New method of modeling the actuation dynamics of a miniature hingeless helicopter using gyroscopic moments

For years, the puzzling cross-coupled responses between the control axes on the hingeless helicopters have long been haunting researchers. Different from previous works that underestimated the gyroscopic moments as a minor off-axis cross-coupling and misinterpreted the precession phenomena on the rotors of the hingeless helicopters as a phase-lag which is physically meaningless, this paper proposes a new method to relate both on-axis and off-axis responses by the influential gyroscopic moments through the actuation mechanism of the hingeless helicopters. Therefore, by this new method the debatable cross-coupling due to actuation dynamics can be directly and analytically quantified. This method is based on the fact that when the angular momentum of the spinning rotor is disturbed by the incremental lift along the main blades due to the varying cyclic pitch angle controlled by the servo mechanisms, the off-axis moments are induced to counteract the changes of the angular momentum according to the principle of gyroscope, and hence these gyroscopic moments directly exhibit the on-axis responses. This new method yields a parametric framework to examine the previously unexplained cross-coupled responses on the hingeless helicopters, and it shows that in hingeless helicopters except the aerodynamics the intricate nonlinearities are also attributed to their unintuitive actuation mechanisms. Finally, simulations as well as experiments have been carried out to validate the proposed modeling method.