Calculating the time-varying regularity of flapping angle and hub forces based on comparison of frequency amplitudes

Abstract Helicopters are widely used in many fields nowadays. However, the higher vibration level compared with fixed-wing planes reduces ride comfort and equipment endurance. The vibration is mainly caused by the transient aerodynamic forces and flapping moment of the rotor blades, which can be useful in designing cyclic pitch control law and fuselage structure. However, the bidirectional coupling between the aerodynamic forces and the flapping angle of a rotor blade makes them difficult to calculate. This article presents a method to acquire the time-varying regularity of flapping angle, aerodynamic forces and, furthermore, hub moment. In this article, the flapping dynamic equation is solved in a stepwise iterative manner, in which an aerodynamic force is assumed and used to calculate the flapping angle, and the flapping angle is then used to calculate the aerodynamic force. This step-by-step process is performed until both the aerodynamic force and the flapping angle converge. In each iteration step, both the flapping angle and the aerodynamic moment are transformed using Fourier analysis and are substituted into the flapping dynamic equation. Then the frequency-component amplitudes on both sides of the equation are compared seriatim to calculate both the flapping angle and the aerodynamic moment. Validation is performed using both reference parameters and actual test data, and the accuracy can reach ±0.1° for simulated rotors and ±1° for actual test data.