Resonance and stability of piezoelectric herringbone gears under time-delay feedback

This study innovatively investigates the resonance characteristics and stability evolution mechanisms of piezoelectric webbed herringbone gears under time-delay control. A nonlinear dynamic model incorporating time-delay feedback control is proposed for the herringbone gear system. The amplitude-frequency response characteristics of both primary resonance and 1/3 subharmonic resonance are analytically investigated using the multiple-scale method. The results demonstrate that the appropriate selection of displacement gain g₁ and velocity gain g₂ can significantly suppress resonance amplitudes, although parametric sensitivity intensifies under high-frequency excitations. Optimal matching of time-delay parameters t_d and t_v can effectively improve dynamic performance, whereas mismatching may lead to system instability. The influence of meshing damping η and load fluctuations e^∗ on resonance characteristics exhibits significant frequency dependence. This study provides the first theoretical framework and parameter optimization guidelines for the time-delay vibration reduction design of piezoelectric webbed gear systems.