Design of an Electromagnet with Low Detent Force and its Control for a Maglev Super-speed Vehicle

Abstract

The vibration and noise caused by the dynamic interaction between electromagnetic suspension and the linear synchronous motor stator beneath a flexible guideway remain problems in designing attractive Maglev trains. One possible method to reduce the sources of vibration is to minimize the detent force in the linear synchronous motor that creates variations in both lift force and thrust. This paper proposes lowering detent force by using separated core instead of single united core. The magnet is designed to adapt to the deflected guideway at a speed of 550km/h. This study will analyze the electromagnetic field and control performance, and how they relate to lift forces and dynamic responses.

1. Introduction

Attractive Maglev trains, such as the German Transrapid, are supported and propelled by combined suspension and propulsion electromagnets (lift electromagnets hereinafter). The vertical attraction force of lift electromagnets is actively controlled to maintain the clearance between the track and the magnet within an allowable range, e.g. 10mm. The lift electromagnets are also used as on-board rotors interacting against stators of the linear synchronous motor mounted on the guideway. Since the attractive-type Transrapid traveling at a maximum operating speed of 430 km/h was first commercialized in Shanghai in 2004, its 10-year record of problem-free operation has proven that the attraction-type Maglev train could be a reliable guided transportation mode [1]. However, owing to the nature of active airgap constant control, these trains have experienced vibration and noise problems, which are caused mainly by the dynamic interaction between electromagnetic suspension and elevated guideway [1, 2].

Such problems may become more serious at very low speed rather than high speeds. One of the ways of reducing the vibration is to minimize the detent forces in the linear synchronous motor, which controls variations in lift force and propulsion thrust. The detent forces are dependent on the shapes of stator teeth and magnet poles [3, 4]. This paper will propose lowering detent force through the arrangement of one pole per core instead of multiple poles. The reduction of detent forces is analyzed by FEM. This proposal will implement the use of the designed lift electromagnet and the airgap control with the state feedback scheme to follow a flexible guideway at a high speed of 550km/h. The lift electromagnet design and control are evaluated through the experimental projects.

 

2. Design and Analysis

Fig. 1 shows the Maglev test vehicle under study, and Table 1 gives its specifications. The vehicle is meant to confirm the performance of the designed electromagnet with less detent force for levitation and propulsion. The vehicle configuration is schematically shown in Fig. 2. It consists of 6 lift electromagnets, 4 guidance electromagnets on both the front and rear bogies, and 2 emergency braking electromagnets on the central bogie. The nominal operational airgap between electromagnets and the linear synchronous motor stator teeth faces is 10mm and 20mm when landing. The maximum design speed is 550km/h.

Fig. 1.Attractive Maglev test vehicle

Table 1.Vehicle specifications

Fig. 2.Vehicle configuration

2.1 Lift magnet design

The following aspects are considered when designing the lift electromagnet for lift and propulsion.

- taking-off from 20mm airgap of landing - sufficient lift force and thrust - variation in lift force due to varying current in the linear synchronous motor winding - displaced magnets along the bogie, but with intervals between bogies chosen in consideration of the pole pitch of the magnet, resulting in less thrust loss - aluminum sheet coil for winding for lightweight and heat dissipation - independent control for each half of the magnet module

Considering the above design considerations and the vehicle configuration and specifications, the preliminary lift electromagnet is designed as shown in Fig. 3(a)-Fig. 3(b) and Table 2. The lift electromagnet module has 12 poles, including two auxiliary poles at the ends. The two auxiliary poles are for reducing fringing effects and ensuring space for the installation of gap sensors. The reduced detent force aspect was essential in the design, which is expected to lower the variations in lift force. Although there are various ways to minimize detent force, such as skewing the pole and pole pitch arrangement of the lift electromagnet, the latter technique is applied in the study because of the need for space for gap sensors, as well as to avoid difficulties in manufacturing. To minimize the net detent force, poles of lift magnet are arranged with intentionally non-synchronizing position. The result of this subdividing effect is that the more module is subdivided into magnets, the less the detent force amplitude will be. This paper proposes to reduce detent force through the arrangement of one pole per core instead of 12 poles. Fig. 3(c) gives the pole pitch adjustment design with 12 individual magnets. Here, the central component of 12 magnets is synchronized with the corresponding linear synchronous motor stator pole, and an interval of 7mm is maintained between magnets.

Fig. 3.Lift electromagnet designs

Table 2.Preliminary design of the electromagnet

Fig. 4 compares the detent forces in both designs. It shows that the detent force of the proposed design is less than 10% of the preliminary one. The suspension force variations are also reduced as in Fig. 5, which would have positive effects on suspension control due to reduced lift force variations. Consequently, the detent force reduction would lead to less vibration between vehicle and guideway. The lift forces are plotted in Fig. 6 with varying current in the magnet at two different airgaps. The rated lift force is achieved at 17A at a nominal operating gap of 10mm. It is noted that the employed design could, to some extent, lower thrust efficiency. In the view of thrust, adjusted pole pitch makes difference in electric current angle and that causes the thrust loss. However, their electric current angle is small enough and thrust loss is less than 10% of its original value.

Fig. 4.Detent force versus position

Fig. 5.Lift force versus position

Fig. 6.Lift force versus current with different airgaps

2.2 Controller design

The configuration of the electromagnet suspension control loop is conceptually shown in Fig. 7. The 5 states from a filter, or observer, serve as feedback to maintain the constant airgap. The following law of determining input voltage(v) to the magnet is used here.

Fig. 7.Configuration of suspension control loop

The 5 states in (1) are airgap(G), airgap velocity(Gp), absolute position(Z), velocity(Zp) and acceleration(Zpp). The gains for the 5 states are airgap gain(kg), airgap velocity gain(kgp), absolute position gain(kz), velocity gain(kzp) and acceleration gain(kzpp). Reference gap(Ref) is trappezoidally shaped for soft lifting and landing. An accurate 5 states estimation is the most important basis for levitation control. The airgap and the acceleration of the lift electromagnet are measured to estimate the 5 states [5]. The states estimations are obtained by applying the following Eqs. (2) and (3) [5].

where,

The main method of estimating the absolute acceleration (Zpp) is to combine the measured acceleration at high frequency and the double differentiation of the measured airgap at low frequency. The reason for this approach is that in practice the measured airgap is more pronounced below a certain frequency, while the measured acceleration is more reliable at above a certain frequency. That is, a low-pass filter and high-pass filter are used for the measured airgap and acceleration, respectively. They are then combined to obtain the absolute acceleration. Based on this concept, the parameters in (2) and (3) are chosen.

Table 3 gives the parameters and gains chosen and the properties of the suspension control system. With the values in Table 3 the transfer functions of the absolute acceleration, velocity and position to the measured acceleration are analyzed by plotting Bode diagrams. In addition, the transfer functions of the airgap and its velocity to the measured airgap are also plotted. From the Bode diagrams in Fig. 9, it can be noted that in the case of gain, the absolute acceleration estimated follows the measured acceleration at above 1Hz, and in case of phase at above 10Hz. The estimated absolute acceleration gain has the form of a high-pass filter as intended. The estimated absolute velocity and position derived by integrating the absolute acceleration have the form of a band filter. The phase differences between them and the estimated absolute acceleration exceed -90°from 10Hz. The gain of the estimated airgap has the form of a low-pass filter going down from above 40Hz. These characteristics must be optimized through the choice of gain and parameters in the control loop and the properties of the suspension system and required performances.

Fig. 8.Definitions of parameters and states

Table 3.Parameters and gains in suspension control system

Fig. 9.Bode diagram for the observer

 

3. Experiments

To verify the design and control of the lift electromagnet in Chapter 2, a tester with a magnet module of 3 magnets was constructed, as shown in Fig. 10.

Fig. 10.Electromagnet Tester

3.1 Static lift force

The static lift forces measured are shown in Fig. 11 with variances in the current in the magnet coil and airgap. The lift forces from both tests and simulations are similar, especially at smaller current. It can be confirmed that the required lift force is sufficiently achieved.

Fig. 11.Lift forces measured and calculated versus current and airgap

3.2 Levitation control

The responses of airgap to ramp reference were measured with 3 different weights: 860kg, 1180kg, and 1500kg. It can be noted that all the three responses well follow the reference with a small steady-state error. The error is due to the lack of integral gain, and thus could be reduced if an integral gain were inserted into the voltage determination of (1).

One of the performance criteria of electromagnetic suspension is the capability of following a deflected guideway. Though there are several frequencies to be followed by a lift electromagnet in order to avoid physical contact with the guideway, the most important frequency is that which is due to the vehicle passing over spans of guideway. If the span length is assumed to be 25m and vehicle speed 550km/h, the vehicle passing frequency is about 6Hz. It thus follows that the control bandwidth of the control loop should exceed 6Hz. The Bode diagram made from these tests is useful for evaluating the control bandwidth. In this test, a sine sweep is used as a reference input to the control loop. Fig. 13 shows the airgap response to a sine sweep input reference. The controlled airgap follows the reference with little magnitude and phase difference. For the sake of clarity Bode diagrams are drawn from these time responses with simulations. The Bode diagram for 860kg presents the control bandwidths of 10Hz in simulation and 7Hz in the experiment, as shown in Fig. 14. The differences in control bandwidth may be due to practical considerations such as mechanical contact between parts. The control bandwidths for two 1180kg and 1500kg weights are similar to that of an 860kg load. The phase at 7Hz is about -60°, which results in it meeting the required 6Hz. The control gains and parameters determined above could be used as a basis for use for the test vehicle of Fig. 1.

Fig. 12.Controlled airgaps following a ramp reference

Fig. 13.Time response of the magnet for chirp reference

Fig. 14.Frequency response of 860kg vertical load

Fig. 15.Frequency response of 1180kg vertical load

Fig. 16.Frequency response of 1500kg vertical load

 

4. Conclusion

We feel that the detent force reduction design and control of the lift electromagnet for a super-speed attractive Maglev vehicle have been accomplished. The pole pitch arrangement of one pole per core rather than multiple poles has significantly reduced detent forces, resulting in less variation in both lift force and thrust. Consequently, it could be expected that the vibration and noise caused by dynamic interaction between the electromagnetic suspension system and guideway could be decreased. The control bandwidth was exceeded 6Hz in the dynamic response test. Hence proposed controller could be utilized in maglev test vehicle.