# Design and Analysis of Novel Low-Cost Linear Vibration Motor for an Electronic Cigarette
## 1 Introduction  
Compared to traditional cigarettes, more and more electronic cigarettes (E-cigarettes) [1] are widely used, which can be useful to quit smoking. They reduce the hazardous effects of some traditional cigarettes and risk of fires, and they keep people away from carcinogens in traditional cigarettes. E-cigarettes do not need to burn but only produce an aerosol by heating the cigarettes. Vibration motors are used to remind the user that E-cigarettes are ready to operate by providing haptic feedback.  
Many studies on vibration motors have been completed. A coin-type vibration motor creates a large acceleration in the form of eccentric vibration, but it has a short product life due to wear of the bushing and bearing. [PERSON] et al. proposed a simpler structure with a longer life span by eliminating small commutation parts [2]. A horizontal linear vibrating actuator was designed by [PERSON] et al. to reduce the thickness of a smartphone and provide better haptic performance compared to a vertical linear vibration actuator. However, the specifications of horizontal linear vibration are 16.5 mm in length and 15.0 mm in width, which are too big to apply in E-Cigarettes [3].  
A new design of a linear actuator with great magnetic force was proposed by [PERSON] et al. to reduce the response time under given constraints on volume and rated power [4]. [PERSON] et al. investigated the linear vibration motor used on a liquid crystal display (LCD) display to reduce the magnetic flux leakage by employing mechanical finite element analysis and experimental verification [5]. These vibrationmotors are widely used in smartphones, tablets, and car touch screens. However, few studies have involved a linear vibration motor inside an electronic cigarette due to the size problem, and previous works do not take a dummy jig into consideration in the analysis. The acceleration of linear vibration is measured by specified equipment (a 100 g dummy jig) with a similar weight to a smartphone or E-cigarette.  
This research proposes a novel linear vibration motor with smaller size (\(\mathcal{O}\)8.0 \(\times\) 2.5 mm), higher motor performance at 250 Hz, and lower manufacturing cost due to a reduced number of fabricated parts and complexity of the manufacturing process. First of all, the comparison between coin-type vibration motor and novel linear vibration motor is discussed, including the working principle, advantages, and disadvantages. Secondly, the electrical material properties are introduced to obtain the average flux density on the voice coil considering nonlinear B-H behavior of the yoke and top plate. The mechanical material properties were used to conduct modal analysis and static analysis to obtain the resonance frequency and von Mises stress distribution on the spring, respectively. They were also used to do an electromagnetic-mechanical coupling analysis.  
Thirdly, a coin-type vibration sample, a linear vibration motor prototype, and experiment setups are discussed. The analysis results of the prototype have been verified. Based on the analysis methods, novel linear vibration motors have been developed to reduce the resonance frequency and improve the magnetic force by considering a novel spring structure and magnetic circuit optimization. Then, two novel types of linear vibration motors were manufactured to check the acceleration on a dummy jig. Both experimental results match well with the analysis results. The novel type (spring thickness = 0.13 mm) shows better acceleration performance than the coin-type vibration motor at a certain frequency range (around 250 Hz). Compared to the coin-type vibration motor, the novel linear vibration motor has a 9.09% reduction in total thickness, an 80.77% reduction in manufacturing cost, and a 40.0% improvement in acceleration at 250 Hz.