Experimental Determination of the Centre-of-Flexure and Centre-of-Torsion Co-Ordinates of an Asymmetrical Aerofoil Cross-Section

Abstract

The differential equations of motion (1)† of a vibrating cantilever blade contain coupling terms dependent upon the co-ordinates of the centre-of-flexure relative to the centroid of the blading cross-section. Complete solution of the equations, therefore, requires a knowledge of the co-ordinates.

The general theoretical problem of flexure of a cantilever blade has not yet been solved but a solution (2) based on St. Venant's theory of torsion is available for the case of a blade of uniform cross-section with symmetry about one of its principal axes but asymmetrical about the other. The accuracy of the theory is confirmed by experiment (***3). The present paper describes an extension of the flexure experiment to the case of a blade of asymmetrical aerofoil cross-section, the most usual form of cross-section found in turbine and compressor blading. For a cross-section with symmetry about one of its principal axes but asymmetrical about the other it has been shown by reasoning and confirmed by experiment (3) that, providing the root fixing is encastré, the centre-of-flexure is coincident with the centre-of torsion. A second experiment is presently described in which the centre-of-torsion coordinates are determined when the cross-section is asymmetric. Close agreement is shown to exist between the co-ordinates of the centre-of-torsion and those of the centre-of-flexure of the asymmetrical aerofoil cross-section blade.