Study Group report
This is the final report on the problem of instabilities in helicopter tail rotors, brought to ESGI46 by Westland Helicopters.

Report author:
Alan Champneys (University of Bristol)

Introduction
Data from Westlands from a modal simulation of a teetered tail rotor shows instability at sufficiently high forward velocity of the aircraft. This report shows that a linearised analysis is sufficient to capture this instability, due to the small teeter angles. Detailed modelling and simulation has been undertaken of a two-degree-of-freedom model, for the teetering motion and the umbrella ‘flap’ mode of the blades.

The report shows that forward velocity enters via parametric excitation terms with frequencies once and twice per revolution. A near 3:1 parametric resonance between the teeter natural frequency and the rotor speed would appear to be responsible for the instability. The report explains this by analysing the classical Mathieu equation for the teeter degree of freedom only where the resonance tongue in question is the 3:2 resonance.

Therefore, the current ‘snapshot’ eigenvalue method within Westlands software is bound to fail to capture this instability. Instead, the report concludes, Floquet theory should be used, applied to the time-dependent system matrices.

Download 'RotorInstability.pdf' (261 Kb).