Understanding rotor flapping behaviour in autorotation using bifurcation and analysis tools

Aeromechanical stability of a rotor in autorotation is a complex nonlinear phenomenon which involves interactions between almost all the sources of nonlinearities, namely; aerodynamic, kinematics, inertial and material property nonlinearities. The fact that the rotor speed is continuously changing in autorotation means that existing methods used in studying the flapping stability of helicopter rotors are not adequate. It is, therefore, the objective of this study to show how bifurcation and continuation analysis tools can be adapted to understand the flapping behaviour of such a rotor. In autorotation, the rotor provides a physical example of self sustained oscillations where blade dynamics are allowed to vary instantaneously in response to the flow excitations. This means that the all the solutions of the system are periodic. The aim of the analysis is to identify the critical parameters governing blade stability; this is achieved by modelling a rotor in autorotation at different levels of complexity and assessing the rotor behaviour using the aforementioned methods. The results yield conditions for bifurcations from stable behaviour and allow this to be understood in the context of parameter changes to the physical system.