## 1 Introduction  
The main role of the braking system is to decrease the speed of a moving vehicle or stop the vehicle. Braking can also be used to maintain the vehicle's position in its state. During its usage, the brake absorbs the kinetic energy, and the drag force to stop the objects is provided by friction. The absorbed energy is then transformed into heat [1]. Good braking performance is crucial for maintaining vehicle speed and vehicle safety. The use of the mechanical braking system produces heat that must be released through cooling using its surrounding free air. Brakes that are used frequently can generate an amount of heat that is larger than the ability of the system to release it. The increase in heat decreases the braking performance, and a high temperature can eliminate braking forces, resulting in braking failure. The use of friction in this braking system has disadvantages. Brake components require maintenance and replacement at certain times. The service life of brake components can be increased by combining braking systems. Mechanical braking supported by engine brakes produces an excellent braking performance and leadsto the extended service life of the braking components [2; 3]. A conventional braking system generally employs a hydraulic system to generate sufficient drag force. This kind of braking system faces several problems, including a delay in braking time, wear of the brake pad, a low braking performance in the high-speed region, and bulkiness in size. Electric and hybrid vehicles have been massively produced and adopted [4; 5]. Electric vehicles show better energy efficiency and are more environmentally friendly. Different to conventional vehicles, electric vehicles employ no engine brake, and regenerative braking is adopted in order to substitute the engine brake. It is used as a support for braking and, additionally, to produce electricity [6; 7]. The generated electricity is then utilized to charge the battery. In order to solve the problems of a friction-based braking system and to provide an excellent braking performance even in the high-speed region, a contactless braking system has been developed. This kind of braking system is believed to have a longer lifetime and require less maintenance. One form of contactless braking system is the eddy current brake (ECB). The ECB is an electric braking system that employs the eddy currents principle. The main components of the ECB consist of a magnetic field in the exitation winding and brake caliper and conductor sources, as shown in Figure 1. An eddy currents is an induction current that is formed in the conductor section to produce braking force. The ECB can be combined with regenerative braking to improve energy efficiency [8]. In addition, the ECB can also be adopted as a braking support system. Furthermore, compared to using resistive loads on regenerative braking, the ECB has a superior braking performance because the torque components produced by the ECB are more effective in terms of braking performance [9]. The ECB has been widely used in various scientific and application fields. It is generally used to improve braking performance and reduce the risk of mechanical failure. It can be applied to wind turbines as a turbine speed control system, so the rotation speed can be suppressed such that it is lower than its critical speed [10]. In addition, the ECB can be used in high-speed vehicles that have a low risk of failure, such as planes and trains. There are also several studies evaluating its application in light vehicles such as cars and motorbikes [11; 12]. The improvement in ECB performance can be carried out by increasing the density of the magnetic field in the air gap. In general, inductance receives the magnetic field from one side. However, recent research shows that the use of magnetic fields from both sides can increase the magnetic field density [13]. The changes in the air gap have been evaluated in [14]. It was shown that a change in the gap effect generated the braking performance.