Abstract: The flexible planetary ring gear is taken as the research object. In order to formulate a more accurate mathematical model in compliance with common engineering practices, the tension, transverse shear, and bending deformation, of the ring gear are considered. According to the structure and boundary, vibration analysis model for flexible spur ring gear with elastic foundation is established by using the plane beam element, and the inherent characteristics are investigated. Based on the superposition principle and force to a point translation theorem, the combined excitation apporach is appled to simulate the meshing excitation acting along the line of action. Effects of meshing excitation on the vibration response of flexible ring gear is revealed from the frequency domain. The results indicate that, the vibration type of flexible ring gear with elastic foundation can be divided into three categories:Translational vibration mode (each point of the ring gear has the same motion), flexural vibration mode (the ring gear occurs vibration of bending deformation), and extensible vibration mode (each point of the ring gear has only radial vibration). The meshing excitation has a slight impact on extensible vibration mode, while it influences the flexural vibration mode apparently. For the spur ring gear, flexural vibration mode is the main cause of vibration and noise. When extensible vibration mode (wave number m=0) occurs resonance, each point of the ring gear has equal vibration amplitude. When the ring gear occurs resonance and the wave number m is not zero, the ring gear has m waveform.

Key words: elastic boundary, inherent characteristic, planetary gears, ring gear, vibration response