Modeling of Cross-Coupling Responses on Hingeless Helicopters via Gyroscopic Effect

The perplexing cross-coupled responses between the control axes on hingeless helicopters have puzzled researchers for years. Unlike previous studies, which introduced a physically meaningless phase-lag to account for the cross-couplings, this paper proposes a new method to relate both on-axis and off-axis responses by the gyroscopic moments through the actuation mechanism of hingeless helicopters. This new method allows investigators to directly and analytically quantify the debatable cross-coupling due to the complex actuation of the rotor. This method is based on the fact that when the angular momentum of the spinning rotor is disturbed by an incremental lift along the main blades due to the varying cyclic pitch angle controlled by the servo mechanisms, off-axis moments are induced to counteract the changes in angular momentum according to the principles of the gyroscope, and hence these gyroscopic moments directly exhibit on-axis responses. This new method yields a parametric framework for examining the previously unexplained cross-coupled responses of hingeless helicopters and demonstrates that, in addition to aerodynamics, intricate dynamic nonlinearities also occur due to non-intuitive actuation mechanisms on the rotor of hingeless helicopters. Finally, simulations and experiments were performed to validate the proposed modeling method.