Design for Manufacturing Using B-Spline Developable Surfaces

1998 ◽  
Vol 42 (03) ◽  
pp. 207-215 ◽  
Author(s):  
Julie S. Chalfant ◽  
Takashi Maekawa
Keyword(s):  
Heat Treatment ◽  
Design For Manufacturing ◽  
Optimization Techniques ◽  
Developable Surface ◽  
Planar Surface ◽  
Complex Objects ◽  
B Spline ◽  
Developable Surfaces ◽  
Manufacturing Applications ◽  
User Friendly

A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. Developable surfaces are widely used in the manufacture of items that use materials that are not amenable to stretching such as the formation of ducts, shoes, clothing and automobile parts including upholstery and body panels (Frey & Bindschadler 1993). Designing a ship hull entirely of developable surfaces would allow production of the hull using only rolling or bending. Heat treatment would only be required for removal of distortion, thus greatly reducing the labor required to form the hull. Although developable surfaces play an important role in various manufacturing applications, little attention has been paid to implementing developable surfaces from the onset of a design. This paper investigates novel, user friendly methods to design complex objects using B-spline developable surfaces based on optimization techniques. Illustrative examples show the substantial improvements this method achieves over previously developed methods.

Design and Tessellation of B-Spline Developable Surfaces

1998 ◽  
Vol 120 (3) ◽  
pp. 453-461 ◽  
Author(s):  
T. Maekawa ◽  
J. Chalfant
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
New Method ◽  
Engineering Applications ◽  
Element Analysis ◽  
B Spline ◽  
Developable Surfaces ◽  
Spline Representation ◽  
User Friendly

Developable surfaces are widely used in various engineering applications. However, little attention has been paid to implementing developable surfaces from the onset of a design. The first half of the paper describes a user friendly method of designing developable surfaces in terms of a B-Spline representation whose two directrices lie on parallel planes. The second half of the paper investigates a new method for development and tessellation of such B-Spline developable surfaces, which is necessary for plate cutting and finite element analysis.

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

1994 ◽  
Vol 116 (4) ◽  
pp. 1042-1048 ◽  
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.

Geometric Design and Fabrication of Developable Bezier Surfaces

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.

scholarly journals Barothermal Processing of Animal Feed Ingredients

2019 ◽  
Vol 29 (3) ◽  
pp. 428-442 ◽  
Author(s):  
Vladimir I. Syrovatka ◽  
Natalya V. Zhdanova ◽  
Aleksandr N. Rasskazov ◽  
Dmitriy I. Toropov
Keyword(s):  
Heat Treatment ◽  
Superheated Steam ◽  
High Pressures ◽  
High Efficiency ◽  
Animal Feed ◽  
Raw Materials ◽  
Digital Technologies ◽  
Feed Ingredients ◽  
System P ◽  
User Friendly

Introduction. The article substantiates the need for high-temperature processing of feed ingredients. Principles of operation and design features of the applied methods and equipment for feed production are considered. Phase transitions, along with advantages and energy, technological, and technical drawbacks are highlighted. The aim of the study is to justify a possibility of creating high-efficiency production lines using heat treatment of feeds by application of heat valves ensuring continuous loading of raw materials into a reactor and discharge of the treated feed at high pressures and temperatures. Materials and Methods. It is proposed to transfer the process of barothermal processing to a higher zone of the phase diagram of the system p,t (pressure and temperature). This is a section of the superheated steam zone with temperature 300–374 °C, pressure 12–21 MPa and treatment exposure 30–60 seconds, which replaces costly processes of normalizing, expansion, extrusion and granulation. The change in enthalpy in the pressure range 0–21 MPa and temperature range 0–600 °C is shown. Thermal modes are presented as formulas which is the basic condition for the use of digital technologies. Results. The design of the reactor with a thermal gate for loading and unloading, being the main unit of the production line of the feed heat treatment, was proposed. The results of the study are fundamental for the development of the sample flow low-capacity line. Discussion and Conclusion. The transfer of the process of barothermic processing of feed into the zone of superheated steam allows for the transfer of poorly digestible elements of grain and legumes in easily digestible, pathogen-free feed. Advantages of the reactor and line include the user-friendly design, energy saving and possibility of implementation of advanced digital technologies.

scholarly journals BladeCAD: An Interactive Geometric Design Tool for Turbomachinery Blades

1996 ◽  
Author(s):  
Perry L. Miller ◽  
James H. Oliver ◽  
David P. Miller ◽  
Daniel L. Tweedt
Keyword(s):  
Design Tool ◽  
Software Implementation ◽  
Blade Design ◽  
Nurbs Surface ◽  
Surfaces Of Revolution ◽  
B Spline ◽  
Turbomachinery Blades ◽  
Flow Through ◽  
Manufacturing Applications ◽  
Primary Contribution

A new methodology for interactive design of turbomachinery blades is presented. Software implementation of the methods provides a user interface that is intuitive to aero-designers while operating with standardized geometric forms. The primary contribution is that blade sections may be defined with respect to general surfaces of revolution which may be defined to represent the path of fluid flow through the turbomachine. The completed blade design is represented as a non-uniform rational B-spline (NURBS) surface and is written to a standard IGES file which is portable to most design, analysis, and manufacturing applications.

Design of a Two-Piece Brassiere Cup From its Data Points Toward its Automation

2020 ◽  
Author(s):  
Kotaro Yoshida ◽  
Hidefumi Wakamatsu ◽  
Eiji Morinaga ◽  
Takahiro Kubo
Keyword(s):  
Three Dimensional ◽  
Developable Surface ◽  
Two Dimensional ◽  
Trial And Error ◽  
Design Efficiency ◽  
Developable Surfaces ◽  
Data Points ◽  
Dimensional Shape ◽  
The Given ◽  
Three Dimensional Shape

Abstract A method to design the two-dimensional shapes of patterns of two piece brassiere cup is proposed when its target three-dimensional shape is given as a cloud of its data points. A brassiere cup consists of several patterns and their shapes are designed by repeatedly making a paper cup model and checking its three-dimensional shape. For improvement of design efficiency of brassieres, such trial and error must be reduced. As a cup model for check is made of paper not cloth, it is assumed that the surface of the model is composed of several developable surfaces. When two lines that consist in the developable surface are given, the surface can be determined. Then, the two-piece brassiere cup can be designed by minimizing the error between the surface and given data points. It was mathematically verified that the developable surface calculated by our propose method can reproduce the given data points which is developable surface.

scholarly journals Developable mechanisms on developable surfaces

2019 ◽  
Vol 4 (27) ◽  
pp. eaau5171 ◽  
Author(s):  
Todd G. Nelson ◽  
Trent K. Zimmerman ◽  
Spencer P. Magleby ◽  
Robert J. Lang ◽  
Larry L. Howell
Keyword(s):  
Mechanical Systems ◽  
Relative Orientation ◽  
Developable Surface ◽  
Curved Surfaces ◽  
Surface Type ◽  
Complex Tasks ◽  
Rigid Link ◽  
Developable Surfaces ◽  
Flat Sheet ◽  
Wide Range

The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces “developable mechanisms” as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.

scholarly journals Parameterisation of developable surfaces by asymptotic lines

1996 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Vitaly Ushakov
Keyword(s):  
Explicit Form ◽  
Gaussian Curvature ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Asymptotic Lines

An example of a “non-developable” surface of vanishing Gaussian curvature from W. Klingenberg's textbook is considered and its place in the theory of 2-dimensional developable surfaces is pointed out. The surface is found in explicit form. Other examples of smooth developable surfaces not allowing smooth asymptotic parametrisation are analysed. In particular, Hartman and Nirenberg's example (1959) is incorrect.

V. On certain developable surfaces

1863 ◽  
Vol 12 ◽  
pp. 279-280 ◽  
Keyword(s):  
Developable Surface ◽  
Developable Surfaces

If U = 0 be the equation of a developable surface, or say a developable, then the hessian HU vanishes, not identically, but only by virtue of the equation U = 0 of the surface; that is, HU contains U as a factor, or we may write HU = U. PU. The function PU, which for the developable replaces, as it were, the hessian HU, is termed the prohessian; and since, if r be the order of U, the order of HU is 4 r —8, we have 3 r —8 for the order of the prohessian. If r =4, the order of the prohessian is also 4; and in fact, as is known, the prohessian is in this case = U.

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