Bezier Curve Fitting of Blade Profile considering Curvature Variation

Abstract

This paper presents a single C2 -continuous Bezier curve fitting procedure for a blade profile. The fitting procedure is based on nonlinear least squares approach and it also contains fairing term to achieve a minimum variation in the curvature of fitted Bezier curve. The Levenberg-Marquardt method is employed to find Bezier curve control points and parameters for each data points. For validation, a wellknown LS89 blade profile data is used and a 12th degree single Bezier curve is obtained via proposed procedure for this blade profile. Thanks to the fitting procedure, we are able to represent LS89 blade profile, accommodating 405 data points, with only 13 control points, which is a quite efficient way in terms of blade profile design and optimization processes, and determination of manufacturing tolerances. Thus, the proposed fitting procedure has a great potential for practical applications.