Pantograph Dynamics and Control of Tilting Train

Transcription

1 Proeedings of the 17th World Congress The International Federation of Automati Control Pantograph Dynamis and Control of Tilting Train Ren Luo, Jing Zeng, Weihua Zhang Tration Power State Key Laboratory, Southwest Jiaotong University, Chengdu , P R China (Tel: , vehile@home.swjtu.edu.n) Abstrat: The modeling methodology of tilting train is studied. The vehile and pantograph are onsidered as nonlinear multiple rigid body systems, and the atenary is modeled by FEM method. The eletrial mehanial atuators for arbody and pantograph tilting ontrol are also onsidered in the tilting train model. The method of on-line urving detetion, filtering and ontrol is adopted for the tilting train. The passive and ative ontrols for the pantograph lateral motions during tilting train urve negotiation are analyzed. The pantograph guideway on top of the arbody is designed, and the ontrol strategy for the pantograph ative ontrol is investigated. It is known that the pantograph lateral and vertial displaement and the flutuation of pantograph-atenary ontat fore an be minimized by the use of ative ontrol. 1. INTRODUCTION Together with the rapid development of modern ontrol and omputer tehnologies, the ative suspension ontrol tehnologies have been inreasingly applied in railway vehile systems in order to improve the dynami performane [Goodall,1997; Bruni, 007]. Tilting train is one of the examples of ative seondary suspensions with arbody tilting ontrol during urve negotiation. Tilting the arbody inwards on urve an redue the unbalaned lateral aeleration experiened by passengers, whih an permits higher speeds and provides a variety of operational benefits [Harris, 1998; Cheli, 001; Zolotas, 00]. Therefore, the appliation of arbody tilting tehnology is an effiient way to inrease train speed and to shorten travelling time for existing railways. The study on pantograph-atenary interation is an important issue for effiient urrent olletion of pantograph-atenary system [Zhai, 1998; Zhang, 00]. Ative pantograph vibration ontrols were also investigated in the past years in order to improve the vibration behaviour [Wu, 1997; Diana, 1998]. Beause the tilting train and onventional train run in the same railway lines with the same atenary systems, the pantograph of the tilting train faes more serious dynami problems ompared with the one of onventional train. When the arbody tilts, the pantograph head will result in large lateral displaement, whih may exeed the pantograph normal working range, for example, ±500mm. Thus the pantograph an not satisfy the arbody tilting ondition if without lateral displaement ontrol [Zhang, 004; Luo, 007]. In this paper, the eletrial mehanial atuators are adopted for arbody tilting and pantograph moving ontrol. The lateral aeleration and roll veloity of the leading bogie of the first ar in the train set are measured by using aeleration sensor and gyrosope. Then the measured signals are filtered and modified to generate the ontrol signals for arbody tilting ontrol and pantograph ontrol. The time delay of the ontrol signals aused by the measuring and ontrol system an be ompensated by using foreast method [Luo, 007]. The models of the tilting train and the pantograph-atenary system are built in the paper. The passive and ative ontrols for the pantograph lateral motions during urve negotiation and the dynami performane are investigated.. DYNAMIC MODELS.1 Tilting Train Model The dynami model of a tilting passenger ar with 34 degrees of freedom (DOF) is set up. The degrees of freedom are longitudinal, lateral, vertial, roll, pith and yaw motions of arbody and eah bogie frame, longitudinal, lateral, yaw and spin motions of eah wheelset. The motion of the tilting bolster is also onsidered, whih is related to the ontrolled atuator displaement. Then the model of a train set with three ars is built by onsidering the oupler fores between ars, and the tration fore and resistant fore. The shemati diagram of the tilting ar is shown as Fig.1. The four swing arm mehanism is loated between the bogie frame and the tilting bolster. The eletrial mehanial atuator is mounted between the bogie frame and bolster. Aording to the urving signals, the eletri mehanial atuator pushes or pulls the bolster and further drives the arbody to tilt a ertain angle. The general equation of the tilting train is written as: M X& + CX& + KX = P( X, X&, + (1) where M, C, K are the mass, damping and stiffness matries, X the displaement vetor, P the nonlinear fore vetor, F p the fore between the ar body and the pantograph. F P /08/$ IFAC / KR

2 .3 Catenary FEM Model The atenary struture with 3 span setions is shown in Fig.3 (a). The atenary is onstituted by ontat wire, dropper and support wire. The wires are supported by the tower. The atenary is a wire struture with anti-bending stiffness, espeially when there is large tension on the wires. Thus the atenary an be meshed by -D elasti beam FEM element. The atenary FEM model an be expressed as Fig.1 Shemati diagram of tilting ar. Pantograph Model The nonlinear pantograph model with two degrees of freedom is shown in Fig.. The frame rotational angle α and the head vertial displaement z are the two independent variables. In the frame, m 1, m, m 3, J 1, J, J 3, l 1, l, l 3 and l 4 are the masses, inertia moments and lengths of the bars. The value δ is not hanged, and γ and β are hanging with α. The m denotes the mass of the head, and, k, u indiate the vertial damping, stiffness and frition oeffiient between the head and the frame. z, z&, & z are the exitation inputs from the arbody to the pantograph. F represents the dynami fore between the pantograph and the atenary, and M p is the pantograph rising moment. Then the dynami equations of the pantograph is derived as below by using Lagrange equation f & + & & & & & () 1 ( α ) α f( α + f3( α+ f4( sgn( + f5( α, = f6( z m& z + ( z& z& & & = F (3) E ) + k( z ze ) + u sgn( z ze ) Where f i ((i=1~6)are the oeffiients hanging with α. and the parameters of pantograph [Zhang, 00]. M q& & + C q& + K q Q (4) e e e = Where Me, Ce and Ke indiate the generalized mass, damping and stiffness matries respetively. q is the generalized variable, and Q the generalized fore ating on the atenary. In order to redue the DOF of the atenary and the simulation time, the FEM element length of the ontat wire is hosen as 1.0m, and only the ross points of the other wires are onsidered as nodes. The DOF of the atenary with 1 span setions is 664. When the fore F is exerted on the ontat wire at the distane x, we get a stati displaement z(x). Then the stati stiffness of the atenary is k ( x) = z( x) / F, as shown in Fig.3(b). If the train speed is not very high, this model an be used to simulate the atenary. The Wilson-θ algorithm is adopted in the dynami simulation. The ontat fore between the pantograph and the atenary is alulated as 0 z( z j( x, F ( x, = (5) k( x)[ z( z j( x, ] z( > z j ( x, Where x is the longitudinal distane of the ontat point at time t. The z( and z j (x, are the vertial displaements on the ontat point of the head and the atenary, here the ontat stiffness k(x)=8300n/m. If the atenary vibration is not onsidered, k(x) an take the value as shown in Fig.3(b). (a) Catenary struture Fig. Pantograph model (b) Catenary stasti stiffness Fig.3 Struture and stiffness of atenary 894

3 Control Signal 3. PANTOGRAPH CONTROL MODELS 3.1 Carbody Tilting Control A lateral aeleration sensor and a gyrosope are loated on the leading bogie of the first ar to obtain the tilting signals, and an eletri mehanial atuator is mounted on eah bogie to tilt the arbody with maximum angle 8 0. The arbody tilting ontrol system is depited by Fig.4. The tilting train an negotiate urves with a speed about 35% higher than the onventional train. A/D Computer D/A Sensor Servo Driver Atuator 3.. Ative ontrol with four-bar linkage By fixing the point J on the arbody and replaing the linkage JK by an eletri mehanial atuator as shown in Fig.5, the pantograph movement an be atively ontrolled. When the arbody does not tilt, point K and point J are in the same horizontal plane. The pantograph ontrol signal an be obtained by modifying the arbody ontrol signal. J R A B N P K C D H p Car body Fig.4 Eletri mehanial servo system Car body 3. Pantograph Lateral Control Three lateral ontrol strategies for pantograph are onsidered: S L 1 bogie H 1) Passive ontrol with four-bar linkage (see Fig.5): The base of pantograph is onneted with the ar body by a four-bar linkage. One node of the four-bar linkage is onneted to the ar body and the bogie frame by a three-bar linkage. Beause the bogie frame does not tilt during urving, the pantograph an maintain in the position orresponding to trak enter line. ) Ative ontrol with four-bar linkage: The base of pantograph is also onneted with the ar body by a four-bar linkage (see Fig.5). But the linkage is not onneted with the bogie frame instead of driving by an eletri mehanial atuator. 3) Ative ontrol with guideway (see Fig.6): the base of pantograph is onneted with the ar body through a guideway. And the lateral movement of the pantograph is ontrolled by an eletri mehanial atuator Passive ontrol with four-bar linkage The mehanial system is shown in Fig.5, in whih points A, D and N are fixed on ar body, point S is fixed on the bogie frame. The optimized parameters of system are[zhang,004]: Height of AD to rail top: 4300mm AB=60mm, BC=1175mm CD=60mm, AD=145mm The oordinates of eah point in the trak oordinate system are: R (-108.8, 309.8), N(-784.6,3058.0), J(-899.8,3731.4) L J L Titling system L 3 Fig.5 passive ontrol pantograph 3..3 Ative ontrol with guideway As shown in Fig.6, the guideway is loated on the roof of the arbody, and the base of the pantograph is positioned on the guideway by rollers. Point J is on the ar body and point K is on the base. The JK represents the atuator. The ontrol signal is also modified from the arbody tilting signal. The shape of the guideway is designed based on the motion of arbody top when arbody tilts, and to maintain the movement of pantograph head (point P) as small as possible. In the arbody oordinate system, the oordinate of point K is: L P K Guideway Roof of ar body θ M (x,y) Coordinate of arbody Fig.6 Pantograph with guideway 895

4 L 3 H L 1 osθ1 + H os[artan + θ ] x osθ L3 = y osθ L 3 H H sin + sin[artan p L1 θ1 H + θ ] L3 (6) where L3 + L1 L1L3 osθ L3 θ = + 1 π aros artan L L3 L1 The parameters L 1, L, L 3, Hp and H are shown in Fig.5. The variable θ is shown in Fig.6. The oordinates of point L and M an be easily derived from the oordinate of point K. 4. NUMERICAL SIMULATION RESULTS The trak ondition used for the simulation is: 10m straight+100m transition+100m onstant urve +100m transition urve+100m straight Curve radius: 800m, superelevation: 0.1m Speed: 160km/h displaement /mm displaement/mm (a) vertial dispalement s/m non-tilting tilting (b) lateral dispalement s/m Fig.8 Displaements of arbody enter of gravity The trak irregularity inputs are also onsidered in the simulation. The train-set is omposed of a motor ar + a trailer ar + a trailer ar. The total DOF of the train-set and the pantograph is =105. The pantograph is loated on the roof of the first ar or the seond ar, above the rear bogie of the ar. The stati fore F 0 between the pantograph and the ontat wire is 80N. There are five working onditions alulated in this paper. The arbody tilting signals and tilting angles of the train set are shown in Fig.7. The tilting signal of the 1st arbody an be obtained by using a foreast method. When the train negotiates the urve with 160km/h, the vertial and lateral displaements of the tilting arbody are larger than non-tilting arbody, as shown in Fig.8. The lateral displaement of the pantograph head is larger than its working range when the arbody tilts, as shown in Fig.9. Control signal/v Angle/rad time/s the 1st ar the nd ar the 3rd ar tilting ontrol signal of eah ar the 1st arbody the nd arbody the tilting angle of the arbody Diatane/m Fig.7 Control signal and tilting angle of tilting train Fig.9 Lateral displaement of pantograph head Three shemes of pantograph ontrol strategy are simulated in this paper. The passive four-bar linkage system is simple and reliable, and an be mounted on the top of every arbody. The ative four-bar linkage system needs ontrol signal and ontrol system, thus the first arbody is not suitable for plaing the pantograph. Ative pantograph ontrol is able to keep the lateral displaement small, although the system is more omplex. Even though the ative four-bar linkage system is simple than the guideway system, it annot redue the pantograph vertial displaement while reduing the lateral displaement. 4.1 Passive Four-Bar Linkage System During urve negotiation, the pantograph head results in small lateral displaement and ertain vertial displaement. The lateral displaements of the pantograph head are almost the same whih less than 5m when the pantograph is on the top of the first arbody or the seond arbody. But the vertial displaement of pantograph head an reah to 1.5m. In the passive ontrol ase, the pantograph-atenary ontat point an always keep in the pantograph working range. The simulation results are illustrated in Fig.10 and Fig

5 Fig.10 Contat fore of the pantograph-atenary Fig.1 Results of pantograph on the first arbody Fig.11 Displaement of pantograph-atenary ontat point 4. Ative Four-Bar Linkage System The ontat fore and displaement of pantograph in this ative ase are almost the same as the passive ase. The pantograph lateral displaement is smaller when the pantograph is on the seond arbody. The simulation results are shown in Fig.1 and Fig. 13. Fig.13 Results of pantograph on the seond arbody 4.3 Ative Guideway System The design priniple of the pantograph guideway is to realize minimum lateral and vertial displaements of pantograph simultaneously. The simulation results are shown in Fig.14 with the pantograph on the seond arbody. It an be seen that the lateral displaements of the pantograph head are smaller than 0m and the vertial displaements of the pantograph head smaller than 7m. The ontat fores are less than 00N. 897

6 Fig.14 Pantograph displaement and ontat fore 5. CONCLUSIONS The tilting train model and pantograph-atenary model are set up. The vehile and the pantograph are onsidered as nonlinear multiple rigid body systems, and the atenary is modelled by FEM method. The eletrial mehanial atuators for arbody and pantograph tilting ontrol are onsidered. The method of on-line urving detetion, filtering and ontrol is adopted for the tilting train. When the tilting train is passing through urves, the lateral and vertial displaements of arbody and pantograph head will inrease duo to arbody tilting motion. Thus pantograph lateral ontrol is neessary in order to satisfy the urrent olleting performane. Three shemes for pantograph motion ontrol, ether passive or ative, are studied in this paper. The ontat fore between pantograph and ontat wire, the displaements of pantograph head are simulated by using numerial method. It an be seen from the results that the use of pantograph ontrol for tilting train an improve the pantograph/atenary ontat performane, and sheme of the ative ontrol with guideway an ahieve better performane. Bruni S., Goodall R. M., Mei T. X. and Tsunashima H. (007). Control and Monitoring for Railway Vehile Dynamis. Vehile System Dynamis, 45(7-8), pp Harris N.R., Shmid F. and Smith R.A. (1998). Introdution: Theory of Tilting Train Behaviour. Journal of Rail and Rapid Transit, 1(1), pp1-5. Cheli F., Diana G. and Resta F. (001). Numerial Model of a Tilting Body Railway Vehile Compared with Rig and on Trak Tests. Vehile System Dynamis, 9 (6), pp Zolotas A.C., Goodall R.M., Halikias G.D. (00). New Control Strategies for tilting trains. Vehile System Dynamis, 37 (suppl.), pp Zhai, W.M and Cai, C.B. (1998). Effet of Loomotive Vibrations on Pantograph-Catenary System Dynamis. Vehile System Dynamis, 9 (suppl.), pp Zhang, W.H., Mei G.M., Wu X.J. and Shen Z.Y. (00). Hybrid Simulation of Dynamis for the Pantograph- Catenary System. Vehile System Dynamis, 36(6), pp Wu T.X. and Brennan M.J. (1997). Ative Vibration Control of a Railway Pantograph. Journal of Rail and Rapid Transit, 11(F), pp Diana G., Fossati F. and Resta F. (1998). High Speed Railways Colleting Pantographs Ative Control and Overhead Lines Diagnosed Solutions. Vehile System Dynamis, 30(1), pp Zhang, Y.H. (004). Study on the pantograph tilting system of tilting train, Master degree thesis. Southwest Jiaotong University, China (In Chinese). Luo, R. (007). Study on the eletrial-mehanial oupled dynamis and ontrol of tilting train, Ph.D thesis. Southwest Jiaotong University, China (In Chinese). ACKNOWLEDGEMENT The authors would like to aknowledge the support from the National Natural Siene Foundation of China (projet no ), whih made this study possible. REFERENCES Goodall R.M., Paejka H.B. and Sharp R.S. (1997). Ative Railway Suspension: Implementation Status and Tehnologial Trends. Vehile System Dynamis, 8(-3), pp