Modeling of the Large Torsional Deformation of an Extremely Flexible Rotor in Hover

Abstract

This paper describes the refined modeling of the large torsional deformation of extremely flexible rotor blades with negligible structural stiffness. Equations of motion including flap bending and torsion, specifically tailored toward unconventional blades with a tip mass and experiencing large elastic twist angles, are derived using the extended Hamilton’s principle. In particular, the foreshortening of the twisted blade arising from the trapeze effect (also called bifilar effect) is explicitly included. Quasi-steady aerodynamic forces are calculated using the blade element momentum theory. The nonlinear coupled equations of motion are solved using a finite-element method. The analysis is used to predict the thrust as well as the spanwise distribution of flap bending and twist of an 18-in.-diam rotor with extremely flexible blades rotating at 1200 rpm at various collective pitch angles. These predictions are correlated with the measurement of loads obtained using a load cell, and the measurement of the deformation obtained using a noncontact optical technique called digital image correlation. It is found experimentally and analytically that tip twist angles in the range of 10 to 40 deg, depending on the blade design, are attained. This torsional deformation is dictated by the combined action of the propeller moment and the trapeze effect. A detailed explanation of the contribution of the trapeze effect to the equations of motion is presented, and it is shown that omitting the axial foreshortening due to the trapeze effect leads to a 50% error in the computation of blade-tip twist.