An Analytical Study of the Mechanical Stability of Two-Bladed Rigid Rotor Systems.
Research and development rept.,
DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD AVIATIO N AND SURFACE EFFECTS DEPT
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An analytical study was conducted to determine the boundaries for mechanical stability of two-bladed rigid rotors, as applied to VTOL aircraft. The two degree of freedom system consisted of a rigid rotor and shaft at constant rpm, a set of springs, and a set of dampers. The shaft was considered to be mounted on a gimbal. The springs and dampers, which were in a rotating coordinate system with the rotor and shaft, produced restoring forces when the shaft deflected from the normal, static position. Parametric equations for the stability boundaries were derived from the quartic, characteristic equation. Graphs of these boundaries are included for some of the nondimensional parameters showing their effect on the stability boundaries. The boundaries shown represent upper limits on the rotor speed ratio for mechanical stability. Damping in the system introduces the possibility of an oscillatory divergence, whereas, the non-damped system can only have a pure divergence. However, proper orientation of the damping axes eliminates the possibility of oscillatory divergence while causing the pure divergence boundary to be somewhat less restrictive. The pure divergence boundary is also made less restrictive by additional stiffness about an axis corresponding to the rotor axis of minimum moment of inertia. Stability boundaries were also obtained for a two-bladed, circulation controlled, rigid rotor. These boundaries indicated that such a system would not encounter mechanical instability if conventional mounting system techniques were employed. Author