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Théorie des bifurcations appliquée à l'analyse de la dynamique du vol des hélicoptères

Sébastien Kolb 1
Abstract : This study aims at exploring the interest of using bifurcation theory to analyse concretely helicopter flight dynamics.
A state-of-the-art allows to show how the methodology was applied with success in the case of fixed-wings aircrafts flight dynamics and presents some phenomenons highly nonlinear coming from the helicopter world.
The first step is to set up the issue. Informatical works end up with the coupling of the HOST code of helicopter flight mechanics from EUROCOPTER and the ASDOBI code of dynamical systems analysis from ONERA. An analytical helicopter model absolutely dedicated and adapted to this application is also developed. Moreover, it is shown that the required mathematical formulation of the evoked problems is based on a differential algebraic system representation.
In a second step, three illustrative cases of this approach are studied. Firstly, the aerodynamic instability due to the vortex rings formation at the rotor periphery in some flight cases is analysed and bifurcations of real eigenvalues are diagnosed. A new criterion to delimit the region of instability is given by the calculation of the locus of these bifurcations. Then, the case of the Dutch roll is examined showing that the underlying (supercritical) Hopf bifurcation turns out to give rise to stable limit cycles. Finally, the study is interested in aircraft-pilot coupling. Pilot induced oscillations are determined for the chosen command channel. Saddle-node bifurcations of limit cycles and jumps of periodical orbits corresponds to the handling qualities cliffs observed.
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Submitted on : Wednesday, December 19, 2007 - 3:47:28 PM
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Sébastien Kolb. Théorie des bifurcations appliquée à l'analyse de la dynamique du vol des hélicoptères. Mathématiques [math]. Institut National Polytechnique de Grenoble - INPG, 2007. Français. ⟨tel-00199793⟩

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