## 2 Tubular Permanent Magnet Actuator (TPMA) Specifications  
A schematic diagram of an active lateral secondary suspension system is shown in Figure 1. In the design, the electromechanical (EM) actuator is installed between the car body and the bogie. Using a spherical rubber joint consisting of a connecting rod and high-stiffness rubber, the stationary part of the actuator is connected to the bogie, and the moving part is connected to the interface bolster under the car body. Two EM actuators are installed at each end of the car body. The size, bandwidth, thrust, stroke, and allowable temperature make up the specifications of the TPMA for active lateral secondary suspension. These specifications must be clearly defined to utilize the active lateral secondary suspension effectively. The size specifications were determined by considering the size of the prototype test bogie and bolster to be developed for the railway vehicle with active lateral secondary suspension. The stator outer diameter and axial length were set to 200 mm and 1000 mm, respectively, by considering the available space between the bogie and the interface bolster where the TPMAs were installed, as shown in Figure 1.  
In a railway vehicle, the ride comfort of passengers is decreased by vibration disturbances. There are two different methods that can be used to evaluate the effect of active lateral secondary suspension: Wz and ISO [3; 27]. In the Wz method, 3-7 Hz is the sensitive range for lateral vibration, and the 0.6-2 Hz component of lateral vibration has a large influence on ride comfort in the case of ISO 2631 [28]. To reduce the lateral vibration of a railway car, a high thrust force is required to move the car body, which weighs dozens of tons, and a low cogging ripple is necessary to provide excellent servo characteristics. The design must achieve the thrust goal under conditions that do not exceed the allowable temperature, and a sufficient axial stroke must be ensured to avoid failure of the railway vehicle and actuator due to sudden shocks. When traveling around a curve with a small radius at high speed, the car body tends to move laterally outward in relation to the track and bogies; thus, a quasi-static displacement arises between the stationary part connected to the bogie and the moving part connected to the car body due to centrifugal force; the moving part may collide with the stationary part, which could ultimately lead to actuator failure. To determine the target thrust force and stroke, driving tests were performed using a test train with conventional lateral passive dampers. In order to measure the behavior of the convectional passive damper, a non-contact laser sensor was installed between the car body and bogie. The relative velocity and displacement between the damper and the car body were measured. Figure 2 shows the relative lateral velocity and displacement distributions of the front and rear conventional lateral passive dampers. In real track experiments where the maximum speed of the test train was 210 km/h,  
Figure 1: Schematic diagram of active lateral secondary suspension. the lateral relative velocities were generally less than 0.05 m/s, and the relative displacements were generally less than 10 mm. However, the maximum displacement was 40 mm and the maximum velocity was 0.22 m/s. According to the real track experimental results, the stroke of the TPMA must be greater than \(\pm\)40 mm. Thus, the stroke of the TPMA was set to \(\pm\)50 mm. The maximum target thrust force was 7700 N, calculated by considering the measured maximum velocity and the damping coefficient of the passive damper, which was 35 kNs/m. As the operating temperature of the electromagnetic actuator increases, the life of the insulator decreases. If the actuator constantly operates above the maximum allowable temperature, it causes a thermal problem and the actuator will not operate [29].