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Purdue University
Purdue e-Pubs
I5'#5+# C' E+''+ C''%' S%* M'%*#+%# E+''+
1994
Control of Acoustic Vibrations Inside RefrigeratorCompressors by Means of Resonators
V. CossalterUniversity of Padova
A. DoriaUniversity of Padova
F. GiustoElectrolux Compressors
F8 5*+ #& #&&+5+# 8 #5: *://&%.+$.&'.'&/+%'%
+ &%'5 *# $'' #&' #7#+#$' 5** P&' '-P$, # ' 7+%' 5*' P&' +7'+5 L+$#+'. P'#' %5#%5 '$@&'.'&
#&&+5+# +#5+.
C'5' %''&+ # $' #%2+'& + +5 #& CD-ROM &+'%5 5*' R# . H'+% L#$#5+' #5 *://'+''+.&'.'&/
H'+%/E7'5/&'+5.*5
C#5', !.; D+#, A.; #& G+5, F., "C5 A%5+% !+$#5+ I+&' R'+'#5 C' $ M'# R'#5"(1994).International Compressor Engineering Conference. P#' 1036.*://&%.+$.&'.'&/+%'%/1036
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wh
ereS i
s the
area
of vi
brati
ng
sourc
es exc
ludin
g re
sonat
or or
ifice.
Sinc
e the
are
a AR
o
f
reso
nator
or
ifice
is
s
ma l l
, P;(x
,y,z)
is
assu
med co
nstan
t ov
er th i
s sur
face
an
d
e
qua l
to P
i(R),
th
us the
equ
atio
n
o
f a c
avity
mod
e
cou
pled to
the
Helm
holtz
reso
nator
is
2 Q
pc2
p
cz
~ +
2
(w ,P
,
+
w;P
; =
p: f
v.
JI,(x,
y,z)d
V-v
f
w
+ ;(x
,y,z )d
S-
v
A
R lJI
,(R)w
R
v
sl
,
(
1())
In
ord
er to
co
uple
res
onato
r
equ
ation
w
ith
the ca
v ity,
pre
ssure
p
in eq
uatio
n (4) is
expr
essed
a
s a
summation
ofthe pressures caused
by
the
modes
of the enclosure. The fo llowing seto f s econd
order
dif feren tial
eq
uatio
ns
i
s obta
ined
2
.
2
2
P
2(J
l) };
w
,
2
P;
=
P:
~
\f
;( x
,y ,z )d V
-
p:
I
w + ; (x
,y z )dS
- p:
A
R
+ ; (R
)w
R
V
S
wR +
2(Rw
Rw
R
w ~ w
R
1
-
IP ,l
.J I ;(
x ,y ,
z )
i
=
l n
pR
i
1
1)
wh
ere n is
the
nu
mber
of
mo
des wh
ich ar
c ta
ken in
to a
ccoun
t in
the
dyn
amic
m o
del .
If the
sou
rce
ofexci
tat ion
is th
e v ib
rat io
n of
a sm a
ll
part
A,
of th
ebou
nda r
ysu r
face
th e su
rface
in teg
ra l b
ecom
es
pc
z I
uJ
i
pc2 A
HI S)
WT-
x,y,z
)t . \
.
r .
w
1
v
l
v
l
j
12)
where
w
is thevibra t ion acce lerat io n
and
P;(S) is the constant va lue ofP;(x,y,z) ove r the smal l a rea
As.
INTE
RAC
TION
O
F
T
HE
RE
SON
ATO
R WITH
C
OMP
RESS
OR CA
VITY
M
ODE
S
A
ty p
ical
com
pres
sorcav
ity
was
co
nside
red,
it h
ad a v
olum
e V
o f 0
.0013
59m
2
an
d it
was
fill
ed w
ith
re
frige
ratin
g flu
id R
l34A
, h
avin
g de
nsity
p=
3.73
K
g/m
3
and sou
nd
sp
eedc= 1
72.3 m
/s
at 70
c
0
T
he fi
rst six
mod
es of the
cav
ity we
re ta
ken i
nto a
ccoun
t in
the m
athem
atic
a l m o
del;
the i r
frequ
encie
s, sha
pes
an
d dam
ping
s
are
su
mma
rized
i
n th e
table
.
M od
e
fiHzl
Type
V;
Si
1
39
4.4
axia
l
V
/2
().{)1
2
53 4
.6
axial
V /
2
0.01
3
644.4
a
xial
V /2
0
.01
4
856.6
tang
entia
l
V /4
().()1
100
40
300
5
6
E
nclo
sure
a
lone
(i()()
F
requ
ency
[H z
]
873.2
8
93.3
xo
o 900
F
igure
2:
Resp
onse
sp
ectra
( P
1
(R
)=l ,
P;(R)
=O i=
2,6)
axial
=ax
ial
1
9
0
5
0
4
0
3
00
V /2
0.01
V /2
0.
01
x
oo 9
00
Fre
quen
cy
[H z
]
F
igure
3: Re
spons
e spe
ctra
( t
1
R
)=l, t ;(R
)=0.3
i=2,6
)
565
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