Analysis of Natural Characteristics of the Dual-Path Nutation Face Gear Transmission System

The nutation face gear transmission combines the high contact ratio of face gears with the large reduction ratio of nutation drives, making it a promising transmission solution. However, the natural characteristics of the dual-path system under multi-stiffness coupling remain insufficiently understood. A 22-degree-of-freedom bending–torsional–axial coupled dynamic model is established using the lumped parameter method, incorporating axial vibration of the face gears and torsional deformation of the input shaft. By solving the undamped free vibration equations, the natural frequencies, mode shapes and stiffness effects are obtained, and the key stiffness parameters governing lower-order modal behavior are identified. The results indicate that no rigid body modes exist, while structural symmetry leads to repeated frequencies in specific modes. The lower-order modes are dominated by torsional vibration of the input shaft. The intermediate modes are characterized by the coupled vibration of the local branch and the output face gear. The higher-order modes are dominated by the vibration of the nutation face gear and exhibit coupled characteristics. The results identify input-shaft torsional stiffness as a key parameter for lower-order modal tuning, while support stiffness mainly affects local modes and exhibits saturation behavior. This study provides theoretical guidance for resonance avoidance and load-sharing optimization.