Computer Aided Engineering Applications …oscar/wp-content/uploads/2015/01/1A...2015/01/01 ·...

Computer Aided Engineering

Applications

1A.Geometric Modeling1.1 Geometric modelling methods

Engi 6928 - Fall 2014

1.1 Geometric modelling methods

1.2 Data representation

1.3 Modeling functions

1.4 Structure of a CAD system

1.Geometric modeling1.Geometric modeling

• Geometric modeling attempts to replace a

physical model with a mathematical description

capturing its geometry.

• This mathematical description should assist in

different tasks in the design process. Ex:

manipulation, deforming, adding removing

material, similar to a physical model.

Clay model [9] CAD model [10]

1.1 Geometric modelling methods1.1 Geometric modelling methods

• A Geometric modeling system determines how the product geometry is represented. Evolved over four geometric modelling systems :

1. Wireframe modeling

– Keeps only Vertices and Edges– Keeps only Vertices and Edges

– Representation is ambiguous

– No surface or mass information

extractable

– Not ideal for CAM CAE tasksAmbiguous representations of

the same wire frame [1]


2. Surface modeling

• Carries information of surfaces

• Additionally carries surface connectivity information

• Good for surface machining, surface shading

• Hard to form fully closed (water tight) models.• Hard to form fully closed (water tight) models.

• Allows surface normal verification, curvature analysis

Surfaces and boundaries [4] Surface normal analysis [5]


3. Solid modeling

• Only geometries of closed volumes are kept

• Solid information can be derived (e.g. mass,

centre of gravity, etc.)

• Carries complete info for CAM CAE tasks. Ex: Finite

element meshing, NC machiningelement meshing, NC machining

• Complicated data structures in modern systems

Solid model [4]


4. Non Manifold modeling

• Manifold modelling creates closed volumes.

• This is only required by the final solid design.

• The design process greatly benefits from allowing

Non manifold models (hybrid solid, surfaces, and

wireframes). wireframes).

• Non manifold modeling captures the evolution of

a design.

Non manifold geometries [1]

1.2 Data representation1.2 Data representation

There are different ways the software manages

the geometric data of solids.

1. CSG – Constructive Solid Geometry

– Positioned Primitives and Boolean operations are

used to generate a solidused to generate a solid

Boolean operations [1]

Primitives

1.2 Data representation 1.2 Data representation -- CSGCSG

• Allows easy parametric edits

in the CGS tree

• The tree structure becomes

complex due to limited

operations

Editing the diameter of the primitive [1]

Long tree structures [2]

1.2 Data representation 1.2 Data representation -- CSGCSG

• No information of boundary surfaces and

edges. Therefore simple operations like a

chamfer is quite involved.

• Simple extrusions require multiple

decompositions in to primitive shapesdecompositions in to primitive shapes

The edge corresponding to the

chamfer is not available in the

CGS tree [1]

Extrusion and decomposition [2]

1.2 Data representation 1.2 Data representation –– BB--RepRep

2. B-Rep – Boundary representation

– Carries geometric information. i.e . Points, Curves,

Surfaces

– Carries topological (connectivity) information i.e.

Vertices, Edges, Faces, ShellsVertices, Edges, Faces, Shells

B-Rep data structure [2] CSG vs. B-Rep [2]


• Curve and surface geometries can be non

planar. (quadratic, circular etc.)

• Curve and surface geometries not required for

the planar case.

Example B-Rep data structure table for a polygon [1]


• To handle Inner boundaries and outer

boundaries of faces a bridge edge is used.

• Inner boundaries and outer boundaries of

solids are kept as separate shells.

Inner boundary

A hollow cube

Outer boundaryInner boundary

Bridge edge to handle inner boundaries [1]

1.2 Data representation1.2 Data representation--ExerciseExercise

• B-rep for a simple cube

B-Rep data structure [2] Edges and vertices of a cube [2]

1.2 Data representation 1.2 Data representation -- OctreeOctree

3. Decomposition model

[6]

The Stanford bunny [8]

[6][6]

쀀!

1.3 Modelling functions1.3 Modelling functions

• The data structure is at the heart of the CAD

system.

• The user simply calls on modeling functions

(extrude, sweep etc..) which modifies this data

structure.structure.

Geometric modelling

kernel

Layered modeling kernel [2]


• Sweeping [1]

• Skinning [1]


• Edge rounding, Vertex rounding [1]

• Lifting [1] – Lift a portion of a full face

1.3 Modelling functions 1.3 Modelling functions

• Boundary modeling

– Add, delete or modify lower entities of a solid.

(Vertices, edges, surfaces)

Vertex modification [1]

Edge replacement [1]Surface replacement [2]


• Parametric modeling

• The geometry of the models are linked to constraints

and parameters.

• Allows generating many derivative designs.

• Change of parameters rebuilds the model by solving

the geometric constraints and equations for the new the geometric constraints and equations for the new

parameters.

•Parameters

•Constraints

A B-Rep data structure linked to parameters [2]


• Feature based modeling

– CGS like editable history tree, composed of

elementary shape units (features <- not primitives).

– The designer can capture the desired

manufacturing process sequence in the tree. Ex:

chamfer, drill a hole, cut a slot, etc.chamfer, drill a hole, cut a slot, etc.

– The design is limited to the available features.

CAD feature tree

1.4 CAD system structure1.4 CAD system structure

• Modern CAD system structure [2]

• GUIs

•Modelling devices (keyboard ,mouse)

•Proprietary files

•Standard product data exchange files

•OpenGL

•DirectX•CAE apps

•Design apps


• Geometric modeling kernel

The working engine of a CAD system. Performs the

essential mathematics and data representation for

different operations.

• Current software are mainly based on two kernels:• Current software are mainly based on two kernels:

– ACIS - AutoCAD

– Parasolids –Solidworks, Abaqus, Ansys, NX


• Databases (output files)- Are the files created by a

CAD system to store the data.

• The output file structure greatly resembles the

data structure adopted by the modelling kernels.

• Standard product data exchange files are used to • Standard product data exchange files are used to

allow the CAD data to be easily transferred

between applications.

– STL (Stereo Lithography)

– IGES (Initial Graphics Exchange specification)

– STEP (ISO 10303)

STL filesSTL files

• STL files – decomposes the solid to a set of

polygon surfaces. Composing of triangular faces.

• Used mainly for stereo lithography 3D printing

• Used to generate meshes from point cloud data.

• A detailed comparison of other different types will

be made during the next part of the course.

Point clouds, STL surfaces, and Smooth surfaces [7]

ExerciseExercise

• Visualize the resulting STL file of a cube

STL file of a cubeThe cube

ReferencesReferences

[1] K. Lee, Principles of CAD/CAM/CAE systems. Addison-Wesley, 1999, p. 582.

[2] I. Stroud and H. Nagy, Solid Modelling and CAD Systems: How to Survive a CAD

System. Springer Science & Business Media, 2011, p. 711.

[3] I. Zeid, Mastering CAD/CAM. McGraw-Hill Higher Education, 2005, p. 962.

[4] X. Xu, Integrating Advanced Computer-aided Design, Manufacturing, and

Numerical Control: Principles and Implementations. IGI Global Snippet, 2009, p.

397.

[5] http://www.studiorola.com/tutorials/miscellaneous/basic-tips-for-preparing-files-[5] http://www.studiorola.com/tutorials/miscellaneous/basic-tips-for-preparing-files-

for-rapid-prototyping/

[6] A. Hornung, K. M. Wurm, M. Bennewitz, C. Stachniss, and W. Burgard, “OctoMap:

an efficient probabilistic 3D mapping framework based on octrees,” Autonomous

Robots, vol. 34, no. 3, pp. 189-206, Feb. 2013.

[7] http://www.cs.mun.ca/~omeruvia/philosophy/philosophy.html

[8] http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter37.html

[9] http://www.machine-language.com/

[10] http://www.creativecrash.com/3d-model/bicycle-helmet

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