
.30 ii frequency
.10
0 2O00
4X
(a) Experimental noise.
I I
80O0 10O0O4000 600O
Frequency, Hz
(b) Predicted noise.
IRgure 11 .--Frequency spectra results from microphone number 1at the operating speed of 3000 rpm.
.50
.25
i 0,o2
1.002:
I
II
I I I I I I
I
(a) Experimental data.
I I I I I I
.75 -
.50 -
| , ,,
2 3 4 5
Frequency harmonic
(b) Numerical predictions.
6 7 8
F'K3um12.--Hypercoherence function of the noise signal frommicrophone number I at 3000 rpm.
15
Form ApprovedREPORT DOCUMENTATION PAGE OM_ No. 0704-0188
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1. AGENCY USE ONLY (Leave blank)
4. TITLE AND SUBTITLE
REPORT DATE
June 1993r
Vibration and Noise Analysis of a Gear Transmission System
6. AUTHOR(S)
F.K. Choy, W. Qian, J.J. Zakrajsek, and F.B. Oswald
7. PERFORMING oRGANIZATION NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135-3191
9. SPONSORING/MONITORING'AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
3. REPORTTYPE AND DATES COVERED
Technical Memorandum
FUNDING NUMBERS
WU-505--62-10
L PERFORMING ORGANIZATIONREPORT NUMBER
E-7859
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
NASA TM- 106162
AIAA-93-2150
ARL--MR-77
11. SUPPLEMENTARY NOTES
Prepared for the 29th Joint Propulsion Conference and Exhibit cosponsored by the AIAA, SAE, ASME, and ASEE, Monterey, California,
June 28-L30, 1993. EK. Choy and W. Oian, The University of Akron, Department of Mechanical Engineering, Akron, Ohio 44325-3903;
and J.L Zakrajsek and F.B. Oswald, NASA Lewis Research Center. Responsible person, J.J. Zakrajsek, (216) 433--3968.
l:;a. DISTRIBUTIONIAVAJLABILn'Y STATEMENT 12b. DISTRIBUTION'CODE
Unclassified - Unlimited
Subject Category 37
13. _BSTHACT (lllaJcimurn200 words")"
This paper presents a comprehensive procedure to predict both the vibration and noise generated by a gear transmission
system under normal operating conditions. The gearbox vibrations were obtained from both numerical simulation and
experimental studies using a gear noise test rig. In addition, the noise generated by the gearbox vibrations was recorded
during the experimental testing. A numerical method was used to develop linear relationships between the gearbox
vibration and the generated noise. The hypercoherence function is introduced to correlate the nonlinear relationship
between the fundamental noise frequency and its harmonics. A numerical procedure was developed using both the linear
and nonlinear relationships generated from the experimental data to predict noise resulting from the gearbox vibrations.
The application of this methodology is demonstrated by comparing the numerical and experimental results from the gear
noise test rig.
14. SUBJECT TERMS
Gears; Vibration; Noise
17. SECURITY CLASSIFICATIONOF REPORT
Unclassified
NSN 7540-01-280-5500
18. SECURITY CLAssIFIcATIONOF THIS PAGE
Unclassified
19. SECUR'FFY("L'ASSIFICATIONOF ABSTRACT
Unclassified
15. NUMBER OF PAGES17
le. PR|CECOOEA03
20. LIMITATI()N OF ABSTRACT
Standard Form 298 (Rev. 2-89)Prescribedby ANSI Std. Z39-18298-102