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Geometric Modeling Geometric modeling plays a crucial role in the overall application of CAD-CAM-CAE systemRequirements of Geometric Modeling Information entered through geometric modeling is utilized in number of downstream applications like: Design Analysis Evaluation of centroid, area (cross-sectional & surface) & volume Estimate the mass & inertia properties Interference checking in assemblies Analysis of tolerance build-up in assemblies Kinematic/ Dynamic analysis & simulation Finite element analysis for stress, vibration, thermal & optimization Drafting Automatic 2D view generation Automatic planar cross-sectioning Automatic dimensioning 3 Geometric Modeling Manufacturing Part classification & Process planning NC tool path generation & verification Manufacturing process simulation Robot program generation Production & Preparation of Bill of Material (BOM) Industrial Engineering Material requirement planning Manufacturing resource requirement Scheduling Marketing Computer-Aided Inspection & Quality control etc….. 4 2
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Geometric Modeling Hence, It is important that the geometric model generated should be as clear & comprehensive as possible so that the other modules of CAD-CAM-CAE system are able to use this information in the most optimal way. Two Dimensional (2-D)Geometric model Wireframe Modeling Three Dimensional Surface Modeling (3-D) Solid Modeling 5 Geometric Model Two Dimensional (2-D) Utility of 2-D model lies in many of the low end drafting packages which is required for preparing manufacturing drawings Their utility is limited because of their inherent difficulty in representing complex objects. Three Dimensional (3-D) The 3-D geometric modeling has the ability to provide all the information required for CAD-CAM-CAE applications Basic Requirement A 3-D geometric model should be an unambiguous representation of an object. A 3-D model should be complete to all engineering function from documentation (drafting & shading) to engineering analysis to manufacturing. 6 3
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Wireframe Modeling In this method the complete object is represented by number of lines, points, arcs & curves and their connectivity relationshipsAdvantages The construction of a wireframe model is simple It does not require much computer time & memory. It can be used for simple NC tool path generationDisadvantages It can not be used for calculation of mass, inertia properties The interpretation of wireframe models having many edges is very difficult 7 Surface Modeling The surface model is constructed essentially from surfaces such a s planes, rotated curved surfaces & even very complex synthetic surfaces. Surface creation on existing CAD system usually requires wireframe entities as a start Surface & wireframe form the core of all existing CAD systemAdvantages Surface model of an object is a relatively more complete & less ambiguous representation than its wireframe model This method is very much useful for specific non-analytical surfaces ( free-form surface/ sculptured surfaces) such as those used for modeling automobile & airplane bodies & turbine blades etc. From an application point of view, surface models can be utilized in Finite Element Modeling, NC tool path generation, sectioning & interference detections.Disadvantages The calculation of mass & inertia properties would be difficult 8 4
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Solid Modeling Solid model of an object is a more complete representation than surface model, as all the information required for engineering analysis & manufacturing can be obtained with this technique. Advantages Solid modeling produces accurate design, provides complete 3D definition Improves the quality of design Improves visualization has potential for functional simulation of the system 9 Wireframe Modeling Point Lines Analytic Entities / Arcs Curves Circles Ellipse Conics ParabolasWireframe entities Hyperbolas<Geometric Primitives> Cubic spline Bezier curves Synthetic Curves B-spline NURBS (Non-Uniform Rational B-spline) Analytic Curve Synthetic Curve - are described by analytic equations - are described by a set of data points (i.e. control points) 10 5
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Analytic Curve are defined as those that can be described by analytic equations such as lines, circle, conics etc. provide very compact forms to represent shapes & simplify the computation of related properties such as areas & volume. Analytic curves are usually not sufficient to meet today’s geometric design requirements of complex mechanical parts like automobile bodies, aeroplane wings, propeller blades, bottles etc. That require synthetic curves & surfaces (free-form surfaces) Synthetic Curve are defined as those that can be described by a set of data points (i.e. control points) such as Splines, Bezier curve etc. Synthetic curves provide designers with greater flexibility & control of a curve shape by changing the positions of the one or more data points or control points. 11Synthetic Curve The need for synthetic curves in design arises on two occasions: i) when a curve is represented by a collection of measured data points (in case of Reverse Engineering) [graphical visualization of experimental data] ii) when an existing curve must change to meet new design requirements.Synthetic Curve Construction Techniques : Interpolation technique Curve passes through the data points Approximation technique Curve do not passes through the data points Mathematically, synthetic curves represent a Curve-fitting problem to construct a smooth curve 12 6
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Surface Modeling Plane surface Analytic Surface Ruled surface/ Lofted surface Entities Surface of revolution Tabulated cylindrical surfaceSurface entities Bi-cubic Hermite spline surface Synthetic Surface B-Spline surface Entities Bezier surface or patch Coons patch Curve segment : is the fundamental building block for curve entities Surface patch : is the fundamental building block for surfaces 13Plane Surface is the simplest surface which requires three non-coincident points to define a plane. The plane surface can be used to generate cross-sectional view by intersecting a surface model with it. Ruled Surface is a surface constructed by transitioning between two or more curves by using linear blending between each section of the surface It interpolates linearly between two boundary curves that define the surface. Lofted Surface is a surface constructed by transitioning between two or more curves by a smooth i.e. higher order blending between each section of the surface. Used for modeling engine manifolds, turbine blades etc. 14 7
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Surface of Revolution is an axi-symmetric surface that can model axi- symmetric objects. is generated by a rotating a planar wireframe entity in space about the axis of symmetry a certain angle.Tabulated Cylindrical Surface is a surface generated by translating a planar curve a certain distance along a specified direction (axis of cylinder). Plane of the curve is perpendicular to the axis of the cylinder. is used to generate surfaces that have identical curved cross-sections. 15 Solid Modeling Solid model are known to be informationally more complete, valid & unambiguous representation of objects than its wireframe or surface model. The completeness & unambiguity of a solid model are attributed to the fact that CAD database stores both its geometry & topology. Solid models are complete & unambiguous but they are not unique because same object may be constructed in various ways. Solid modeling has been acknowledged as the technological solution to automating & integrating design & manufacturing functions like…Design / Engineering Analysis Drafting CAPP, CNC tool path generation MRP Computer-Aided Inspection & Quality control 16 8
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A solid model of an object consists of both the geometrical & topological data of the object. Geometry - Geometry of an object defines the actual dimensions of its entities. Topology - Topology of an object defines the connectivity & associativity of the entities. - it determines the relational information between entities. From user point of view, Geometry is visible. Topology is considered to be non-graphical relational information that is stored in solid model databases & are not visible to users. 17 Geometry The geometry that defines the object is the - the length of lines L1, L2, L3 - the angle between the lines - radius ‘R’ & the centre ‘P’ of semi-circle Topology The topology of the object can be stated as - L1 shares a vertex (point) with L2 & C1 - L2 shares a vertex with L1 & L3 - L3 shares a vertex with L2 & C1 L1 - L1 & L3 donot overlap - ‘P’ lies outside the object L1 R RL2 C1 P L2 P C1 L3 L1 L3 L1 R RL2 L2 P P C1 C1 L3 L3Same Geometry but Different Topology Same Topology but Different Geometry18 9
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Solid ModelingModern CAD systems offer two approaches to creating solid models : - allows designers to use pre-defined shapes (primitives) as building blocks to model solid object.Primitive Approach - Boolean operation are used to combine the primitives to create complex objects. - is limited by the restricted shapes of primitives - Features are more flexible as they allow the construction Feature Approach of more complex solid than what the primitive offer. Feature is defined as a geometric shape (i.e. feature profile or 2-D sketch) and feature operation to build parts. Feature Feature Profile (Sketch) + Feature Operation The entities required for Feature profile (Sketch) are wireframe & surface entities Feature Operation is an activity that converts the Sketch (2-D) into 3-D shape 19 Constraints Geometric Constraints Dimension Constraints Fix Coincidence Concentricity Tangency Parallelism Perpendicular Horizontal Vertical Mid point Equidistant point Geometric constraints is defined as a geometric condition that relates two or more sketch entities. 20 10
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Constraint-based Feature Modeling Select a Sketch Plane Sketching the feature profile (2D profile) Apply Geometric & Dimensional Constraints Apply feature operations Create Base Feature Combine feature to build part- is considered the best tool to create solids because of its ability to edit & change the shape of the solid in the future by using its relations & constraints. It has flexibility to create complex shape. 21 Common Feature Operations & Features Extrude Protruded Feature Revolve Sweep LoftFeature RibOperations Pocket Hole Slot Shell 22 11
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Common Feature Operations & Features Fillet Chamfer Rectangular Pattern Pattern Feature Circular Pattern Operations Translation Rotation Transformation Scaling Mirror Thread 23 Common FeaturesExtruded or Protruded feature Extrude command is used to create a solid object by extruding a given closed profile. It requires a closed profile (sketch of cross-section of solid object) & an extrusion vector (length & direction). The extrusion direction is always perpendicular to the sketch plane of the profile.Revolved feature Revolve command is used to create an axi-symmetric objects by revolving the selected geometry about an axis. It requires a profile (sketch of cross-section of solid object) & a revolution vector (axis & angle of revolution). The axis of revolution is always in the sketch plane of the profile. 24 12
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Common FeaturesSweep feature is a generalization of extrusion. Creates a feature by moving a sketch (closed or open) along a linear or non-linear path, which is not necessarily perpendicular to the sketch plane. Loft feature Use to blend multiple cross-section (two or more) along the linear or non-linear guide curve to create a solid. Hole feature is equivalent to subtracting a cylinder from a solid. Simple and Taper hole Counter-bored hole Type of Hole feature Counter-sunk hole Threaded hole 25 Common Features Slot feature Removes material from solid. Rectangular slot Type of Slot feature T- slot Dovetail slot Shell feature Shell operation is used to create hollow or thin-walled solids by removing material out. The input to a shell operation is the faces to be removed & a wall thickness. 26 13
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Common FeaturesRib feature is a special type of extruded feature. Creates an extension of geometric element by creating a feature connecting the two faces of the part. The input to create a rib is a contour & a thicknessPattern feature Rectangular Pattern Used to create multiple copy of given feature in rectangular (linear) array. Circular Pattern Used to create multiple copy of given feature in circular array. 27 Common FeaturesFillet are used to smoothen (round) the sharp edges of solid. input to create a constant radius fillet feature is to select the edges to be filleted & fillet radius.Chamfer use to remove sharp edges (or corners) from parts input to create a chamfer is angle-distance, distance- distance. 28 14
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Boundary representation (B-rep) Constructive Solid Geometry (CSG) Sweeping Half spaces Analytic Solid Modeling (ASM)Solid Representation Schemes Cell decomposition Spatial enumeration Octree encoding Primitive Instancing 29 Boundary representation (B-rep) B-rep is based on the topological notion that an object is bounded by a set of faces. A face is a closed, orientable & bounded (by edges) surface. Each face is bounded by edges & each edge (bounded curve) is bounded by vertices. B-rep model of an object consists of faces, edges, vertices. Vertices (v) - The database of a boundary model contains both its Edge (E) topology & its geometry. Topology & Geometry are interrelated & cannot be Face (F) separated entirely from each other 30 15
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B - repAdvantages B-rep is very appropriate to construct solid models of unusual or complex shapes ( like turbine blades, auto body etc.) that are difficult to build using primitives. It is relatively simple to convert a B-rep model into a wireframe model because the model’s boundary definition is similar to the wireframe definition. Disadvantages It requires large amounts of storage because it stores the explicit definition of model boundaries i.e. faces, edges & vertices which tend to grow fairly fast for complex model. 31Constructive Solid Geometry (CSG) CSG model is based on the topological notion that a physical object can be divided into set of primitives (basic elements & shapes) that can be combined in a certain order following a set of rules (Boolean operation) to form the object. Primitives are considered as building block Primitives are simple, basic shapes which can be combined by a mathematical set of Boolean operations to create the complex solid object. Primitives Block Cylinder Cone Sphere Wedge 32 16
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Boolean Operations Union Intersection Difference (U) (∩) (-)Used to combine or Intersecting two Used to subtract oneadd two primitives/ primitives give a primitive from other & objects shape equal to their results in shape equal common value to the difference in their volume 33 CSG Advantages It is easy to construct out of primitives & Boolean operation. It is concise & requires minimum storage. Disadvantages Major disadvantage of CSG is in its inability to represent sculptured surfaces i.e. non-analytical (synthetic surface) cannot be modeled using CSG scheme. - Modern CAD systems provide both approaches to increase their modeling domain 34 17
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Coordinate Systems World Coordinate System Working Coordinate System Screen Coordinate System Device coordinate systemModel coordinate systemMaster coordinate systemDatabase coordinate system World Coordinate System is defined as the reference space of the model with respect to which all the geometrical data is stored in CAD database. Default coordinate system used by a particular software. can be displayed on the computer screen. Input information is transformed to coordinates relative to the world coordinate system before being stored in the database. 35 Working Coordinate System It is convenient in the development of geometric models & the input of geometric data to refer to an auxiliary coordinate system instead of world coordinate system. The user can define a Cartesian coordinate system whose XY plane is coincident with the desired plane of construction (sketch plane). While the user can input data in reference to the working coordinate system, the CAD software performs the necessary transformations to the world coordinate systems before storing the data. Screen Coordinate System is defined as a 2D device –dependent coordinate system whose origin is usually located at the lower left corner of the graphics display. The physical dimensions of a device screen & type of device determine the range of the SCS. A 1024×1024 display has an SCS with a range of (0,0) to (1024, 1024). This SCS is used by the CAD/CAM software to display relevant graphics by converting directly from world coordinates to SCS coordinates. A transformation operation from world coordinate systems coordinates to SCS coordinates is performed by the software displaying the model views and graphics. For a geometric model, there is a data structure to store its geometric data (relative to world coordinate system) & a display file to store its display data (relative to SCS) 36 18
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Solid Model-based Down-stream Application Solid Model-based Assembly Design Solid Model-based Drafting Solid Model-based Mechanism Design Finite Element Modeling from Solid Models CNC machining based on Solid Modeling … 37 19
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Solid Model-based Down-stream Application Solid Model-based Assembly Design Solid Model-based Drafting Solid Model-based Mechanism Design Finite Element Modeling from Solid Models CNC machining based on Solid Modeling … 37 19
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Solid Model-based Down-stream Application Solid Model-based Assembly Design Solid Model-based Drafting Solid Model-based Mechanism Design Finite Element Modeling from Solid Models CNC machining based on Solid Modeling … 37 19
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Solid Model-based Down-stream Application Solid Model-based Assembly Design Solid Model-based Drafting Solid Model-based Mechanism Design Finite Element Modeling from Solid Models CNC machining based on Solid Modeling … 37 19
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