Research on Reliability for Wind Turbine Transmission System Based on Random Theory

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Ernest Robinson
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1 Advaced ciece ad Techology Leers Vol8 (CT 5) pp3-9 hp://ddoiorg/457/asl58 Research o Reliabiliy or Wid Turbie Trasmissio ysem Based o Radom Theory Xi Gua Huadog Wag 3 Zhili u Da Zhao chool o Mechaical gieerig ad Auomaio Norheaser Uiversiy heyag Chia New power school heyag Isiue o gieerig heyag Chia 3 Liaoig Guidaojiaoog College heyag Chia i_gua@siacom Absrac As srucure wid urbie is ilueced by wid load i he ru ad propery o wid load is srog radomess which is a grea iluece o he reliable operaio I his paper he heory o radom vibraio aalysis is applied o aalysis o he wid load ad calculaio o wid urbie Mahemaics mehod o wid load aalyic calculaio is deailed discussed meawhile simulaig mehod o he srucure is combied which is applied or simulaio aalysis o wid urbie rasmissio sysem Combiig resul o umerical simulaio ad i acual worig codiio We ca hough i value ha aalysis mehod ca be used or egieerig applicaio ad i is pu orward ha ew aalysis hough o wid load Keywords: radom wid load rasmissio sysem reliabiliy wid urbie Iroducio I rece years may epers ad scholars a home ad abroad has carried o urher research o he wid urbie rasmissio sysem For eample buildig oliear dyamic model o he gear - drive sha - body sysem coupled wih muli-gear rasmissio o large wid urbie ad sudyig o he dyamic characerisics o he couplig sysem [] ; buildig muli-gear coac iie eleme model o large wid urbie rasmissio sysem pu orward calculaio mehod ha he acual coac gear pair disribued gear load i he process o iside ad ouside gear pair meshig [] ; buildig ad puig orward aalysis mehod o plaeary gear sysem ieic model i variable load eciaio [] These mehods is buil based o seady or very small chage ouside evirome acually rasmissio sysem o wid urbie is aeced by eeral evirome ad by wid load obviously [] I is cosidered ha eeral wid load aecs wid urbie ad should be cerai egieerig value or research o ruig reliabiliy o he whole wid urbie ad rasmissio sysem IN: ATL Copyrigh 5 RC

2 Advaced ciece ad Techology Leers Vol8 (CT 5) Wid load radomess vibraio aalysis Radom process As srucure iesiy o wid load which is oe o wid urbie load always chages wih ime A characerisic o wid load is ha o oly chages complicaedly wih ime bu also load waveorm do' show same syle i wo ime I is ehibi comple ad chages wih ime o oly waveorm o wid load bu also requecy ad duraio As a radom process radom vibraio ca be o a ucio o ime bu i used o be ucio o spaial coordiae ve i he same evirome i oal impossible o be predic ha he acual waveorm geeraed bu i is occurred by Probabiliy ample ucio may be produced i he codiio o each waveorm Radom vibraio o o-deermiisic pheomea is o be solved by aalyzig he acual ucio o saisics Wid load saioary radom process ad coiuiy Whe i is provided ha all acual sample ucio o wid load radom process ( ) ( ) ( ) or whe i is provided ha oal probabiliy desiy ucio ad probabiliy desiy ucio hese saisics should be solved O course comple sochasic processes o wid load cao eplaied ully by oly hese saisics used I is he mos impora ad he mos basic radom process ha saioary radom process I he acual wid power projec I is simulaed by saioary sochasic process ha may pheomeo is corolled by he probabiliy Whe all saisics () i radom process does o chage wih ime i is ow as sricly saioary radom process Thereore ime o () probabiliy desiy ucio should saisy: r r r () Based o probabilisic basic ormula mahemaical epecaio o are as ollows: d lim () o he meaig o ad ( ) i equaio () is cosise amely +r =( +r ) Accordig o equaio he probabiliy r r r desiy ucio o () as ollows: because i is righ or each r he r ( ) has ohig o ime o i ca be showed equaio d cosa 4 Copyrigh 5 RC

3 Meaime wid load as wo-dimesioal disribuio o radom process he quadraic probabiliy desiy ucio is: r r (3) I projec i addiio o he sricly saioariy above whe oly saisy equaio () ad (3) i is ow as saioary radom process cep i is oed i egieerig projec which is o saisy equaio () ad (3) is ow as saioary radom process 3 Radom gauss process Radom process imes o () probabiliy desiy ucio obeys laws o gauss disribuio () is called as a gauss radom process Tha is: Ad probabiliy desiy ucio is give: j j j j / / ep (4) i he equaio is deermia o he covariace mari as ollow: (5) Whe = equaio (5) is: ep (6) i equaio R (7) is correlaio coeicie o ( ) ad ( ) () Advaced ciece ad Techology Leers Vol8 (CT 5) Copyrigh 5 RC 5

4 Advaced ciece ad Techology Leers Vol8 (CT 5) 3 igle degree o reedom sysem vibraio aalysis Whe srucure is applied by eeral orce ad i ca be regarded as radom process he dyamic aalysis mehod is called radom vibraio heory Chage o wid load because o is o-repeiive is show as radom process ad ha graspig reacio o wid urbie srucure sysem is reliable saey mehod o Quaiaive evaluaig srucure Origially i is regarded as limied duraio problem ha vibraio respose o wid urbie or wid load so i should be cosidered o o-saioary radom process Bu he acual aim is diere we ca cosider i as saioary radom process i addiio whe saic wid urbie sar ruig especially i he iiial sage o he moveme we ca serve i as a o-saioary radom process or aalyzig Radom vibraio heory ca be divided io wo ypes oe is ha cosiderig he srucure maerial ad mechaical properies o oliear large deormaio eecs vibraio aalysis he oher is ha cosiderig idealized liear vibraio aalysis I addiio srucure isel also ca' be cosidered as radom srucure i saisical properies o srucures are cosidered Radom vibraio is mos impora ha evaluaig reliabiliy problem o he dyamic load Whe srucure is desiged ad reliabiliy is cosidered boudary limied ad deorm should be deied For eample whe wid urbie srucure sress eceeds allowable sress From agle o reliabiliy i should be hough ha wid urbie has eered io a dagerous rage Whe solvig problem o dyamic load by applyig radom vibraio heory we hi ha i more high ha reacio value i more sae ha wid urbie rus i eire duraio I he umerical value o probabiliy has bee obaied we ca hi i as quaiaive evaluaio o reliabiliy i is called radom damage problem whe reacio value is higher ha limied value ad we hi i as crierio I heory i is problem o irs ime misregisraio probabiliy I is o cosidered ha elaso-plasic properies accumulaio aigue sregh degradaio o wid urbie bu because o providig he more impora problem o dyamic reliabiliy heory 3 igle degree o reedom sysem vibraio For sigle degree o reedom paricle-sprig sysem ca be illusraed by he ollowig equaio: m c g (3) z y (3) m c m y (33) 6 Copyrigh 5 RC

5 Advaced ciece ad Techology Leers Vol8 (CT 5) I equaio m= qualiy c= viscous dampig coeicie =sprig cosa moio equaio o paricle displaceme () is show whe paricle m is disurbed by eeral orce g(t) meawhile moio equaio o oudaio displaceme () i absolue coordiae z() ad relaive displaceme () is show as equaio (3) The sigle degree o reedom sysem vibraio model is ha chages he mos comple srucure io he simple idealizaio model i will become he basis o muli degree o reedom sysem vibraio aalysis quaio (3) ad (3) is rasormed io a sadard orm: 或 g - y / m (34) I equaio: =dampig raio; =sigle degree o reedom irisic circular requecy; / m ; c / m I o iiial codiio we ca solve: I equaio: h d (35) h e ; si ; (36) udyig o harmoic moio codiio o he dampig raio wid load disurbace () is cosidered as absolue value o isaaeous orce whe = Tha is ubsiue i io equaio (4) (37) h d h e ; si ; (38) Copyrigh 5 RC 7

6 Advaced ciece ad Techology Leers Vol8 (CT 5) Thereore physical sigiicace o ucio h() is reacio displaceme h i sigle degree o reedom sysem whe surgig orce i = i is called ui impulse reacio ucio ecodly we research o wid load disurbig as saioary harmoic ucio uppose i e H H i subsiue i io (3) e (39) i H is called wid urbie (rasmissio) sysem requecy reacio ucio or (rasmissio) sysem raser ucio i oher word i is displaceme reacio o wid load ipu () 3 Radom vibraio aalysis Cosiderig ipu o equaio (33) wid load disurbace as sochasic process A his ime is o all samplig ucio bu should be regarded as collecio o ucios For reacio () o ipu is meaig ad becomes radom process uppose is g (3) s g is o-saioary coirm ucio s is saioary radom process Whe g cosa is o-saioary radom process As is represeed by equaio (39) i is used o mahemaical model o wid load vibraio ad is requecy compoe disribuio proporio o power specral desiy is ohig o ime I we ae soluio o equaio (33) epeced value o equaio (34) is h I reacio epeced value O he basis o equaio (34) d (3) will be h h d d (3) oluio will be give i ac epeced value o wid load wo-dimesio seady radom mahemaic is 8 Copyrigh 5 RC

7 Advaced ciece ad Techology Leers Vol8 (CT 5) h h d d Ad worig ou wo-dimesio radom probabiliy o wid load is R h h d d (33) (34) 4 Coclusio I is more sigiica ha wid urbie is aeced i acual process o wid urbie ruig so o oly he whole wid urbie bu also rasmissio sysem is aalyze i srucure load dyamic load or saioary load i mus be cosidered ha eec o eeral load (wid load) Wid load has srogly radomess so i is pracical applicaio value ha usig heory o radom o deermie wid load Reereces WANG J G WANG Y HUO Z P: sablishme o mahemaic model ad sudy o vibraio modes o muli-sage plaeary gear rai o wid urbie gearboes [J] Joural o ichua Uiversiy (egieerig sciece ediio) 5 89 (3) ZHU C-C HUANG Z H TANG Q ec: Aalysis o oliear couplig dyamic characerisics o gearbo sysem abou wid-drive geeraor Chiese joural o mechaical egieerig 4 3 (5) 3 ZHU C-C HUANG Q TANG Q: udy o muli-eeh coac ad load disribuio o speed icrease gearbo rasmissio sysem or he wid-drive geeraor [J] Joural o agriculural machiery (6) 4 GUAN X UN Z-L ZHAO Y ec: Based o heory o aerodyamic eciaio wid urbie blade useady low eec aalysis [J] ciece echology ad egieerig 7 4 (4) 5 ZHAO Y MUTLLIP Ahma UN -D H Y-M: Dyamic o-liear aalysis o helical plaeary gear sysem or wid urbie gearbo Reewable eergy resource 8: 45-5 (3) Copyrigh 5 RC 9

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