Blade Vibration and Its Effect on the Optimal Performance of Helicopter Rotors

Abstract

In this paper, we develop a computationally efficient frequency-domain model that can be used to compute the required shaft power and vibratory loads for a trimmed helicopter rotor with flexible blades in forward flight. The aerodynamic forces and power are modeled using a vortex-lattice method. A finite element model based on the linearized form of the Hodges–Dowell rotating beam equations is used to model the vibrating blades. Guyan reduction and harmonic balance are used to reduce the number of degrees of freedom. The model is validated against several previous computational and experimental models, with generally good agreement. For rotors that use higher harmonic control, the problem of minimizing the required power and/or vibratory loads is cast as a quadratic programming problem requiring a single linear matrix solve to find the optimum. We show that for moderate and high advance ratios, higher harmonic control can substantially reduce vertical hub forces, but only with an increase in required cruise power. For example, using four-per-revolution higher harmonic control, the vertical vibratory loads on the four-bladed HART II rotor can be decreased by about 30% for a 3.0% increase in induced power for at a forward flight advance ratio of 0.45.