Stability analysis of whirl flutter in rotor-nacelle systems with freeplay nonlinearity

Abstract

Tiltrotor aircraft are growing in prevalence due to the usefulness of their unique flight envelope. However, aeroelastic stability—particularly whirl flutter stability—is a major design influence that demands accurate prediction. Several nonlinearities that may be present in tiltrotor systems, such as freeplay, are often neglected for simplicity, either in the modelling or the stability analysis. However, the effects of such nonlinearities can be significant, sometimes even invalidating the stability predictions from linear analysis methods. Freeplay is a nonlinearity that may arise in tiltrotor nacelle rotation actuators due to the tension–compression loading cycles they undergo. This paper investigates the effect of a freeplay structural nonlinearity in the nacelle pitch degree of freedom. Two rotor-nacelle models of contrasting complexity are studied: one represents classical whirl flutter (propellers) and the other captures the main effects of tiltrotor aeroelasticity (proprotors). The manifestation of the freeplay in the systems’ dynamical behaviour is mapped out using Continuation and Bifurcation Methods, and consequently the change in the stability boundary is quantified. Furthermore, the effects on freeplay behaviour of (a) model complexity and (b) deadband edge sharpness are studied. Ultimately, the freeplay nonlinearity is shown to have a complex effect on the dynamics of both systems, even creating the possibility of whirl flutter in parameter ranges that linear analysis methods predict to be stable. While the size of this additional whirl flutter region is finite and bounded for the basic model, it is unbounded for the higher complexity model.

Bifurcation Analysis and Sticking Phenomenon for Unmanned Rotor-Nacelle Systems with the Presence of Multi-Segmented Structural Nonlinearity

“…This free body diagram is then used to derive the governing equations of motion for the coupled second-order ordinary differential equation system. The governing equations of motion, given in Equation ( 1), outline the response of the system in pitch and yaw [7,19,20,25]:…”

“…A similar wind tunnel rotor-nacelle system is considered in this study. Using the lift calculated along each blade for a specified number of propellers, and breaking them into their respective directional component in the pitch and yaw axis, the following moments in Equations ( 2) and (3) are developed [7,19,20,25,26]: The governing equations of motion, given in Equation ( 1), outline the response of the system in pitch and yaw [7,19,20,25]:…”

“…A two-degree-of-freedom rotor nacelle assembly can provide valuable insight and information on the physical nature of the aeroelastic phenomenon of whirl flutter. Most of the research on this aeroelastic phenomenon focuses on the linear structural stiffness responses and is limited to the possible existence of nonlinearities and/or freeplay in the pitch and/or yaw degrees of freedom [19][20][21][22]. In the research performed by Mair et al [19], the authors looked into the impact of nonlinear pylon stiffness on whirl flutter stability.…”

“…This study demonstrated the coexistence of stable and unstable limit cycles in the nonlinear system, while focusing on the importance of the nonlinear whirl flutter model and analysis method. Further investigation was examined by Mair et al [20] where they studied the inclusion of freeplay in tiltrotor aircraft design. The findings of the study outlined the effects of freeplay on the model complexity and deadband edge sharpness.…”

Aeroelastic Tailoring of the Next Generation Civil Tiltrotor Technological Demonstrator Composite Wing

“…If the system is not suitably stiffened and, therefore, able to dampen the oscillations, these are amplified with fatal consequences. The research today focuses on nonlinearities (e.g., free play in the tilting mechanism), and for such research purposes, more advanced models are used, which catch the rotor-nacelle system with higher fidelity and features a gimballed hub, rotor blade dynamics, and wing degrees of freedom [36]. For a gimballed hub model, a gimballed hub connects the rotor to the end of the shaft, allowing the rotor disc to pitch and yaw separately from the motion of the wing.…”