Aeroelastic optimization of a helicopter rotor using orthogonal array-based metamodels

Aeroelastic optimization of a four-bladed, soft-inplane hingeless rotor is performed to reduce hub loads and blade root loads with blade stiffness design variables. An aeroelastic analysis based on the finite element method is used. Aerodynamic modeling includes a time domain unsteady aerodynamic model and a free wake model. Metamodels (models of models) of the aeroelastic analysis are investigated in a systematic manner including various experimental designs such as factorial designs, central composite designs (CCD), gradient-enhanced CCD, and orthogonal arrays (OA). Linear, quadratic, and cubic polynomial response surfaces are obtained, and graphical, statistical, and,optimization results obtained are used to compare the different designs. It is found that the CCD and OA are able to capture the basic trends of the analysis using sequential second-order polynomial response surfaces and are further investigated for use in optimization. However, the OA, which is a fractional factorial design, requires significantly fewer analysis runs than the CCD. Numerical results obtained for single-objective and multiobjective optimization problems show a 16-22 % reduction in vibratory hub loads for a nonuniform-blade with six elastic stiffness design variables. The multiobjective optimization problem based on the min-max method reduces the vibratory hub loads by about 16% and the 1/rev and 2/rev blade root loads,which are the principal cause of dynamic stresses, by about 18 and 31 %, respectively. The OA-based metamodels provide an efficient and interactive approach to perform preliminary design studies using comprehensive simulation codes and is suitable for use in an industrial setting.