TELKOM
NIKA
, Vol. 11, No. 6, June 20
13, pp. 3327
~ 333
2
e-ISSN: 2087
-278X
3327
Re
cei
v
ed
Jan
uary 16, 201
3
;
Revi
sed Ap
ril 14, 2013; Accepted Ap
ril 25, 2013
Rotating Cantilever Beam Dynamic St
rain Measurement
and Analysis b
ased on
FBG
Jiang Xi-Xin
Schoo
l of Mechan
ical/El
e
ct Eng, W
uhan U
n
i
v
ersit
y
of T
e
chnol
og
y , Hub
e
i,
W
uhan ,Chi
na
, 027-87
85
950
5
Corresp
on
din
g
author, e-mai
l
: jian
g
x
i
x
i
n20
06
@16
3
.com
A
b
st
r
a
ct
T
he mai
n
for
m
of machi
n
e
’
s
w
o
rking pr
inci
p
l
e is r
o
tatio
n
. T
he mech
anic
a
l pr
operti
es o
f
rotatin
g
compo
nent ar
e
signific
ant i
m
p
o
rtance to
i
m
pr
ove the
ma
chi
n
e
’
s re
li
abi
lity. In the meas
ure
m
e
n
t, the diffic
u
lt
thing
is to tra
n
smit sig
nals
form se
nsors
on a r
o
to
r to
a station
a
ry
part . In this
pap
er, usin
g t
h
e
F
B
G
’
s(F
i
bre
B
r
agg Ga
ug
e)
prop
erties
of w
i
reless
tra
n
s
miss
ion,
auth
o
r meas
ure th
e loc
a
l stra
ins
of
rotating c
anti
l
e
v
er be
a
m
ca
nti
l
ever
by util
i
z
i
n
g the
strai
n
pr
i
n
cipl
e g
a
u
ge F
B
G(F
i
bre Brag
g Gaug
e) a
nd t
h
e
rotary signal trans
m
i
t equipment,.
The result of analysis s
howed that rot
a
ting cant
ilever have complic
at
e
dyna
mic ph
en
omen
on, dy
na
mic stra
in
not
only r
e
l
a
ted t
o
spe
ed
but
also r
e
late
d to
fluid
actio
n
, th
e
dyna
mic stiffing phe
no
me
no
n
w
e
re observe
in the sa
me
ti
me. F
i
na
lly, au
thor offer an i
m
prove
d
insi
ght i
n
to
a strain
m
e
asurement tec
hnique fo
r
a r
o
tating
mechanic
al system
. The
r
e
searc
h
work
could pr
ovide
an
effective w
a
y for me
asur
ing r
o
tating co
mpo
nent
’
s
mec
h
a
n
i
c
al pro
perties.
Key wo
rd
s:
fib
e
r Bragg gr
atin
g (F
BG) , dyna
mi
c stress , me
asure
m
ent , be
am
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Rotating
co
m
pone
nt ca
n b
e
found
on
al
most eve
r
y u
n
it of machin
ery eq
uipme
n
t, and is
the main co
mpone
nt for reali
z
ation of
mecha
n
ic
al function conv
ersi
on. In the developme
n
t
o
f
mode
rn i
ndu
stry, equi
pm
ent continu
o
u
sly d
e
velop
s
to
wards th
e directio
n of
larg
e-si
ze, h
i
gh-
spe
ed and fle
x
ible, the unit load of rotating com
pon
en
t tends to become la
rge
r
and larger, a
nd
factors su
ch
as control of machi
n
e
r
y vibration,
re
du
ction of stre
ss level, and enha
ncement
of
usa
ge life
of
mechani
cal
com
pon
ent
and
u
s
ag
e
relia
bility are be
comi
ng
more
an
d m
o
re
importa
nt. Usually, dyna
mics d
e
si
gn
will be pe
rfo
r
med fo
r imp
o
rtant compo
nents, so as to
determi
ne its
mode
(di
s
pla
c
eme
n
t, sp
ee
d and
accel
e
ration mod
e
),
but these pa
rameters
refle
c
t
overall dyn
a
m
ics
pe
rform
ance of
structure, and
are
not se
nsitive
for local cha
nge of
stru
cture,
damag
e of st
ructure no
rmal
ly occurs at t
he lo
cati
on
of the largest
st
ress, rathe
r
than the l
o
cation
of the maxim
u
m displa
ce
ment, spe
e
d
and a
c
cele
ration, in re
ce
nt years, n
u
m
ero
u
s
scho
lars
have starte
d to study mea
s
urem
ent of dy
namic re
spo
n
s
e
thro
ugh stress
and strai
n
[
1,2].
For rotating
comp
one
nt, the key p
o
int of strain m
e
a
s
ureme
n
t is
how d
o
e
s
th
e sign
al
transmit
bet
ween rotating
comp
one
nt
a
nd stationa
ry comp
one
nts, method
s
avai
lable at
prese
n
t
inclu
de ele
c
tric sli
p
rin
g
, telemetry, optical fiber
slip ri
ng,
and
FB
G collimato
r
.
In literature
[3-6
],
resea
r
cher
m
easure
s
stre
ss dist
ri
butio
n of steam t
u
rbin
e impell
e
r bla
de an
d
air comp
re
ssor
blade un
de
r rotation con
d
ition by adopti
ng slip ri
ng, and sign
al is transmi
tted th
rough
stationa
ry
comp
one
nt (electri
c
bru
s
h
)
an
d rotatin
g
com
pone
nt
(armatu
r
e
)
of slip ring,
the disa
dvantag
e
of
this metho
d
i
s
the p
h
ysi
c
al
conta
c
t bet
ween el
ec
tri
c
b
r
ush an
d a
r
m
a
ture
will cau
s
e n
o
ise, whi
c
h
will overcom
e
signal under ci
rcum
stance
of hi
gh
rotation
speed. The telem
e
try, was fi
rstly
utilized by Westho
use in 1
958 for me
asurem
ent of
ro
tating comp
o
nent [7], rather than u
s
e
s
slip
ring, this typ
e
of techn
o
lo
gy enlarge
s strain
si
g
nal
before tran
smitting strain
signal to a
radio
freque
ncy tra
n
smitter
whi
c
h tran
smits it in fo
rm
of freque
ncy-mod
u
lated
wave,
then receive
s
freque
ncy
mo
dulated
si
gna
l by a
n
tenna,
and
the
n
d
e
m
odulate
s
an
d enl
arges
strain
si
gnal.
T
he
disa
dvantag
e
of
this method is rotation
spe
ed of
test can
not be hig
h
due to the extra weig
ht o
f
radio f
r
eq
uen
cy tran
smitter, but the tran
smissio
n
di
stance is l
a
rg
e, rea
c
hin
g
up
to nearly 1
0
0
0
k
m
. No matter for
s
lip ring
or for
wi
reless telem
e
try, there is a
sa
m
e
difficulty-strain respon
se
of
vibration
is d
i
fferent for di
fferent ex
cita
tions,
a
n
d
di
stributive
me
asu
r
em
ent i
s
re
quired,
while
each strain
gaug
e
n
eed
s
two pie
c
e
s
of
wire,
la
rg
e qu
antity of wires will
cause difficulty of
dynamic
bala
n
ce, at the
same time, re
quire
ment
s
of strain g
aug
e
mounting te
chniqu
e are hi
gh,
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
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TELKOM
NIKA
Vol. 11, No
. 6, June 201
3 : 3327 – 33
32
3328
there
are n
u
m
ero
u
s in
stal
lation difficulties. A
s
a
ne
w type of
se
nsor
device,
op
tical fibe
r B
r
a
gg
grating
(FBG
) feature
s
sm
all volume, in
tegrati
on
of sensi
ng an
d transmi
ssion, explosi
on-pro
o
f,
fire-p
roof,
el
e
c
trom
agn
etic interferen
ce resi
stan
ce, ea
sy constitutio
n
of FBG i
n
telligent
sen
s
i
ng
netwo
rk
by adoptio
n of wavele
ngth
division mult
i
p
lex, time division multipl
e
x and interval
multiplex te
chnolo
g
y, and
has got
more
and
mo
re
attention [8
-9].
Usage
of FB
G for eq
uipm
ent
strain
mea
s
u
r
eme
n
t
ca
n solve
p
r
o
b
le
ms su
ch
a
s
remote data transmissio
n,
elect
r
oma
g
n
e
tic
interferen
ce resi
stan
ce a
nd
dist
ributiv
e
me
a
s
urem
ent, and re
q
u
irem
ents o
n
strai
n
gau
ge
mounting te
chniqu
e are
sub
s
tantially
lowe
r,
main
method
s u
s
ed i
n
FBG
dynamic
stress
measurement
are optical fiber sli
p
ring
method an
d optical fibe
r-collimator met
hod, optical fiber
slip
ring
met
hod i
s
to pl
a
c
e t
w
o pi
ece
s
of o
p
tical fi
ber i
n
on
e pi
ece
of thin pi
pe, in
whi
c
h
one
piece of opti
c
al fiber
rotate
s with
rotatin
g
co
mpo
nent,
the othe
r pie
c
e of
opt
ical
fiber stan
ds st
ill,
optical
sign
al is tran
smitted out from en
d of
rotating
optical fiber,
and enters stationary opti
c
al
fiber th
rou
g
h
air. T
o
reali
z
e
sig
nal tra
n
smi
ssi
on, th
e di
sadvanta
ge of thi
s
m
e
thod i
s
fri
c
ti
on
betwe
en pip
e
wall an
d opt
ical fibe
r ca
u
s
e
s
low
rotat
i
on sp
eed,
which i
s
no
rm
ally lowe
r than
2000
rpm. Lit
e
ratu
re [10]
has
re
sea
r
ch
ed mea
s
u
r
e
m
ent of rotat
i
ng compo
n
e
n
t stre
ss th
ro
ugh
FBG-optic
a
l fiber s
l
ip ring, but its
ro
tation s
p
eed is
lower than 2000r/m.
In this article,
FBG-colli
mat
o
r metho
d
is
adopte
d
for measurement
of
dynamic strain of
rotary
cantilever beam, its
theory
i
s
simil
a
r
with literat
ure [], but
rot
a
tion
speed i
s
up to
3000rpm
.
Thro
ugh
se
ri
al co
nne
ction
of 3 FBG
st
rain
se
ns
o
r
s on
rotary can
t
ilever
bea
m modal su
rface,
cha
nge
of
ca
ntilever
bea
m
strai
n
u
n
der 80
0r
p
m
has be
en
re
sea
r
ched,
an
d dyna
mic st
rain
distrib
u
tion a
nd re
spo
n
se
of rotating cantileve
r be
am unde
r rotation con
d
i
t
ion has be
en
analyzed, in
dicatin
g
that
this metho
d
can m
e
a
s
u
r
e dyna
mic
strain
of hig
h
-spee
d rota
ting
comp
one
nt effectively.
2. Rese
arch
Metho
d
2.1 The FBG Sensor
A FBG is co
mposed of p
e
riodi
c chan
g
e
s of the
refractive index that are form
e
d
by th
e
exposure
to a
n
inten
s
e
UV
interferen
ce
pattern i
n
the
co
re
of an
o
p
tical fibe
r.
When lig
ht from
a
broa
d ba
nd source inte
ra
ct with t
he grating, a sin
g
le
wavele
ngth,
know a
s
Bragg
wave len
g
th, is
reflecte
d b
a
ck while
re
st of the si
gnal
is tra
n
smitted. A FBG sh
ows sen
s
itivity to strain
a
nd
temperature
cha
nge
s. The
Br
agg conditi
on is expressed as:
B
=2
ef
f
n
(1)
Whe
r
e
B
is the Bragg wavelength of F
B
G,
e
n
is the effective refracti
ve index of the
fiber c
o
re,
is the gratin
g pe
riod.
If the grating
is exp
o
sed to
extern
al p
e
rt
ur
batio
ns, su
ch as
st
rain
and
te
mpe
r
at
ure,
th
e
Bragg
wavel
e
ngth will
cha
nge
s. By me
asu
r
ing
the wavelength ch
ange accu
rat
e
ly,
the
physi
cal
prop
ertie
s
, su
ch a
s
strain a
nd tempe
r
atu
r
e, ca
n be m
easure
d
. The
shift of a Bragg wavel
engt
h
due to strain and tempe
r
at
ure an
d pressure can be ex
pre
s
sed a
s
:
BT
aa
T
(2)
Whe
r
e
a
is the
strain
sensitiv
ity coefficient
，
T
a
the tempe
r
ature
sen
s
itivity coefficient,
with the a
s
su
mption of no
pre
s
sure ch
a
nge an
d no t
e
mpe
r
ature chang
e, we
ca
n mea
s
ure the
strain from wavelength
shi
ft as:
B
a
(3)
2.2. Working
Principle Of Non-Con
t
ac
t Optic
a
l Signal Transmi
ssion
Figure 1 sh
o
w
s the
wo
rki
ng prin
cipl
e of t
he non-contact opti
c
al
signal tran
smissi
on,
broa
dba
nd lig
ht emitted from a light sou
r
ce an
d pr
o
p
a
gates al
ong a
n
optical fibe
r, The C-le
nse
s
cha
nge the li
ght in the fiber to colli
mat
ed bea
m of parall
e
l light
，
and collima
t
ion light tran
smit
betwe
en ai
r
gap, then, th
e optical sig
nal co
uld tr
a
n
smit bet
wee
n
station
a
ry
part an
d rota
ting
part.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Rotating
Cant
ilever Beam
Dynam
ic Strain
Measurem
ent and Anal
ysis... (Ji
ang X
i
-Xin)
3329
Figure 1. Wo
rking Pri
n
ci
ple
for Rotary O
p
tic Signal Transmi
ssion
2.3. Working
Principle Of D
y
namic Str
a
in Detectio
n
Dynami
c
strain
te
sting system
of rot
a
ting
rect
an
gular
sheet
con
s
i
s
ts of person
a
l
comp
uter, int
e
rrogato
r
, optical fiber
rotat
i
ng joint, FBG, rotating shaf
t and blade.
After coupli
n
g, light emitted by wi
deb
and
light
so
urce in FBG
demod
ulato
r
enters
optical fib
e
r,
move forward
in polyline
s
,
and rea
c
he
s
FBG on
rotati
ng bla
de thro
ugh o
p
tical fi
ber
rotating joint,
in whi
c
h, light
meeting Bra
gg co
nditi
on
are reflecte
d, light of other wavelen
g
th are
transmitted throu
gh FBG,
the reflecte
d
light re
turns back to FBG demo
dulat
or thro
ugh
o
p
tical
fiber
after
p
a
ssing
opti
c
al fibe
r
rota
ting joint, F
B
G dem
odul
ator m
odul
ates/dem
odul
ates
wavele
ngth signal
of FBG
,
and com
m
u
n
icate
s
with
PC throug
h
TCP/IP proto
c
ol, thu
s
sig
nal
attache
d
on rotating ca
ntilever bea
m an
d detec
te
d by FBG can be
measured an
d recorded.
Figure 2. Experime
n
tal Set-Up fo
r Dyna
mic Strain De
tection by FBG
3. Simulation
Dynami
c
stra
in re
spo
n
se
of rotary can
t
ilever beam
will cha
nge
unde
r excit
a
tion of
different rotation spee
ds, in
orde
r to m
o
u
n
t FBG at the
positio
n of m
a
ximum st
rai
n
, and e
nha
n
c
e
measurement
effect, strai
n
mode of
canti
l
ever
be
am h
a
s b
een
anal
yzed, a
s
sho
w
n in th
e figu
re,
dimen
s
ion of
analytic mo
del and mat
e
rial p
r
op
ert
y
are de
scri
bed in 2.1, model bo
und
ary
con
d
ition
s
are co
nfigured
as: complet
e
soli
d
co
nn
ection at
en
ds wit
hout consi
deration of
deform
a
tion a
l
ong di
re
ction
x, i.e. deform
a
tion alo
ng
cantilever
bea
m width
direction, its 1
s
t, 2
n
d
and 3
r
d
natu
r
al fre
que
ncy
are
re
sp
ecti
vely
60.199
Hz, 37
5.2Hz a
nd 10
45.6
H
z,
the maximu
m
strain
po
sitio
n
s a
r
e respe
c
tively 0mm, 159.3
mm a
nd 90.4mm,
with co
nsi
d
e
r
ation of actu
al
length of FBG, the actual
in
stallation positio
ns
of FBG
ar
e respectively 5m
m, 159.3mm
and
90.4mm, as
shown in Figu
res 3-5.
Figure 3. The
1
st
Strain Mode Shape
Figure 4. The
2
nd
Strain Mode Shape
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
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TELKOM
NIKA
Vol. 11, No
. 6, June 201
3 : 3327 – 33
32
3330
Figure 5. The
3
rd
Strain Mode Shape
4.
D
y
namic
Strain
Meas
urement Of Rotating Bla
d
e
4.1. Experimental Set-Up
As con
s
titutio
n
of dynamic stre
ss mea
s
u
r
em
e
n
t syste
m
of rotary ca
ntilever beam
shown
in figure 7, the driving d
e
vice is a A
C
va
riation fre
quen
cy moto
r of 45KW a
n
d
rotation
sp
eed
30
～
30
00rpm,
rotation
spe
ed
can
be
ad
justed
by
sp
e
ed regul
ation
software
of i
ndu
strial
co
ntrol
comp
uter, o
r
by manual a
d
justme
nt of adju
s
t
able re
sista
n
ce, motor drive
s
a speed
-in
c
reasi
n
g
gear b
o
x, of whi
c
h ge
ar ra
tio is 1:5, gea
rbox dr
ive
s
b
earin
g box, cantilever be
a
m
is install
e
d
o
n
end fa
ce
of b
earin
g b
o
x, a
nd i
s
built i
n
-hou
se,
with l
ength
280m
m, thickne
s
s
6mm a
nd m
a
terial
Q235,
modul
us
of ela
s
ticit
y
2.09E11
an
d de
nsity
7
8
0
0
kg/m,
sp
ecifi
c
sha
pe
as shown in
figure 6,
rotary collima
t
or holdin
g
de
vice is in
stall
ed on
en
d of high-sp
eed
shaft of speed
-incre
asi
ng g
ear
box, so that
optical
shaft center
of rotary collim
ator i
s
located
at
the rotating center of
rotati
ng
shaft, adj
ust
the
stationary collimator on five
-dim
ensi
on fine
adjustment bracket
fixed
on
foundatio
n, so that o
p
tical
sh
a
ft ce
nters of t
w
o
colli
mators
coin
ci
dent
with e
a
ch
other, th
u
s
optical
signal comm
uni
cati
on can be realiz
ed between rotary-stationary collim
ators.
Figure 6. The
Cantilever B
eam and FB
G
Figure 7. Experime
n
tal Set-Up
4.2. Result
Und
e
r e
n
viro
nment of ro
o
m
temperature 20
, pe
rfo
r
m mea
s
u
r
e
m
ent test of
dynamic
stre
ss, firstly in ord
e
r to av
oid discrep
an
cie
s
between boun
dary con
d
itions
of sim
u
lation
an
alysis
and a
c
tual
condition
s, im
pact te
st is p
e
rform
ed
fo
r
cantileve
r be
am und
er
st
atic conditio
n
, to
determi
ne na
tural freq
uen
cy of cantilev
e
r bea
m, as
sho
w
n in the
figure, the 1
s
t orde
r freq
ue
ncy
is 54.9
H
z a
n
d
the 2nd ord
e
r
frequ
en
cy is 331.8Hz.
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TELKOM
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e-ISSN:
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Rotating
Cant
ilever Beam
Dynam
ic Strain
Measurem
ent and Anal
ysis... (Ji
ang X
i
-Xin)
3331
Figure 8. Impact sig
nal of Cantileve
r Be
am
Fi
gure 9. Analysis of Impa
ct Signal Resp
onse
Spectrum
Rotation
spe
ed test sta
r
ts from 100rp
m
, and rotati
on sp
eed ri
ses to 800
rpm
stably as
per i
n
terval
of
app
roximatel
y
100rpm
poi
nt by poi
nt, reco
rdin
g FB
G outp
u
t valu
e of all
recording
points i
n
turn, after rea
c
hin
g
800
rpm,
de
cre
a
ses to
0
r
pm sta
b
ly as
per i
n
terval
o
f
100rpm p
o
i
n
t
by point, ma
ke re
co
rd
s of
retractin
g
stro
ke FB
G
outp
u
t value of
all
test poi
nts i
n
reve
rse
o
r
de
r,
and re
peat th
e cycle a
s
pe
r the above
mentione
d
m
e
thod for 3 times, then su
btract the ave
r
age
value of Bra
gg wavelengt
h of all gratings fr
om FB
G Brag
g wa
velength of
all ch
annel
s,
the
results a
r
e pl
otted in figure
s
a
s
follows, figure
10 sho
w
s the
ch
ang
e of micro strain of ca
ntile
ver
beam un
de
r con
s
tant rot
a
tion sp
eed
420 rp
m, an
d figure 11
sho
w
s analy
s
is of re
sp
o
n
se
spe
c
tru
m
of sign
al in figu
re 10, in
whi
c
h, freq
uen
cy
7.26Hz is a
freque
ncy rel
a
ted to rotati
on
spe
ed, 1
4
.53
H
z is dou
ble
d
-fre
que
ncy
of 7.26
Hz,
no
rmally d
ouble
d
-fre
que
ncy
related to
rota
tion
spe
ed exi
s
ts in rota
ry sy
stem d
r
iven
by motor,
55
Hz i
s
1
s
t o
r
d
e
r n
a
tural f
r
e
quen
cy of rotary
cantileve
r be
am.
Figure 10. Th
e Rotating
Ca
ntilever Beam
Dynami
c
Stra
in Data From
1#FBG in 42
0RPM
Figure 11. Th
e Rotating
Ca
ntilever Beam
Dynami
c
Stra
in From 1# F
B
G in Freq
ue
ncy
Domai
n
in 42
0 RPM
Figure 1
2
sh
ows the
micro-st
rain
chan
ge
of ca
ntile
ver
be
am un
der 660
rpm,fi
gure
13
sho
w
s analy
s
is of freq
ue
ncy sp
ectru
m
in fi
gure 12, whi
c
h shows existen
c
e of frequ
e
n
cy
10.93
Hz relat
ed to rotation
spee
d, existence
of frequ
ency spe
c
tru
m
21.85Hz re
lated to rotation
spe
ed d
ouble
d
-fre
que
ncy,
and exi
s
ten
c
e of a
la
rge
amplitude f
r
e
quen
cy 55.1
8
H
z
nea
r natu
r
al
freque
ncy 54
.9Hz of canti
l
ever bea
m, the re
a
s
on f
o
r app
ea
ran
c
e of freq
ue
ncy 55.18
Hz is
dynamic
stiffening of ca
n
t
ilever beam
unde
r the ac
t
i
on of cent
rifu
gal force, whi
c
h ma
ke n
a
tu
ral
freque
ncy
of
cantileve
r b
e
a
m raise
ap
proximately
0
.
28Hz, the
re
aso
n
for rapi
d ri
se
of dyn
a
mic
stre
ss amplitude of cantil
ever
beam at
55.18Hz is similarity
between natu
r
al freque
ncy and
4-
time-freq
uen
cy of rotation spe
ed, and reso
nan
ce o
c
curs , mean
while, with th
e rise
of rota
tion
spe
ed, effect
of fluid emb
o
d
ies
graduall
y
, t
he 2nd n
a
tural frequ
en
cy 333.8Hz
of cantileve
r b
e
a
m
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e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 6, June 201
3 : 3327 – 33
32
3332
and its
dou
bl
e frequ
en
cy a
r
e ex
cited, bu
t its frequ
en
cy
value is la
rger tha
n
static value,
whi
c
h is
also a p
hen
o
m
enon of dyn
a
mic stiffenin
g
.
Figure 10. Th
e Rotating
Ca
ntilever Beam
Dynami
c
Stra
in Data From
1#FBG in 65
5RPM
Figure 11. Th
e Rotating
Ca
ntilever Beam
Dynami
c
Stra
in From 1# F
B
G in freque
ncy
domain in 6
5
5RPM
5. Conclusio
n
This a
r
ticl
e in
trodu
ce
s a n
e
w
strain
me
asu
r
em
ent m
e
thod of rotat
i
ng compo
n
e
n
t, strain
of con
s
tant se
ction cantilever bea
m unde
r rota
ry condition i
s
measu
r
e
d
throu
gh com
p
lex
stru
cture of F
B
G-opti
c
al
co
upler,
dynami
c
st
rain
of co
nstant
se
ctio
n ca
ntilever
b
eam u
nde
r hi
gh-
spe
ed rotary
con
d
ition i
s
measured through th
e ch
a
r
acte
ri
stics of
FBG su
ch
a
s
multiple
-p
oi
n
t
with one lin
e ,distributiv
e measure
m
ent and no
n-conta
c
t tra
n
smi
ssi
on of
optical sig
nal,
mean
while, t
e
st
re
sults are an
alyze
d
,
as i
ndi
cated
i
n
test
analy
s
i
s
, cantilever
beam
emb
o
d
i
es
abun
dant
kin
e
tic
cha
r
a
c
teristics u
nde
r rotary condi
tio
n
, su
bsta
ntial
theoretical
rese
arche
s
ha
ve
been
perfo
rm
ed on
so
me o
f
these
kineti
c
cha
r
a
c
teri
st
i
cs,
while
re
se
arch on
othe
r cha
r
a
c
teri
sti
cs
has ju
st be
en
sta
r
ted. T
h
is ar
ti
cle
ha
s p
r
ovided
some
funda
ment
al
expe
riment
helpful fo
r th
ese
resea
r
che
s
, a
nd the
s
e th
eo
ries can
be v
e
rified i
n
exp
e
rime
nt. Due
to re
stri
ction
of experi
m
ent
al
con
d
ition
s
, the high
est
rot
a
tion spee
d reached i
n
th
i
s
the
s
is is
onl
y 800rpm, bu
t it is po
ssi
ble
to
rea
c
h 20
000
rpm in theo
ry, and stress mea
s
u
r
em
ent requi
rem
ents of exist
i
ng machine
r
y
equipm
ents
can be met ba
sically.
Ref
e
ren
c
e
[1]
Li De
bao. A Genera
l
Revi
e
w
o
n
Sev
e
ral
F
undam
enta
l
Points Of Exp
e
riment
al Strai
n
/Stress Moda
l
Anal
ys
is.
Journ
a
l Of Vibration
And Shock
. 1996; (1).
[2]
Lu Qiuh
ai, Li D
eba
o. T
he Advances of Mod
a
l
T
heor
y
.
Adv
a
n
c
e in Mech
anic
s
. 1996; (4).
[3
]
H
A
N
Zh
o
n
g
h
e
,
ZH
U
Xi
a
o
y
a
n
,
D
I
N
G
C
h
an
g
fu
. R
e
se
a
r
ch
an
d
De
ve
lo
p
m
en
t o
f
Vi
b
r
a
t
i
onal
Measur
ement T
e
chnolog
y of
Steam T
u
rbine
Blade.
T
u
rbi
n
e
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e
chnol
ogy
. 2
002; 44(
3): 129
-131.
[4]
Z
H
EN Shuc
he
n, HE Li to
ng
. Non-co
ntacti
ng me
asurem
ent of vibr
atio
n par
ameters
for rotati
n
g
bla
des.
Ga
s Tu
rb
ine
Te
ch
no
log
y
.
2002; 1
5
(1)
:
7-12.
[5]
AL-Bed
oor BO
. Blade Vi
brati
on Meas
urem
e
n
t in T
u
rbo-Ma
chin
er
y
:
C
u
rre
nt Status.
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he Shock an
d
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on Di
ges
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[6]
Che
n
Ji
ngmi
n
g, W
ang
Z
o
n
g
bo. A S
u
rve
y
of
Vibr
atio
n M
onitor
i
ng
T
e
chnol
og
y Of Ste
a
m T
u
rbin
e
Blad
es Both At Home And Ab
roan.
T
her
ma
l Pow
e
r Generat
ion
. 19
97; 3: 5
3
-57.
[7]
V Do
nato, etc.
Meas
urin
g b
l
ade
vibr
atio
n of
lar
ge lo
w
p
r
essure
st
eam
turbi
ne.
Jo
urn
a
l of
Pow
e
r
Engi
neer
in
g
. 1981; 3.
[8]
More
y
W
W
,
Meltz GW
,
Glenn
H. F
i
bre optic Bragg gr
atin
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210
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[9]
Kerse
y
AD, D
a
vis MA, Patrick
HJ, et al. F
i
b
e
r grati
ng s
ens
ors. J Lig
h
t W
a
ve T
e
chno
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5
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144
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63.
[10]
K
y
u
ngm
ok Ki
m, Jong Mi
n L
ee,
Yoh
a
H
w
a
ng. Determ
inat
ion
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in
ee
ring strai
n
d
i
stributi
on i
n
a
rotor bl
ad
e
w
i
th fibre Br
ag
g
gratin
g arr
a
y and
a r
o
tar
y
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oup
ler
.
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g
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