Dynamic stability of hingeless and bearingless rotors in forward flight

Abstract The aeroelastic stability of flap bending, lead-lag bending and torsion of hingeless and bearingless rotor blades in forward flight is examined, using a finite element formulation based on Hamilton's principle. The hingeless blade is idealized as an elastic beam, and is discretized into beam elements. Each beam element consists of fifteen nodal degrees of freedom. Between the elements there is a continuity of displacement and slope for lag and flap bending, and a continuity of displacement for twist and axial deflection. For a bearingless rotor blade the flexbeam, the torque tube and the main blade are assumed as elastic beams, and these are discretized into beam elements. Quasisteady strip theory is used to evaluate the aerodynamic forces, and the unsteady aerodynamic effects are introduced approximately through a dynamic wake induced inflow modelling. The natural vibration characteristics of a rotating blade are calculated from the finite element equations. The blade finite element response equations are transformed to the model space in the form of a few normal mode equations. These nonlinear response equations containing periodic terms are solved iteratively using Floquet theory. The periodic perturbation equations linearized about the nonlinear response position are solved for stability using Floquet transition matrix theory as well as constant coefficient approximation in the fixed reference frame. Results are presented for both stiff-inplane and soft-inplane blade configurations. Stability results are also obtained for a bearingless blade configuration consisting of single flexbeam with a wrap-around type torque tube and the pitch links located, one on the leading edge and the other on the trailing edge of the torque tube. The effects of several parameters on the blade stability are examined, including, the blade modelling, lag stiffness, dynamic inflow, constant coefficient approximation and forward speed.