構造最適化による低振動ロータ・ブレードの設計

Abstract

A new low vibration rotor blade design methodology using modal based structural optimization is proposed. The blade is substituted for a cantilevered rotating plane tapered beam subjected to sinusoidally varying distributed loads. Structural optimization problems to minimize dynamic loads and moments at the blade root are formulated as non-linear optimal control problems in continuous system and their optimum cross sectional area distributions are determined numerically by SCGRA. The features of this procedure are (1) in favor of modal approach, the low vibration blade design problems can be practicable by treating each blade mode separately, (2) utilizing the modal equation as one of equality constraints imposed on the problem, there is no necessity to specify the natural frequency ranges in advance and feasible natural frequency ranges are determined automatically during numerical processes. Numerical studies are conducted for five different kind of combinations of objective functions, constraints for minimum cross sectional area and exciting frequencies of external loads. To clarify the effects of structural optimization to vibration reduction, optimum solutions are compared with numerical results for a uniform blade. It is revealed that little difference can be recognized between the optimum solutions to minimize vertical shear force and those for out of plane moment. However, for optimum area distributions, large difference can be found depending on dominant vibration modes which are related to the exciting frequencies of external loads.