# Magnetic Force Enhancement Using Air-Gap Magnetic Field Manipulation by Optimized Coil Currents
## 1 Introduction  
Electromechanical devices, such as electromagnetic actuators and electric motors, are one of the main components for automobiles, aerospace, and robotics applications. The primary design goal of the electromechanical devices might be a strong magnetic force generation in a limited device volume and mass, which means a high force density. To achieve this design goal, a magnetic field distribution is a key design factor because the strength and direction of the magnetic force are determined by the magnetic field distribution inside the devices. The magnetic field distribution inside the electromechanical devices is mainly affected by the structural shape of the device components (i.e., soft magnetic material (i.e., iron), hard magnetic material (i.e., permanent magnet), and coil) [1]. Thus, various structural optimization studies have been performed to find the optimal shape and configurations of the device components maximizing the magnetic force. The structural shape of the soft magnetic (i.e., iron) material has been optimized to maximize the magnetic force of actuators [2; 3; 4; 5] and electric motors [6; 7; 8]. The structural optimization of permanent magnet material was studied in [9; 10; 11; 12] to determine the optimal magnet shape and magnetization directions. In [13; 14; 15; 16; 17], both iron and permanent magnet materials were simultaneously designed using structural optimization techniques. In [18; 19], all three device components (i.e., iron,permanent magnet, and coil) were co-designed for maximizing the magnetic force of electromagnetic actuators. While the structural optimization techniques [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19] are certain to be an efficient approach for enhancing the magnetic force of electromechanical devices, they have a limitation that the magnetic field distribution is indirectly handled through optimizing the shape and configuration of the device components. As a technique to directly treat the magnetic field distribution, the magnetic field manipulation scheme was developed in [20; 21; 22]. In [20], the magnetic field focusing was proposed using an induced current in a periodic-ladder structure consisting of a conductivity material. Subsequently, it was shown that the focused magnetic field distribution in the air-gap enhanced the magnetic force in the normal direction of the air-gap line [21]. The force enhancement by the focused magnetic field was then experimentally validated in an actuator [22]. In these previous works [20; 21; 22], the magnetic field distribution in the air-gap was directly optimized using the induced current, and the force enhancement by the manipulated magnetic field was experimentally validated. However, passive manipulation using the induced current is limited in the resultant field distribution and force enhancement. Specifically, it has been observed that the force enhancement in the direction tangential to the air-gap line might not be available by the passive field manipulation based on the induced current. Thus, the manipulation by the induced current would not be useful for electric motors and actuators because they operate by the magnetic force in a tangential direction. Meanwhile, the magnetic field manipulation using an actively controlled external current was proposed in [23; 24; 25; 26]. In [23], a switch-mounted loop array was proposed for the active control of the magnetic field, and its analytical model was presented. In [24], the design of a programmable coil array was presented for the manipulation of the electromagnetic field. In [25], a current-controlled coil array was proposed for the magnetic field focusing. In [26], the active control of the magnetic field was implemented using multiple electromagnets. In these previous works [23; 24; 25; 26], the active manipulation of the magnetic field distribution using the external current was theoretically studied and experimentally validated for wireless power transfer, magnetic field communication, and biomedical imaging applications.