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The influence of freeplay on the whirl flutter and nonlinear characteristics of rotor-nacelle systems

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Abstract

Rotor-nacelle systems are susceptible to aeroelastic instabilities, such as whirl flutter, which is affected by structural and/or aerodynamic nonlinearities. This phenomenon can lead to structural fatigue and possible failure in propeller-driven aerodynamic systems. A nonlinear reduced-order model using quasi-steady aerodynamics for a rotor-nacelle system is considered to study the effects of whirl flutter and structural freeplay nonlinearity on the performance of rotor-nacelle systems. The results of the freeplay with various gap sizes and stiffnesses are explored in the dynamical responses of these rotor-nacelle systems. A particular focus is paid to the interaction between the freeplay nonlinearity and inherent structural nonlinearities in the system's degrees of freedom. First, several polynomial nonlinearities considering a two-degree-of-freedom rotor-nacelle model are tested to research possible structural nonlinear effects with freeplay. Results show that the gap size affects the bifurcation diagrams resulting in a variation in the oscillation amplitudes with period-adding behaviors. The characterization of one specific case is considered, deeply investigated, and discussed. For particular transition points, characterizations are analyzed using the time histories, power spectra, phase portraits, Poincaré maps, and basin of attraction. Lastly, case studies are performed to determine the impacts of freeplay, structural nonlinearities, and particular parameters on the system’s dynamics (i.e. blade length, chord length, rotor moment of inertia, nacelle moment of inertia, and number of blades). Based on the result found, the six-blade propeller case is selected and studied as a case of interest, where complex and period-adding behavior are uncovered.

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Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

\(a\) :

Ratio of pivot length to rotor radius

\(A_{i}\) :

Various aerodynamic integrals that arise from the total in-plane forces and moments

\(\beta\) :

Velocity ratio of freestream velocity to velocity at the blade

c :

Blade chord length

\(C\) :

Damping matrix

\(c_{K,a}\) :

Consolidation of terms

\(c_{l,\alpha }\) :

Sectional blade lift slope

\(C_{\psi }\) :

Structural yaw damping

\(C_{\theta }\) :

Structural pitch damping

δ :

Freeplay gap size

\(F_{\psi }\) :

Moment about the pivot of yaw

\(F_{\theta }\) :

Moment about the pivot of pitch

\(\gamma\) :

A local spanwise coordinate over the length of the element

\(I_{n}\) :

Nacelle moment of inertia

\(I_{x}\) :

Rotor moment of inertia

\(J\) :

Jacobian matrix

K :

Stiffness matrix

\(K_{\psi }\) :

Structural yaw stiffness

\(K_{\theta }\) :

Structural pitch stiffness

\(N_{B}\) :

Number of blades

\({\Omega }\) :

Rotor angular velocity

\(\rho\) :

Air density

R :

Rotor radius

\(\psi\) :

Angular deflection off the off the y–z-plane

\(\dot{\psi }\) :

Angular velocity off the y–z-plane

\({\uptheta }\) :

Angular deflection off the off the x–y-plane

\(\dot{\theta }\) :

Angular velocity off the x–y-plane

V :

Freestream velocity

\(V_{tip}\) :

Velocity at the tip of the propeller blade

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Acknowledgements

The authors A. Quintana and A. Abdelkefi acknowledge the financial support from New Mexico Space Grant Consortium. The idea of this work was presented in the 2022 SciTech conference and a short conference paper containing preliminary results were published in the conference [45].

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM, USA

    A. Quintana, B. E. Saunders & A. Abdelkefi

  2. Sao Paulo State University, São João da Boa Vista, Brazil

    R. Vasconcellos

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Quintana, A., Saunders, B.E., Vasconcellos, R. et al. The influence of freeplay on the whirl flutter and nonlinear characteristics of rotor-nacelle systems. Meccanica 58, 659–686 (2023). https://doi.org/10.1007/s11012-023-01658-1

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