A vibration model of a flexible multiple shaft gear system with the tip relief modification

The fixed-shaft gear system (FSGS) is one critical part in gear transmission systems (GTSs), whose vibrations can significantly influence performances of GTSs. To reduce the vibrations of rigid FSGS caused by installation and manufacture errors, the tooth profile modifications without the shaft deformation were widely introduced. This paper establishes a flexible multiple shaft gear system (FMSGS) model of an unmanned underwater vehicle, which can obtain vibrations of rotor at different axial positions. However, the previous rigid FSGS model cannot obtain those vibrations. In the FMSGS model, the Timoshenko beam elements are applied to the establishment of shaft segments considering flexibility. The meshing stiffness for helical gears with different ranges of tooth profile modification are quantitatively expressed by a gear slicing method. Based on the kinetic relationship between the gear pairs, shaft segment, and bearings, the dynamic equations of FMSGS are derived. By comparing the time-domain waveforms and spectra of FMSGS, the effects of the tooth profile modification amounts and lengths on the vibrations of FMSGS are revealed. The proposed FMSGS model is validated by an experiment. This study extends the dynamic methods of FSGSs, and some suggestions on the vibration control of FSGSs are given.