A Study on the Dynamic Behavior of Wheel-Type Train Propelled by Superconducting Linear Synchronous Motor

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1 Modern Mechanical Engineering, 4, 4, Published Online August 4 in SciRes. A Study on the Dynaic Behavior of Wheel-Type Train Propelled by Superconducting Linear Synchronous Motor Jinho Lee, Changyoung Lee, Jeongin Jo, Yongjae Han Maglev Train Research Tea, Korea Railroad Research Institute, Uiwang-si, Republic of Korea Eail: jinholee@krri.re.kr, cylee@krri.re.kr, jjo@krri.re.kr, yjhan@krri.re.kr Received 7 June 4; revised 6 July 4; accepted 6 August 4 Copyright 4 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Coons Attribution International License (CC BY). Abstract This paper deals with a study on the dynaic behavior of 6 k/h wheel-type train propelled by superconducting linear synchronous otor (LSM). This train is of a traditional wheel-on-rail type with traction otors on wheel-bogies. However, for the 6 k/h speed, on the both sides of each vehicle, superconducting LSMs are attached and the ground coils are installed on the guideway. In this case, the guideway irregularities act as disturbance to the vehicle causing deterioration of ride cofort. And besides thrust force, the noral force could be created in superconducting LSM control, which influences vehicle dynaics during running. In this study, to exaine the effect of guideway irregularity and noral force on dynaic behavior of proposed train, the vehicle dynaic odel is driven and frequency analysis is perfored through siulation. The siulation results show that the lateral directional acceleration is ainly influential to ride cofort; however this could be reduced effectively by electroagnetic daping force fro linear generator. It is also shown that the noral force effect fro superconducting LSM control is liited even though the attractive noral force acts favorably to ride cofort. Keywords High Speed Railway, Superconducting Linear Synchronous Motor, Dynaic Behavior. Introduction Technology copetitions for increasing the speed of rail transportation constantly becoe fierce around the world. Conventional wheel-type railways such as TGV, ICE, Shinkansen, etc. are being coercialized with axiu speed of 3 k/h and now under developent for over 5 k/h speed. Meanwhile, as an alterna- How to cite this paper: Lee, J.H., Lee, C.Y., Jo, J.M. and Han, Y.J. (4) A Study on the Dynaic Behavior of Wheel-Type Train Propelled by Superconducting Linear Synchronous Motor. Modern Mechanical Engineering, 4,

2 tive for high speed rail transportation, the aglev using linear synchronous otor (LSM) is also being coercialized in Shanghai China with 43 k/h as axiu speed []. And Japan has built a construction plan of Tokyo-Nagoya route by aglev until 7 and conducted the perforance test in 4.8 k test line [] [3]. Despite the superiority in high speed, the drawback such as interoperability proble that aglev could not interoperated with the existing wheel-on-rail track is the ain obstacle for aglev coercialization [4]. To resolve this proble while aiing at the high speed, copared with the 3 k/h level wheel type railway and 4 k/h level aglev, the new concept of high speed railway aiing at 6 k/h level is recently introduced by C. Y. Lee [5]. In [5], author proposed the dual-ode propulsion syste propelled by traction otors in low speed and superconducting LSM in high speed. As shown in Figure, by adopting the traditional wheel type rail, the interoperability proble with existing railroad could be resolved and by installing superconducting electroagnets on vehicle sides and ground LSM coils on the exclusive high speed line, the powerful thrust force could be achieved. In superconducting LSM propulsion, since the thrust force is produced fro interactive force between electroagnets on vehicle and LSM coils on guideway, the irregularities of guideway cause deterioration of ride cofort [6]. Since the precise construction of guideway requires excessive aount of cost, active vibration control based on vehicle dynaic analysis should be considered to iprove the ride cofort. And in superconducting LSM propulsion control, the noral directional force in respect of thrust direction could be created by adjusting the agnetic field angle [5], so the noral force effect on the vehicle dynaic behavior is also needed to be analyzed. In this study, as a odel for dynaic analysis, the Korea high speed wheel type train (KTX) attaching superconducting electroagnets on vehicle sides is assued. Based on the proposed odel, the coputation odel and atheatical equations including external disturbance are established. Then, through the siulations, syste dynaic behavior according to the guideway irregularities and noral forces is analyzed and the ride cofort iproveent ethod is suggested.. Vehicle Dynaic Model.. Configuration of Proposed Vehicle Model The configuration of vehicle odel for dynaic analysis is shown in Figure. The forehead otor car of KTX with two wheel bogies is adopted as ain body and it is assued that superconducting electroagnets are attached on sides without shape odification of ain body. Therefore, the ajor vehicle characteristics are deterined by wheel-bogies whose detail coponents are described in Figure 3 [7]. Based on this, the vehicle dynaic odel for vertical, lateral and rolling direction could be established like Figure 4. The descriptions of sybols in this odel are as follows:, : asses of bogie and car body I, I : oent of inertial of bogie and car body k py, k pz : spring constants of bogie in lateral and vertical direction k sy, k sz : spring constants of car body in lateral and vertical direction c py, c pz : daping constants of bogie in lateral and vertical direction c sy, c sz : daping constants of car body in lateral and vertical direction h k, h k, h k : lateral spring attachent height h c, h c, h c : lateral daper attachent height b k, b k : half of the lateral distance between vertical springs b c, b c : half of the lateral distance between vertical dapers y, y : lateral displaceent, : rolling angular displaceent z, z : vertical displaceent y, z : guideway irregularity of lateral and vertical direction The characteristic values of dynaic odel are described in Table [7]. In here, the subscript (p) eans bogie(priary) and (s) eans car body(secondary). And the subscript a and b eans different co- 45

3 Figure. Concept of high speed railway with dual-ode propulsion syste [5]. Figure. Configuration of proposed vehicle. Figure 3. Bogie syste of KTX forehead otor car [7]. 46

4 Table. Characteristic values of dynaic odel [7]. Figure 4. Dynaic odel of proposed vehicle. Description Sybol (unit) Value Sybol (unit) Value Mass (kg) 4 (kg) 5496 Moent of inertia I (kg ) 593 I (kg ) 38 Spring constant (vertical) Spring constant (lateral) Daping constant (vertical) Daping constant (lateral) k (N/) pza 75 k (N/) sza 634 k (N/) pzb 5 k (N/) szb 83 k (N/) pya 583 k (N/) sya 5 k (N/) pyb 45 k (N/) syb c (N s/) pza c (N s/) sza c (N s/) szb 6 c (N s/) sya c (N s/) syb 43 h ().85 k a Lateral spring height h () kb.45 h () ka.3585 ka h ().85 h () kb.5 kb h (). Lateral daper height Half of lateral distance between vertical springs Half of lateral distance between vertical dapers h () ca.5 ca h () cb.5 cb b () ka ka b () kb kb b () ca ca b () cb cb h (). h (). b () b ().5 b () b () 47

5 ponents with sae function... Dynaic Equation for Vertical Direction Based on the dynaic odel achieved previously, the dynaic equations for vertical direction could be expressed as follows: Bogie vertical otion ( pza sza szb ) ( sza szb ) ( pza pzb sza szb ) ( sza szb ) ( ) z + c + c + c z c + c z + k + k + k + k z k + k z = c z + k + k z Car body vertical otion pz pza pzb If we set the state variable like and the state space equation like ( ) ( ) ( ) ( ) z c c z c c z k k z k k z () sza + szb + sza + szb sza + szb + sza + szb = then, the syste atrix A could be expressed like [ z, z, z, z ] T x = (3) x = Ax + B z, (4) ( kpza + kpzb + ksza + kszb ) ( cpza + csza ) ( ksza + kszb ) csza A = (5) ( k ) ( ) ( ksza kszb ) ( csza c szb ) sza + kszb csza + c + + szb And the external input ter, B z can be express like c pza ( kpza + kpzb ) z z z + B =. (6) If input is sinusoidal such as z H ( ωt) = sin, the second eleent in Equation (6) can be re-expressed as follows: where ( ) ( ) c k + k c k + k z + z = Hωcos( ωt) + Hsin ( ωt) = Ωsin ( ωt α) (7) pza pza pzb pza pza pzb Then, Equation (6) can be siplified like H Ω = ( cpza ) + ( kpza + kpzb ), α = tan k + pza k pzb c pza B z = Ωsin ( ωt α). (8). () 48

6 .3. Dynaic Equation for Lateral and Rolling Direction To achieve the dynaic equations for lateral and rolling direction of proposed syste, the siilar procedure to previous section could be applied. However, in this case, since the energy balanced equation about oentu should be constructed, the distance between coponents position and ass center described in Table should be considered. And it is assued that the lateral disturbance, y originated fro guideway irregularity acts on the ass center of bogie for siplicity. The dynaic equation for lateral and rolling direction could be expressed as follows: Bogie lateral otion y+ ( kpya + kpyb ) y+ cpy y ( ksya + ksyb )( y y) ( csya + csyb )( y y ) + ( kpyahk a + kpybhk b ) + cpyhc ksya ( hk a + hk a ) (9) k h + h c h + h c h + h Car body lateral otion syb ( k b kb ) sya ( ca ca ) syb ( cb cb ) ( kpya kpyb ksya ksyb ) y = ( sya syb )( ) ( sya syb )( ) sya ( k a k a ) syb ( k b k b ) ( ) ( ) y + k + k y y + c + c y y + k h + h + k h + h + c h + h + c h + h = sya c a c a syb c b c b Bogie rolling otion I + kpyahk a + kpybhk b y + cpyhco y + ksyahk a + ksybhk b y y + csyahc a + csybhc b y y + k b + k b + c h + k h h + h + k h h + h ( ) ( )( ) ( )( ) ( pya k a pyb k b ) py co sya ka ( k a ka ) syb kb ( k b kb ) csyahc a ( h ca h cb ) csybhc b ( h cb h c b ) ( kpzabk a kpzbbk b ) ( cpzabc a cpzbbc b ) ksza ( bk a bk a ) kszb ( bk b bk b ) csza ( b ca b ca ) cszb ( b cb b cb ) = Car body rolling otion I + ( ksyahk a + ksybhk b )( y y) + ( csyahc a + csybhc b )( y y ) + ksyahk a ( hk a + hk a ) + ksybhk b hk b + hk b + csyahc a hc a + hc a + csybhc b hc b + hc b + ksza bk a bk a + k b b + c b b + c b b = ( ) ( ) ( ) ( ) ( ) ( ca ) szb ( cb cb ) szb k b k b sza c a If we set the state variable like and the state space equation like () () () T x = y, y, y, y,,,, (3) x = Ax + B z, (4) then, the eleents of atrix A and B could be achieved in a siilar way described in previous section. 3. Siulation Results Based on dynaic equations driven in previous section, the siulation regarding ride cofort by using the frequency response analysis in vertical, lateral and rolling direction was perfored. For the vertical directional siulation, as an input z, a sine wave with a agnitude and wavelength is used [8]. And as a lateral and rolling direction disturbance input y, a agnitude and wavelength sine wave is used [6]. In both cases, the travel speed of train is assued as 5 k/h. 3.. Ride Cofort Analysis The frequency response of car body in vertical direction is shown in Figure 5. The peak value with. /s / 49

7 .6.4. Aplitude (/s /) Figure 5. Frequency response of car body in vertical direction. at.6 Hz is found. According to the [9] which studied about ride cofort of high speed train based on ISO- 63 (guide for evaluation of huan exposure to whole-body vibration), the vibration of frequency range in 4 - Hz for the vertical direction and.6 - Hz for the lateral direction are sensitive to huan body. Since the vibration of frequency for vertical direction is outside of the range 4 - Hz, it sees that the ride cofort for vertical direction couldn t be a ajor concern in this case. The frequency response of car body in lateral and rolling direction is shown in Figure 6. In this case, since the peak values are found at.5 Hz in both cases, uncofortability in lateral direction could be an issue, so, this value is needed to be reduced by further vibration reduction ethods. 3.. Effect of Noral Force In this section, the effect of noral force produced in superconducting LSM propulsion control is exained. Since the typical relation between thrust and noral force in superconducting LSM control is trigonoetrical with respect to the agnetic field angle as shown in Figure 7, the noral force with respect to the angle could be siply calculated [5]. In our case, due to the syetry for in lateral direction, only vertical directional noral force is considered. By assuing that the axiu thrust force per one car is 46 kn (This value can be achieved at 9 of agnetic field angle, [5]) and the slope of lateral guideway is 6, the noral forces with respect to the different agnetic field angle (i.e. 75, 8, 85, 9, 95,, 5 ) are added in right side of Equation () for siulation. As shown in the siulation results in Figure 8, it is found that attractive noral force acts favorably to ride cofort while the repulsive force acts unfavorably. However, in both cases, these effects are negligible (i.e. change rates are under %) as suarized in Table Ride Cofort Iproveent Method Frequency (Hz) As reviewed in Section 3., the vibration frequency of lateral direction positioned within the range of.6 - Hz is expected to influence ride cofort un-favorably. To itigate this vibration, the electroagnetic force fro the linear generator is considered. The linear generator is usually installed in high speed aglev to generate power in traveling vehicle by using the haronic agnetic interaction with ground LSM coil. And during linear generator operation, the electroagnetic force is generated additionally fro linear generator and this force could act as daper in priary suspension []. On condition that this ethod is also applicable to our syste, the vibration reduction effect by electroagnetic force fro linear generator is investigated. By assuing that the generated force with axiu value of f has the switched polarity according to the polarity of lateral velocity [], the electroagnetic force can be expressed like: F = sign y f (5) f is in- To exaine the effect of this force on the vehicle dynaics, Equation (5) with different value of serted in right side of Equations () and (9). ( ) 5

8 Aplitude (/s /) Frequency (Hz) Aplitude (rad/s /) Frequency (Hz) Figure 6. Frequency response of car body in lateral and rolling direction. Figure 7. Typical thrust and noral force as functions of the agnetic field angle [5]. Figure 8. Frequency response of vertical directional car body according to agnetic field angle. The siulation results about effects of daping force fro linear generator results are shown in Figure 9 and Figure. As shown in figures, the ride coforts are iproved effectively in both cases, and the aount of i- 5

9 Table. Noral force effect according to the agnetic field angle in vertical direction. Magnetic field angle (degree) Created noral force (kn) Peak value of acceleration (/s /) Change rate (%) Rearks Repulsive Attractive Figure 9. Frequency response of vertical directional car body according to linear generator force. Figure. Frequency response of lateral and rolling directional car body according to linear generator force. proveent is ore rearkable in lateral and rolling direction than vertical direction. This result is suarized in Table Conclusion In this study, to analyze the dynaic behavior of dual-ode propulsion syste which is proposed for 6 k/h 5

10 Table 3. Ride cofort iproveent according to linear generator force. Direction Vertical Lateral Rolling Generated force, (N) f Peak value of acceleration (/s /) Change rate (%) level high speed, the dynaic odel including guideway irregularities is established and nuerical siulations are perfored. Fro the frequency response analysis regarding ride cofort, lateral direction is expected to be ore influential to ride cofort than vertical direction. And it is shown that the noral force effect on the vertical directional vehicle behavior according to the agnetic field angle would be liited even though the attractive noral force acts favorably to ride cofort. And as a ride cofort iproveent ethod, the electroagnet force fro linear generator acting as a daper is introduced and its effectiveness is confired. Acknowledgeents This work was supported by Ministry of Science, ICT and Future Planning. (PK47B) References [] Dories, W. and Viola, B. (4) Further Developent Prograe for the Transrapid of the Federal Ministry of Transport, Building and Housing. In: Maglev 4, Vol. I, 3-3. [] Miyaoto, S., Katsui, Y. and Tsutou, F. (4) The Status of the Running Tests of JR-Maglev. In: Maglev 4, Vol. I, [3] The Final Stage of Test Line Extension Construction (3) [4] Kluhspies, J. (8) Prospects and Liitations of High-Speed Maglev Systes: Aspects of an Interdisciplinary Approach. The th International Conference on Magnetically Levitated Systes and Linear Drives, 5-9 Deceber 8, No. 39. [5] Lee, C.Y., Lee, J.H., Jo, J.M., Park, C.B., Rue, W.H., Chung, Y.D., Hwang, Y.J., Ko, T.K., Oh, S.-Y. and Lee, J. (4) Conceptual Design of Superconducting Linear Synchronous Motor for 6 k/h Wheel-Type Railway. IEEE Transaction on Applied Superconductivity, 4, Article No [6] Watanabe, K., Yoshioka, H., Suzuki, E., Tohtake, T. and Nagai, M. (7) A Study of Vibration Control Systes for Superconducting Maglev Vehicles. Journal of Syste Design and Dynaics,, [7] Ki, J.C. (3) A Study on Running Perforance for KTX. Korea Railroad Research Institute (KRRI) Report. [8] Choi, I.-Y., Koo, D.-H., Hwang, S.-Y. and Li, Y.-S. () Analysis on Safety and Ride Cofort of KTX According to Track Surface, Journal of the Korean Society for Railway, 3, [9] Ki, Y.-G., Park, C.-K., Ki, S.-W., Ki, K.-H. and Lee, T.-H. () A Study on the Ride Cofort of High Speed Train in Korea. Proceeding of Fall Conference of Korean Society for Railway, [] Suzuki, E., Shirasaki, J., Watanabe, K., Hoshino, H. and Nagai, M. (8) Vibration Reduction Methods for Superconducting Maglev Vehicles. Proceedings of the 8th World Congress on Railway Research, Seoul, 8- May 8, CD-ROM Paper R

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