## 1 Introduction  
With the increasing use of railway vehicles, many countries have become interested in the development of high-speed trains, as they have been proven to be an effective and economical means of transportation. However, increased train speeds cause significant vibration problems, which degrade passenger comfort and operational safety, and increase track maintenance costs [1, 2]. Because modifications and improvements to railway vehicles to reduce vehicle vibration are less costly than modifications to the track, various types of suspension systems linking the bogies and the car bodies have been studied. One method, active lateral secondary suspension, has been developed to enhance or maintain passenger comfort in the face of increased vehicle speeds and inferior track conditions [3, 4]. To apply active lateral secondary suspension, an actuator with high power density, high thrust force, and excellent servo characteristics must be installed between the car body and the bogie, to handle the heavy, floating weight of the car body and passengers. Over the last few decades, a variety of railway actuator types have been studied. Hydraulic actuators are compact and can easily be installed in the narrow spaces between the car body and the bogie [5, 6]; however, they have a low control bandwidth and are at risk of oil leakage [7, 8]. Furthermore, in order to control the force of hydraulic actuators, the hydraulic valve must be driven by an additional low-power electromagnetic actuator [9]. Moreover, a highly complex controller design is required to account for severe nonlinear dynamics of hydraulic actuators [10; 11; 12]. Although pneumatic actuators are relatively cheap and there is no liquid leakage, the controllable frequency bandwidth is restricted to 2-3 Hz and they suffer from an air consumption problem [13; 14]. Semi-active magnetorheological fluid damper can generate high yield strength, have low cost of production, require low power [15; 16]. However, the force remains dependent upon the speed of damper movement, which means that large forces cannot be produced with low speed. Electromagnetic (EM) actuators exhibit good frequency response and allow for bidirectional power flow, thus enabling both active and passive modes [9; 17; 18; 19]. In addition, EM actuators do not require continuous power, intricate control, or any fluid [20]. Among the various types of EM actuators, the tubular permanent magnet actuator (TPMA) is one of the most suitable actuators with all of the required characteristics [21; 22; 23]. Numerous studies have focused on a TPMA design to ensure maximum performance under constraints using electromagnetic and thermal analysis. [PERSON] et al. [21] developed a high force density linear actuator for active vehicle suspension, which consists of a brushless tubular permanent-magnet actuator. A thermal network model has been established using the thermal resistances derived using the governing principle of heat conduction, assuming the thermal dissipation in the machine is predominant in the radial direction. The model was used to maximize thrust density against a given set of volumetric and thermal constraints. Although these methods provide analytical means for establishing a rough temperature distribution, they require a subsequent series of assumptions and experimental verification to obtain accurate results. In particular, several thermal parameters have a large effect on the temperature distribution of a TPMA, but it is difficult to obtain these data without experiments. Some of the data regard investigation of the interface gap between components, the forced convection heat transfer coefficient, the thermal conductivities of laminated stator cores, etc. [24]. Furthermore, since the cooling effect on the housing of the actuator is not considered during the design process, the temperature distribution of the final prototype with the housing may have a large error under forced convection conditions. [PERSON] et al.