acoustic radiation efficiency

7/24/2019 Acoustic Radiation Efficiency

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NASA

TechnicalMemorandum

107226

ArmyResearchLaboratory

Technical

Report

ARL-TR-1111

Acoustic

Radiation

Efficiency

Models

of

aSimple

Gearbox

MarkF .

Jacobson

and

RajendraSingh

Ohio

State

University

Columbus,

Ohio

FredB.Oswald

Lewis

Research

Center

Cleveland,

Ohio

CNJ

**3Q

9

*U^

$8is

Preparedfo rth e

SeventhInternationalPower

Transmission

and

Gearing

Conference

sponsoredb y

th e

American

Society

of

Mechanical

Engineers

San

Diego,

California,

October

6-9,

1996

National

Aeronaut ics

an d

Space

Administrat ion

DIS

TRTBUTION

STATEMENT

A

Approvedor

public

elease;

Distribution

U nlimited

U.S.

RMY

RESEARCH

LABORATORY


2/7

ACOUSTIC

RADIATIONEFFICIENCY

MODELS

OFASIMPLEGEARBOX

MarkF

Jacobsoman dRajendra

Singh

Ohio

State

University

Co lumbus,

Ohio 43210

Fred

B .

Oswald

NASA Lewis

ResearchCen te r

Cleve land,Ohio 44135

ABSTRACT

Acousticintensitymeasurementswereconducted

on

a

simple

spur

geartransmissionina weldedsteelhousing.Theradiationefficiency

of

th e

housing

was

computed

from

the

intensity

data

fo r

the

first

three

harmonics

of

mesh

requency.

initeelementan dboundaryelement

methods (FEM/BEM)

were

used jointlyto

model

acoustics

an d

dynamics

ofthe

top

plate

ofthe

housing.

or

a

simply

upported

elastic

plate,

reasonable

greement

wa s

chieved

between

experimental

radiation

efficiencies

an d

those

predicted

withFE M/B E M.However,predictions

of

th e

housing

characteristics

were

only

partially

successful.

Four

simple

analytical

modelswere

examined

to

judge

theirabilitytopredictth e

radiation

efficiency.

These

models

do

no t

simulate

th e

modal

characteris-

tics

of

a

gearbox;

therefore

their

predictionsyieldonlygeneral

trends.

Discrepancies

are

believed

to

be

related

to

inaccurate

modeling

of

the

excitationofth e

structure

as

well

as

to

interactions

betweenmodes

of

vibration.

INTRODUCTION

Much

effort

ha sbeen expended

during

thedesign

processin

recent

yearstopredict

th e

noise

of

machinery

in

order

to

reduce

it.

The

mesh

excitation

of

geartransmissions

ha s

been

analyzed,

an d

a

method

ha s

beendeveloped tomodelth e

transmission

of

vibration

through

bearings

intothe

housing

Lim,

989).Theremaining

tep

s

o

predict

the

characteristics

ofnoiseradiation

ro m

vibratingtructure.Seybert

discusses

method

or

predicting

radiation

y

boundary

element

analysis

of

a

vibrating

surface (Seybertet al.,1994).

Several studies

have

examined

the sound

radiation

characteristics

ofsingle

flat

plates

(panels)

under

various

boundary

conditions.

A

general

reviewis

given

in

Li m

an d

Singh1989).

Other

workincludesWallace

1972),

Beranek

(1971),

Fahy

(1985),

Guyader

(1994),

an d

Cremer

et

al .

(1973).

Othershave

tried

to

correlate

gearbox-radiated

noise

with

structural

excitation

(Oswald

et

l. ,

992;Seybert

et

al.,

991;Kato

et

al.,

994 ;

Sabot

nd

Perret-Liaudet,

994;VanRoosmalen,

994;

Lim,

989;

an d

Heath

an d

Bossier,

1993).Many

other

studies

re

summarizedinLim

an d

Singh

(1989).

Since

acoustic

radiation

efficiency

is

the

link

betweenstructural

vibrations

nd

the

r di ted

ound

power,t

hould

betudied

when

attempts

re

being

made

to

predictnoise.

This

paper

looks

t

several

acoustic radiation

efficiency

models

an d

compares

them

to

experimental

results.Identifyingth eusefulness

of

these

modelsin

housingdesignis

th e

main

focus

of

this

paper.

APPARATUS

Th e

gear

noise

test

rig at

NASA

Lewis

Research

Center

is

equipped

to

accommodate

spuran dhelical

gears.Several

typesof

measurements,

including

sound

pressure,

acoustic

intensity,

an dhousingacceleration,

ca nbe

madeon

this

rig(Oswaldet

al.,1992).

The

testrig

consists

of

a

single-mesh

gearpair

powered

by

50-kW

20 0

hp )

variable-speed

electric

motor.

An

eddy-current

dynamometer

loads

th e

output

shaft. The

gearbox

ca n

operate

at

speeds

up

to

6000

rpm.

F orthis

study,

th e

gears

wereidentical28-toothspur

gearswith

a

6.35-mm

ace

width;

hey

weremanufacturedoA G M Aclass-15

accuracy.

The

ears

have

linear

profile

modification

tip

relief)

of

11mm

(0.00045

in.)

that

extends

90 percentof

thedistance

from

th etip

to

th e

high

pointof

single

tooth

contact. F or

these

gears, the

transmission

erroris

minimized

at aloadof45

N-m

(400

in-lbf). The housing is

made

of6.35-mm-thick

steel

plates.

Th e

four

corners

of

th e

base

plate

are bolted

to

foundation

that

is

ssumed

to

be

rigid.The

sides

of

the

bo x

re

weldedto

each

otheran dto

the

baseplate;

the

to p

plate

isbolteddown,

bu t

can beremovedto

changetestgears.The wholerig

is

within

a

room

whose

floors,

walls,

nd

ceiling

re

covered

with

acoustic

bsorbing

'Currentlyat Ford

Motor

Company,

Dearborn,

Michigan.


3/7

material.

This

providesasemi-anechoictest

chamberthatabove50 0H z

attenuates

reflected

soundby

at least20 dB .

ME SUREMENTS

The sound

power

radiated

from

thegearbox

was

measured

by

using

an

acoustic

ntensity

probe

consisting

of

a

pair

of

phase-matched

microphonesmountedface-to-facean dspaced6mmapart.Theprobe

wa s

positioned

with

th e

id

of

a

computer-controlled

robot

(Oswald

et

al.,

1992).

Th e

robot

wa s

commanded

tomovethe

probe

to20

locations,

each

approximately

60

m m

above

the

top

of

th e

housing.

The 20 intensity

spectra

were

averaged

an d

multiplied

by

the area

of

the

top

of

th e

housing

to

yield

th e

radiated

sound

power

at that

operating

condition.

During

th e

course

of

th e

experiments,

we

noticedthat

the

ampli-

tudesof

the

sidebands

were

ignificant

relativeto

helevelst

mesh

frequency

f,

an dtheharmonicsof/

m

.

Thiswa sparticularly

trueatth e

higher

peeds.Figurehows

he

ound

power

pectrumfor

peed

Q=

00 0

rp m

an d

torqueT

=

8

N-m.

Here,

hemeshfrequencyis

2800

H z,

and the

shaft

frequencyis10 0H z.In the

spectrum

some

of

th e

sidebands

have significant

amplitudes

relative

to

the

mesh

frequency

peak.

We

decided

that

a

characterization

of

th e

sound

power

should

include

threepairs

of

sidebands

in

th e

computation.

The

meanquare

velocity

wa s

obtained

from

the

accelerometers

located

onth e

gearboxhousing

(w e

assumed

sinusoidal

responsean d

integrated).Threehousingocationswere

chosen

orhe

patial

averagingse e

Fig.

).Thevelocitypectra

containedignificant

sideband

activity,

just

as

the

soundpower

spectradid.

Sound

intensitymeasurementswere

taken

onlyoverth eto pplate

ratherthanover

the

surface

of

anenclosing

volume.

This

limitationwas

dictated

by

th e

difficulty

an d

danger

of

taking

measurements

nexttoa

rotatinghaft.Limitingmeasurements

o

he

op

platereduced

he

unwantedeffectsof

noisefrom

couplings

adjacentto

the

gearbox.

One

justification

fo rlimiting

th e

measurements

was

ha t

the

top

plate

wa slessstiff

than

th e

sides

and,thus,

could

vibrate

more

than

th e

others,

specially

at

low

requencies.

Although

th e

to p

plate

s

more

flexible,

ho w

much

this

ffects

he

vibratory

powerflow

through

the

housing

is

no t

clear.

Th e

peak

velocities

of

th e

bearing

ca p

were

an

order

of

magnitudelower

than

hoseof

theide

ortop

plates.Thiss

s

expected

since

th espur

gears

generateno

thrust

force

that

would

cause

1st

harmonic

+ 6

sidebands

2n dharmonic+

6

sidebands

3rd

harmonic

+

6 sidebands

2000

3000 4000

5000

6000

7000

8000

9000

Frequency,

Hz

Figure1.Typicalsoundpowerspectrum 6000rpm,

torque=

68 N-m).

significantmotion

along

th e

axis

of

th eshaft.In

addition,

the

bearing

mounting

plates

a re

verystiff

relative

to the

housing.Th e

peak

velocities

of

the

side

plate

were

about

the

same

order

of

magnitude

asthose

of

the

to p

plate.

This

uggests

hat ignificant

mount

ofpower

m ay

be

flowingthroughth eside

plates

an dcould

be

radiated

as

sound.Future

experiments

houldattemptto

examine

sound

radiation

from

the

side

plates

by

using

more

accelerometer

locations.

The

acoustic

radiationefficiency

of

a

structuresuch

asa

gearbox

m ay

be

defined

asthe measured

sound

power

radiated

from

th e

structure

divided

by

thesound

power

radiated

bya

pistonin an

infinite

baffle.

The

area

ofthe

piston

is

equal

to

the

surface

area

of

the

structure,

an d

th e

vibrationvelocityof

the

piston

equals

thatof

thestructure.

Th e

radiation

efficiencymaybecomputedfo reachfrequency

of

interestan dit

may

exceedone.

The

experimental

radiation

efficiency

m

of

the

gearbox

housing

under

operating

onditions

was

stimated

from

th e

ound

power

nd

velocityby

th e

following(Cremeret

al.,1973):

U/i

Q

w f

T a

pcS

M i

(1)

whereW *sheradiatedound

power

inwatts,pcis

he

acoustic

impedance

of

th esurrounding

medium in

rayls,5

isth e

radiatingarea

of

thehousing

n

meters

quared,nd(v

t

] she

patially

nd

temporally

veraged

mean

quare

velocityof

th e

housing

in

meters

squaredpe r

second

squared.In

Eq .

(1),the

*

indicates

that

these

arein

situ

quantities,whichdependonhemeasurementandoperating

conditions,

including

harmonic

nd

ideband

frequencies

ft,peed,

an dtorque

load

T .

Intensity

probe

Acceler-

ometer

y

Pft)

Microphone

Acceler-

ometers

Output

shaft

y

(x-axis

normalto

page )

Figure

2. Instrumentation.


4/7

RADIAT ION

EFF IC IENCYRESULTS

Theradiation

efficiency

wa s

computed

from

Eq.

(1).

Theacoustic

impedance

of

ai r

is

415rayls

at

25

Can d

atmos.The

surface

area

5

ofth e

op

an d

foursides

of

the

housingis

.4 1m2.No

cceleration

measurements

were

taken

on

th ebottomplatebecause

it

is

no teasily

accessible.Therefore,th e

area

of

the

bottom

platewa sno t

includedin

the

computed

surface

area.

The

bottom

plate

is

somewhatthickerthan

the

sides

nd

ha s

tiffeners,

oweexpectitisnotaneffective

sound

radiator.

Th e

radiation

efficiency

omputed

from

hese

parameters

s

plotted

in

Fig.

3.

Ingeneral,

theradiationefficiency

tendsto

increase

with operating speed

for

each

harmonic

an dapproachesunityasthespeed

becomeslarge enough

so

that

the

acoustic

wavelength

isno longer

large

relative

to the

dimensionsoffnegearbox.

Several exceptionstothe

trend

ca n

be

bserved.

Most

notably,

hest

harmonic,

t

Q

=00 0

rp m

f

m

= 467

Hz),ha d

a

radiation

efficiency

nearly

0

times

as

large

asat

Q=1500

rpm

f

m

=70 0Hz).

This

variation

inth eradiation

efficiency

across

he

peed

range

is

most

probably

heresultof

the

interaction

(coupling)

between

vibration

modes

of

the

housing.

Atleast

five

housing

modesare

present

below90 0H zalone,

as

reportedbyLim (1989),

so

th epossibility

of

multimode

excitation

is

likely.

Each

ofthese

modes

should have

different

modal

radiation

efficiencies,

so

an

examination

of

th e

radiation

efficiency

on

a

modal

basis

would

be

useful.Thiswill

be

leftfo ra futurestudy.

Thehree

races

n

Fig.

partially

overlap.

This

llowsso

compare

th e

radiation

efficiency

fo r

different

harmonicst

th e

am e

frequency.

F or

example,at 2800 Hz,th e

mesh

frequency

(1st

harmonic)

occurst

00 0

pm ;wice

he

meshrequency2nd

harmonic),t

3000

pm ;

nd

hree

imes

hemesh

requency

3r d

harmonic),

t

2000

pm.nmanycasesexceptat

heowest

requencies)

he

overlapping

curvesagree

reasonably

well.This

suggests

that

datafrom

higherharmonicstakenatfairly

lowspeeds

may

be

used

topredict

th e

radiation efficiencyfo rlo wharmonicsat

higherspeeds.

Inotherwords,

perhaps

weca npredictth eradiationefficiencyforspeedsbeyondou r

operating

range

by

examining

datafromhigherharmonics

within

the

operating

range.

This

would

be

useful

or

future

high-power-density

rotorcraft

transmissions.

Range

for

3r d

harmonic

i

~ Range for2n dharmonic*]

c

o

1

0 1

A.

.

Range

for

r

1s t

harmonic

1

r, 1-t\

A

..A

A

Harmonic

+

6 sidebands

1st

2n d

3rd

_L

_L

3000

000

Gear meshharmonic

frequency,

H z

9000

Figure3.Radiationefficiencyforfirst

three

harmonics

over

speed

range

of

1000

to6000

rpm

andtorqueof

68 Nm.

Analytical

Dimensions,

mode lm

onopole

ipole

late

ylinder

a

=20

a

=50

h

=

8.65

r

h

=

6.35

I

d

=

o

D

A

xperimental

1

stharmonic

2nd

harmonic

3rd

harmonic

S

c

a

o

E

0)

c

o

' =

TD

0

D C

0 1

0 0 1

J_L

3000

000

Mesh

frequency,

Hz

9000

Figure

4.Summary

ofanalyticalacousticradiation

models

a

radius,

h

=

height,

d=diameter).

Idealcousticource

modelsuc hs

hemonopole

pulsating

sphere

of

radius

a)an d

the

dipole

(acoustic

doublet

tw osimple sources

of

equal

trength,

eparatedy

distance

a,

vibrating

at

th e

am e

frequency

bu t

180

ou t

ofphase

with

each

other)

yield

fast

estimations

of

the

housingradiation

efficiency,

ut

the

utility

ofthesemodelsis

difficultto

justify

on

th ebasis

of

an y

apparenthousing

geometry.An

equivalent

(same massand estimated

modaldensity as

gearbox

housing)

plate

model

that

relieson

an

approximation

of

th e

modal

densityof

the

housing

ppears

o

bebetter

estimator.U nfortunately,

he

modal

densities

of

transmissionhousings

m ayno tbeknown.)An

equivalent

cylindermodelbased

on

he

eometryof

th ehousing,

where

plate

thicknesses

h

are

equal

an dcylinder

diameter

d

equals

the

length

of

th e

gearbox

housing,

may

also

be

a

good

estimator

(Guyader,1994).Figure

4

compares

some of

the

better

modelsstudied, along

with

th e

experimental

radiation

efficiency

values.Obviously,

none

ofthese

models

capture the

variation

that

is

presentin

th e

experimentalradiation

efficiency

curves.

DYNAMIC

AND

ACOUST IC MODELSOF THE TOP PLATE

Thetestgearbox

is

arectangularhousingmadefrom

steel

plates

weldedtogether

an d

a

top

plate

bolted

on .

F or

a simple

analysis,

afinite

elementmethod(FEM)modelwa s

generatedfo r

only

theto p

plate.

Th e

to p

plate

s86

y62

y.3 5

mm .

Shell

elements

were

used

o

generatemodel

with20

lementsnd43

odes.

The

boundary

conditions

of

the

plate

were

modeled

so

that

the

nodes

at

the

four

corners


5/7

ha d

al l

degrees

of

freedom

se t

tozero (clamped

condition),an d

th e

nodes

alongthe

dgeslternated

between

being

ompletelyfree

ndbeing

clamped.

Thisscheme

simulated

th eboltedconnection

betweenthe

top

plate

and th e

top

flange

of

th e

housing,

which

is

depictedin Fig.

5. With

thismodel,

thefirstfournatural

frequencies

were

determined.

They

are

shownin

Table

Ialong

with

th e

previous

experimental

measurements

(Oswald

et

al

1992).

The

modal

index

is

the

number

of

antinodes

along

th e

widthan dlength

of

the

plate.The

discrepancybetween

the

F EM an d

measured

results

is

lessthan

9percent.

Table

I.NaturalFrequenciesof

th e

Gearbox

Top

Plate

Modal

Frequency,

H z

index

Predicted

Measured

3

Error,

percent

(1.1)

50 8

511

0.6

(1.2)

89 8

97 5

8.6

(2,1)

1175

1273

83

(2,2)

1530

1631

6.6

a

Oswaldetal.

1992) .

Th e

F EM

an d

measured

mode

shapes

(not shown)

were

also

similar.

Thisindicates

that

th emodelreasonablysimulatesthe

response

of

the

gearbox

to p

inthe

frequency

rangestudied.U sing

this

platemodel,we

applied

three

rbitrary

loading

onditions

o

conductforced

response

an d

acoustic

radiation

studies.

These

loadingconditionswere

no tmeant

to

represent

actual

loadsseen

by

the

test

gearbox; rather, they

were

meant

to

bea

starting

pointfo r

comparing

th eeffects

of

different

loads

on

the

acoustic

efficiency

of

the

platean dth e

housing.

The differentloads were

(i)a-Nforce

normal

toth e

plate,

pplied

at

a

point

onth e

edge

as

shown

inFig.6(a);

(ii)

a1-N-mmomentabout

the

y-axis

ofFig.

6(b),

applied

at

thesame

node

as

fo r

case

(I);

an d

(iii) several

1-N

forces

normal

to

th e

plate

an d

equal

in

phase,

applied

along

th e

plate

edgeat

the

free

nodes

as

shownin

Fig.6(c).

For

a

linear

system,

th e

predicted

radiation

efficiency

s

not

affectedby

he

magnitude

ofth epplied

orce.To

simulate

the

rangeof

speeds

in

the

experiment,

the

loads

wereapplied

at

frequencies

of

400

to

2900

H z

in

steps

of

10 0

H z.

Clamped

nodes

nodes

Figure

5.Plate

used

to

model

housing.

Cornernodesand

every

other

edge

node

clamped;otheredgenodesfree.

Figure

6.Loadcases, a)

Case i) ,point

load

appliedat

free

edgenode,

b)Case

ii),point

moment

applied

at

free

edge

node,

c)

Case

iii),point

loads

applied

at

eachfree

edge

node.

The

forced

vibration

responsepredicted

by

th e

F EM

model

was

used

as

th e

input

to a

boundary

element

method

( B E M)

model.

Th e

B EM

modelcalculated

he

acoustic

esponse

of

the

plate,

ncluding

he

radiation

efficiency.

Figure

7showsth eradiation

efficiencies

predicted

for

th e

hree

loading

cases

y

he

combinedBEM/FEM

model.

An


6/7

Case (i),

point

load

- A -

Case

(ii),

pointmoment

case

(iii),

severa lpoint

loads

Exper imenta l ,

st

harmonic

1000

2000

3000

Gearmesh

frequency,H z

Figure

7.Effect

of

differentloadings

of

Fig.

6

on

predictedradiationefficiencyof

abaffledplate.

experimental

alue

based

n

hest

harmonic)

s

lsohown

or

comparison.The

resultsin

Fig.

ndicatethat

the

loadingcondition

strongly

influences

th epredicted

acousticresponse,

especiallyatlower

frequencies.

The

single

normal

force

(case

(i))seems

to

bestreproduce

th e

variation

in

radiation

efficiency

displayed

in

the

experimental

results.

Th e

peaks

seenincase

(i)at

500,

900,

an d

1500H zcorrespond

tothe

(1,1),

(1,2),

and (2,2)modes

ofTable

I,which

indicatesthat

these

modes

arefairly

efficient

radiators.These

peaks

arealso

seen

in

the

predicted

radiationefficiency,although

at

generallylowervalues.

SUMMARYAND

CONCLUS IONS

Acousticintensity

and vibration measurementswereperformedon

a

simple

gearbox

made

from

welded steel

plates.

Th e

radiationefficiency

fo r

the

housing

wa scomputed

from

the

intensityan d

vibration

data.

This

was

ompared

with

the

ntensity

predicted

by

ideal

coustic

models.

Finally,

a

combined finiteelement/boundaryelementmodelw asusedto

predict

th e

radiation

fficiency

of

th e

to p

plate

of

th e

housing.

The

following

conclusions

weredrawn:

1.

A

finite

element

modelca n

simulate

th e

vibration

modesof

a

structureuc hs

ge rbox

op .

f

th egear

dynamic

excitations

adequately

simulated,

th e

model

ca n

predict

the

structuralresponse

of

the

actual

gearbox.

2. A

boundary

element

modelc an

predict

the

acoustic

response

of

a

vibratingstructure

if

th e

vibration

characteristics

are

known.

A combined

finite

element/boundary

elementmodel

ma y

e

used

o

predictth e

operatingnoise

characteristics.

3.

Idealacoustical

models(such asa

monopole,dipole,

flat

plate, or

cylinder)

dono tadequately

simulate

the

modalvibrationbehavior

ofa

gearbox.

These

ideal

models

annot

predict

the

variation

in

coustic

response

dueto

vibration

modes.

Therefore,

idealmodelspredictonly

general

trends.

REFERENCES

Beranek,L.L.,

971,

Noisean dVibrationControl,

McGraw-Hill,

Inc.,

Ne w

York.

Cremer,

L. ,

Heckl,

M,nd

Ungar ,

E.E. ,

973,

tructure-Borne

Sound,

Berlin:Springer-Verlag.

Fahy,

.,

985,SoundandStructural

Vibration-Radiation,

Transmission

an d

Response, Academic

Press

Limited,

Sa n

Diego.

Guyader,

. -L. ,

994,

Methods

o

Reduce

Computing

Time

in

Structural

AcousticsPredictions,

Third

InternationalCongresson Air-

and

Structure-borne

Sound

and

Vibration,

Montreal,

pp .

5-20.

Heath,

G. F . ,

nd

Bossler,R . B . ,Jr.,

993,

Advanced

Rotorcraft

Transmission(ART)ProgramFinal

Report, NASACR-191057.

Kato,M.,

Inoue,

K.,

an d

Shibata,

K.,994,

Evaluation

of

Sound

Power

Radiated

yGearbox, nternational

Gearing

Conference,

Newcastle

U p o n Tyne.

Lim,

T.C,1989, VibrationTransmissionThrough

Rolling

Element

Bearingsn

Geared

Systems, Ph.D.Dissertation,

TheOhioState

U niversity,

Columbus,

OH .

Lim,

T.C. ,ndSingh,R.,989,

A

ReviewofGear

Housing

Dynamics

an dAcousticsLiterature,

NASA

CR-185148

or AVSCOM

Technical

Memorandum

89-C-009.

Oswald,

F . B . ,

Seybert,

A.F. ,

W u,

T.W.,

ndAtherton,

W.

992,

Comparison

of

Analysis

and

Experiment

orGearbox

Noise,

Proceedings

of

th e

International

Power

Transmission

and

Gearing

Conference,

Phoenix,pp .

675-679.

Sabot,

J. ,an d

Perret-Liaudet,J. ,1994, Computation

of

the

Noise

RadiatedbyaSimplifiedGearbox,

International

Gearing

Conference,

Newcastle

upon

Tyne.

Seybert,

A. F . ,

W u,

T.W.,

W u,

X.F. ,

and

Oswald,

F.B.,

991,

Acoustical

Analysis

of

Gear

Housing

Vibration, NASA

TM-103691.

Seybert,

A. F . ,

W u,T.W.,andW u,X . F . ,

994,

Experimental

Validation

of

FiniteElementandBoundaryElementMethods

or

Prediction

of

Structural

Vibrationan d

Radiated

Noise, NASA CR-4561.

VanRoosmalen,A.N.J. ,

1994,

DesignToolsfo rLo w

Noise

Gear

Transmissions, Ph.D.

Dissertation,

Eindhoven

U niversity

of

Technology.

Wallace,

C.E. ,1972, Radiation

Resistance

of

a

Rectangular

Panel,

Journal

of

th e

AcousticalSocietyofAmerica,

vol.

51 ,n o.

3,pp.

946-952.


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ONLY

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blank

2.

EPORTDA TE

September1996

REPORT TYPE

ND

D TES

COVERED

TechnicalMemorandum

4.

rTLE

AND

SUBTITLE

AcousticRadiation

Efficiency

Models

of

aSimpleGearbox

6.

UTHOR S)

Mark

F .Jacobson,RajendraSingh,and

Fred

B .Oswald

7.

ERFORMINGORGANIZATIONNAME S)ANDADDRESS ES)

NASA

L e w i sResearchCenter

C l e v e l a n d O h i o

4135-3191

and

Vehicle

Propulsion

Directorate

U . S .A r m y Research

Laboratory

C l e v e l a n d O h i o

4135-3191

9 .

PONSORING/MONITORINGAGENCYNAME S)

ANDADDRESS ES)

NationalAeronauticsa n d S p a c e A d m i n is t ra t io n

Washington,

D . C .0546-0001

and

U . S .A r m y Research

Laboratory

Adelphi,

Maryland

0783-1145

5. FUNDINGNUMBERS

WU-505-62-36

1L162211A47A

8. PERFORMINGORGANIZATION

REPORTNUMBER

E-10264

10 .

PONSORING/MONITORING

AGENCY

REPORTNUMBER

NASATM-107226

ARL-TR-1111

11 .

UPPLEMENTARYNOTES

Prepared fo rtheSeventhInternationalPowerTransmissionan dGearingConferencesponsoredbytheAmericanSocietyof

MechanicalEngineers,Sa nDiego,California,October

6-9,

1996.Mark F .Jacobson,OhioStateU niversity,Columbus,Ohio

43210,

presently

at

Ford

Motor

Company,

Dearborn,

Michigan;

Rajendra

Singh,

Ohio

State

U niversity,Columbus,Ohio

43210;

FredB .

Oswald,

NASA

Lewis

Research

Center.

Responsible

person,

FredB .

Oswald,

organization

code

2730,

(216)

433-3957.

12a.

ISTRIBUTION/AVAILABILITY

STATEMENT

l2b.

DISTRIBUTIONCODE

U nclassified-Unlimited

Subject

Category

7

This

publication

is

available

from

the

NASA

Center

for

AeroSpace

Information,

(301)

621-0390.

1 3 .

B S T R A C T M aximum 200 words)

Acousticintensitymeasurementswere

conducted

onasimple

spur

gear

transmission

in

a weldedsteelhousing.

The

radiationefficiencyof

th e

housing

was

computed from

th e

intensity

data

fo rth efirstthreeharmonicsof

meshfre-

quency.Finiteelementan d

boundary

elementmethods

( F E M / B E M )

wereused jointlytomodel

acoustics

an ddynamics

of

th e

to p

plateof

th e

housing.F or

a

simply

supported

elastic

plate,reasonableagreementwas

achieved

between

experimentalradiation

efficiencies

and thosepredictedwithF E M / B E M .However,predictionsofth ehousingcharac-

teristics

wereonly

partially

successful.Foursimple

analytical

models

were

examined

to judgetheirability

to

predict

th e

radiation

efficiency.

These

models

do

notsimulateth e

modal

characteristicsof

agearbox;thereforetheirpredic-

tions

yield

only

general

trends.

Discrepancies

are

believed

to

be

related

to

inaccuratemodelingof

th e

excitationof

th e

structure

aswellas

to

interactions

betweenmodesofvibration.

14 .

UBJECTTERMS

Acoustic

intensity;

Gears;

Gearbox;Radiationefficiency

17 .

ECURITY

CLASSIFICATION

OF

REPORT

U nclassified

18 .

ECURITYCLASSIFICATION

OFTHISPAGE

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19 .ECURITY

CLASSIF ICAT ION

OF

ABSTRACT

U nclassified

15 .

NUMBER

OF

PAGES

07

16 . PRICECODE

A02

20.IMITATIONOF

ABSTRACT

NSN

7540-01-280-5500

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298

Rev.

2-89)

Prescribed

by

ANS I

Std.

239-18

acoustic radiation efficiency

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