A closed-form analysis of rotor blade flap-lag stability in hover and low-speed forward flight in turbulent flow

Abstract

An approximate, closed-form analysis of the stability of coupled flap-lag motion of a helicopter rotor blade in the presence of turbulence is presented. The longitudinal, lateral, and vertical components of turbulence are modeled as uncorrelated physical white noise processes and a special case of the stochastic averaging method is applied to obtain the equations governing the first moments of the stochastic system. A closed-form first moment stochastic stability criterion is obtained using approximations based on realistic rms values of turbulence velocities. This closed form analysis is a generalization of a previous analysis by Peters for the deterministic case. Based on the stability criterion obtained, an interpretation is given for the result, previously obtained by the authors, that in hover the turbulence increases the stability of the coupled flap-lag motion. The interpretation is that the turbulence increases the damping in the least-stable, lead-lag mode by providing the same stabilizing effect as an increase in the profile drag coefficient in both hover and low-speed forward flight. Of the three turbulence components, the vertical turbulence is shown to have the dominant effect on this increase in stability. Numerical results are presented for the hover case and comparison with the more stringent case of second moment stability is made.