principle 2 Testing pantograph

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1 Che Taglog, a Feghao, Zhou Ya The Study of Novel Detetio Aoah fo OCS Dyami Paametes of High-seed Eletified Railway CHEN TANGLONG, A FENGCHAO, ZHOU YAN College of Eletia l Egiee ig Southwest Jiaotog Uivesity Noth Ehua oad #, Chegdu, Sihua 6, CHINA CHINA tl_he@6.om Abstat: This ae stats with dyami esose of atogah slide, ad omutes the dyami aametes of atogah-ateay system suh as otat foe, had sot, ull-off value ad otat wie height by utilizig the tasfe futio matix gaied befoehad ad the dislaemets of atogah slide measued with the lase age sesos ofigued at the low voltage side. The ae also deduts the umeial algoithm of esose matix ad tasfe futio matix, demostates the feasibility of eduig the umbe of lase age sesos, ad veifies its effetiveess by simulatio with a simle examle. Key-Wods: OCS(Ovehead Cotat System; Patogah; System Resose; Cotat Foe; Pull-of f Value; Had Sot; Cotat Wie Height; Lase Testig Dislaemet Itodutio Patogah slide is movig fast ude the ovehead ateay whe eleti loomot ive is uig. Fig. shows the effet of atogah-ateay otat foe ad dyami esose of hoizotal vibatio of atogah slide [-, ]. The study of this ae, whih is helful to ostut the high-seed atogah vibatio test latfom, a be veified ad geealized by alyig diffeet fequeies, otat foes, ad atig ositios. Testig iile of atogah ateay system s otat esose Fig. Aalysis of system sigal Diet testig methods of atogah-ateay otat foe ae ommoly used i the wold. Howeve, beause of fast motio, testig sigals ae vuleable to the itefeee of eletomageti saks aused by atogah-ateay otat vibatio, ad the istalled essue seso ieases the weight of slide ad hages its shae. Theefoe, the stability ad safety of atogah has bee affeted. The testig method oosed i this ae is to istall seveal lase age sesos symmetially at the to of the loomot ive, alulates the dyami aametes of the atogah-ateay otat foe, ull-off value, had sot ad otat wie height aodig to testig the hoizotal vibatio dislaemet at the bottom of the atogah slide. Fig. Resose testig model of atogah slide The vibatio of slide i the atogah-ateay oeatio a be osideed aoximately as omoud motio whih iludes hoizotal bedig vibatio of elasti beam suoted by fixed eds, vetial flutuatio ad laay wheelig of igid beam suoted by elasti eds. Slide s bedig vibatio mode a be solved by usig Eule-Beoulli beam [5]. F i exesses atogah-ateay otat ulse foe exetig at the sot of the slide s beam. It i th ISSN: Issue, Volume, Jauay 8

2 Che Taglog, a Feghao, Zhou Ya idiates hages of the ull-off value i diffeet loatios. Y i eesets testig value of dislaemet fom the high-seed lase seso i th o the to of loomot ive oesodig to the bottom of the atogah slide. Thei dyami esoses a be exessed as the followig matix fom i tems of tasfe futio: F Y F Y F Y ( a be obtaied fom uit im ulse esose. Theefoe, aodig to ovolutio iile, atogah-ateay otat foe P a be exessed as follows: P F Y i i i j i ( The imat aeleatio of atogah ateay G, otat wie height H ad Pull-off value Z a be obtaied istatly fom disete dislaemet sigal y( t, i tested by those lase sesos, whih ae exessed as follows: d y( t, i G max{ } dt i,,, ( H h y( t, i ( Z Whee h i W i i i i W y( t, i (5 the base height of sesos o the to of loomot ive. the umbe of lase sesos the distibutig ode umbe of lase sesos symmetial weightig oeffiiets at geometi loatio of those lase sesos. Kietis aalysis of slide s beam The model show i Fig. a be deomosed ito a atogah elasti slide s beam suoted by fixed eds ad a atogah igid slide s beam suoted by elasti eds. Afte solvig thei dyami esose, hoizotal esose dislaemet y( t, i a be added togethe at the same oit of the axis ude stati equilibium.. Viba tio of atogah slide s igid beam i lae Suosig that the baig sig stiffess is k, legth of slide s beam is l, the lie desity is, mass is m, etiod is, momet of ietia of slide s igid beam ilig the etiod is I, hoosig etoid s hoizotal dislaemet y ad agula dislaemet of slide s igid beam ilig aoud the etiod as geealized oodiate( y,, aalyzig the foes exetig o the slide, diffeetial equatio of foed vibatio a be established as follows: m y ky P ( x l (6 I kl P ( x l ( l l (7 Assumig P, fom whih the atual fequey of hoizotal vibatio ad the ylig fequey of igid beam aoud its etoid a be obtaied esetively: k k (8 m l kl I 6k l Fig. ehai model of slide s igid beam imosed by exteal foe (9 Adotig Duhamel itegal method to solve (6 ad (7: t y P ( x l si t d ( P ( x l ( os t ( ISSN: Issue, Volume, Jauay 8

3 Che Taglog, a Feghao, Zhou Ya t P ( ( si x l l l ( t d P ( os ( x l ( l l t ( The omosite hoizotal vibatio dislaemet y( x, t aused by hoizotal vibatio ad the wheelig aoud the etoid at x sot of slide s igid beam a be exessed as ( whe atogah-ateay otat foe affets o l sot as show i Fig.. y ( x, t y ( l / x si P ( x l ( os t P ( x l( l l( os t ( l / xsi( (. Bedig viba tio mode futio of atogah slide s elasti beam Cosideig hoizotal dislaemet y of slide s elasti beam suoted by the fixed eds i the oss setio s symmetial lae as geealized oodiate, suosig that lie desity of the beam is, the oss setio s bedig stiffess is EI, aalysis of foes a be obtaied as show i Fig.. The exeted foes o the elemet whih is iteeted fom setio x o the beam a be aalyzed. Suosig that the sheaig foe effeted o setio x is Q, momet is ; the sheaig stess effeted o setio x is Q Q / x, momet is / x. Aodig to D Alembet s Piile, the followig equatio a be obtaied: Q y Q Q x t ( omet equilibium equatio a be obtaied by keeig abitay sot o setio x as the etoid of the momet o the ight side of the uit. y Q x t ( Igoig miodose of the seod ode i the above equatio, the elatioshi of momet ad sheaig foe a be obtaied: Q x (5 Aodig to the kowledge of mateial mehais, momet oesodig to geealized dislaemet y a be exessed as follows: y EI (6 x Puttig (5 ad (6 ito (, a fou ode homogeeous PDE of beam s hoizotal vibatio a be obtaied: y y EI (7 x t Fig. Hoizotal fee vibatio of slide s elasti beam The atue fequey ad mode about slide s elasti beam a be solved by usig vaiable seaatio method [, 7]. Suosig y x, t ( x at (8 Diffeetiatig the above equatio ad uttig it ito (7,the followig equatio is available: EI d ( x a t (9 ( x a ( t Beause a be exessed as follows: d ( x ( x EI a ( t a( t is a ostat, the above equatio ( ( is the atual fequey of slide s beam, the solutio about ( is: a t A os t A si t ( A ad A ( i the above equatio a be detemied by iitiative oditio. Assumig ( EI The solutio of ( is: ( x B si x B osx B shx Bhx ( Substitutig ( ad ( ito (8, the solutio ISSN: Issue, Volume, Jauay 8

4 Che Taglog, a Feghao, Zhou Ya about hoizotal fee vibatio of slide s beam is: y x t ( B si x B os x B shx B h A, x *( A ost A si t (5 A ad Thee ae six ostats to be detemied. elies o the iitiative oditio of vibatio. Thee of the B j s( j =,,, ad whih is imliated i a be detemied by bouday oditios. Puttig bouday oditios ito the exessio of vibatio model futio, the atual vibatio model a be solved. The exessio of vibatio model futio a be show as follows by usig Colleov futio: ( x C S x C Tx C U x C V x (6 Whee C C B, C C B, C C B, C C B Fidig the deivative of (6, the followig equatios ae available: d C Vx C Sx C T x C U x (7 d C U x C V x C Sx C T x (8 d C T x C U x C V x C S x (9 Dyami esose of slide s elasti beam show i Fig. a be osideed as hoizotal bedig vibatio mode about elasti beam suoted by fixed eds. Fo the elasti beam suoted by fixed eds, its bouday oditio is that eds dislaemet ad oe of the beam ae zeos. Namely, x d, x ( xl, d xl ( Puttig ( ad ( ito (6 ad (7, the followig equatios a be obtaied: C C ( C U l C V ( l ( C ( T( l CU ( l C ad C ( aot be so that the solutio is ot. Theefoe, the followig equatio must be equied. U ( l V( l (5 T ( l U ( l Puttig Colleov futio ito the above equatio: ( hl os l ( shl si l ( shl si l (6 The followig idetial equatios always exist: h l sh l l si l (7 os (8 Puttig (7 ad (8 ito (6, fequey equatio of hoizotal vibatio about slide s elasti beam a be obtaied: oslhl (9 The followig solutio a be gaied fom solvig this hyeboli equatio: i i l ( i,, ( Puttig the above equatio ito (, omutatioal exessios of atual fequey about slide s beam a be obtaied: i EI ( i ( i,, l Fo the faility of alulatio, aametes of vibatig slide s beam a be hose as Table. Table Calulatio aametes of vibatig slide s beam Lie desity of slide s beam.5 kg / m Elasti modulus of slide s 7 Nm beam EI Legth of slide s beam. m Elasti oeffiiet of sigs o the eds of slide s beam k 5 N/m The atual fequey of st ode model is 9.5Hz, the atual fequey of d ode model is 58Hz, the atual fequey of d ode model is 55Hz, the atual fequey of th ode model is 89Hz. Puttig (, ( ad ( ito (6, the vibatio mode futio of the hoizotal bedig vibatio of slide s elasti beam a be obtaied as ( shows. x C U ( x C V( ( x shl si l Dhx osx ( shx si x hl osl ( I (, D a be abitay ostats. ai vibatio mode of the oesodig ode about hoizotal bedig vibatio of slide s elasti beam a be obtaied as log as l oesodig to i ISSN: Issue, Volume, Jauay 8

5 Che Taglog, a Feghao, Zhou Ya those atual fequeies is ut ito (.. Dyami imulse esose to atogah slide s elasti beam Fig.5 Slide s beam affeted by uit imulse foe Suosig thee exists a atogah-ateay otat foe P, the movig equatio of fee vibatio a be obtaied at x l sot of slide s beam: y y EI P ( ( x l x t ( is the vibatio mode futio of slide s elasti beam. Regulaizig the mai vibatio mode, usig its othogoal featues, the equatio ( is available. D l ( shl si l hx os x ( shx si x os h l l Suosig that those atual fequeies ae, mai vibatio mode is ( x, whee,,,, the dyami esose to elasti beam a be exessed by modal sueositio (oodiate tasfomatio as: y x, t ( x q ( t (5 q t is the mode oodiate i the above equatio. The esose of eah detemied mode a be solved esetively; the luses them togethe. Theefoe, eah detemied mode hages ito oblem of sigle degee of feedom. Usig othogoal featue of mai vibatio mode, th d q ( t ode mode a be exessed as follows: dt q ( t Q ( t(,,, (6 Whee, l Q ( t ( x P ( x l P ( l It a be solved by Duhamel itegal method: t q ( t Q ( t si ( t d P ( l ( - os t (7 Puttig (7 ito (5, esose to the geealized oodiates about slide s elasti beam (8 a be obtaied. P ( l y x, t [ (- os ( ] (8 t x Solutio of esose matix ad tasfe futio matix with umeial method To solve tasfe futio matix [ ] i (, the esose matix [ D ] i the followig equatio (9 should be solved fist, whih is just as the alibatio oess of system detetio. Y D D D F Y D D D F Y D D D F (9 The elatioshi of tasfe futio matix [ ] ad esose matix [ D ] is exessed by the followig equatio: [ ] [ D ] (5 Stes of omutatio based o aalysis of system esose ae as follows: ( As Fig. shows, suosig a etai atogahateay otat foe F, imosig o the slide at the fist etai sot fom left to ight, the dislaemet esose values, Y,, Y Y oesodig to those lase sesos a be alulated seaately fom ( ad (8. a D i be alulated fom (5: Yi Di F (5 It eeds to exlai that the uose o takig the maximum of the value is to avoid effets fom Y i time aametes i the futio. Coesodigly, the maximum measued values of the lase sesos should be hose i uit samlig time. ( The method to solve the othe elemets D of the matix is simila to the way above-- suosig a etai atogah-ateay otat foe F j imosed o the slide at the j etai sot. D a be obtaied by alulatig fom the followig equatio: th ISSN: Issue, Volume, Jauay 8

6 Che Taglog, a Feghao, Zhou Ya Y D F i D j a also be alibated ad tested i lab. (5 ( [ ] a be alulated fom (5. ( F a be alulated fom ( ad (. (5 Geometi aametes ad dyami aametes of ateay a be alulated fom (, (, ad (5 seaately. 5 Feasibility study o eduig the umbe of lase age sesos Fom evious disussio, it s eessay to use lase sesos as muh as ossible to esue the testig eisio of dyami aametes suh as atogah-ateay s otat foe et. Howeve, it s also imotat to edue the umbe of sesos ude the eoditio of keeig testig auay fom the view of ost. Geeally seakig, dyami haateistis of atogah a be desibed though the vibatio modal sueositio iile. I the atual wokig oditio of atogah-ateay s system, if the highest vibatig fequey is th f, the we egad the ode mode as the highest fudametal mode whih is oesodig to the smallest atual fequey that is o less tha f. The, low- ode modal ideedet aametes ould be obtaied ad the oblem be well solved by ayig out modal sueositio. I othe wods, testig eos a be deeased by utilizig lase sesos loated at the sesitive dislaemet sots oesodig to the highest fudametal vibatig mode. The tasfe matix elemets i ( a be exessed as follows:, (5 Whee, is the tasfe elatioshi betwee the testig aametes samled at the jth lase sesos ad mode of the th ode oesodig to the i th atig sot of otat foe. I ase that otat foe of i th oit a be exessed just by sesos, W exesses the weight oeffiiet,, the followig futio is available. Fi Y j j k W ik ik Y k (5 Patogah slide ad atogah famewok is a attahed sig-damig system, so dyami esose of atogah slide s beam a be exessed as follows. Y j l l (55 Whee, is the i ow ad j olum s elemet of the mode matix, of the l th l is the dislaemet mode. Puttig (55 ad (5 ito (5, the followig futio is obtaied. (56 l, Wlk lk, l j k The followig futio omes ito existee as log as the above futio is always available to disetioal l. j, W ik k W ik ik, (57 Whee is ukow vaiables, othe aametes all a be solved fom the system esose elatioshi. So (57 is a matix. Theefoe, dyami esose of the system a be tested auately by lase sesos, ad fom whih, atogah-ateay s otat foe a be estimated aoximately. 6 System testig simulatio of esose Aodig to the oess of bakwad aalysis, ofiguig five lase testig dislaemet sesos symmetially to test dislaemets of suh five oits as -.m, -.m, m,.m,.m at the bottom of atogah slide, the esose testig mode show i Fig. a be simulated as show i Fig.6. Whee is.5 kg / m, EI is 7Nm, is.8m, k is 5 N/m. Followed by the assumtio that atogahateay otat foe N vetially imosed dowwad to the atogah slide odely at -.m, -.m, m,.m,.m, dislaemet esose values Y, Y,, Y of the sots oesodig to those lase sesos a be alulated esetively fom ( ad (8. Resose elatio matix (58 a be obtaied fom (5. ISSN: Issue, Volume, Jauay 8

7 Che Taglog, a Feghao, Zhou Ya Fig.6 Slide beam s defomatio whe aly 5N otat foe o the atogah Fig.7 Cotat foes of eah oesodig oits whe aly 5N otat foe o the atogah.787e-6.55e-6-8.9e e-7-6.9e-7.888e-6 8.8e e e e-7 D -9.97e e e e-8-8.9e e e-8 8.8e-7.55e e-9.888e e-6 (58.688e e e+5.587e e+6.9e e e e+7.9e+7.587e e+5 -.9e+7.5e e e+5.688e+ 5 (59 Tasfe futio matix (59 a be obtaied fom ivesio of the matix D. I the ase of usig the atogah-ateay otat foe 5N agai, imosig vetially o -.m ad -.m sots dowwads, fom whih Y a be obtaied, ad the otat foe 5N a be solved by uttig ito ( i tu. I the ase Y of usig the otat foe N agai, imosig vetially o -.5m sots dowwad, fom whih Y a be obtaied, i tu, otat foe 98.77N a be solved by uttig ito (. The eo is Y ISSN: Issue, Volume, Jauay 8

8 Che Taglog, a Feghao, Zhou Ya about %, whih is maily eated by ofiguig loatio of those sesos. Suosig the atogah-ateay otat foe 5N imosed vetially o -.m sots dowwad, as Fig.7 (a shows, whee absissa is detetio oit of slide s beam ad odiate is otat foe; dislaemet esose to the sesos eah sot is show i Fig.6 (a, whee absissa is detetio oit of slide s beam ad odiate is defomatio of slide s beam. Suosig the foe imosed o -.m, m,.m,.m, the futio hat of foes (Fig.7 (b - (e is oesodig to dislaemet esose hat(fig.6 (b - (e. The simulatio esults usig tasfe futio omutatioal method ofom to the eal situatio ad veify the effetiveess of this method. To distiguish fom ovetioa l mixed detetio method, this aoah make fully o-otat detetio of OCS beome eality, ad theefoe avoid the side effet o testig esults by itself. 7 Colusio I atial aliatio, the dyami aametes suh as otat foe ad geometi aametes suh as ull-off value a be obtaied though a seies of alulatios with the tasfe futio matix ad the measued data of atogah slide s dislaemets, whih ae samled by the lase testig dislaemet sesos aay istalled at those vibatio sesitive ositios ude slide s beam. The method of testig dyami aametes of high-seed ailway OCS based o the system esose iile makes sese to take the testig sesos away omletely fom the atogah slide, whih is the goal of dyami testig of high-seed ailway OCS o loomot ive. Owig to the limit of sa yle ad oessig time, othe o-otat detetio suh as image oessig ad lase ada a ot meet the testig eeds of dyami haateisti ude high-fequey oditio. I atual aliatio, the authos oside that data should be tested dietly i the lab ad disosed by eusive aalysis, ad omutatioal model should be etified ad veified. Refeees: [] Yu WaJu, Cateay system of high-seed eletified ailway, Southwest Jiaotog Uivesity Pess,. [] Gukow, Kiesslig Pushma, Shmide, Shmidt, Fahleituge elekttishe, Bahe.B.G.Teube Stuttgat, 997. [] Zhag WeiHua, The study of dyami esose about quais-high-seed ailway ateay, Southwest Jiaotog Uivesity Pess, 997. [] Fujii Yasukazu, Theoy o ovidig uet fo high-seed ailway ateay, Railway ad eletial tehology, 99. [5] Xia YogYua, Zhag Azhou, Calulatio method of mehaial vibatio, atioal defese idusty ess, 99. [6] Li GuoHao, Stability ad vibatio of bidge, Chia Railway ublishig house,. [7] Xi ShaoZhog, Qiu BigQua, Egieeig mehais, Southwest Jiaotog Uivesity Pess, 5. [8] itsuu LKEDA, The oat foe betwee atogah ad otat wie, QR of RTRI, Vol.5, No., ay,. [9] Zhag Ce, ehaial dyamis, Highe Eduatio Pess,. [] Zhag Xiada, ode sigal oessig, Tsighua Uivesity Pess,. [] Che AHua, Liu DeShu, Dyamis theoy ad methods of vibatio diagosis, ahiey Idusty Pess,. [] Zhag Jiami, ehaial vibatio, Chia Uivesity of Geosiees Pess, 995. [] Che Taglog, Xiao Jia, Sythetial aalysis of OCS dyami testig data, WSEAS TRANSACTIONS o SYSTE Issue 5, Volume 5, 6, [] Che Taglog, Xiao Jia, The OCS testig data aalysis of had sot based o data-miig tehique, 6th Idustial ofeee o Data iig ICD 6 Juy -5, 6, Leizig/Gemay. [5] Che Taglog, Xiao Jia, Novel detetio methods fo ovehead otat system zigzag based o eual etwoks, Poeedigs of the 9th WSEAS It. Cof. o SYSTE(CSCC 5, [6] Che Taglog, a Feghao, Zhou Ya, The study of OCS dyami aametes testig based o system esose, Poeedigs of the 7th WSEAS It. Cof. o ISCGAV 7, [7] Che Taglog, Xiao Jia, Sysmati aalysis of OCS testig data, Poeedigs of the WSEAS It. Cof. O ICAS 6, [8] Che Taglog, Xiao Jia, The study ovel detetio method fo ovehead otat system zigzag of high-seed eletified ailway, WSEAS TRANSACTIONS o SYSTE Issue 5, Volume, 5, ISSN: Issue, Volume, Jauay 8