Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR...

18
/7 77S NASA Techn.ical Memorar_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 _._ _0 F.. 0 ......... 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

Transcript of Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR...

Page 1: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

/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 _._

_0 F..

0

......... 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

Page 2: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron
Page 3: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

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_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,

Page 5: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

Page 6: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

Page 7: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

Page 8: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

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_Dynamic Measurements of Geax Tooth Friction

and Load," NASA TM-103281, 1991.

20. Seybert, Wu, T.W., and Wu, X.F., "Acoustical

Analysis of Gear Housing Vibration,_ NASA

TM-103691, 1991.

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

Page 10: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

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9

Page 12: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

Page 13: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

.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

Page 14: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

,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

Page 15: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

Page 16: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

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

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

Page 17: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

.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

Page 18: Vibration and Noise Analysis of a Gear - NASA€¦ · VIBRATION AND NOISE ANALYSIS OF A GEAR TRANSMISSION SYSTEM F.K. Choy and W. Qian Department ofMechanical Engineering The UniversityofAkron

Form ApprovedREPORT DOCUMENTATION PAGE OM_ No. 0704-0188

Public reporting burden fo'r this collection Of information Is estimated to average 1 hour per response, including the time for reviewing instruCtiOns, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection Of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway. Suite 1204, Arlington. VA 22202-4302. and to the OWce of Management and Budget. Paperwork Reduction Project (0704-0188). Washington. DC 20503.

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