Analysis of harmonic forces produced at hub by imbalances in helicopter rotor blades
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Preliminary wind tunnel tests of the hill-size Model 412/IBC rotor at the Ames Research Center, NASA, are described. Blade flapping motion was excited by swash plate oscillation, and the flapping response was measured using blade-mounted accelerometers and compared with flapping motion inferred form blade strain measurements. The recorded open-loop accelerometer signals were used as input to the flapping-IBC system in the laboratory. The resulting controller cyclic pitch outputs are compared with the original cyclic pitch excitation inputs, and the potential effectiveness of the controller in suppressing the original excitation is evaluated. Control of blade flapping excites blade lagging, and vice versa; the paper describes a theoretical investigation of these coupling effects.
An advanced higher harmonic control (HHC) analysis has been developed and applied to investigate its effect on vibration reduction levels, blade and control system fatigue loads, rotor performance, and power requirements of servo-actuators. The analysis is based on a finite element method in space and time. A nonlinear time domain unsteady aerodynamic model, based on the indicial response formulation, is used to calculate the airloads. The rotor induced inflow is computed using a free wake model. The vehicle trim controls and blade steady responses are solved as one coupled solution using a modified Newton method. A linear frequency-domain quasi-steady transfer matrix is used to relate the harmonics of the vibratory hub loads to the harmonics of the HHC inputs. Optimal HHC is calculated from the minimization of the vibratory hub loads expressed in term of a quadratic performance index. Predicted vibratory hub shears are correlated with wind tunnel data. The fixed-gain HHC controller suppresses completely the vibratory hub shears for most of steady or quasi-steady flight conditions. HHC actuator amplitudes and power increase significantly at high forward speeds (above 100 knots). Due to the applied HHC, the blade torsional stresses and control loads are increased substantially. For flight conditions where the blades are stalled considerably, the HHC input-output model is quite nonlinear. For such cases, the adaptive-gain controller is effective in suppressing vibratory hub loads, even though HHC may actually increase stall areas on the rotor disk. The fixed-gain controller performs poorly for such flight conditions. Comparison study of different rotor systems indicates that a soft-inplane hingeless rotor requires less actuator power at high speeds (above 130 knots) than an articulated rotor, and a stiff-inplane hingeless rotor generally requires more actuator power than an articulated or a soft-inplane hingeless rotor. Parametric studies for a hingeless rotor operating in a transition flight regime and for an articulated rotor operating at the level-flight boundary (high speed and high thrust conditions) indicate that blade parameters including flap, lag, torsion stiffness distributions, linear pretwist, chordwise offset of center-of-mass from elastic axis and chordwise offset of elastic axis from aerodynamic center can be selected to minimize the actuator power requirements for HHC.
A new formulation for the Ffowcs Williams-Hawkings quadrupole source, which is valid for a far-field in-plane observer, is presented. The far-field approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r(exp -2) and r(exp -3) dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.
Measurements of the time-averaged induced velocities were obtained for rotor tip speeds as great as 1,100 feet per second (tip Mach number of 0.98) and measurements of the instantaneous induced velocities were obtained for rotor tip speeds as great as 900 feet per second. The results indicate that the small effects on the wake with increasing Mach number are primarily due to the changes in rotor-load distribution resulting from changes in Mach number rather than to compressibility effects on the wake itself. No effect of tip Mach number on the instantaneous velocities was observed. Under conditions for which the blade tip was operated at negative pitch angles, an erratic circulatory flow was observed.