Nonlinear coupled rotor-fuselage vibration analysis and higher harmonic control studies for vibration reduction in helicopter

In this dissertation, a fundamental study of vibration prediction and vibration reduction in helicopters using active controls is performed. The nonlinear equations of motion for a coupled rotor/flexible fuselage system have been derived using computer algebra on a special purpose symbolic computing facility. The details of the derivation using the symbolic manipulation program MACSYMA are described. The analysis is carried out for two different rotor-fuselage configurations, namely one which has an offset hinged spring restrained rigid blade model and another with fully elastic blades. The trim state and vibratory response of the helicopter are obtained in a single pass by applying the harmonic balance technique for all rotor and fuselage degrees of freedom. The influence of the fuselage flexibility on the vibratory response is studied. Open loop higher harmonic control (HHC) studies are performed to determine the optimal HHC inputs necessary to minimize either the vibratory hub shears or accelerations at various fuselage locations. It is shown that when the fuselage is modelled as a flexible body conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage accelerations but not both simultaneously. It is demonstrated that for simultaneous reduction of hub shears and fuselage accelerations a new scheme called multiple higher harmonic control (MHHC) is required. The fundamental aspects of this scheme are described in detail. A physical explanation of the MHHC control inputs for simultaneous reduction of hub shears and fuselage acceleration is provided. The effects, on the MHHC scheme, of varying the advance ratio, changing the fuselage flexibility and using the acceleration levels at different locations inside the fuselage as the objective function to be minimized are studied. Furthermore, a multiple blade tracking (MBT) analysis capability is developed which enables one to determine the response of each individual blade comprising the rotor system. This treatment allows the evaluation of the vibratory response of the rotor and the fuselage when the blades are not tracking. Finally, effectiveness of the MHHC scheme combined with MBT is demonstrated. The results obtained indicate that MHHC has very significant potential for vibration reduction in rotorcraft.