Investigation of the divergence stability boundary of an extremely flexible helicopter rotor in hover

Abstract

This paper describes the analysis of the divergence stability boundary in hover of an extremely flexible rotor. The rotor blades are clamped at the root and stiffened in flight by the centrifugal force acting on a tip mass. The first torsional natural frequency of such blades is on the order of 3.3 per rev. The analysis shows that the contribution from the structural stiffness to the torsional natural frequency is negligible, and torsional stiffening is dictated by the propeller moment and the bifilar effect. Previous studies suggest that the divergence stability boundary of a torsionally soft rotor is dependent upon the position of the elastic axis relative to the aerodynamic center. For a rotor blade experiencing large angles of twist and under centrifugal loading, this paper shows that the elastic axis is located at the centroid of the radial stress field induced by the centrifugal forces. In addition, an analytical model is derived to predict the divergence stability boundary of the flexible rotor. The model, based on a linearized eigenanalysis of the perturbed equations of motion, includes the bifilar effect due to the large angles of twist incudes along the span of the blade. It is found that the torsional natural frequency of a flexible blade depends upon the chordwise position of the tip mass and the rotational speed. Furthermore, the divergence stability boundary is also found to be a function of the rotational speed. This result qualitatively agrees with experimental measurements of the stability boundaries of flexible rotor blades in hover.