Parametric Instability of a Rotating Circular Ring With Moving, Time-Varying Springs

Parametric instabilities of in-plane bending vibrations of a rotating ring coupled to multiple, discrete, rotating, time-varying stiffness spring-sets of general geometric description are investigated in this work. Instability boundaries are identified analytically using perturbation analysis and given as closed-form expressions in the system parameters. Ring rotation and time-varying stiffness significantly affect instability regions. Different configurations with a rotating and non-rotating ring, and rotating spring-sets are examined. Simple relations governing the occurrence and suppression of instabilities are discussed for special cases with symmetric circumferential spacing of spring-sets. These results are applied to identify possible conditions of ring gear instability in example planetary gears.