Parametric Instability of Face-Gear Drives due to Meshing Loads

We investigate the parametric instability behavior of face-gear drives with a spur pinion by modeling face-gear and pinion tooth geometry and kinematics. The out-of-plane dynamics of the face-gear are excited by periodically time-varying gear tooth meshing load variations. Here an annular spinning Kirchhoff plate with centrifugal stiffening effects and a meshing load unit with prescribed movements are used to model face-gear drive, and Floquet theory is employed to determine the system stability. Additionally, we consider the maximum bending stresses at the root of pinion tooth to restrict the face-gear size. Tregold's approximation is utilized to calculate the contact ratio of face-gear drives. Finally, an example of prototype helicopter face-gear drives is studied at different operating speeds and meshing loads. The results characterize the parametric instability regions as a function of rotation speed, meshing load, and face-gear disk thickness. Moreover, the minimum critical thickness to sustain the system stability over the entire operating speed region is determined as well. These analyses and results provide novel and important insights into the dynamics and design of the lightweight face-gear drives.