Use Of Twisted Principal Coordinates In Blade Analysis

Unlike the case of untwisted blades, using a system of principal coordinates in the case of pretwisted blades does not result in uncoupled equations for blade bending motion in two planes. In this paper a system of coordinates is defined which yields such an uncoupling in the case of pretwisted blades. When combined with a generalized coordinate technique, where the generalized coordinates are the modes of free vibration of corresponding flat blade, it is possible to obtain the system stiffness matrix without direct structural modeling of the pretwisted blade. Describing the blade twist in terms of piecewise constant pitch angles presents certain advantages in the calculations. The method described here is used to calculate the static deflections of a pretwisted blade and its rot ting and nonrotating free vibrations. The results show the efficiency and accuracy of the method, particularly for situations in which one wishes to evaluate the effect of variations in blade twist. Computing time for 6 natural rotating coupled bending modes for a twenty-station model is up to two orders of magnitude less than a transfer matrix approach.