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 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 mien th&i gian - tdn so (Time-Frequency Analysis - TFA) la mpt cong cu hihi hiiu di phdt hiin hu hong 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 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 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 tren mo hinh thi nghiem Kit qud phdn tich chi rdng day Id mpt phuang phdp co hieu qud viec gidm sdt tinh trgng hogt dpng cua bo truyin banh rang van hdnh 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 transform, gear fault, time-frequency analysis synchrosqueezing ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, Sd 1+2 nam 2015 w « w.cokhivietnam.vn ^ NGHIEN CljrU-TRAODOl DAT VAN DE Trong qua trinh van hanh, bd truyen banh rang thudng tao cac dao dgng co hpc Cac dao ddng chiia cac thdng tin phan anh tinh frang boat dpng cua bg truyen banh rang Cd the cac dao dpng co hpc dudi dang tin hieu dao ddng bang each thiet lap dau gia tdc ganfrenvd hop sd chiia bp truyen banh rang [ I ] Khi bg truyen banh rang cd hu hdng se sinh 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 - tan so [1] Randall [2], cho rang cac dai phu sinh 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, dd cd han ehe de khai thac cac thdng tin huu ich nham chan doan chinh xac hu hdng 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 cdngfrinhnghien ciiu cho toi thdi diem [9-10] Trong bai bao nay, tac gia trinh bay trieu chiing hu bdng cua bp truyen banh rang phan Phan tae gia tdm tat lai co sd ly thuyet cua phep bien ddi GST Phan 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 DAU HIEU HU" HONG BQ TRUYEN BANH RANG CO TOC DO QUAY BIEN DOI Phuang phap phan tich thdi gian - tan Tin hieu dao ddng cua hop sd co banh sd ddi cho phep phan tich nhirng tin hieu dao dgng vdi tdc quay bien ddi Trong nhiing rang hu hdng dugc bieu diln theo dang sau nam gan day cd nhieu phuong phap phan tich [II]: 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 phan giai phan bd thdi gian Trong do: A la bien do, B la mo - tan sd cua cac phuang phap van cdn dang dun cua dieu bien bien dp, k la bac dieu hoa dupe nghien ciiu (k=0,1,2,3 ), Z la sd rang,fii(t)la tin s6 quay Nam 2011, Daubechies [7] dl xuit mpt bien ddi theo thdi gian, (p(t) la ham dieu bien phuong phap nang cao dp phan giai ciia phan tan sd Phuang trinh (I) cd the dugc bien doi bd thdi gian - tin sd duafrenCWT, dugc ggi la tuong duong dudi dang sau [I I]: 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 (2) cac dai bien xung quanh tin sd an khdp frong trudng hgp tdc dp quay bien ddi ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, Sd 1+2 nam 2015 www.cokhivietnam.vn NGHIEN cufu - TRAO DPl Vai phan tin s6 ca ban cong thiic dung phep bien doi Hilbert [12]: (3) va cac dai bien tren cong thiic (4), dai bien duoi cong thiic (5): i{t) = x(t) + iH(x{t)) = A{t)e"^''' (9) / ( ' ) = 2/".+ip'(()/(2it) (3) / ( ' ) = (Z + *)/.+^""«) (10) Vdi x„(t) duoc tinh tCl cong thiSc [10]: Budc 3: Neu chpn pha tham chieu X(,(t) tdphaongtrinh(ll) thayvao(lO) tathudiigc: Trong ^6:fjt) la bac dieu hoa an khop ii) = Aii)JS^-^'''-^'S^''-^^-^)^^^,^,'^-'S^^ (12) thii m, f„^j^Jt) \2Lf„^J1) lan luat la dai bien tren va dai bien duoi cua bac dieu hoa an khop thii Ddi vdi tin hieu mo phdng, biet tnrdc :E dugc 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 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 phan cua bai *bao Ddi vdi tin hieu thuc dau pha cung cip phin tin sd an khdp cua he thdng | '""y'^^-^-' | banh rang Tu 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 phan cua bai bao Chpn tan s6 I ^ ^ CO SO LY THUYET PHEP BIEN DOI GST Hinh Sddo thudt gidi phep bien dSi GST [10] Phep bien doi GST la phep bien doi tong hop ket hop giiia hai phep bien doi GFT va Budc 4: De loai bd anh hUdng cua WSST diloc diia bdi Ming Liang [10] Cac budc thuc hien phep bien doi GST nhu sau [10]: phan tan sd am phep bien ddi Hilbert lai dUgc Budc 1: Tao mpt tin hieu giai tich si( ap dung: ISSN 0866 - 7056 TAP CHf CO KHI VIET NAM, Sd +2 nam 2015 www.cokhivietnam.vn NGHIEN CUTU-TRAO DOI Tan so quayif = -4.S.t' + JOl + 12 Digu bi6n 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: 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 (14) (20it(- 4.3/' + 10(+ 12)+ 1.6cos(0.3m)) (17) dd/T [0.1 1.1] Budc 6: Khdi phuc tm hieu bdi biln ddi GFT ngugc [8]: Ro rang ring x(t) bao gdm phan diSu bien bien - tin sd: Tiin sd an khdp, dai tan tren, dai tan dudi Theo dd ta cimg thu dugc (15) tiin so tren bieu dien mi8n thdi gian - tiin s6 theo cong thiic (3), (4), (5) WT,{, s) = dill^'V-{s