Rotor Rpm Research Articles

The application of complex coordinates to the study of the dynamic characteristics of the tip-pathplane of a helicopter rotor is considered. The coordinates describing rotor blade motions can be transformed from individual blade flapping angles to linear combinations of flapping angles. Two of the transformed coordinates can be interpreted as describing the tilting motion of the tip-path-plane. In a stationary reference frame, these two new coordinates are coupled. However, by defining a set of complex coordinates, for near hovering flight these two coupled differential equations can be combined into a single second-order differential equation describing the tilting motion of the tip-path-plane. This formulation provides a convenient and natural framework for investigation of the response characteristics of fully articulated and hingeless rotors. Considerable insight into the influence of various physical parameters on the behavior of the tip-pathrplane can be gained. The approach is illustrated by consideration of the transient and frequency response characteristics of the tip-pathplane and the influence of flapping feedback. An extension of the root locus method is described which makes the investigation of flapping feedback convenient. Nomenclature! a - rotor blade lift curve slope b = number of blades A(s) = transfer function c = rotor blade chord Ci = rotor hub rolling moment coefficient, positive for right roll, Ci = L/pKR2(VR)2R Cm — rotor hub pitching moment coefficient, positive nose up, Cm = M/pirR2(QR)2R Cmz = complex rotor hub moment coefficient, Cmz— Cm + iCi /i = rotor blade flapping moment of inertia j = constant of proportionali ty between complex inflow and complex rotor aerodynamic hub moment coefficient KH = gain parameter associated with integral flapping feedback Kp,e = parameters associated with proportional flapping feedback mz — dimensionless aerodynamic moment acting on rotor blade due to forward speed. Effect of cyclic pitch, angular rates and flapping not included p = rotor blade natural frequency in flapping divided by rotor rpm, also roll rate nondimensionalized by rotor rpm, positive roll right q = pitch rate nondimensionalized by rotor rpm, positive nose up

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