Transfer matrix of parametric excited system for noise and vibration analyses of helical gear system

This study proposed a transfer matrix with harmonic frequencies for a parametrically excited system. The proposed transfer matrix applied to noise and vibration of a helical gear system. Gears are part of the parametrically excited system because of mesh stiffness variation. The nonlinear equation of motion for gears was linearized to an equation with the excitation of harmonic frequencies. Transfer matrix with harmonic frequencies for gear vibration was derived. The helical gear system was modeled using a shaft-bearing-circular plate with helical gears. The assembled transfer matrix of the helical gear system was obtained. Moreover, the assembled transfer matrix with harmonic frequencies was used to investigate the effects of dynamic and noise characteristics of the helical gear system owing to axial excitation. Result showed that sound-pressure level was closely related to the first-harmonic plate displacement caused by the first-harmonic axial force. Significant peaks of sound pressure were closely related to the first-harmonic component and had some peaks in the second and third components. The proposed transfer matrix can easily show the contribution of the harmonic components.