Helicopter Ground/Air Resonance Including Rotor Shaft Flexibility and Control Coupling

The results of an investigation into the effects of rotor shaft flexibility and the associated rotor control coupling on the so-called ground/air resonance instability of helicopters are presented in this paper. Several types of advanced helicopters appear to be designed with relatively flexible shafts. Since the literature reports no studies of their influence, a ground/air resonance study varying shaft flexibility and shaft-blade coupling, therefore, seems pertinent. Linearized equations of motion for a mathematical model with a rigid airframe, a rotor shaft flexible between the swash plate and hub, and a fully articulated rotor with rigid blades were derived and are presented in a form which emphasizes the differences between hub motions resulting from fuselage motion and those due to shaft flexibility. Twelve degrees of freedom are included: two blade lag modes and two blade flap modes; fuselage pitch and roll about and translation along lateral and longitudinal axes; and shaft flexibility allowing hub translation and bending slope in each of these two directions. Since the study concentrates on the unique aspects of rotor shaft flexibility, only uncocked hinges and rather rudimentary aerodynamic forces are included. The nature of the shaft-pitch coupling is shown to be similar to a "virtual ƍ3"; however, bending of the rotor shaft in a given plane affects the pitch of a blade both in that plane and perpendicular to it. Multiblade coordinates were employed to eliminate periodic coefficients and stability examined using an eigenvalue solution. To ensure a reasonable range of parameters, helicopter dimensions published for the OH-58D helicopter were used, as a guide. Ground and air instability (in hover) were examined with and without shaft flexibility. A range of values for control linkage parameters and ƍ3 were also examined. In addition, because such can influence rotor shaft bending, all cases were studied both with and without a mast-mounted sight.