The existing research on the dynamics of noncircular gears can be roughly divided into two categories: rigid dynamics and elastic dynamics.
In the first category, the elasticity of non-circular gear teeth is ignored, and the influence of variable ratio transmission of non-circular gear on the dynamic characteristics of the system is mainly considered, that is, the rigid body dynamics of non-circular gear. Okada et al. Considered the dynamic characteristics of the bouncing robot driven by non-circular gears, optimized the gear transmission ratio to meet the requirements of high torque and high-speed; Chen et al. Established the dynamic model of transplanting seedlings with denatured elliptical gear by using ADAMS, but did not consider the influence of time-varying torque excitation; pan et al The dynamic model of eccentric noncircular gear crank rocker weft insertion mechanism was constructed, and the dynamic performance of the mechanism was analyzed emphatically, which provided a theoretical basis for the design and optimization of the dynamic parameters of the gear; Wang Ying et al. Established the dynamic optimization model of the eccentric elliptic gear planetary gear train mechanism, optimized it, and proved its dynamic credits through experiments This paper analyzes the reliability of the model; oleksii Karpov et al. Applied non-circular gear to the vibration suppression of gear mechanism; Hu Ziyang et al.  combined non-circular gear and crank slider mechanism to apply it to the main transmission mechanism of horizontal flow pump, and verified the feasibility of theoretical design through simulation, which effectively suppressed the fluctuation of pump pushing speed; Li Hongxun et al Matlab optimized and analyzed the design parameters of the non-circular gear CVT, realized the optimization goal of reducing the maximum adjusting torque of the phase adjusting device, and gave full play to the excellent performance of the transmission; Xu et al carried out the coupling dynamics numerical calculation and Experimental Research on the differential vane pump driven by the non-circular gear, and optimized the dynamic performance of the differential vane pump; Yu et al Aiming at the problem of low efficiency of transplanting seedlings in dry land in our country, a kind of non-circular gear transmission planetary gear system rotation seedling picking mechanism with incomplete eccentric circular gear and non-circular gear combination was designed by using the optimization parameters obtained by human-computer interaction optimization method and optimization software, and the indoor seedling picking test was carried out; ye Bingliang and others used the dynamic static analysis method and dynamics The dynamic model of rice bowl seedling rotation transplanting mechanism was constructed by solving the equation group sequence method, and the model was optimized, analyzed and designed. The above researchers all think that the non-circular gear is the rigid contact without backlash, so it is called the non-circular gear rigid dynamics research.
In the second category, the influence of the comprehensive stiffness excitation caused by the tooth elasticity on the dynamic behavior of the non-circular gear is considered. The tooth of the non-circular gear is considered as the elastic contact, and the internal excitation such as the comprehensive stiffness excitation, the error excitation and the meshing impact excitation exist in the non-circular gear. Zhang Aimei et al.  replaced non-circular gear locally with circular gear, and deduced a convenient and practical non-circular gear model by using the principle of boundary continuity, and preliminarily analyzed and discussed the solution of the dynamic model of non-circular gear, but did not consider the influence of time-varying stiffness excitation; Liu Dawei et al. Established a non-circular gear considering multiple system parameters based on the elastic angle separation method For pure torsional vibration model of wheel, the vibration response of non-circular gear under different parameters is solved by numerical method; Zhang Guofeng and others put forward the sequential solution method of dynamic equations to improve the solution process of dynamic equations of elliptic gear, but the nonlinear relationship between driven wheel angle and driving wheel angle is ignored in the process of establishing dynamic equation; Dong Changbin established time-varying meshing stiffness and static state In this paper, the nonlinear dynamic model of elliptic gear with the factors of state transfer error and backlash is analyzed, and the nonlinear vibration characteristics of the elliptical gear are analyzed. The dynamic characteristics of the non-circular gear are studied through the simulation and modal analysis of the non-circular gear, but the influence of time-varying stiffness and torque excitation is not considered. Chen Jianneng et al. Has a good understanding of the dynamic characteristics of elliptical gear A lot of research work has been done through theory and experiment, and the influence of time-varying stiffness and moment excitation is not considered. Zhang Hongwen applies the finite element theory of elasticity and adopts CosmosWorks, a finite element analysis software Through the modal analysis of elliptical gear, it is concluded that eccentricity has great influence on the natural frequency of elliptical gear; Yan Zhaochao and others have carried out parametric modeling and finite element modal analysis of elliptical gear pair, and obtained the results Based on the study of the natural frequency of the elliptical gear, Huang Zhidong et al. Gave the selection range of the eccentricity of the elliptical gear Then, the theoretical analysis is carried out, and the theoretical model of the gear is constructed. Through the theoretical analysis, the structure of the numerical analysis and the experimental results are compared to verify the correctness of the theoretical analysis results This paper focuses on the study of virtual simulation model of non-circular gear, puts forward a good dynamic design model construction method, and constructs the dynamic model, as shown in the figure. A variety of gear dynamic parameters are simulated and analyzed, and compared with the analysis results of traditional circular gear, the correctness of the new gear model construction method is verified.