Stability Analysis Of Helicopter Rotor Flapping

The rotor blades are important parts for helicopters. The stability of dynamic behavior of the system determinates the flight quality directly. With the dynamic balance testing process, a method is proposed that building the nonlinear Duffing's flapping equation with complex aerodynamics for primary standard rotor blade. The stability on flapping and sensitivity on testing environment is analyzed in the field of chaotic threshold analysis by Melnikov method. The results have been proved by simulation and experiments.Firstly the flapping model is built and the Duffing's flapping equation for primary standard rotor blade is derived by expanding the flapping angle with the method of Taylor series, which has nonlinear terms of three power and periodical slippery damping and complex periodic excitation. The stability of the linearized system of the rotor blade is analyzed by the Lyapunov Theory. The chaotic threshold which could be lead to unstable vibrations is analyzed in terms of Melnikov method.The influence of the aerodynamic stiffness, aerodynamic damping and double-period aerodynamics perturbation on the stability of flapping equation of rotor blade is analyzed by Melnikov method. The stability on flapping and sensitivity on testing environment for flapping equation of standard rotor is also analyzed.Finally, the validity of the theoretical results is shown by the Simulink programming based on Matlab and the experiments in dynamic balance test. It indicates that the Duffing model of flapping equation, derived here, is appropriate for primary standard rotor blades. The wind speed in the process of calibration is determined for primary standard rotor blade,and the base of calibration process is settled.