Investigations on the Effect of Blade Torsion on the Dynamics of the Flapping Motion

Abstract
The report, which is an extension of Reference 1, investigates the effect of the blade torsional degree of freedom on the stability boundaries and response characteristics of rotors operating at high advance ratios. It is based an classical rotor theory and, with the exception of the damping of blade feathering and torsion, uses steady‐state aerodynamics. The investigations refer to a blade for which the elastic axis coincides with the 25‐percent chord line. For this case the blade elements operating in the reversed flow region experience zero torsional damping. In addition, the lifting forces acting at the 75‐percent chord line produce negative torsional spring effects. As a result of this, two undesirable characteristics show up. (a) The dynamic stability of the rotor system deteriorates which means that, depending on the blade torsional frequency parameter f, the stability boundary shifts to lower advance ratios. (b) At operating conditions where large torsional displacements occur, the blade flapping response to excitations may be amplified. The unstable modes are characterized by frequencies which are an integral order of one half of the rotor angular velocity. The results obtained are discussed and compared with those of Perisho, Reference 2. The agreement between the two analytical studies is quite satisfactory.