Modal and whirling analysis of coupled lateral and torsional vibration of herringbone gear

Abstract

The coupled lateral and torsional motions are significant for the herringbone gear in high-speed applications. The present work attempts to investigate the influences of damping, eccentric mass and time varying mesh stiffness of gear pair on the modal vibration of a herringbone gear pair. Under high-speed condition, the gyroscopic performance as a result of coupled lateral and torsional motions cannot be ignored. To achieve a targeted analysis, the equivalent mesh stiffness of the herringbone gear pair is calculated in preprocessing based on the finite element method by considering the thin rim and web. Subsequently, an analytical model for coupled lateral and torsional motions of the herringbone gear is proposed. Then, the natural frequencies, synchronous whirling speed, critical speed, as well as the transient behaviors with time invariant and time varying stiffness, are calculated numerically. The results in Campbell diagram show that the damping affects the critical speed slightly while the eccentric mass will reduce the critical speed significantly. Transient dynamics analysis shows that no matter which stiffness models are used, the high frequency components are predominant, which may be the results of frequency veering phenomena at high order natural frequency. The present work indicates the necessity of paying attention to the critical speed relative to mesh frequency in high speed gear applications.