## 1 Introduction  
Over the past decades, the development of micro actuators and motors for providing an efficient approach to realizing the arrival of digestive tract lesions has trigged enormous interest from both academia and industry [1; 2; 3; 4]. This is because even making use of modern advanced minimally invasive surgery, such as Endoscopic Submucosal Dissection (ESD), negative consequences, including perforation [5] and postoperative bleeding, may be induced [6; 7], thus posing a threat to the patient's life. It has been found that employing endoscopic hemostatic forceps or other surgical methods can temporarily stop bleeding; however, over 30% of patients still suffer from postoperative bleeding [8; 9; 10]. In addition, it should be noted here that ESD treatment is strictly prohibited for patients with blood clotting disorders and blood diseases [11; 12; 13]. On the other hand, chemotherapy-targeted drugs have been demonstrated to be effective for curing major gastrointestinal diseases [14; 15]. However, the traditional oral approach for taking chemotherapy-targeted drugs is prone to causing systemic allergic reactions and serious side effects [16; 17]. Therefore, there is an urgent need to develop a new and efficient approach to realizing the arrival of digestive tract lesions for local targeted applications of drugs in endoscopes.  
Currently, for the practical and safe operation of micro actuators inside the human body, two main issues still exist, including the lack of linear motion and the temperature increase when operating in the endoscopic biopsy channel [18]. In particular, the temperature rising issue induced by the thermal effect of actuators can cause overheating, giving rise to histologic damage [19; 20; 21], i.e., burns and tissue necrosis, thus making it difficult to realize long-term safe operation inside the human body. Due to their distinguished features of a high precision [22; 23], quick response [24; 25], simple structure [26; 27], and miniature size [28; 29], piezoelectric actuators have emerged as one of the promising candidates. Our recent work demonstrated the capability of a small-sized piezoelectric actuator (diameter 3 mm) being operated in an endoscopic biopsy channel (OLYMPUS, Tokyo, Japan) for releasing targeted drugs [30]. However, the operation of a piezoelectric actuator in the endoscopic biopsy channel can also yield an elevated temperature of over 42 \({}^{\circ}\)C, which has been suggested to be the safe temperature limit, resulting in a temperature rising problem, as mentioned above. Therefore, exploring an effective approach to address this issue still remains a challenge for their practical and commercial application.  
Herein, in this work, with the aim of preventing the temperature issue of our piezoelectric actuator, we propose a thermal finite element method (FEM) based on COMSOL Multiphysics software to achieve thermal analyses. Additionally, systematic work is performed to study the effect of the duty ratio on the temperature and speed of the actuator because, when the actuator is installed in the endoscope, the permanent magnet orbit is ground to a thickness of 0.35 mm, and its magnetic induction intensity is 43 mT, making it difficult to decrease the temperature by decreasing the driving voltage amplitude (the minimum driving voltage is 200 V\({}_{\mathrm{pp}}\)). Therefore, only modulating the duty ratio of the actuator is applicable to control the temperature rises of the actuator. According to the theoretical analysis and experimental results, it is found that a 60% duty ratio with a driving voltage of 200 V\({}_{\mathrm{pp}}\) can more effectively decrease the temperature rise from 44.4 \({}^{\circ}\)C to 41.4 \({}^{\circ}\)C in the first 3 min. Moreover, the temperature of the actuator is significantly reduced to around 36.6 \({}^{\circ}\)C when the duty ratio is modulated to less than 30%. Furthermore, the speed of the actuator can be well-held at a certain level, proving its safe usability for operation in the endoscopic biopsy channel.