Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Abstract

Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty.