Optimal placement of trailing-edge flaps for helicopter vibration reduction using response surface methods

This study aims to determine optimal locations of dual trailing-edge flaps to achieve minimum hub vibration levels in a helicopter, while incurring low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithm to determine the flap time history for vibration minimization. The reduced hub vibration levels and required flap control power (due to flap motion) are the two objectives considered in this study and the flap locations along the blade are the design variables. It is found that second order polynomial response surfaces based on the central composite design of the theory of design of experiments describe both objectives adequately. Numerical studies for a four-bladed hingeless rotor show that both objectives are more sensitive to outboard flap location compared to the inboard flap location by an order of magnitude. Optimization results show a disjoint Pareto surface between the two objectives. Two interesting design points are obtained. The first design gives 77 percent vibration reduction from baseline conditions (no flap motion) with a 7 percent increase in flap power compared to the initial design. The second design yields 70 percent reduction in hub vibration with a 27 percent reduction in flap power from the initial design.