Determination of Critical Speeds and Divergence Instability Boundary for a High- Speed Double- Helical Planetary Gear System

Abstract

High-speed planetary gears, or more generally, gyroscopic systems are not preserve energy and therefore subjected to instability. In this research, the dynamic equations for double- helical planetary gear system in 3-D space and considering 6-DOF for each member are extracted. Then, the system stability in the range of critical speed is investigated. In the extraction of equations, the constant mesh stiffness is assumed and the gyroscopic effects due to rotating carrier are considered. The critical speeds of gyroscopic systems occur at speeds in which one or more natural frequencies are zero. To calculate the critical speeds, the eigenvalue problem of the system is solved by numerical methods. In order to validate the equations and the process of extraction of critical speed, the obtained results for a high-speed spur planetary gear system are compared with the results of the existing research. Finally, by plotting the variations of the real and imaginary parts of the Eigenvalues of the double-helical planetary gear system versus a range of carrier speeds investigate the system stability near critical speeds. The results of the current study indicate that the double- helical planetary gear system is stable at some critical speeds and in others subjected to divergence instability.