Nonlinear stability analysis of whirl flutter in a rotor-nacelle system

Abstract

Whirl flutter is an aeroelastic instability that affects propellers/rotors and the surrounding airframe structure on which they are mounted. Whirl flutter analysis gets progressively more complicated with the addition of nonlinear effects. This paper investigates the impact of nonlinear pylon stiffness on the whirl flutter stability of a basic rotor-nacelle model, compared to a baseline linear stiffness version. The use of suitable nonlinear analysis techniques to address such a nonlinear model is also demonstrated. Three types of nonlinearity were investigated in this paper: cubic softening, cubic hardening and a combined cubic softening-quintic hardening case. The investigation was conducted through a combination of eigenvalue and bifurcation analyses, supplemented by time simulations, in order to fully capture the effects of nonlinear stiffness on the dynamic behaviour of the rotor-nacelle system. The results illustrate the coexistence of stable and unstable limit cycles and equilibria for a range of parameter values in the nonlinear cases, which are not found in the linear baseline model. These branches are connected by a number of different bifurcation types: fold, pitchfork, Hopf, homoclinic and heteroclinic. The results also demonstrate the importance of nonlinear whirl flutter models and analysis methods. Of particular interest are cases where the dynamics of the nacelle are unstable despite linear analysis predicting stable behaviour. A more complete stability envelope for the combined model was generated to take account of this phenomenon.

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

“…12, crucially both the bowtie LCO and the double main branches are attached to the zero main branch, and there is no homoclinic bifurcation connecting the bowtie LCO to the whirl flutter branch from each double main branch. In [31], this bowtie LCO was demonstrated through time simulations though no analysis of any kind was conducted.…”

“…CBM is selected for obtaining results as it enables comprehensive exploration of a range of nonlinear system steady-state behaviours, while identifying the bifurcations that interlink the branches of various solution types. The authors have previously used CBM to explore the effects of polynomial stiffness nonlinearities on the whirl flutter stability of a basic rotor-nacelle system [28,29], and a higher complexity gimballed rotor-wing model [30]. In all cases, the effects of the nonlinearities were complex, though a recurring finding was the possibility of flutter behaviour when linear analysis predicted stability.…”

“…It is, however, completely distinct from freeplay, which is a non-smooth nonlinearity that arises inherently in mechanical interfaces and joints, and is exacerbated by cyclic loading. A preliminary investigation of the effects of freeplay on the aforementioned basic model was presented in [31]. The work constitutes initial exploratory research and motivates a more systematic and structured analysis which is conducted in this work.…”

“…The work constitutes initial exploratory research and motivates a more systematic and structured analysis which is conducted in this work. Crucially, [31] suggested that model complexity was an axis of investigation that could provide an understanding of the effects of freeplay in tiltrotor aeroelastic systems. Although the basic model's stability boundary was redrawn to take account of the whirl flutter behaviours found by CBM, it is, however, only in this article that both the basic model and the gimballed hub model are analysed, and in greater depth: the newly presented analyses of the gimballed hub model are substantially more comprehensive.…”

Parametric whirl flutter study using different modelling approaches

“…[16] used multibody simulation to study the effect of nonlinear spring stiffness on a whirl flutter wind tunnel model using linearisation and nonlinear time simulation. Mair et al used nonlinear analysis techniques like bifurcation and eigenvalue analysis to demonstrate the effect of nonlinearities for tilt rotor gimbal stiffness [18] and propeller pylon stiffness [19] using analytical models. They concluded that in some cases there can be areas for pylon (or gimbal) stiffness which are unstable in the non-linear case but predicted as stable by the linear methods.…”