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Challenge E: Bringing the territories closer together at higher speeds

A Model Experiment Investigation of Superconducting Maglev Vehicle Dynamics and Vibration Control

Erimitsu SUZUKI, Ken WATANABE, Hironori HOSHINO, and Takenori YONEZU Railway Technical Research Institute, Tokyo, Japan

Abstract

In the research and development of the superconducting magnetically levitated transport (Maglev) system being developed in Japan, studies on the characteristics of vehicle dynamics and car body vibration reduction methods until recently mainly involved computer simulations followed by full-scale vehicle running tests. An experiment apparatus using a reduced-scale model of a train car body was constructed to study the characteristics of vehicle dynamics of Maglev systems that differ from conventional railway systems. Consisting of six-axis parallel link motion bases to reproduce bogie motions, an aluminum car body, and secondary suspension units, this apparatus is expected to be useful in examinations of control methods to reduce vehicle vibrations and to generate data useful in eventually improving the precision of computer simulations. This report provides an overview of the Maglev vehicle model experiment apparatus and results of initial tests examining its fundamental characteristics. Key words: Maglev, vehicle, vibration, suspension

1. Introduction

The superconducting magnetically levitated transport (Maglev) system being developed in Japan is designed for travel at high speeds of over 500 km/h, and has previously achieved a world record speed of 581 km/h. Maglev can provide high speed mobility with vehicles capable of traveling faster than any other known existing fixed-guideway ground transport system, and is capable of high acceleration and deceleration. This transport system is particularly useful for access between densely populated cities separated by long distances, with optimal routes that can include terrain with steep gradients difficult for conventional steel wheel-on-rail systems to handle. The Maglev system utilizes electromagnetic interactions between ground coils installed on the sidewalls of the guideway and superconducting magnet coils on board the vehicle to generate forces of propulsion, levitation, and lateral guidance (Fig. 1). Methods of reducing vehicle vibrations are being examined with respect to suitability of the Maglev system for commercial operation as a public mode of transportation. Maglev vehicle vibrations are caused by disturbances in the electromagnetic forces that result from deviations in the alignment of ground coils (guideway irregularities). Countermeasures on the vehicle can reduce vibrations by controlling the suspension and improve ride comfort. In addition to improving ride comfort, suspension control systems implemented to reduce vibrations on Maglev vehicles can lead to the reduction of construction costs by enabling the relaxation of the limits of tolerated irregularities in the guideway coil alignment, and the reduction of management costs by minimizing the extent of guideway maintenance. In the research and development of Maglev systems, studies on the characteristics of vehicle dynamics and car body vibration reduction methods until recently mainly involved computer simulations followed by full-scale vehicle running tests. However, numerous limiting factors of full-scale vehicle running tests made it difficult to perform experiments in which the various parameters could be changed freely. In this study, an experiment apparatus using a reduced-scale model of a Maglev vehicle was constructed, that is expected to be useful in examinations of control methods to reduce vehicle vibrations and to generate data useful in eventually improving the precision of computer simulations. This Maglev vehicle model experiment apparatus (MAGMOX) can be used to reproduce conditions of experiments that are difficult to perform on a full-scale vehicle.

Fig. 1: Overview of the superconducting Maglev system

Guideway

Propulsion coil Levitation/guidance

coil

Bogies


Bogie (Motion base)

Secondary suspension vertical

vertical pitching

Fig. 2 View of the MAGMOX setup

Car body

This report provides an overview of the MAGMOX system and results of initial tests examining its fundamental characteristics. Experiments of model Maglev vehicles will generate data that are expected to be useful in improving the accuracy of computer simulations, and will make it easier to reproduce conditions of the Maglev vehicle that are difficult to test on the full-scale guideway.

2. Overview of the superconducting Maglev system and the MAGMOX project

As shown in the schematic diagrams of the superconducting Maglev system in Fig. 1, the vehicle is equipped with superconducting magnet (SCM) coils on the left and right sides of each bogie. Levitation/guidance coils and propulsion coils are installed along the sidewalls of a concrete guideway. The vehicle travels on this guideway at high speeds of over 500 km/h.

2.1 The MAGMOX apparatus

The MAGMOX project has the objective of modeling a three-car Maglev train set with an articulated bogie arrangement, in which each single intermediate bogie connects and supports the ends of two adjacent car bodies (resulting in three car bodies and four bogies). In the initial phase of this project, a 1/12-scale car body and two bogies were constructed. Each bogie consists of a hydraulically-powered motion base that can recreate 6 degrees of freedom (6-DOF: vertical, lateral, and longitudinal translation and yaw, pitch, and roll rotation). The car body was made of aluminum and designed to be flexible enough to study bending vibrations. Each end of the car body was connected to each bogie by mechanical coil springs to model the secondary suspension. Figure 2 shows a view of the MAGMOX setup.

2.2 Motion base, for reproducing bogie motion and primary suspension

The initial brainstorming of the project plans raised ideas about using mechanical spring equivalents to model the electromagnetic spring characteristics of the primary suspension. However, this idea was not pursued in detail, considering the difficulties of changing the spring constant to adjust for changes in parameters such as the vehicle speed and bogie-supported load. Moreover, a mechanical spring structure would be difficult to construct in a manner that can simultaneously model multiple DOF, such as the combination of vertical and pitching motions with lateral and rolling motions. Therefore, a hydraulic actuator system with a 6-DOF mechanism (motion base) was selected to directly reproduce the motions of the bogie. Specifically, a parallel-link motion base was chosen because of the relative simplicity of controlling the posture of the motion base. A hydraulic-based actuator driving method was chosen in order to minimize the size of the motion base and to generate motions of high frequency vibrations. Table 1 includes an example of specifications of the motion bases that were constructed.

2.3 Model car body

The model car body was constructed with aluminum in 1/12 scale, 2 meters in length, and designed to have a characteristic frequency of the first-order bending vibration below 50 Hz, which is the maximum possible frequency of vibration that can be generated by the motion base. Two types of car bodies were constructed; one with a first-order bending vibration characteristic frequency of 45 Hz,


Tension/compression load cell (to measure forces of interactions between the car body and bogie)

Car body

Bogie

Coil spring

Linear bearing

Rod bearing

Shaft component

Coil component

｝ Fig. 3 View of the secondary suspension unit

Shaft motor for vibration control

Table 1 Main specifications of MAGMOX

Specification Value

Bogie Maximum oscillation frequency 50 [Hz] Maximum load 500 [N]

Car body

Length 2000 [mm] Width 250 [mm] Height 30, 35 [mm] Plate thickness 3 [mm]

and the other of 50 Hz (equivalent to about 13 Hz and 14.5 Hz in a full-scale vehicle, respectively). The length and width of both types of car bodies are equivalent to about 1/12 of a full-scale vehicle. The heights of the two types of car bodies are 30 mm and 35 mm, since it was necessary to minimize the second-order cross-sectional moment. Table 1 includes an example of specifications of the car bodies. MAGMOX was designed such that the magnitude of vibration acceleration is equivalent to that of a full-scale vehicle. Accordingly with the laws of scale model similitude ratios, the frequency values are about 12 times that of a full-scale vehicle.

2.4 Secondary suspension

The secondary suspension between the car body and bogie in a full-scale vehicle consists of air springs and hydraulic dampers. Because small air springs sufficiently suitable for use in a 1/12 scale model could not be found, coil springs were used in MAGMOX. While air springs function in both vertical and horizontal (lateral and longitudinal) axes, coil springs function only in one axis, in this case the vertical axis. Therefore, the secondary suspension structure was designed to allow vertical translation and pitching rotation of the car body, and constrain lateral, rolling, and yawing motions. The bottom end of the secondary suspension structure was linked with the bogie using pin joints to allow rotation on the pitch axis. The top end was linked to the car body using linear bearings with shafts inserted in the axial center spaces of the coil springs to allow vertical translation while constraining lateral translation. Moreover, the secondary suspension was assembled into a single unit on each of the two ends of the car body, such that the types of coil springs can be easily changed by simply removing the secondary suspension unit.

2.5 Vibration control actuator

A shaft motor, which is one type of linear motor, was selected to serve as the actuator for the vibration control of the secondary suspension, because of its compact dimensions and superior response characteristics. Shaft motors were installed at the four corners of the car body, but since only vertical vibration was controlled at this stage of the project, the left and right shaft motors at each end of the car body were paired and controlled to move together in parallel. Each shaft motor transmits control force to the car body through a rod bearing connecting the car body to the coil component of each shaft motor, resulting in a structure that allows pitching motion while also preventing any strenuous


Car body

Bogie

Load cell Virtual

magnetic spring

External disturbance (Vertical irregularities)

Direction of travel

Time delay

Forces of interaction between the

car body and bogie

Secondary suspension

Bogie (Motion base)

Bogie displacement computed by solving dynamic equations in real time using inputs of vertical irregularities and load cell measurements

of forces of interaction between the car body and bogie.

Fig. 4 MAGMOX reproduction of coupled vibrations resulting from interactions between the car body and bogie

forces from acting on the shaft motor. The shaft component of the shaft motor contains a magnet, and its top and bottom ends are rigidly fixed to the actuator frame. Figure 3 shows a view of the secondary suspension unit.

3. Motion base control system

3.1 Bogie control device

The bogie control device sends bogie displacement commands through D/A converters and amplifiers, to the actuators of the motion base. Stroke sensors embedded in the actuators send actuator displacement measurement signals through amplifiers and A/D converters, providing feedback to the bogie control device. A forward kinematics algorithm in the computer program of the bogie control device uses these stroke sensor measurements to compute the bogie displacement. In addition, laser gap sensors measure the bogie vertical displacement directly. The bogie control device can compare these external laser sensor measurements with values computed from stroke sensor data.

3.2 Control of coupled vibrations resulting from interactions between the car body and bogie

Because MAGMOX consists of a car body linked with bogies as are full-scale vehicles, MAGMOX needs to be able to reproduce coupled vibrations of the car body and bogie. Specifically, when the amplitude of car body vibration decreases by vibration control, reaction forces acting on the bogie cause the amplitude of bogie vibration to change. To reproduce the interaction of forces between the car body and bogie, compact load sensors (load cells) that can measure both compression and tension were inserted between the secondary suspension and motion base (Fig. 4). The forces of interaction between the car body and bogie measured by these load cells are fed back into the bogie control device, to reproduce coupled vibrations. In the bogie control device, the bogie was modeled by a 1-DOF system, using dynamic equations. The bogie displacement is computed by solving these dynamic equations in real time using external disturbance inputs of simulated vertical irregularities in the guideway coil alignment and forces of interaction between the car body and bogie measured by the load cells.

4. Vibration control of the secondary suspension

4.1 LQ control

Linear quadratic (LQ) control is a type of feedback control that applies weighting factors to certain state values and output in an evaluation function that includes quadratic terms, and is designed to minimize this evaluation function. In this study, the evaluation function included state variables of the vertical acceleration of the center of the car body and the relative displacements between the car body and bogies, and the actuator control forces as the output of the control law. The relative displacements between the car body and bogies was included in the evaluation function to model the emergency limiting stopper installed in a full-scale vehicle that serves to limit the maximum allowed relative displacement[1][2]. The dynamic equations used in the control method were discretized and expressed in state-space form as follows:

0

0

( 1) ( ) ( ) ( )( ) ( ) ( ) ( )

k k kX k A X k B u k W x kY k CX k Du k Ex k

(1)


Bogie Direction of travel

Vibration data from the foremost bogie used to control the car bodies to the rear

Secondary suspension and control system

Fig. 5 Representation of preview control

Here, k represents the discrete time step, X the state variables, u the control input, 0x the rate of change of the external disturbance 0x with respect to time, Ak the discretized system matrix, Bk the driving matrix, and Wk the coefficient matrix corresponding to the external disturbance input. C represents an observer matrix, and both D and E are coefficient matrices applied respectively to the control input and external disturbance input to derive the output Y. When this system can be stabilized, the following evaluation function is used:

1

( ( ) ( ) ( ) ( ))T T

kJ X k QX k u k Ru k

(2)

Here, Q is a weighting factor matrix for the state variables used in the control and is a square matrix with the same dimensions as Ak, and R is a weighting factor matrix for the control input and is a square matrix with dimensions corresponding to the number of control inputs. The feedback gain values are derived by finding the solution to the optimal regulator problem that minimizes this evaluation function.

4.2 Optimal preview control

Optimal preview control consists of preview feed-forward and optimal feedback components, and uses information on vibration in the front of the vehicle in the control of vibrations in the rear of the vehicle. This type of control is considered to be effective in railway systems and other modes of transport in which vehicles travel on a fixed track or guideway, where all bogies of a train pass through a common path. In particular, the repeatability of patterns in vehicle dynamics over any given guideway interval is higher for Maglev systems than for conventional railway systems. In this study, the MAGMOX car body represents the intermediate (second) car body within a train consisting of three car bodies and four bogies, and a control system was designed to use information on vibrations of the foremost bogie (Fig. 5). The values of the external disturbance 0x in the dynamic equation of Eq. (1) used in the control law described in the previous section are considered as known values for MR number of steps ahead of the current time step k. The current time refers the instant at which the external disturbance is input to the point on the bogie closest to the secondary suspension unit to be controlled, and steps ahead of this current time refer to times at which data was taken from the foremost bogie, ahead of the point to be controlled. The external disturbance is expressed by the following equation[3][4]: 0 0 0( ) [ ( 1) ( 2) ( )]T

R RZ k x k x k x k M (3) Using Eq. (3), an equation using expanded matrices is formed that includes the matrices of the state variables X and known external disturbance values ZR:

( 1) ( )

( )( 1) ( ) 00

k k

R RR

A W HX k X k Bu k

Z k Z kG

(4)

Here H represents a matrix that extracts 0x from ZR, and GR a transformation matrix that derives ZR(k+1) from ZR(k). From these equations, the evaluation function of the preview control system is expressed as:

1

( )0[ ( ) ( )] ( ) ( )

( )0 0R

T T TR

k M R

X kQJ X k Z k u k R u k

Z k

(5)


Wave number [1/m]

Gui

dew

ay ir

regu

larit

y PS

D

[(mm

2 )/(1/

m)]

Fig. 6 Power spectral density of guideway irregularities

The matrices Q and R are weighting factors. In this study, the external disturbance in form of vertical irregularities in the alignment of the coils along the sidewalls of the guideway (vertical irregularities) was excluded from the evaluation function. Consequently, the elements of the weighting factor matrix including Q that correspond to the external disturbance components are set to zero, such that the ZR components of the evaluation function are omitted. As in the case of LQ control described in the previous section, the feedback gain values are derived by finding the solution to the optimal regulator problem that minimizes this evaluation function.

5. Results of experiments

5.1 Simulated guideway irregularities for external disturbance input

To assess the reproduction of vehicle vibrations and the effects of the vibration control using MAGMOX, vertical irregularities were generated, and used as simulated external disturbance input. A transfer function was formed based on Reference [5], and a uniformly random number was used to compute the vertical irregularities. The power spectral density (PSD) of the vertical irregularities is shown in Fig. 6. In accordance with similitude laws for scale model ratios, the vertical displacement magnitude and vibration frequencies were set to 1/12 and 12 times that of a full-scale vehicle, respectively.

5.2 Characteristics of the passive case

5.2.1 Time-domain results

To confirm the performance of MAGMOX with respect to reproducing coupled vibrations resulting from the interaction of forces between the car body and bogie, time-domain plots of vibration characteristics were examined for the case without vibration control of the secondary suspension (passive). External disturbance of vertical irregularities were input to the front and rear bogies with a time delay between the two bogies equivalent to that of a full-scale vehicle traveling at a constant speed of 500 km/h. Figure 7 shows sample time-domain plots. The analysis in this preliminary study focused on a frequency range that includes characteristic frequencies of the primary and secondary suspension, and a low-pass filter cutting out frequency components of over 34 Hz, equivalent to 10 Hz in a full-scale vehicle, was used to remove high frequency noise from the vibration data. The vertical displacement of the bogie center shown in Fig. 7 is within 1 mm, which is equivalent to the vertical displacement magnitude of a full-scale vehicle, considering similitude laws. The magnitude of acceleration of MAGMOX is the same as that of a full-scale vehicle according to similitude laws, and is independent of the scale of the model. The vertical accelerations of the centers of both the bogie and car body are equivalent in magnitude to those of a full-scale vehicle. To confirm to the reproduction of coupled vibrations, a small external downward load was applied to the secondary suspension unit of MAGMOX. Applying the load caused the motion base to descend slowly, and removing the load caused it to ascend and return to its neutral position, resulting in a slow bobbing motion. This behavior indicates that MAGMOX reproduces coupled vibrations, in which such downward force acting on the bogie results in a bogie vertical displacement in the downward direction.

5.2.2 Computation of the bogie posture using forward kinematics

The computation of the posture of the motion base using measured stroke values of actuators in the parallel link structure of the motion base involves a forward kinematics algorithm that typically requires


-1

0

1

-10

-5 0

5 10

-10

-5 0

5 10

Dis

plac

emen

t [m

m]

A

ccel

erat

ion

[m/s

2 ] A

ccel

erat

ion

[m/s

2 ] Time

(a) Front bogie center vertical displacement (measurement)

Time (b) Front bogie center vertical acceleration (measurement)

Time (c) Car body center vertical acceleration (measurement)

5 s

Fig. 7 Time-domain plot of MAGMOX vibration data (passive case)

-1

-0.5

0

0.5

1

D

ispl

acem

ent

[mm

]

Command Measurement Computation

Time 0.2 s

Fig. 8 Bogie vibration characteristics (front bogie center vertical displacement)

101

10-3

10-2

10-1

100

101

Second derivative of displacement command Acceleration measurement

Acc

eler

atio

n PS

D [(

m/s2 ) 2

/Hz]

Frequency [Hz]

Fig. 9 Bogie vibration characteristics (front bogie vertical acceleration)

many steps in a time-consuming converging iterative process[6]. However, the fluctuations in the displacement of the vibrating motion base are very small, such that the iteration converges quickly enough to enable accurate real-time computation of the motion base posture. To confirm the practicality of this method, the values computed from the actuator stroke data were compared with those of direct measurements by an external laser gap sensor. Figure 8 shows the bogie vertical displacement command signal (command), laser gap sensor output (measurement), and the values computed by forward kinematics (computation). The three values are in good agreement, indicating that the forward kinematics computation can be used as feedback in the bogie control device, in the same manner as laser gap sensor measurements, in terms of measurement precision and response characteristics.

5.2.3 Frequency-domain analysis

The reproduction of coupled vibrations shown in Fig. 4 involved a 1-DOF model using parameters such as the bogie mass and spring constant of the vertical electromagnetic spring in the primary suspension between the bogie and guideway. These constants were set to values such that the characteristic frequency of the primary suspension of a full-scale vehicle (about 5 Hz) is reproduced in MAGMOX in accordance with similitude laws (about 17 Hz). Figure 9 shows a plot of the computed power spectral density (PSD) of the bogie acceleration. Since the bogie control device uses feedback of bogie displacement and not acceleration, a virtual bogie “acceleration command” data was represented by the second derivative of the bogie displacement command signal with respect to time. The PSD of the bogie acceleration measurement values are in good agreement with that of the “command.” The plot also


Fig. 11 MAGMOX apparatus expanded to test a 2.5-car train

Bogie No. 1

Bogie No. 2

Bogie No. 3 車 Car body No. 1

Car body No. 2

Car body No. 3 (half car)

shows the characteristic frequency peak of the primary suspension at about 17 Hz, confirming the adequacy of the parameter settings and 1-DOF model of vertical bogie vibration.

5.3 Characteristics of the vibration-controlled case

The aforementioned optimal preview control method was applied to MAGMOX, and the effect of this control method was analyzed in the frequency domain. Figure 10 shows a PSD plot of the vertical acceleration of the car body. In both the passive and controlled cases, there are noticeable frequency peaks at around 17 Hz corresponding to motions of the primary suspension, and at about 8 Hz corresponding to motions of the secondary suspension. The results indicate that optimal preview control reduced the vibrations corresponding to the motions of the secondary suspension at around 8 Hz to about 1/2 that of the passive case, and the primary suspension frequency peak at around 17 Hz to about 2/3 that of the passive case. Applying the control method resulted in increased vibrations at around 11 Hz, between the two frequency peaks corresponding to the motions of the primary and secondary suspension, presumably because the actuators in the secondary suspension unit were not designed to cope with pitching motion of the car body, since the actuators are designed to reduce only vertical car body vibrations at this stage of the project.

6. Conclusions

A scale model experiment apparatus was constructed to reproduce vehicle dynamics of a superconducting Maglev system. A bogie control device was designed to generate coupled vibrations using the forces of interaction between the car body and bogie, and experiments reproduced characteristics equivalent to that of a full-scale vehicle. Testing of control laws to reduce vertical vibrations in the secondary suspension confirmed the fundamental characteristics of vibration control using this apparatus. Current plans for future work include modifications in the design of the secondary suspension and vibration control method of the actuators to improve the performance of the apparatus in the reproduction of vehicle dynamics, and the expansion of the MAGMOX apparatus to test a 2.5-car train (Fig. 11).

Acknowledgment

The authors would like to express their sincere gratitude to Mr. Yukio Nishiyama of the Design and Manufacture group at RTRI, for his indispensable contributions to the MAGMOX project, with his expertise on the design and construction of the model car

Passive Preview control

Acc

eler

atio

n PS

D [(

m/s2 ) 2

/Hz]

Frequency [Hz]

Fig. 10 Car body vibration characteristics (car body vertical acceleration)

101

10-1

10-2

10-3

10-4

10-5


body and the secondary suspension system. This research is financially supported in part by the Ministry of Land, Infrastructure, Transport and Tourism, of the government of Japan.

References

[1] E. Suzuki, J. Shirasaki, K. Watanabe, H. Hoshino, M. Nagai. “Proposal of vibration reduction methods for Maglev vehicles,” Proceedings of the 19th Symposium on Electromagnetics and Dynamics (SEAD 19), JSME, Paper A135, pp. 53-54, in Japanese (2007).

[2] H. Hoshino, E. Suzuki, K. Watanabe. “Reduction of vibrations in Maglev vehicles using active primary and secondary suspension control,” Quarterly Report of the Railway Technical Research Institute (QR-RTRI), Tokyo, Japan, Volume 49, Number 2, pp. 113-118 (2008).

[3] E. Suzuki, J. Shirasaki, K. Watanabe, H. Hoshino, M. Nagai. “Vibration reduction methods for superconducting Maglev vehicles,” Proceedings of the 8th World Congress on Railway Research (WCRR 2008), CD-ROM Paper R.3.3.7.2 (2008).

[4] J. Shirasaki, E. Suzuki, K. Watanabe, H. Hoshino, M. Nagai. “Improvement of vibration reduction performance of superconducting Maglev vehicles using optimal preview control,” Proceedings of the Dynamics and Design Conference (D&D 2007), JSME, CD-ROM Paper OS11-410, in Japanese (2007).

[5] J. Shirasaki. “Study on vibration suppression methods for superconducting Maglev vehicles using optimal preview control,” Master’s degree thesis, Tokyo University of Agriculture and Technology, in Japanese (2008).

[6] Vincent De Sapio. “Some approaches for modeling and analysis of a parallel mechanism with Stewart platform architecture,” Sandia Report, Sandia National Laboratories, SAND98-8242, (1998).

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