Application of optimization methods to helicopter rotor blade design

The minimum weight design of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies is studied in this paper. A constraint is also imposed on the minimum value of the autorotational inertia of the blade to ensure sufficient autorotational inertia to autorotate in case of an engine failure. A stress constraint is used to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of the nonstructural weights. The program CAMRAD is used for the blade modal analysis and the program CONMIN for the optimization. In addition, a linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function, the autorotational inertia constraint and the stress constraints. A central finite difference scheme is used for the derivatives of the frequency constraints. Optimum designs are obtained for both rectangular and tapered blades. The paper also discusses the effect of adding constraints on higher frequencies and stresses on the optimum designs.