## 1 Introduction  
With the recent widespread use of haptic devices [1], better haptic performance and more efficient linear vibration motors are in high demand, particularly in smartphones, vehicle infotainment displays, and video game controllers. Numerous studies on linear vibration motors have been conducted. [PERSON] et al. designed an integrated microspeaker and linear vibration motor, which showed better performances compared to the conventional type [2]. A horizontal linear vibrating actuator was designed to reduce the thickness of a smartphone, which represents an improvement in haptic performance compared to a vertical linear vibration actuator [3]. In addition, [PERSON] et al. proposed a novel design of a linear actuator with a large magnetic force to reduce the response time without decreasing the vibration magnitude [4]. A resonant piezoelectric vibrator was also designed by using a resonant amplification mechanism to have a high output displacement at a low frequency for haptic device applications [5]. Most of these related studies have focused more on improving motor performance without considering the influence of the magnetic flux leakage when these devices have been applied. A neodymium iron boron magnet has been widely used to obtain sufficient displacement. However, this produces strong magnetic flux leakage, which has a harmful effect on passengers who have a cardiac pacemaker or an ICD (implantable cardioverter defibrillator). The strong magnetic flux leakage may damage these medical devices and cause life-threatening malfunction [6]. According to the engineering specification when considering the above situation, the magnetic flux leakage requirement at the measurement point should be under 50 G. Furthermore, metallic dirt can easily be collected on the vehicle LCD display due to magnetic flux leakage, creating an uncomfortable experience for people using a haptic device. It is therefore necessary to reduce the magnetic flux leakage while maintaining the same performance. The motor performance requirements were decided by previous research [7; 8] with consideration for the human mechanoreceptors that are the nerve endings in the skin responsible for sensitivity to vibration and pressure [9]. The maximum displacement of a linear vibration motor is around 0.4 mm, and the range of resonance frequency is from 138 Hz to 150 Hz, while the working frequency is from 50 Hz to 500 Hz, and the electrical resistance is around 8 ohms. These requirements are enough for haptic feedback to users. The magnetic flux leakage calculation [10; 11] used for the 3D finite element method is employed to obtain the magnetic flux leakage at a certain measurement point. The voltage equation and the equation of motion are used to obtain the displacement and the impedance by considering the electromagnetic-mechanical coupling: these parameters indicate the performance of a linear vibration motor. The analysis results of the prototype were analyzed and verified based on the experimental results. The experimental results satisfied the motor performance requirements except for the magnetic flux leakage. Three types of new designs were proposed to reduce magnetic flux leakage. The first design attempted to reduce the magnet source and magnetic flux conducting path, which included the magnet grade, the magnet thickness, and the top plate thickness. However, the analysis results of the first design were unacceptable owing to the high magnetic flux leakage exceeding 50 G. To reduce the magnetic flux leakage as much as possible, the second design was developed by reversing the prototype with a lower magnet grade and a thicker top plate, limiting the reduction on the force factor to less than 5%. The second design had a new plate, a protector, and two inserted plates. There was an 87.09% reduction between the second design and the prototype without much reduction in the force factor.