Typical Bellows Design Analysis

Db=Bellows inside diameter
nc=Number of convolutions
q=Convolution pitch
w=Convolution height
t=Thickness of one ply
n=Number of plies
P=Design pressure
Temp=Design temp (°F)
xc=Axial compression
xe=Axial extension
xl=Lateral deflection
xf=Angular rotation
Ø=Torsional rotation
xp=Axial preextension
nb=Number of bellows
Db=16 in
nc=6
q=1.125 in
w=1.5 in
t=0.05 in
n=2
P=450 psi
Temp=250
xc=0 mm
xe=0 mm
xl=13.5 mm
xf=2.0 deg
Ø=0 deg
xp=0 in
nb=2
Type=2 reinforced, 1 unreinforced
Ls=Spool pipe length
ts=Spool pipe thickness
tpipe=Pipe end thickness
tc=Collar thickness
Lc=Collar length
Lt=Bellows neck length
odr=OD of the reinforced rings
tdr=ID of the reinforced ring
matb=Bellows material code
matr=Bellows material code
pm=Fluid density (water)
Type=2
Ls=8 in
ts=0.5 in
tpipe=0 in
tc=0.05 in
Lc=0.5 in
Lt=0.5 in
odr=0.375 in
tdr=0 in
matb=5
matr=2
pm=62.2 lb ft3
A
Sab=Allowable stress3
Syb=Yield strength3
Eb=Moduli of elasticity3
At Design Temp.
Sab=19.5·103psi
Syb=25.8·103 psi
Eb=27.3·106 psi
At Room Temp.
Sab1=20·103psi
Syb1=20·103 psi
Eb1=28.3·106 psi
Bellows free length
Univ EJ. free length
Development length
Bellows weight
Effective area2
Equiv. Mov./Conv.
Lb=6.75 in
Lu=21.5 in
Lbd=22.85 in
Wb=15.7 lb
Ae=243.3 in2
ex=0.12 in
Convolution factors:   Cd=1.57   Cf=1.47   Cp=0.71    ce<cre=1   ce<ere=1    Ce=0.375   Cy=0.558   cwb=1
SRcmp=Reinf ring circumf. membrane stress
S2=Number of convolutions
S3=Convolution pitch
S4=Convolution height
S5=Thickness of one ply
S6=Number of plies
St=Design pressure
SRcmp=9678 psi
S2=9733 psi
S3=2332 psi
S4=40630 psi
S5=1695 psi
S6=129083 psi
St=160851 psi
Stress Verification
SRcmp<=CwbSab=1
S2<=CwbSab=1
S3+S4<=CwbSab=1
Ss<=0.6Sab=1
Ss=0· psi

Axial vibration (Hz) fna=16.1
Lateral vibration (Hz) fnl=149.1
Rocking Vibration (Hz)fnr=71.8
fia=Axial spring rate3
fil=Lateral spring rate3
Mif=Angular spring rate3
Mit=torsional spring rate3
fia=1744·lbf in -1
fil=1160·lbf in -1
Mif=1179·lbf in deg -1
Mit=1.35·106lbf in deg -1
fia=305399·N mm-1
fil=203222·N mm-1
Mif=133·N mm-1
Mit=152401.26·N mm-1
Nc=56484
Nc8=1132
Nc3=1800
E.J.M.A.-7th Ed.
ASME Sec.VIII App.26 1998 Ed.
ASME B31.3 App.X 1996 Ed. 1997 Add.
Max. flow without liner
for induced vibration
v=16.4·ft/sec


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