Analyses of Contact Force Fluctuation between Catenary and Pantograph in a hanger span cycle.

Transcription

1 Analyses of Conac Force Flucuaion beween Caenary and Panogra in a anger san cycle. ABOSHI Misuo Cief Researcer, Curren Collecion Laboraory, Railway Tecnical Researc Insiue -8-38, Hikari-co Kokubunji-si, Tokyo, Jaan Tel: Fax: abosi@rri.or.j IKEDA Misuru Senior Researcer, Curren Collecion Laboraory, Railway Tecnical Researc Insiue -8-38, Hikari-co Kokubunji-si, Tokyo, Jaan Tel: Fax: mikeda@rri.or.j NAGASAKA Sei Senior Researcer, Curren Collecion Laboraory, Railway Tecnical Researc Insiue -8-38, Hikari-co Kokubunji-si, Tokyo, Jaan Tel: Fax: nagasaka@rri.or.j Absrac: One of e mos imoran subjecs of overead conac line and anogra sysem is o imrove e conac erformance in ig-seed oeraion. In e exising caenary equimen for Sinkansen lines, e conac force flucuaion in a suor san cycle is comaraively small because a comound-ye caenary is used and e wole ension is ig. Terefore, e conac force flucuaion in a anger san cycle is comaraively large. I as been confirmed in as researces a wen e rain seed is close o e wave velociy of conac wire, e conac loss raio becomes exremely large and conac loss occurs in a anger san cycle. I is necessary o clarify e causes of e conac force flucuaion beween caenary and anogra, and o roose an imrovemen meod o reduce e conac force flucuaion. In is researc, e relaion beween e wave moion of conac wire and e conac force flucuaion of anogra is sudied; e conac force flucuaion in a anger san cycle is analyzed; and meods o reduce e conac force flucuaion are roosed. Te mecanism of conac force flucuaion in a anger san cycle is considered as follows. Ta is, wave moion is generaed by anogras running under e di of conac wire beween angers, reflecs a e neares anger, becomes inciden o e anogra and causes conac force flucuaion. I is confirmed by eoreical analyses and fundamenal exerimens a e magniude of e conac force flucuaion is roorional o e verical velociy amliude of e wave inciden o e anogra. Te ransfer coefficien of conac wire wave moion a anger oins is measured on a real overead conac line by e wave searaion measuring meod and secrum analysis meod. Te unevenness of conac wire is also measured on a real overead conac line by e unevenness measuring meod alied wi e laser ecnique. From e above sudy, we obain e conclusions summarized below abou e mecanism of conac force flucuaion and e imrovemen meods for ig-seed oeraion. () I is sown a e conac force flucuaion of anogra in ig-seed oeraion is mainly caused by e inciden wave of conac wire a is generaed by e unevenness of conac wire and is refleced a angers. () Tis influence becomes exremely large wen e rain seed is close o e wave velociy of conac wire. Te amliude of conac force flucuaion exceeds e saionary ulif force of a anogra a e non-dimensional seed of abou.7 or over. (3) Increasing e wave velociy of conac wire or decreasing e reflecion facor of wave moion a angers is effecive o reduce e conac force flucuaion. keywords: Curren collecion, overead conac line, conac wire, anogra, wave moion

2 . Inroducion For ig-seed oeraion of elecric railways, reducing e conac force flucuaion of anogra is one of e mos imoran subjecs. I as been confirmed in as researces ) a wen e rain seed is close o e wave velociy of conac wire, e conac erformance becomes exremely degraded and conac loss occurs in a anger san cycle. I is necessary o clarify e causes of e conac force flucuaion beween caenary and anogra and roose an imrovemen meod o reduce e conac force flucuaion. In is aer, e relaion beween e wave moion of conac wire and e conac force flucuaion of anogra is sudied; e conac force flucuaion in a anger san cycle is analyzed; and meods o reduce e conac force flucuaion are roosed.. Conac force flucuaion Te bes conac condiion is a e conac force beween conac wire and anogra is always consan and equal o e saionary conac force. Bu e conac force canges in ig-seed oeraion due o several causes. Te main causes are considered as () e flucuaion mecanism in a suor san cycle, () flucuaion mecanism in a anger san cycle, (3) unevenness of conac wire (undulaing wear, for examle), (4) aerodynamic disurbance and oers. Te magniude of e conac force flucuaion in a suor san cycle and a in a anger san cycle are indices o evaluae e dynamic erformance of overead equimen. Concerning e conac force flucuaion in a suor san cycle, e following imrovemen meods ave been sown in as researces ), () reducing e variabiliy of caenary elasiciy, and () increasing e wole ension of caenary. A eavy-comound caenary is normally used for Sinkansen lines in Jaan. Fig. sows an ouline of is caenary. Because is equimen consiss of ree wires (so-called comound ye ), e elasiciy a e suor oin is comaraively small. Te oal ension of is caenary amouns o 53.9kN. Terefore, i is considered a e conac force flucuaion in a suor san cycle is comaraively small, and a in a anger san cycle is influenial in ig-seed oeraion. Fig. Sandard overead equimen for Sinkansen (Heavy-comound caenary)

3 3. Analysis of conac wire wave moion 3. Meod of measuring wave moions 3) Te wave roagaing velociy (ase velociy) of e conac wire is one of e mos imoran indices for e curren collecing erformance. Te wave velociy is obained by esimaing e frequency a wic e addiion or subracion of acceleraions a wo oins is equal o. A measuremen examle is sown in Fig.. I is found a e wave velociy increases a ig frequencies because of is flexural rigidiy and a e measured values agree well wi e calculaion resul. In order o esimae e wave moion of e conac wire, i is necessary o searae e measured vibraion of e conac wire ino e forward roagaing wave and e backward one. If e wave moion y(x,) is exressed by Eq.(), wo wave moions roagaing in oosie direcions are obained by Eq.() by using e gradien and e wave velociy of e wire c. y( x, ) f ( x c ) g( x c ) f ( x g( x c ) c ) { y( x, ) { y( x, ) c c y( x, ) d} x y( x, ) d} x...()...() A measuremen examle of e wave searaion is sown in Fig.3 (verical acceleraion limied under 6Hz). Te wave moions roagae on e conac wire in differen direcions (forward and backward). Fig. Measuremen examle of wave roagaion velociy 3

4 Fig.3 Measuremen examle of wave searaion. 3. Conac force flucuaion caused by wave moion of conac wire 3) If e dislacemen of e wave moion inciden o e anogra y is exressed by Eq.(3) in e analysis model sown in Fig.4, e amliude of conac force flucuaion F caused by e inciden wave is obained by Eq.(4), y Aex i ( x / c )...(3) F ( ) A,...(4) / / were A and are e amliude and e angular frequency of e inciden wave, resecively; is e raio of e moving seed of anogra o e wave roagaing velociy of conac wire; and are e mecanical imedance of conac wire and anogra; and i is e imaginary uni. In e rig and side of eq.(4), e sign "+" is used wen e wave moion comes inciden from e fron of e anogra, wile "-" is used for e wave moion from beind. Eq.(4) means a e magniude of e conac force flucuaion is roorional o e verical velociy amliude of e wave inciden o e anogra. 4

5 Fig.4 Analysis model for conac force flucuaion caused by wave moion of conac wire. In order o verify e above-menioned eoreical analysis, we measured e wave moion of e conac wire inciden o e anogra and e conac force flucuaion a e same ime 4). An acual caenary and anogra are available for e exerimen wi e curren collecing es equimen of R.T.R.I. In order o measure e conac force, load-cells and acceleromeers are se under e conac sris of PSA-ye anogra. A conac wire is only rovided for e running exerimen, in order o simlify observaion of e wave roagaion. Te resul of e exerimen in rigid suor is sown in Fig.5 (seed: km/, =.8). "V_F"_"V34_G" indicae e verical velociies of e wave moion assing roug e measuring oins (limied under 6Hz). I is found a e wave moion roagaes forward ()(), reflecs a e forward suor oin (3), comes inciden o e anogra (4), and reeas e reflecion beween e suor oin and e anogra (5) ~(). A large conac force flucuaion is caused wen e wave moion comes inciden o e anogra. Te measuring resuls agree well wi eoreical calculaion. 5

6 Fig.5 Resul of e fundamenal exerimen. 3.3 Generaion of wave moion by unevenness of conac wire As sown in Fig.6, we suose a e conac wire is an infinie sring wic as e unevenness of a wave leng and one-side amliude B. Wen a anogra runs under e conac wire (seed, v), e amliude of verical velociy of e generaed backward wave and forward wave V, V and e angular frequency, are obained by Eq.(5) and Eq.(6). Te conac force flucuaion caused by e unevenness of conac wire F ue is obained by Eq.(7). 6

7 Fig.6 Analysis model for wave generaion by unevenness of conac wire V V F i B, B,...(5)...(6) B ex i...(7) ue, were v, v c Tese equaions indicae a e frequency and e verical velociy amliude of e forward wave increases wen e anogra seed becomes iger, and e forward wave is esecially influenial a ig-seed. Concerning e relaion beween e unevenness of conac wire and e amliude of generaed wave moion, we ave confirmed a e measuremen resuls of fundamenal exerimens wi low sring consan angers agree well wi e eoreical analysis 5). 3.4 Reflecion of wave moion a anger oin As sown in Fig.7, we suose an analysis model in wic wo infinie srings are combined wi a sring-damer elemen. Te comlex reflecion facor R (e raio of amliude of refleced wave A r o a of inciden wave A i ) is obained by Eq.(8), were k, D, m, and m m denoe e sring consan, e daming facor and e mass of a anger, resecively, wile, m, T, Tm reresen e line densiy and e ension of conac wire and messenger wire, resecively. 7

8 Fig.7 Analysis model for wave reflecion a anger. R i A A r i m m i m m D k / i...(8), and m are e mecanical imedance of conac wire and messenger wire, resecively, sown in Eq.(9). T, T...(9) m m m Fig.8 is an examle of e ransfer coefficiens of conac wire a a anger oin (eavy-comound caenary; beween conac wire and auxiliary messenger wire). Tese are calculaed by aking ino consideraion e line flexural rigidiy. Tese coefficiens are measured on a real overead conac line by e wave searaion measuring meod and secrum analysis meod 6). I is confirmed a e measured values are mosly in agreemen wi eoreical values, and e line flexural rigidiy is influenial on e ransfer coefficien even a low frequencies. 8

9 Fig.8 Coefficien of wave ransfer a anger. 4. Mecanism of conac force flucuaion in anger san cycle As sown in Fig.9, we suose a e wave moion () is generaed by e di of conac wire beween angers, () reflecs a e neares anger, (3) becomes inciden o e anogra and causes e conac force flucuaion. Fig.9 Analysis model for conac force flucuaion in a anger san cycle. 9

10 Te unevenness of conac wire is also measured on a real overead conac line by e unevenness recise measuring meod alied wi e laser ecnique 7). Fig. sows a measuremen examle of unevenness of conac wire of Sinkansen. Te unevenness of waveleng =5m (wave number =.) is equivalen o e di beween angers. Te sorer wavelengs are also seen in is measuremen resul. Fig. Measuremen examle of conac wire unevenness in Sinkansen. If e di beween angers is assumed o be a secondary curve, e k- coefficien of Fourier series a k is exressed by Eq.(), were L is e san leng beween angers. g L ak cos k k.....() T k Te amliude of e k- unevenness is /k imes e rimary unevenness, and is waveleng is /k imes. Terefore, i is sown from Eq.(6) a e verical velociy amliude of e conac wire wave moion generaed by e k- unevenness becomes /k imes in e case of rimary unevenness. In oer words, e influence of e iger order unevenness of e di beween angers on e generaion of conac wire wave moion is comaraively small. If e conac wire unevenness can be regard as a firs armonic of e di beween angers, e amliude of conac wire unevenness B is simly exressed by Eq.(). g L B a...() c Te verical velociy amliude and e angular frequency of e generaed wave moion of conac

11 wire (forward wave) V, are obained by Eq.(), and e amliude of e conac force flucuaion caused only by e unevenness of conac wire F ue is obained by Eq.(3). V F ue g gl c L c L L c.().(3) Fig. sows a measuremen examle on Sinkansen line in wic e forward wave is generaed by e di of conac wire beween angers and roagaes in fron of e anogra. Under e condiions of =5m, c = 4m/s, and v=6.m/s (km/), e frequency of e generaed wave moion is calculaed as 6Hz from Eq.(). Te frequency of e forward wave observed by is measuremen is mosly in agreemen wi is calculaed value. I is confirmed a e conac wire wave moion is also generaed by e di beween angers in acual equimen. Fig. Examle of wave generaion by di beween angers. Nex, if i is assumed a e forward wave moion reflecs and reurns R imes a a anger oin, e verical velociy amliude and e angular frequency of e inciden wave o a anogra

12 V, 3 3, and e amliude and e angular frequency of conac force flucuaion wv wv obained as follows. F, are V F 3 3 wv wv g R gl c L ( ) R c L L c.(4) ( ) wv.(5) Fig. sows e conac force flucuaion caused by e conac wire wave moion F wv resumed from e measuremen resul of e conac wire unevenness and residual diameer in e case of Sinkansen. Te resumed conac force flucuaion by e conac wire wave moion F wv is obained by subracing e conac force flucuaion by conac wire unevenness F ue from e conac force flucuaion F ue +F wv, wic is equivalen o e residual diameer under e suosiion a conac wire wear is roorional o e conac force. Tis examle is resumed for e PS-ye anogra wen i runs a km/. Te endency of e conac force caused by e conac wire wave moion F wv becoming iger is regularly seen a e.7~. ar of anger san. Te enomenon in wic e generaed conac wire wave moion reeas e reflecion beween a fron reflecing oin and a anogra is observed by e above-menioned fundamenal exerimen. In is case, e firs and second osiions x and x a wic e conac wire wave moion becomes inciden o a anogra locae.7 and.9, resecively, in a anger san. Tese oins agree well wi e oin were e conac force flucuaion caused by wave moion F wv is large in is Figure. Tis means a e wave reflecion a e neares anger is mos influenial for e wave inciden o e anogra. I as been confirmed a e conac loss in a anger san cycle occurs near e cener beween angers and a e residual diameer near e cener beween angers is larger ). I is oug a ese enomena resul from is mecanism. Ta is, e conac force flucuaion in a anger san cycle is considered o be e enomenon in wic e conac force flucuaion by e di of conac wire beween angers F ue and a by e conac wire wave moion refleced a a anger F wv are comounded.

13 Fig. Conac force flucuaion by wave moion resumed from measured unevenness and residual diameer. 5. Conac force flucuaion in ig-seed oeraion 5. Seed caracerisic of conac force flucuaion in a anger san cycle Fig.3 sows an examle of e amliude of conac force flucuaion F ue and F wv wic is calculaed by Eq.(3) and Eq.(5). Tese curves sow e caracerisics of non-dimensional seed in e condiion of eavy-comound caenary and >>. Te conac force flucuaion caused by conac wire unevenness F ue increases linearly wi seed. On e oer and, wen exceeds abou.7, e conac force flucuaion caused by e reflecive wave moion F wv increases remarkably. Tis caracerisic is based on e so-called Doler effec as sown in Eq.(5). Consequenly, i is sown a e influence of wave reflecion becomes larger esecially in ig-seed oeraion. Tis caracerisic of conac force flucuaion agrees well wi e radically increasing endency of conac loss raio. Terefore, we ink a e enomenon, in wic e conac loss raio increases remarkably as e running seed aroaces e wave roagaion velociy of conac wire, is mainly based on e conac force flucuaion in a anger san cycle. Te amliude of conac force flucuaion caused by e reflecive wave moion F wv is comared and sown in Fig.4 for e case of eavy-comound (HC) caenary and e case of ig-ension eavy-comound (HTHC) caenary for wic e ension of conac wire is increased o 9.6kN. In is case, ese values are calculaed wi e arameer of PS anogra. In e case of igension eavy-comound caenary, e wave roagaion velociy of conac wire is abou 5% iger, and e reducion effec of conac force flucuaion by decreasing is seen. Fig.5 sows e comarison of ese cases a non-dimensional seed, and i is found a ese caracerisics ave almos e same curves. As sown in Eq.(5), is is because e amliude of e conac force 3

14 flucuaion F wv mainly deends on e non-dimensional seed if e conac wire is e same ye and e reflecive coefficien is e same. Fig.3 Calculaed examle of conac force flucuaion Fig.4 Comarison of conac force flucuaion 4

15 Fig.5 Comarison of conac force flucuaion (non-dimensional seed) By using Fig.4, we will esimae ere e maximum seed wiou conac loss. We suose a e saionary ulif force of e moving anogra is 74N (saic ulif force 54N + aerodynamic ulif force N) and conac loss will occur wen e amliude of conac force flucuaion caused by wave moion reflecion of conac wire exceeds e saionary ulif force. In regard o e seed deendence in is Figure, i is indicaed a e maximum seed wiou conac loss (criical seed) is abou 7km/ for e eavy-comound caenary, and 3km/ for e ig-ension eavycomound caenary. In e acual case, i is oug a conac loss occurs below ese seeds because of oer causes. However, e seed sown ere becomes e sandard value for e maximum oeraion seed as a conac erformance index of overead equimen. Te ig-ension eavy-comound caenary is one of e sandard yes for 3km/ ig-seed oeraion in Jaan. 5. Imrovemen meods of caenary for ig-seed oeraion Based on Eq.(5), imrovemen meods for ig-seed oeraion are sown as follows. () Increasing e wave roagaion velociy of conac wire. () Decreasing e densiy of conac wire. (3) Reducing e wave reflecion of conac wire. (4) Sorening e anger san leng. Te resen overead equimen of Sinkansen for 3km/ oeraion as a ig wave roagaion velociy of conac wire by increasing e ension of conac wire, and adoion of ligweig conac wire. Tis is desirable from e viewoin of is researc. Moreover, if i as e same wave roagaion velociy, e smaller e line densiy of conac wire is, e beer e erformance is. In order o reduce e reflecion of conac wire wave moion a a anger oin, use of angers wic ave a sring and a damer mecanism is effecive. Aloug e use of ese daming ye angers canno remarkably cange e increasing endency of conac loss deending on e relaion beween e rain seed and e wave roagaion velociy of conac wire, ese angers are execed 5

16 o reduce e conac force flucuaion below e criical seed. Te reflecion facor of wave moion wi a daming anger will be calculaed as sown in Fig.6. A coil sring is used in e fricion daming anger, and a iece of rubber is used in e rubber daming anger. From e resuls of e field es carried ou on Sanyo Sinkansen line, i is found a ere is a close correlaion beween e conac loss raio and e verical velociy of backward wave moion 8). Te rubber daming angers can reduce e magniude of e wave moion inciden o e anogra and e conac loss raio. Fig.6 Reflecion facor of wave moion a anger. Te measuremen resuls for Sinkansen lines sow a e conac loss raio in e secion of a 3.5m-long anger san is smaller an a in e secion of 5m-long one. We ink a our eory can exlains suc measuremen resuls. 6. Conclusion In e exising caenary equimen for Sinkansen lines, e conac force flucuaion in a suor san cycle is comaraively small because i is a comound ye and e wole ension is iger. Terefore, e conac force flucuaion in a anger san cycle is comaraively large. From e above sudy, we ave obained e conclusions summarized below abou e mecanism of conac force flucuaion and imrovemen meods for ig-seed oeraion. () I is sown a e conac force flucuaion of anogra in ig-seed oeraion is mainly caused by e inciden wave of conac wire a is generaed by e unevenness of conac wire and is refleced a angers. () Tis influence becomes exremely large wen e rain seed is close o e wave velociy of conac wire. Te amliude of conac force flucuaion exceeds e saionary ulif force of a anogra a e non-dimensional seed of abou.7 or over. (3) Increasing e wave velociy of conac wire or decreasing e reflecion facor of wave moion a angers effecively reduces e conac force flucuaion. 6

17 References () Manabe, K.: Hig-seed conac erformance of caenary -anogra sysem, JSME, Vol.54, No.54, , 988 () G. Gilber,: Panogra moion on a nearly uniform railway overead line, PROC.IEE, Vol.3, No3, 966 (3) Abosi, M.: Researc for conac loss reducion meod by daming caenary vibraion, WCRR 97, Vol.C,.5-59, 997 (4) Abosi, M.: Influence of wave moion of conac wire on conac force flucuaion (s reor, eoreical analysis and fundamenal exerimens), JSME, Vol.63, No.64,.9-96, 997 (5) Abosi, M.: Relaion beween wave moion and unevenness of conac wire, JSME, D&D 98, 998 (6) Abosi, M.: Transfer caracerisics of conac line wave a anger oin, JSME, No.-5,.59-6, (7) Abosi, M.: Measuremen and is esimaion meod of conac wire unevenness, RTRI Reor, Vol.5, No.6,.45-5, (8) Abosi, M.: Influence of wave moion of conac wire on conac force flucuaion (nd reor, exerimens in racical caenary-anogra sysem), JSME, Vol.64, No.6,.3-37, 998 7