Blade geometry design with kinematic ruled surface approximation

Authors:
Yayun Zhou;Jörg Schulze;Stefan Schäffler
Affiliations:
Siemens AG, CT, Munich Germany;Siemens AG, CT, Munich Germany;Universität der Bundeswehr München, Neubiberg, Germany
Venue:
Proceedings of the 2010 ACM Symposium on Applied Computing
Year:
2010

Citing 3
Cited 0

Approximation by ruled surfaces

Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Spherical averages and applications to spherical splines and interpolation

ACM Transactions on Graphics (TOG)
Computational Line Geometry

Computational Line Geometry

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Abstract

A blade geometry design method is proposed in this paper, which adopts a novel kinematic ruled surface approximation algorithm. The algorithm is applied to approximate a free-form blade surface as a ruled surface in order to reduce the manufacturing cost. By applying Klein mapping and Study mapping, a ruled surface in Euclidean space is transformed to a curve on a Dual Unit Sphere (DUS). The kinematic ruled surface approximation algorithm is set up based on the novel definition of a spline on the DUS and the corresponding spline interpolation algorithm. This representation of ruled surface links directly to the manufacture procedure.