Computer Aided Engineering Applications

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1 Computer Aided Engineering Applications 1A.Geometric Modeling 1.1 Geometric modelling methods 1.2 Data representation 1.3 Modeling functions 1.4 Structure of a CAD system Engi Fall 2014

2 1.Geometric modeling Geometric modeling attempts to replace a physical model with a mathematical description capturing its geometry. Clay model [9] CAD model [10] This mathematical description should assist in different tasks in the design process. Ex: manipulation, deforming, adding removing material, similar to a physical model.

3 1.1 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 Representation is ambiguous No surface or mass information extractable Not ideal for CAM CAE tasks Ambiguous representations of the same wire frame [1]

4 1.1 Geometric modelling methods 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. Allows surface normal verification, curvature analysis Surfaces and boundaries [4] Surface normal analysis [5]

5 1.1 Geometric modelling methods 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 machining Complicated data structures in modern systems Solid model [4]

6 1.1 Geometric modelling methods 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). Non manifold modeling captures the evolution of a design. Non manifold geometries [1]

7 1.2 Data representation There are different ways the software manages the geometric data of solids. 1. CSG Constructive Solid Geometry PositionedPrimitives and Boolean operations are used to generate a solid Primitives Boolean operations [1]

8 1.2 Data representation -CSG Allows easy parametric edits in the CGS tree Editing the diameter of the primitive [1] The tree structure becomes complex due to limited operations Long tree structures [2]

9 1.2 Data representation -CSG No information of boundary surfaces and edges. Therefore simple operations like a chamfer is quite involved. Simple extrusions require multiple decompositions in to primitive shapes The edge corresponding to the chamfer is not available in the CGS tree [1] Extrusion and decomposition [2]

10 1.2 Data representation B-Rep 2. B-Rep Boundary representation Carries geometric information. i.e. Points, Curves, Surfaces Carries topological (connectivity) information i.e. Vertices, Edges, Faces, Shells B-Rep data structure [2] CSG vs. B-Rep [2]

11 1.2 Data representation B-Rep 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]

12 1.2 Data representation B-Rep 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. Outer boundary Inner boundary Bridge edge to handle inner boundaries [1] A hollow cube

13 1.2 Data representation-exercise B-rep for a simple cube B-Rep data structure [2] Edges and vertices of a cube [2]

14 1.2 Data representation -Octree 3. Decomposition model [6] [6] The Stanford bunny [8]

15 1.3 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 쀀! structure. Geometric modelling kernel Layered modeling kernel [2]

16 1.3 Modelling functions Sweeping [1] Skinning [1]

17 1.3 Modelling functions Edge rounding, Vertex rounding [1] Lifting [1] Lift a portion of a full face

18 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]

19 1.3 Modelling functions 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 parameters. Parameters Constraints A B-Rep data structure linked to parameters [2]

20 1.3 Modelling functions 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. The design is limited to the available features. CAD feature tree

21 1.4 CAD system structure Modern CAD system structure [2] GUIs Modelling devices (keyboard,mouse) CAE apps Design apps OpenGL DirectX Proprietary files Standard product data exchange files

22 1.4 CAD system structure 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: ACIS - AutoCAD Parasolids Solidworks, Abaqus, Ansys, NX

23 1.4 CAD system structure 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 allow the CAD data to be easily transferred between applications. STL (Stereo Lithography) IGES (Initial Graphics Exchange specification) STEP (ISO 10303)

24 STL 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. Point clouds, STL surfaces, and Smooth surfaces [7] A detailed comparison of other different types will be made during the next part of the course.

25 Exercise Visualize the resulting STL file of a cube STL file of a cube The cube

26 References [1] K. Lee, Principles of CAD/CAM/CAE systems. Addison-Wesley, 1999, p [2] I. Stroud and H. Nagy, Solid Modelling and CAD Systems: How to Survive a CAD System. Springer Science & Business Media, 2011, p [3] I. Zeid, Mastering CAD/CAM. McGraw-Hill Higher Education, 2005, p [4] X. Xu, Integrating Advanced Computer-aided Design, Manufacturing, and Numerical Control: Principles and Implementations. IGI Global Snippet, 2009, p [5] [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 , Feb [7] [8] [9] [10]

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