NGHIEN ClifU - TRAO 061 PHU'aNG PHAP NHAN DANG HU* HONG BO TRUYEN BANH RANG TRONG DIEU KIEN VAN HANH V d | TOC DO QUAY BIEN DOI BANG PHEP BIEN DOI NEN WAVELET SUY RONG FAULT IDENTIFIC
Trang 1NGHIEN ClifU - TRAO 061
PHU'aNG PHAP NHAN DANG HU* HONG BO TRUYEN BANH RANG
TRONG DIEU KIEN VAN HANH V d | TOC DO QUAY BIEN DOI
BANG PHEP BIEN DOI NEN WAVELET SUY RONG
FAULT IDENTIFICATION METHOD IN GEARBOXES OPERATING
AT VARIABLE ROTATION SPEEDS USING THE GENERALIZED
SYNCHROSQUEEZING TRANSFORM
ThS Nguyen Trong Du
Khoa Cdng nghe Co khi, Trudng Dai hgc Dien lire
T6M TAT
Phdn tich tin hiiu trong mien th&i gian - tdn so (Time-Frequency Analysis - TFA) la mpt
cong cu hihi hiiu di phdt hiin hu hong trong he truyen dpng co toe dp quay biin doi Trong bdi
bdo ndy tdc gid de cgp t&i mpt phucmg phdp phdn tich tin hieu trong miin thai gian - tdn s6 m&i
tren ca s&phep biin doi nen Wavelet suy rpng (Generalized Synchrosqueezing Transform - GST)
V&i phuang phdp ndy tin hiiu dao dpng do dugc se dugc xu ly bdng GST, co khd ndng nhdn dang
tot tdn so dn kh&p vd cdc ddi bien Phuong phdp ndy dugc tdc gid kiem chicng bdng tin hiiu dao
dpng mo phong vd tin hiiu dao dpng thifc do tren mo hinh thi nghiem Kit qud phdn tich chi ra
rdng day Id mpt phuang phdp co hieu qud trong viec gidm sdt tinh trgng hogt dpng cua bo truyin
banh rang van hdnh trong dieu kien toe dp quay biin doi
Tur khoa: Phep bien doi Wavelet, phep biin doi nen Wavelet, phep bien doi nen Wavelet
suy rpng, hu hong hdnh rdng, phdn tich thai gian - tdn so
ABSTRACT
Time-Frequency Analysis (TFA) Is an effective tool to detect gearbox faults at variable
operating speeds The present study deals with an advanced method of TFA based on Continuous
Wavelet Transform (CWT), called generalized synchrosqueezing transfrom (GST) Using this
method, the measured vibration signal is transformed into time-frequency domain to obtain its
Time-Frequency Distribution (TFD) having high resolution in time and frequency domain The
gearbox fault, if any, can then be detected by observing the presence of the meshing frequency
and side band components in the TFD The TFA-approach used is evaluated using both simulated
and measured vibration signals at a test-rig The results have shown that this approach is effective
for gearbox condition monitoring
Keywords: Wavelet transform, synchrosqueezing transform, generalized synchrosqueezing
transform, gear fault, time-frequency analysis ^
ISSN 0866 - 7056
TAP CHi CO KHi VIET NAM, Sd 1+2 nam 2015
Trang 2NGHIEN CljrU-TRAODOl
1 DAT VAN DE
Trong qua trinh van hanh, bd truyen
banh rang thudng tao ra cac dao dgng co hpc
Cac dao ddng nay chiia cac thdng tin phan anh
tinh frang boat dpng cua bg truyen banh rang
Cd the do cac dao dpng co hpc dudi dang tin
hieu dao ddng bang each thiet lap dau do gia
tdc gan fren vd hop sd chiia bp truyen banh rang
[ I ] Khi bg truyen banh rang cd hu hdng se sinh
ra nhiing dao dpng bat thudng, duoc phan anh
bang cac tin hieu dao dgng Tin hieu dao dpng
dupe dua vao phan tich phd bang phep bien ddi
Fourier, se thu dugc dd thj bien do - tan so [1]
Randall [2], cho rang cac dai phu sinh ra xung
quanh tan sd an khdp cd the la trieu chiing cho
thay cd hu hdng frong bd truyen banh rang
Tuy nhien, nhugc diem ciia phuong phap phan
tich phd la khd phan tich tin hieu dao ddng vdi
tdc dp van hanh bien ddi, do dd cd han ehe de
khai thac cac thdng tin huu ich nham chan doan
chinh xac hu hdng
Phuang phap phan tich thdi gian - tan
sd ra ddi cho phep phan tich nhirng tin hieu dao
dgng vdi tdc do quay bien ddi Trong nhiing
nam gan day cd nhieu phuong phap phan tich
thdi gian - tan sd dua fren cac phep bien ddi
nhu phep bien ddi CWT [3-4], phep bien ddi
Hilbert-Huang (HHT) [5], phep gan lai [6]
Van de cai thien do phan giai phan bd thdi gian
- tan sd cua cac phuang phap nay van cdn dang
dupe nghien ciiu
Nam 2011, Daubechies [7] dl xuit mpt
phuong phap nang cao dp phan giai ciia phan
bd thdi gian - tin sd dua fren CWT, dugc ggi la
phep biln ddi nen Wavelet (WSST) WSST cd
kha nang nang cao dp phan giai thdi gian - tin
sd nhung cd nhugc diem khdng thi tach dupe
cac dai bien xung quanh tin sd an khdp frong
trudng hgp tdc dp quay bien ddi
Phep bien ddi GST la mdt phuang ph^ ket hgp giira phep bien ddi Fourier suy rpng (Generalized Fourier Transform - GFT) [8] va phep bien ddi WSST [7] cd the khac phuc dugc nhugc diem ciia phep bien ddi WSST ChSn doan hu hdng cua bd truyen banh rang di;a tren phep bien ddi GST van cdn la mpt dieu mdi me
va mdi chi ed hai cdng frinh nghien ciiu cho toi thdi diem nay [9-10]
Trong bai bao nay, tac gia trinh bay trieu chiing hu bdng cua bp truyen banh rang 6 phan 2 Phan 3 tae gia tdm tat lai co sd ly thuyet cua phep bien ddi GST Phan 4 tac gia sii dung phep bien ddi GST nham chan doan hu hong
bd truyen banh rang dua tren cac dau hieu hu bdng, frong hai trudng hgp tin hieu mo phong
va tin hieu thuc
2 DAU HIEU HU" HONG BQ TRUYEN BANH RANG CO TOC DO QUAY BIEN DOI
Tin hieu dao ddng cua hop sd co banh rang hu hdng dugc bieu diln theo dang sau [II]:
Trong do: A la bien do, B la mo dun cua dieu bien bien dp, k la bac dieu hoa (k=0,1,2,3 ), Z la sd rang, fii(t) la tin s6 quay bien ddi theo thdi gian, (p(t) la ham dieu bien tan sd Phuang trinh (I) cd the dugc bien doi tuong duong dudi dang sau [I I]:
(2)
Trang 3NGHIEN cufu - TRAO DPl
Vai thanh phan tin s6 ca ban cong thiic
(3) va cac dai bien tren cong thiic (4), dai bien
duoi cong thiic (5):
/ ( ' ) = 2/".+ip'(()/(2it) (3)
/ ( ' ) = (Z + *)/.+<P'(')'(2") (4)
/.-(') = ( 2 - ' ) / + * ' ( ' ) ' ( 2 " ' ) (5)
Neu xet bac dieu hoa an khop thii m;
fjt)=mffi), Idii do ta co:
f,{l) = mZf,+if\t)l(l%) (6)
/ (')= ""(2+*)/.+1''(')'M (7)
/.i-(') = '"(Z-*)/.+'P'(')'(2") (8)
Trong ^6:fjt) la bac dieu hoa an khop
thii m, f„^j^Jt) \2Lf„^J1) lan luat la dai bien tren
va dai bien duoi cua bac dieu hoa an khop thii
dung phep bien doi Hilbert [12]:
i{t) = x(t) + iH(x{t)) = A{t)e"^''' (9)
Bu6c 2: Nhan tin hieu -^(^) vdi pha tham
khao e
u{t)^A{ty'-''>e'"'-^''>= ^((y«'>^""«) (10)
Vdi x„(t) duoc tinh tCl cong thiSc [10]:
Budc 3: Neu chpn pha tham chieu X(,(t) tdphaongtrinh(ll) thayvao(lO) tathudiigc:
.ii) = Aii)JS^-^'''-^'S^''-^^-^)^^^,^,'^-'S^^ (12)
:E
Ddi vdi tin hieu mo phdng, do biet tnrdc
dugc thanh phin tin sd an khdp tiic thdi biln I ^,)=x(,)->-iH{x(i)]
ddi (fjt)), Ap dung phep bien ddi GST cd the
dl dang xac dinh dugc hai thanh phan dai bien r
tren (frn^(t)) va dai bien dudi (finftf) dugc tach
'-ra tir tin sd tiic thdi cua he Viec xu ly tin hieu r
md phdng dugc minh hga trong phan 4 cua bai
*-bao nay Ddi vdi tin hieu thuc dau do pha cung
cip thanh phin tin sd an khdp cua he thdng | '""y'^^-^-' |
banh rang Tu thanh phan tan sd an khdp ap
dung phep biln ddi GST dl tach thdng tin xung | i¥Tj^.s) = wjx.!<>e'"''"' |
quanh tin sd an khdp Viec xu ly tin hieu thuc
dugc trinh bay ky trong phan 4 cua bai bao nay
I
1
Chpn tan s6
3 CO SO LY THUYET PHEP BIEN DOI GST
Phep bien doi GST la phep bien doi
tong hop ket hop giiia hai phep bien doi GFT va
WSST diloc diia bdi Ming Liang [10] Cac budc
thuc hien phep bien doi GST nhu sau [10]:
Budc 1: Tao mpt tin hieu giai tich si(
^ ^
Hinh 1 Sddo thudt gidi phep bien dSi GST [10]
Budc 4: De loai bd anh hUdng cua thanh phan tan sd am phep bien ddi Hilbert lai dUgc
ap dung:
ISSN 0866 - 7056
TAP CHf CO KHI VIET NAM, Sd 1 +2 nam 2015
Trang 4NGHIEN CUTU-TRAO DOI
v{t)=£i{t) = u{t)-i-iH{u(t)) (13J
Budc 5: Tinh toan phep biln ddi CWT
cho dn hieu giai tich mdi:
WT,{, s) = dill^'V-{s<a).e"^^''^ (14)
Budc 6: Khdi phuc tm hieu bdi biln ddi
GFT ngugc [8]:
Budc 7: Ap dung phep biSn ddi WSST
[7] cho phuang trinh (15)
(15)
r " ' * (16)
C'(t,a))= f WTlv)ih\
U.1 " I
De cd duoc phep biSn ddi (15) thi tin
hieu trudc khi bien ddi CWT phai co dang:
Tan so quayif = -4.S.t' + JOl + 12 Digu bi6n tkn s6:(|)(()= 1.6cos(0.3n:f) Tin hi?u dao
dgng mo phong dugc bi^u diln:
x{l)= l.l(l+ 0.6cos(2it(- 4.3/'+ 10(+ 12))\cosi
(20it(- 4.3/' + 10(+ 12)+ 1.6cos(0.3m)) (17) trong dd/T [0.1 1.1]
Ro rang ring x(t) bao gdm 3 thanh phan diSu bien bien do - tin sd: Tiin sd an khdp, dai tan tren, dai tan dudi Theo dd ta cimg thu dugc
3 tiin so tren bieu dien mi8n thdi gian - tiin s6 theo cong thiic (3), (4), (5)
/(/) = 10(-12.9(=+20( + 12)-0.24sin(0.3rt) /*(() = ! l(-12.9(' + 20f + 12)-0.24sin(0.3«) /-(() = 9(-12.9/' + 20/ +12) - 0.24sin(0.3it()
Lua chgn lay mau la 4096 Hz va chon tan sd muc tieu la/„=JO Pha ciia ham bifa ddi
cd the dirge tinh toan theo cdng thuc (11) nhu sau:
x(t) = A{t)e"-'^'^ = A{t)e'*[ Nhu vay, tin J,(()= - 43/= +100/' +120/- 0.8cos(0.3rt)/i-30( hieu x(t) da dugc phuc hdi vdi thanh phan tjn
s6/„ dugc tach ra Viec thuc hien lap trinh phep
bien doi GST ddi hdi mgt ky nang tdng hgp sau
khi da nam virng cac phep bijn ddi trong xii ly
tin hieu sd
4 NHAN D^NG DAU HIEU HU HONG
BANG PHEP BIEN DOl GST
4.1 Tin hieu mo phong
Xet mgt trudng hgp mgt bg truySn
banh rang cd hu hdngvdi cac thdng sd: Bien do
A=l 1, dieu bien bien dd B=0.6, s6 rang Z=10
Ap dung phep bifo ddi GST vdi tin s6
/„ va pha tham chiSu x/t) tir phuang frinh tren
ta thu dugc kk qua nhu 2 Hinh 3 diln tm hieu
ket qua xii ly tm hieu tren miln thdi gian - tin
sd vdi ba phuang phap khac nhau CWT, WSST
va GST Ro rang ta thiy tren hinh 3, cac dai bien tren va dai bien dudi trong phan bd thdi gian - tin sd, la trieu chiing gay hu hdng [2], chi cd the duac nhan ra bSng phep biln ddi GST
Trang 5NGHIEN cufu - TRAO OOl
Hinh 2 Ddi bien xung quanh tdn sd an khop dugc
xu ly bdng GST
Hinh 4 Mo hinh thi nghiem
Ket qua phan tich tin hieu trong mien thdi gian va mien tan so khdng cho thay cd su khac nhau giua banh rang binh thudng va banh rang niit Hau nhu khdng the quan sat dugc cac tan sd an khdp va cac dai bien tren phd tan sd,
do tdc do quay bien ddi
Hinh 3 So sdnh cdc phep bien doi
CWT WSST vd GST
4.2 Thvc nghiem v^ ket qua
Md hinh thi nghiem bp truyen banh rang
mpt cap dugc xay dung tai phdng thi nghiem
chan doan ky thuat, thudc Bd mdn Co hpc U'ng
dung, Trudng Dai hgc Bach khoa Ha Ngi So
rang banh dan la 24 rang, sd rang banh rang
dau ra la 40 rang Tdc dp dpng c a dugc thay ddi
bang bien tan Trong qua trinh thi nghiem tdc
do dpng ca thay ddi hi 375 (vg/ph) - 1000 (vg/
ph) Tai trgng dugc tao ra tii phanh tir, cd hai
trang thai tai va khong tai tuong ung vdi ddng
va md phanh tu Banh rang dan dupe tao ra hu
hdng niit rang mpt each cd chu y nham danh
gia va k i i m chiing hieu qua cua phuang phap
trong thuc nghiem Md hinh thi nghiem dugc
thilt lap va mieu ta nhu tren hinh 4
a) Tin hieu hdnh rdng binh thudng
b) Phd tdn so bdnh rdng binh thuang
c) Tin hieu bdnh rang cd vet nut
\ nniii 11 iiiiiiiiii
d) Pho tdn so bdnh rang cd vet nirt Hinh 5: Kit qud phdn tich trong mien th&i gian vd trong mien tdn sd bdnh rdng binh thuang (hinh a, b) vd bdnh rdng cd vet nut (hinh c, d) " ^
ISSN 0866 - 7056
T4.P CHf CO KHI VIET NAM, S6 1+2 nam 2015
Trang 6Tan sofg dugc lua chpn la 70Hz de dam
bao quet bet dai bien xung quanh tan so an
khdp Ket qua ap dung phep bien ddi GST vao
ti n hieu ta thu dugc phan bd thdi gian - tin s6
nhu tren hinh 6 Quan sat hinh 6 ta thiy trong
trudng hgp banh rang binh thudng phan bd thdi
gian - tan sd chi xuat hien tan sd an khdp, cdn
vdi trudng hop banh rang cd vit niit thi phan
bd thdi gian - tan so ed xuat hien eae dai bien
xung quanh tan sd an khdp Nhu vay, ed thi
nhan dinh rang phucmg phap chan doan dua
tren trieu tning dai bien trong trudng hpp tdc
do quay bien ddi bang GST la dang tin cay va
cd thi ap dung nhu la mot phuong phap chin
doan mdi trong cdng nghiep Phuong phap nay
ed the chan doan sdm hu hdng ngay trong qua
trinh tang tdc cua bd truyin banh rang
Tin so in khor
a) Bdnh rdng binh thu&ng
I Daib
7
.1 bien duxTJ I
1
5 KET LUAN
Trong qua trinh nghien ciiu, phuong phap phan tich thdi gian - tin sd dua tren phep bien ddi GST dugc ap dung d l phan tich tin bieu dao dgng cua hop sd banh rang, qua do co
t h i giam sat tinh trang boat dpng va phat hien
hu hdng ciia banh rang trong he truyin dpng
Ve CO ban, day la mdt phuong phap dugc xay dung tren ca sd phep bien ddi Fourier suy rpng
va phep bien ddi Wavelet lien tuc So sanh vdi nhihig ky thuat phSn tich thdi gian tin sd hien
cd, phuang phap GST tao ra phan bd thdi gian
- tan sd cua tin hieu vdi dp phan giai cao khong gay ra nhieu sai leeh, ddng thdi cd kha nang tach cac dai bien xung quanh tin sd an khdp Phuong phap nay phu hpp d l phan tich hpp s6
cd toe dp quay bien ddi nhanh do yeu ciu ciia qua trinh edng nghe Dua vao tin sd an khop
va cac dai dieu hda phu quanh tin sd an khdp dugc nhan dang tu phan bd thdi gian - tin si eua tin hieu, cd the xac dinh dugc diu hieu hu hdng bd truyen banh rang Tuy nhien, viec lira chpn tan sd trung tam nhim tdi uu hda phuong phap GST van edn la van de can dugc quan tam nghien cuu.•>
Ngay nhan bai: 17/01/2015 Ngay phan bien: 18/02/2015
Tai lieu tham khao:
b) Bdnh rdng bj nut
Hinh 6: Kit qud phdn bd thai gian - tdn sd trong
hai tru&ng hgp bdnh rdng binh thu&ng vd bdnh
rdng bi nut
[I] G Meltzer (2000) Technical diagnostics - an
introduction Lecture notes, Dresden University [2] Robert Bond Randall (2011) Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applicadons, Wiley, ISBN 978-0-470-74785-8
Trang 7NGHIEN cufu-TRAODOI
[1] G Meltzer (2000) Technical diagnostics - an introduction Lecture notes, Dresden University [2] RobertBond Randall (2011) Vibration-based Condition Momtonng: Industrial Aerospace and Automotive
Applications Wiley, ISBN 978-0-470-74785-8
[3] Nguyen Phong Dien, & Nguyen Trpng Du, (2012), Phdt hien vet nut rdng cua bp truyen bdnh rdng
bdng phuang phdp trung binh hoa tin hieu dao dpng vd phep bien ddi Wavelet lien tuc Paper presented at
the, Tuyen tap cong trinh khoa hpc hoi nghi co hpc toan quoc Ian thii 9, Ha Npi
[4] Z K Peng, & F L Chu (2004) Application of the wavelet transform in machine condition monitoring
and fault diagnostics: a review with bibliography Mechanical Systems and Signal Processing, 18,
199-221
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decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
[61 F Auger, & P Flandrin (1995) Improving the readability of time-frequency and time-scale representations
by the reassignment method IEEE Transaction on Signal Processing, 43, 1068-1089
[7] I Daubechies, J.F Lu, & H T Wu (2011) Synchrosqueezed wavelet transforms' an empirical mode
decomposition-like tool Applied and Computational Harmonic Analysis, 30, 243-261
[8] S Olhede, & A.T Walden (2QQ5) A generalized demodulation approach to time-frequency projections
for multicomponent signals P Roy Soc Lend A Mat, 461, 2159-2179
[9].ZhipengFeng, Xiaowang Chen, & Ming 'LmxigQ.QXS) Iterative generalized synchrosqueezing transform
for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions Mechanical Systems
and Signal Processing, 52, 360-375
[10] Chuan Li, & Ming Liang (2012) A generalized synchrosqueezing transform for enhancing signal
time-frequency representation Mechanical and Signal Processing, 92, 2264-2274
[11] F.Q Peng, D.J Yu, & J.S Luo (2011) Sparse signal decomposition method based on multi-scale
chirplet and its application to the fault diagnosis of gearboxes Mechanical Systems and Signal Processing
25 549-557
[12] Michael Feldman (2011) Hilbert transform in vibration analysis Mechanical Systems and Signal
Processing, 25, 735-802
ISSN 0866 - 7056
TAP CHi CO KHi VIET NAM, Sd I +2 nam 2015