Development of an extremely flexible, variable-diameter rotor for a micro-helicopter
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This dissertation describes the design, analysis and testing of an unconventional rotor featuring extremely flexible, retractable blades. These rotor blades are composed of a flexible matrix composite material; they are so flexible that they can be rolled up and stowed in the rotor hub. The motivation for this study is to equip the next generation of unmanned rotary-wing vehicles with morphing rotors that can change their diameter in flight, based on mission requirements. Due to their negligible structural stiffness, the static and dynamic behavior of these blades is dominated by centrifugal effects. Passive stabilization of the flexible blades is achieved by centrifugal stiffening in conjunction with an appropriate spanwise and chordwise mass distribution. In particular, such blades are susceptible to large deformations. For example, a combination of the trapeze effect and the tennis racquet effect induces a large negative twist that results in decreased efficiency. Additionally, the rotor blades are prone to aeroelastic instabilities due to their low rotating torsional frequency, and it is seen that without careful design the blades experience coupled pitch-flap limit cycle oscillations. The primary focus of this research is to develop analytical and experimental tools to predict and measure the deformations of an extremely flexible rotor blade with non-uniform mass distribution. A novel aeroelastic analysis tailored towards unconventional blades with negligible structural stiffness is developed. In contrast to conventional analyses developed for rigid rotor blades, the present analysis assumes very large elastic twist. The nonlinear coupled equations of motion for the flap bending, lead-lag bending and torsion of an elastic rotating blade are derived using Hamilton's principle. The virtual work associated with unsteady aerodynamic forces in hover is included in the analysis. An ordering scheme consistent with the relevant physical quantities is defined and terms up to second order are retained in the Hamiltonian. The equations of motion are solved using a nonlinear finite element analysis. The steady-state deformation of the rotor blade is obtained from the time invariant part of the solution. The rotating flap, lag and torsional frequencies are found by solving the eigenvalue problem associated with the homogeneous system of equations. Finally, stability boundaries are computed for various operating conditions and the influence of parameters such as rotational velocity and collective pitch angle is discussed. The analytical predictions are validated by experimental measurements of the blade deformation in hover. These measurements are obtained by a novel, non-contact optical technique called three-dimensional Digital Image Correlation (3D DIC). The use of this technique is demonstrated for the first time to obtain full-field deformation measurements of a rotating blade. In addition, stability boundaries are extracted from experimental observations and correlated with predictions.