# Study on Beat Vibration of a High Temperature Superconducting EDS Maglev Vehicle at Low Speed
## 1 Introduction  
A maglev (magnetic levitation) train can travel along tracks without mechanical contact with the ground; it has the advantages of high speed, low noise, low carbon emissions, and a high degree of safety to meet the requirements of future transportation systems [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Various maglev systems, including electro-magnetic suspension (EMS), electro-dynamic suspension (EDS), and high-temperature superconducting (HTS) pinning maglev, have been developed and tested in Germany, Japan, South Korea, and China for more than 50 years [1; 2; 3; 4; 5; 6]. The EDS system was introduced by [PERSON] and [PERSON] [7], where null-flux figure-eight-shaped coils were built on both sides of the guideway for levitation and guidance. EDS trains have large suspension air-gaps of above 10 cm compared with EMS trains; they also have a better running safety when climbing, going downhill, or under subgrade deformation [8; 9; 10]. The low-temperature superconducting magnet-null-flux coil EDS system was first developed in Japan in the 1980s [8; 9]. Thanksto the efforts of Japanese scientists, the JR maglev was found to be able to travel at a high speed of approximately 603 kmph in 2015. A large amount of research has been carried out to study the dynamic performance of the JR maglev system [8; 9; 10; 11; 12; 13; 14; 15; 16]. [PERSON] [9] studied the mechanical model of the EDS system based on the dynamic circuit theory. Since the damping is too small, efforts were also carried out to improve the damping effect [10; 11]. Because a guideway will always be used, experts should also consider the dynamic interaction between a vehicle and guideway [12; 13; 14]. At the same time, experts should also study a vehicle's dynamic performance under accident conditions, such as with a quenched SC coil [15; 16], and conduct enough running tests [17] to guarantee the vehicle's safety. Generally, the levitation force, guiding force, and drag force, which are generated between ground coils on the ground and the SCM on board, are dependent on the velocity and position of a vehicle [18; 19] and other electric parameters. When predicting a vehicle's dynamic performance, there are two methods which are commonly used. The first method to determine the vertical performance is based on vibration theory with one degree of freedom (DOF) [9], where the magnetic force is calculated first. However, with this method, the pitch angle of a vehicle is ignored. To overcome this shortcoming, the second method [13] considers the full dynamic coupling of magnetic forces, the current, the magnetic field, the movement of a vehicle, and even flexible bodies. However, the calculation of these forces is quite time consuming. Recently, the CRRC Changchun Railway Vehicles Co., Ltd. (Changchun, China) developed a new 200 m straight test line with a high-temperature superconducting EDS maglev vehicle, as shown in Figure 1, unlike the Japanese low-temperature superconducting EDS maglev vehicles. There are eight HTS fixed on both sides of the vehicle. To solve any practical problems in the whole system from low velocity to high velocity step by step, a test vehicle was designed to run at a low velocity of approximately 14 mps to ensure the vehicle's safety. When all problems are solved at a low velocity, the test line can then be upgraded to run at a higher speed to uncover the new phenomenon of the system. It is particularly difficult to make the vehicle run at a rated velocity because the experimental test is limited by the traction system, current SCM, initial vertical displacement, and so on. The vehicle is clamped by four guiding wheels and is in a planar motion. When running at 13.7 m/s (mps), both the vertical displacement acceleration and pitch angle show the phenomenon of beat vibration, as shown in Figure 2. Currently, experimental records show this unexpected phenomenon of beat vibration, which has not yet been reported in other literature despite the low velocity value.