Wind Tunne Test and Wind Deviation Cauation of Catenary System on Raiway *Xi Zhi 1), Zhenyu Yang ) and Qiang Xie 3) 1), ), 3) Struture Engineering, Tongji University, China 1) zhixi083@163.om ) 80956775@qq.om 3) qxie@tongji.edu.om ABSTRACT This paper mainy fouses on the performane of wind deviation of atenary system on raiway. A wind tunne test have been taken to get the dispaement of mid span, showing the onvined figures. Whie the figures are imited by test ondition. Four auation methods in three ountries have been studied, omparing the differenes and figure out the inappropriate points, inuding negeting the funtion of droppers and ength of atera position or just approximate auated it. After that, a new method is proposed to take these questions into onsideration. The ase study shows the differene of theoretia methods mention above by omparing with finite eement method. Finay the orretion of the new method is proved and show the importane of adopting the new method to guarantee the safe of rai. This work an give referene to the design of atenary system, sine wind deviation is a vita measuring indiator to guarantee the operation of raiway system. NOMENCLATURE T /kn Tension on ontat wire T m /kn Tension on messenger wire p /(kn/m) Wind oad on ontat wire p m /(kn/m) Wind oad on messenger wire W /(kn/m) Weight on ontat wire /m Span between eah supporter d /m Shortest ength of dropper a/m Length of atera position H /m Height of atenary system b Wind deviation of ontat wire 1. INTRODUCTION Sine the first raiway took into operation in 185 in Engand, raiway system is paying an inreasing important roe in our daiy ife as we as in the eonomy beause 1),) Graduate Student 3) Professor
of its high effiieny, ow prie and omfortabe environment (Vikerman 1997). So, it is of great soia and eonomi signifiane to guarantee the safe operation of the raiway. Catenary system is a vita omponent on raiway to suppy eetri to trains, so as to guarantee the operation. The main parts of atenary system inude ontat wire, messenger wire, and droppers. Contat wire is used to suppy eetria energy to the train, messenger wire is used to provide stiffness and droppers are used to ink both wires. There are three types of atenary systems, the simpe one, the stith one and the ompound one, whih are shown in Fig.1 (Park and Kim et a. 00). The simpe atenary has the simpe struture with ow onstrution prie, whie it has the poor ontat quaity and short ive span. The differene between simpe one and stith one is that there are easti droppers around the supporters, so as to provide better ontat quaity. At the meantime, its prie in onstrution and maintenane is reativey higher. The third type is the ompound one, whih is widy used in Japan. Beause of the ompex struture, it has better anti- wind abiity, ower stiffness variation and better ontat quaity, in ontrast, the high prie and arge weight are its disadvantages. However, in most ountries, the simpe atenary system is widy used for its effiieny. Many researh have been arried out based on this basi struture. messenger wire ontat wire easti dropper Simpe Stith Compound Fig.1 Types of atenary system In fat, many aidents raised from atenary system have been reported these years and ed to quantities of eonomi osses in China. Sine Beijing-Shanghai highspeed raiway took into operation, four aidents raised from the atenary system under strong wind have been reported. On Juy 10, 011, a power outage of the atenary system aused by arge offset of positive feeder in strong wind made a deay of 19 trains in Shandong Provine. Three trains were fored to derease the speed or ompetey stop beause of the poor ontat of the pantograph in suh bad weather on Juy 1-14, 011 in Jiangsu-Shandong region. On Marh 3, 01, many trains
5.3m 7.8m 6.8m 1.8m between Beijing and Tianjin were deayed owing to the mafuntioned atenary system under intense wind attak. On November 11, 01, aidents on ine feeder in high wind in Shandong ed to outage of the trains. So it has been widey onerned that how to improve the performane of the struture of atenary system and its abiity to resist wind. Beause of speia onnetion and ow rigidity, it is a wind-sensitive struture. Many aidents happened by strong wind, thus ausing atenary system out of operation, making ots of trains deayed and serious eonomi osses. So wind deviation is a vita measuring indiator in the onstrution of atenary system. This artie is fous on the deviation of atenary system on the simpe type. The paper is organized as foows. A wind tunne test is disussed first (Setion ) to test wind deviation in midpoint. In the foowing setion 3, deviation auation methods of different ounties have been ompared. Then a new auation method is proposed (Setion 4) with finite eement method verified (Setion 5). A ase study shows the resuts of different methods and make omparison among them (Setion 6). Conusion goes in Setion 7.. WIND TUNNEL TEST ON AERO- ELASTIC MODEL The prototype of this study is part of the atenary system. The type of atenary is the simpe one, whih is easy to buid and an attain suffiienty uniform eastiity, thus it is widey adopted in China. The span between eah mast is 50m. The height of the mast is 7.8m. The height of hanging point on steady arm from trak pane is 5.3m. The height of messenger wire from trak pane is 6.8m and the height of antiever struture is 1.8m, whih is shown in Fig.. The ross setion of ontat wire is CTMH150 type with the area of 150mm and the messenger wire is JTMH10 type with the ross setiona area of 10mm. Tension on ontat wire is 0kN and that on messenger wire is 15kN, whih are exerted by weights through speia pueys. So the speifiation parameters of this mode are shown in Tab.1. Fig.. Prototype of tie-member struture
Dispaement(mm) Tab.1 Speifiation parameters T /kn T m /kn /m d /m 0 15 50 0.6 a/m h /m m 0.3 1.5 0.9 A wind tunne test have been taken to test dispaement in wind diretion of ontat wire. A mode of 3 posts and spans have been made to test wind deviation, one of the most important measurement index of atenary system (Xie and Zhi et a. 015). Sine the imitation of experimenta instruments, ony the midpoint have been tested on the ontat wire. The mode is shown in Fig.3, inuding the midpoint D1z. A uniform fow has been taken into aount, with the wind veoities of 4m/s, 6m/s, 8m/s, 10m/s, 1m/s and 14m/s. Z diretion means the diretion of wind. D1z Fig.3 Arrangement of the Test Points Fig.4 shows the wind deviation in the midde of ontat wire (D1 z ) in different wind veoities in uniform fow. It an be seen that the dispaement inreases nonineary with the wind veoities, whih is due to the fat that the pressure on the ine posed by wind is square funtion of the wind veoity. When the wind veoities are 10m/s and 14m/s, the tested mean wind deviations are 18.03mm and 41.10mm respetivey whih were onverted to be 81.14mm and 184.95mm in the wind veoities of 1.m/s and 9.68m/s respetivey. 50 40 30 0 10 0 8m/s 6m/s 4m/s 10m/s 14m/s 1m/s 0 5 10 15 0 5 30 35 40 45 50 55 60 Time(s) Fig.4 Time evoution of wind deviation in uniform fow Athough wind tunne an show a reativey onvined resut, it osts a ot and the resuts are imited by many fats inuding experimenta site, measuring equipment and many unontroabe fators. Take this test for exampe, for reason of test ondition, the 1
a a b maximum wind speed an ony reah 14m/s, whih is reativey sma to the deviation researh. Moreover, the tested point annot present the argest deviation, whih ony shows the dispaement in mid span. So the theoretia researh of atenary system is a vita task to figure out the argest deviation. 3. CALCULATION OF WIND DEVIATION IN DIFFERENT COUNTRIES Wind deviation of atenary system is infuened by many fators, inuding the types of atenary, materias of wires, ength of atera position and wind situation. In the atenary system, droppers are used to ink ontat wire and messenger wire, so they transfer the fores between the wires. It is a ompiate work to determine the fores, as we as the wind deviation of ontat wire. Catenary system has the shape of Z aong the road, sine the ends of wires have a distane from the entra road, whih is aed the ength of atera position, (Yu. 003), as shown in Fig.5. In it, x diretion means the diretion aong the rai, and z diretion means the diretion aong the wind, aso y diretion is the diretion of gravity. This diretion setting appy to this paper. T atenary system wind deviation z x T x Fig.5 Genera view and stress state of ontat wire From this figure, it an be seen the stress state, inuding tensions on ontat wire, T, and the wind oad aong the wire, p. So the basi auation method of ontat wire an be dedued from this state by fore and geometria anayzing (Shen and Xu et a. 1997), with foowing expression: Ta p b 8T p (1) This deviation happens at onsideration. af x, whih takes the atera position into p There exists a imitation that x shoud in the range of span, so af 0 x. p
It is known that the parameters in af p are a positive numbers, so the imitation F ony needs to meet the requirement of 4a This is the basi equation to auate the wind deviation of ontat wire. But it is widey known that ontat wire is just a part of atenary system, so its deviation shoud be take the funtion of whoe system into onsideration. 3.1 Chinese Method There are two methods to auate the deviation in China, the equivaent method and the mean vaue method. The equivaent method regards the atenary system as a whoe, introduing a parameter m to revise the basi equation into a new one with the foowing expression: Ta mp b,1 8T mp () Eq. negets the ompex funtion in the system whie ony introdues m, whih is ess than 1, as an equivaent parameter to be timed by wind oad. Sine it is regarded that ontat wire is restrained by messenger wire through droppers. The vaue of m is infuened by its physia harateristis, 0.9 for opper wires and 0.85 for steeauminum wire whih is determined by experiene. The differene of mean vaue method is that it takes the funtion of messenger wire into onsideration. In order to study the ontribution of messenger wire to the ontat wire, the wind deviations of both wires are auated respetivey first. Then their effets are deided by their ratios of wind oad to tension on wire. Finay the deviation is turned out as foows: 1 pm a b, ( ) T 8 1 Tm p p ( ) T m (3) Tm These two methods an auate the wind deviation of ontat wire. The former one needs ess information thus being the more onvenient and ess aurate one by ony onsidering ontat wire. Compared to the equivaent method, the mean vaue method shows a more ompex equation to take the messenger wire into aount. Whie both of them neget the funtion of droppers, whih are important fators. 3. German Method Wind deviations of ontat wire and messenger are different when winds impose on them, thus making the droppers deiver fores between them. This method is to determine the interation fore ΔF first and then figure out the offset deviation Δb by its geometria anaysis (Friedrish. 001), as shown in Fig.6. In this proess, it regards the shortest dropper d as /3 times the height of atenary system H. Finay the wind deviation is shown as beow:
d b, g b b (4) and p p m HF H T T m b 3G 3G 16H 1 1 3G T Tm (5) messenger wire wind oad dropper z y p b ontat wire G Fig.6. Genera view of droppers funtion There exists a probem the Δb is in the midde span of the atenary system, whie b takes the situation at x. So this method just ombines two figures at different paes and assume that it neary equas the maximum dispaement. 3.3 Soviet Method Soviet method aso takes the funtion of droppers into onsideration. Compared with the German one, it auate the offset wind oad Δp on ontat wire aused by droppers and messenger instead of the offset deviation (Wather. 1986). There goes the equation: ( p) b s, 8T (6) and pm F Fm p 8 1 1 G F F d m (7) In this proess, it an be seen eary that it ignores the funtion of atera positon, and just thinks the maximum deviation happened in the midde of the span.
bmz bz bdz 4. WIND DEVIATION PROPOSAL After studying the methods in auating deviation of different ountries, a new equation is proposed by buiding hypothesizes forwardy: a. Droppers meet Hooke s ow, with their interna fores inear inrease with their growth, thus regarding them as springs whih an ony bearing tensions. b. The fores between ontat wire and messenger wire are reated by droppers, and ompared with the wind oad, they are reativey sma. So the wires an sti meet the assumption of paraboa.. Sine ength of atera position is partiuary sma ompared with the span, the fore reated by droppers is in the same diretion with wind oad in top view. z x x wind oad Fig.7 Top view of atenary system under wind oad Here start to anaysis the ontat wire and messenger wire in top view, shown in Fig.7. The deviation of ontat wire b z and the deviation of messenger wire b mz an be determined respetivey as foows: x( x) a( x) b z T (8) pmx( x) a( x) b mz T m (9) So the deviation of droppers b dz an got by Eq.8-Eq.9: x( x) pmx( x) 1 pm b dz ( ) x ( x ) T T T T (10) m m thus fores on droppers p dx an be dedued as foows: 1 pm p dx k ( ) x ( x ) T T m (11) where k is the stiffness of droppers. This equation shows the fat that the fores between ontat wire and messenger wire reated by droppers meet the rue of
pm paraboi distribution, with k and ( ) are onstant. The maximum figure of p dx T Tm an refer to Δb in Eq.7, so the dropper fores an be revised as foows: pm 4 F Fm 4 pdx p x( x) x ( x) (1) 8d 1 1 G F Fm Based on the hypothesis., p dx has the same diretion as p. Then the wind deviation of ontat wire an be dedued as foowing appearane: ( pdx ) x( x) a( x) p 4 4p 3 p a b x, n x x ( ) x ( ) x a T T T T T T (13) so the position of maximum deviation an be auated as foows: d( bx, n ) 8p 3 1p 4p a x x ( ) x 0 dx T T T T T Compared with the former methods, the new one is a quarti equation instead of a quadrati equation. Though it has the ompex expression, it has more aurate resut to give onsut in the design proess. And it an aso be soved quiky by omputationa tehnis. 5. FINITE ELEMENT ANALYSIS In order to verify the orretion of the new method, a finite eement anaysis has been studied on the atenary system. A mode has been estabished with ontat wire, messenger wire and droppers with ink eements, whih annot be subjeted to bending moment. The ends of wires are hinge joints to simuate the onnetion in reaity with the way of pueys, whih an ony shift in one diretion. At the meantime, tensions on the wires are transfer to prestressing fore and keep a baane with their own weights to reah the shape of origina sag. Equivaent stati wind oads are exert to wires in uniform distribution so as to auate the performane of ontat wire. The mode are shown as foows in Fig.8. (14) Fig.8 Finite eement mode of atenary system
6. CASE STUDY In order to ompare the differene in theoretia auation methods mentioned above and verify the orretion of new method by using finite eement method, a ase study is taken. Sine the imitation mentioned above, the wind speed of 35, 40, 45, 50 and 55m/s have been hosen to make auation. Wind deviation an be figured out from wind pressure on atenary system whih are onvert from wind speed. The resuts of wind deviation are shown in Tabe. Tabe. Wind deviation of different methods Wind speed /(m/s) b,1 /m b, /m b,g /m b,s/ m b,n /m FEM/m 35 0.300 0.305 0.31 0.170 0.30 0.303 40 0.311 0.331 0.346 0. 0.3 0.33 45 0.338 0.374 0.388 0.80 0.360 0.357 50 0.379 0.430 0.444 0.346 0.410 0.400 55 0.431 0.497 0.509 0.40 0.473 0.448 The figures of new method are between those of the equivaent method and the mean method and with the inreasing of wind speed, the differenes between them are aso inreasing. This phenomenon is due to the fat that simpified auation of Chinese method bring errors whie the new method has been overed the insuffiienies of those two methods so as to figure out a more aurate resut. The figures of new method is smaer than those of the German method, for the reason of the new method fixing the onfusing in two kinds of dispaements and ombining it to the orret answer. Compared with the Soviet method, the figures of the new one are arger, sine it takes the dispaement of atera position into onsideration. It is just the dispaement in the mid of span. But the wind speed inreasing, the differene with other methods are dereasing, so it shows the fat that, the point of deviation is shifting to the mid of span. Verified by the finite eement method, it an be seen that the resut of the new method is ose to the finite eement method. When the wind speed is ower than 45m/s, the errors between them are ess than 1%. Whie with the inrease of wind speed, their errors are aso inreasing. This phenomenon may due to the different materia and joint ondition. The new method detais the stress distribution of droppers, it may be identified as the most aurate one. In the proess of designing, the new method of deviation auation may bring more onvined situation to guarantee the safer operation. So it is suggested that the new method may give more aurate onsut to the rai design. 7. CONCLUSION
Wind tunne test wi bring the most onvined figure and intuitive resut, showing the fat that the dispaement of ontat wire is inreasing nonineary with wind speed. Whie wind tunne test woud ost a ot and be imited by experimenta site, measuring equipment and many unontroabe fators. Methods in three ountries have been studied and ompared the differenes, inuding two Chinese methods, a German one and a Soviet one. Inappropriate points in them have been figured out, inuding negeting the funtion of droppers and ength of atera position or just auating the deviation approximatey. A new method is proposed to take these questions into onsideration. Compared with the former methods, the new one is a quarti equation instead of a quadrati equation. Though it has the ompex expression, it has more aurate resut to give onsut in the design proess with finite eement software proved. The ase study shows the differene of theoretia methods mention above by omparing with finite eement method. Finay the orretion of the new method is proved and is proved that it is an appropriate and onvenient method to auate the deviation in strong wind with inorret points in other methods reovered. This work an give referene to the design of atenary system, sine it offers a onvenient way to auate the wind deviation whih is a vita measuring indiator. REFERENCES Friedrish K. (001), Contat ines for eetri raiways, Pubis orporate pubishing. Park, T.J., Kim, B.J., Wang, Y.Y. and Han, C.S. (00), "A atenary system anaysis for studying the dynami harateristis of a high speed rai pantograph", Journa of Mehania Siene & Tehnoogy., 16(4), 436-447. Shen SZ, Xu CB, and Z C. (1997), "Suspended abe struture design", China buiding industry press. Vikerman, R. (1997), "High-speed rai in Europe: experiene and issues for future deveopment", Annas of Regiona Siene., 31(1), 1-38. Wan JY. (003), Catenary of high speed rai, Southwest Jiaotong university press. Wather M. (1986), Catenary, China raiway pubishing house. Xie, Q. Zhi, X. Sun, QG. and Xiao, YW. (015), " Wind Tunne Test on Aeroeasti Mode of Catenary System for High Speed Raiway", China Raiway Siene., 36(3), 73-80.