According to the principle of nutation, various nutation mechanisms have been designed and studied from the aspects of structure analysis, transmission characteristics and dynamics analysis. Fanghella et al. Studied the static and dynamic force balance of the designed nutation drive reducer, and carried out the simulation analysis. Frank designed a stapler for medical surgical equipment based on Nutation principle. The dynamic analysis of input shaft and nutation disk in nutation drive is carried out by Itzhak. Based on Nutation principle, uzuka et al. Designed nutation drive devices of different forms, such as nutation magnetic motor and nutation pneumatic motor. Nelson et al. Studied the similar kinematic characteristics of different nutation mechanisms, and used the concept of “equivalent” gear mechanism to analyze the kinematics, force and efficiency of a new swing reducer. Yao Ligang and others designed two-stage double circular arcnutation drive reducer and magnetic nutation drive reducer, and made in-depth research on the transmission ratio calculation formula, tooth surface meshing equation, dynamic analysis and simulation, and structural design of the two-stage nutation transmission mechanism. Wang Guangxin et al. Designed the nutation face gear transmission with conjugate Meshing Based on Nutation principle, and carried out three-dimensional modeling and dynamic meshing force simulation analysis of the transmission system. Yu Yibin introduced nutation into gear transmission and analyzed the calculation method of gyroscopic torque in cone difference nutation transmission based on dynamic theory. Li Yanmin et al. Designed a new type of ball mill based on Nutation principle, and analyzed the key parameters affecting the performance of nutation ball mill. Most of the existing nutation mechanisms of bevel gears are two-stage nutation transmission system. Although they can provide large transmission ratio, there are many problems such as more parts, complex meshing process of two pairs of gears and unstable dynamic characteristics in the transmission process. Therefore, it is of great significance to design a single-stage nutation reducer with simpler structure and more stable transmission.
According to nutation transmission principle, the nutation reducer of single-stage double circular arcis designed. Taking the minimum volume of nutation reducer as the objective function, the optimization model is established, and the relevant parameters of single-stage nutation bevel gear are obtained. Based on the establishment of nutation bevel gear three-dimensional model, the finite element loading strength analysis is carried out to provide a theoretical basis for the subsequent structural improvement.
(1) According to the nutation motion principle of coin rotation, a new single-stage nutation reducer of bevel gear is designed, and its transmission ratio formula is obtained. The bevel gear is driven by double circular arc spiral bevel gear.
(2) Taking the minimum volume of nutation reducer as the objective function, the optimization mathematical model is established. The optimization model includes 4 design variables and 12 optimization constraints. The parameters of single-stage nutation bevel gear are obtained by lingo software.
(3) Based on the establishment of three-dimensional model of single-stage nutation bevel gear, the finite element loading strength analysis is carried out. According to the analysis results, it can be seen that there are multiple teeth contacting at the same time in single-stage nutation bevel gear, and there is a meshing contact trace on the concave and convex tooth surfaces, and the tooth surface contact area is large; the Mises stress distribution is relatively uniform, but the stress value of the outer bevel gear at the small end of the tooth top is large, so it is necessary to modify or improve its structure in the future.