# Characteristics of noncircular gear stepless speed regulation

Since the relevant research of gear pair entered the right track in the 17th century, many scholars at home and abroad have analyzed the tooth shape design, simulation processing and meshing characteristics of gear pair. Liang Chengcheng and others have deduced the mathematical model of gear tooth surface of forming method and generating method respectively by analyzing the mathematical model of forming wheel, and established the accurate modeling process of gear. Li Shuai et al. And Chen Xi et al. Optimized the parameters of the gear pair from the angle of coincidence degree, and analyzed the influence of coincidence degree on the meshing characteristics of the gear pair and the dynamic meshing performance of the system. In Song Dynasty, Sheng et al. Analyzed the influence of installation error on the bending characteristics of tooth root from the angle of bending stress. With the application of gear pair more and more widely, relevant scholars put forward the transmission form of non-circular gear to further expand the application range of gear pair. For pitch curve design of non-circular gears, Bair et al. And Li et al. Based on gear meshing principle, combined with Jarvis stepping algorithm and Fourier series theory, established time-varying series mathematical model of pitch curve of non-circular gears from different angles, According to the given parameters, it can carry out a certain degree of universal design, with a certain degree of accuracy and versatility. Tong Ting et al. And Qiu et al. Discussed the design method of closed pitch curve of non-circular gear, and solved the problem of solving the tooth profile of non-circular gear with concave pitch curve. Li Jiangang et al. And Li et al. Proposed a numerical calculation method of non-circular tooth surface discrete coordinate points based on the idea of tooth surface discrete. At the same time, the undercutting and tooth tip sharpening of non-circular gear were preliminarily explored, the theoretical judgment equation of tooth undercutting was established, and the evaluation index of tooth undercutting was given.

Because the pitch curve of non-circular gear is arbitrary, its motion characteristics are different from that of conventional cylindrical gear pair. Based on the mechanism diagram and incidence matrix theory of complex gear mechanism, penaud et al. And talpasanu et al. Established the kinematic analysis method of non-circular gear and its combined mechanism with bar mechanism. Lin Chao and others put forward a new type of non-circular gear type intermittent rotation mechanism aiming at the defects of the transmission performance of the existing intermittent rotation mechanism, and analyzed the transmission performance of the mechanism from the perspective of kinematics. By analyzing the kinematic and dynamic characteristics of the meshing transmission of non-circular gears, Yang Cun can not only solve the design problems, but also optimize the design, eliminate or reduce the inertial force generated by the components, reduce the mechanical vibration, reduce the noise pollution, and improve the working performance and service life of the whole mechanical system, It provides a reliable and effective research method for the design and development of non-circular gear.

The above research mainly focuses on the theoretical design of non-circular gear and the influence of parameters on the motion characteristics. At the same time, there are few related applications, only combined with the guide bar mechanism, which has been applied more simply. Based on the speed ratio characteristics of non-circular gear, aiming at the limitation of load-carrying capacity and low transmission accuracy of the belt type continuously variable transmission mechanism commonly used in vehicles, a non-circular gear stepless speed regulation mechanism with full gear mesh is designed, which expands the application scope of non-circular gear and continuously variable transmission mechanism. Based on the closeness of pitch curve, the reverse design method of non-circular gear pitch curve is proposed by using the method of multi segment construction; The matching relationship among the number of branches, the speed ratio range and the angle range of the non-circular gear is established, and the correctness of the design of the non-circular gear and the stepless speed regulation mechanism is verified by the ADAMS simulation experiment. 