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
-
7/24/2019 Acoustic Radiation Efficiency
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.
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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.
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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
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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
-
7/24/2019 Acoustic Radiation Efficiency
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.
-
7/24/2019 Acoustic Radiation Efficiency
7/7
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September1996
REPORT TYPE
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4.
rTLE
AND
SUBTITLE
AcousticRadiation
Efficiency
Models
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aSimpleGearbox
6.
UTHOR S)
Mark
F .Jacobson,RajendraSingh,and
Fred
B .Oswald
7.
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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.
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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
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OF
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