Determination of operating conditions of parametric instability is crucial to the design and usage of the inertia asymmetric rotor. Current research mostly focused on the rotor with single inertia asymmetric disk. There are few studies on the multi-disk rotors with multiple inertia asymmetries. In fact, the interaction between the multiple parametric excitations with various phasing and amplitude, which are induced by the multiple unsymmetrical disks, would make the instability behavior of the system differ distinctly from that of the single-disk rotor system. Thus, the parametric instability of the two-disk rotor system with two inertia asymmetries is studied herein. Two important indicators for describing the unstable regions, namely the unstable rotating speed and width of the unstable region, are defined and derived using the parametric instability theory and Taylor expansion technique. For a practical used two-disk unsymmetrical rotor, three design parameters (inertia excitation phasing, relative position of the disk, and inertia ratio) are discussed in detail for their effects on the two indicators. It is shown from the results that the dynamic instability of the two-disk unsymmetrical rotor system indeed has some unique features that differ from that of the one-disk rotor system. The interaction of the two inertia parametric excitations could be utilized to control (or enhance) the unstable regions.
Modal Analysis of Asymmetric Rotor System Using Simple Model