On the basis of previous studies, some scholars have added the influence of other parts of the system, such as the support stiffness of bearings. Wang Allen et al. Have constructed a nonlinear bending torsional coupling model of elliptical gears based on bond graph theory. The influence law of the bending and torsional vibration of elliptical gears is analyzed. The centrifugal force and torsional inertia force produced by the eccentricity of the elliptical gear are regarded as the vibration of the system However, the influence of time-varying pitch diameter on the system vibration is ignored. Ma Qiang et al. Constructed a nonlinear torsional shaft coupling model of elliptical gear, and compared the results obtained by simulation, experiment and numerical analysis. With the rapid development of NC machining technology, spatial non-circular gear pair with more complex structure appears. Lin established a bending torsion shaft coupling dynamic model of curved surface gear, as shown in the figure, and analyzed the influence of system parameters and external excitation on vibration.
The above-mentioned scholars mainly focus on single pair of noncircular gears, while the following scholars have carried out in-depth research on the non-circular gear train with more complex and changeable dynamic characteristics. Ogawa et al. Have carried out theoretical analysis and Experimental Research on the non-circular gear planetary gear train mechanism and investigated the dynamic response of the mechanism under specific working conditions In this paper, the dynamic performance of non-circular gear planetary gear train was studied, and the gear response under specific conditions was obtained by experiments By combining theory and experiment, the authors studied the elastic dynamic performance of transplanting mechanism with plane elliptic gear planetary gear train, and put forward an effective research method of noncircular gear train; Wei Shuang et al. Solved the torsional dynamics of Non-circular Planetary gear hydraulic motor by numerical method, and analyzed the influence of clearance on the dynamic characteristics of noncircular gear system.
From the research results, it can be seen that the characteristics of the time-varying instantaneous center and the structural form of the non-circular gear have a great impact on its vibration. In addition, the dynamic model of the non-circular gear is more complex than that of the circular gear. Many scholars have studied the dynamic equation solving methods of the mechanical system with non-circular gear It is difficult to analyze the relationship between gear dynamic characteristics and system parameters.
Based on the analysis of the instantaneous center excitation, a dimensionless dynamic model of the gear with / without backlash is established. The approximate analytical solution of the gear dynamic equation is obtained by harmonic balance method. The influence law and sensitivity of the system parameters on the vibration are analyzed emphatically The dynamic design and optimization of gear has certain guiding significance.