Stability analysis of time-periodic systems using multibody simulation for application to helicopters

Helicopters are rotating systems with time-periodic characteristics. It means some parameters of the system, e.g. aerodynamic forces, change periodically during the one revolution of a rotor blade. There are simulation tools like “CAMRAD II” for modelling and analysing of any type of rotor-craft like helicopters or tilt-rotors. However, these tools are often limited for a range of special tasks. The aim of this paper [1] is to investigate the multibody simulation tool “SIMPACK” for the stability analysis of a rotating system. Stability or instability is related to the behaviour of a system in the equilibrium state due to a small disturbance. Among all the existing methods of the stability analysis of a time-periodic system “Floquet theory” and “Multiblade coordinates transformation” are applied. Starting from a nonlinear system with time-periodic characteristics, the equilibrium state is first established. This equilibrium state can be static or dynamic (dynamic state: helicopter in forward flight). The system is then linearised about the equilibrium state. Using the Floquet theory allows to predict the stability or instability of the linearised time-periodic system without usage of any approximations. Using the multiblade coordinates transformation allows first reducing the number of periodic terms in the first order linear differential equations of motion of the system. A time average approximation of the remaining periodic terms changes the equations to the linear differential equations with constant coefficients. Afterward for the stability analysis of this approximated equation the classical stability analysis method “Eigenvalue Analysis” is used.