Laser Forming Oriented CAD/CAM for Developable Surfaces

Laser forming of sheet material has been widely investigated for the last 15 years. While researchers encounter severe problems during the forming of a 3D free form shape, at least one category of surfaces can be made with the process of laser forming, namely the developable surfaces, which are widely used in, for example, ship building. Those surfaces show a zero gaussian curvature and can be unrolled onto a plane without distortion. Until now, the forming of such surfaces has been more or less heuristic, but this paper aims to treat the CAD/CAM issues of this problem in a generic way. Once the surface has been defined, in order to obtain a developable surface, the surface is rebuilt into a number of planar flanges. After collision testing, the unfolding of the surface is calculated. The developable surface is scanned on the boundary between two flanges using laser settings that are determined based on efficiency optimisation considerations, keeping in mind the hardware limitations and the possible surface damage for a too high input energy. In this paper, the proposed CAD/CAM procedure is validated by means of a developable parabolic cylinder.

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Geometric Design and Fabrication of Developable Bezier Surfaces

18th Design Automation Conference: Volume 2 — Geometric Modeling, Mechanisms, and Mechanical Systems Analysis ◽

10.1115/detc1992-0172 ◽

1992 ◽

Author(s):

R. M. C. Bodduluri ◽

B. Ravani

Keyword(s):

Geometric Design ◽

Developable Surface ◽

Developable Surfaces ◽

Surface Patches ◽

Bézier Surfaces ◽

Point Representation ◽

Cad Cam ◽

C2 Continuity ◽

Type Construction ◽

Bezier Surfaces

Abstract In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

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Calibration of bending and membrane strains for iterative laser forming of non-developable surfaces

International Congress on Applications of Lasers & Electro-Optics ◽

10.2351/1.5060194 ◽

2004 ◽

Cited By ~ 2

Author(s):

R. McBride ◽

M. Gross ◽

A. J. Moore ◽

D. P. Hand ◽

J. D. C. Jones

Keyword(s):

Laser Forming ◽

Developable Surfaces

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Evolution of Generic Mathematical Models and Algorithms for the Surface Development and Manufacture of Complex Ducts

Journal of Engineering for Industry ◽

10.1115/1.2803292 ◽

1995 ◽

Vol 117 (2) ◽

pp. 177-185 ◽

Cited By ~ 4

Author(s):

P. Sundar Varada Raj

Keyword(s):

Mathematical Models ◽

Cross Sections ◽

Physical Modelling ◽

Theoretical Determination ◽

Spline Curve ◽

Developable Surfaces ◽

Surface Development ◽

Cutting Out ◽

Cad Cam

Complex ducts bound by developable surfaces can be obtained by cutting out the required developed shape on plane sheets and then wedge-bending or folding along certain lines called generators or rulings. The problem then reduces to the theoretical determination of the 2-D shape to be cut so that on folding along the rulings, the required 3-D surface is accurately obtained. The first step in the surface unfolding process is the determination of the parametric β-θ relationship between two adjacent cross-sections of the duct. The cross-sections of the duct can be planar or nonplanar and composed of conic or spline curve segments, placed anywhere in space. In this paper the requisite β-θ relationships of the most generic form have been derived and can be directly applied to any complex duct. Based on these relationships, an efficient and compact algorithm for surface-unfolding has also been derived. The application of this algorithm to numerous prototype cases has been shown. The theory has been verified by physical modelling of various ducts occurring in the field of hydroturbines, and now forms the basis of an Integrated CAD-CAM System.

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Geometric Design and Fabrication of Developable Bezier and B-spline Surfaces

Journal of Mechanical Design ◽

10.1115/1.2919485 ◽

1994 ◽

Vol 116 (4) ◽

pp. 1042-1048 ◽

Cited By ~ 20

Author(s):

R. M. C. Bodduluri ◽

B. Ravani

Keyword(s):

Spline Interpolation ◽

Geometric Design ◽

Developable Surface ◽

Knot Insertion ◽

B Spline ◽

Developable Surfaces ◽

Spline Surfaces ◽

Insertion Algorithm ◽

Cad Cam ◽

Type Construction

In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

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