CAD/CAM Principles and Applications Ch 4 Geometric Modelling
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Objectives • • • • • • • •
Understand the various requirements for the information that is generated during the geometric modeling stage. Study various types of geometric models possible and their applications Develop various methodologies used for geometric construction such as sweep, surface models, solid models, etc. Recognize the various types of surfaces and their application as used used in geome geometri tricc modell modelling ing Appreciate the concept of parametric modeling which is the current mainstay of most of the 3D modeling systems Develop the various mathematical representations of the curves used in the geometric construction Discuss the various CAD system requirements that need to be considered while selecting a system for a given application Understand the concept of rapid prototyping and the various methods available for the purpose. CAD/CAM Principles and
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4.1 Requirements of Geometric Modelling
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Fig. 4.1
Total product cycle in a
manufacturing environment Geometric Modelling
Ideas
Design Analysis
Production
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Functions of Geometric Modelling • Design an analysis: – Evaluation of areas areas and volumes. – Evaluation of mass and and inertia properties. properties. – Interference checking in assemblies. – Analysis of tolerance build-up build-up in assemblies. assemblies. – Analysis of kinematics — mechanics, robotics. – Automatic mesh generation generation for finite element analysis.
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Functions of Geometric Modelling • Drafting – Automatic planar cross sectioning. – Automatic hidden line and surface su rface removal. – Automatic production of shaded images. im ages. – Automatic dimensioning. – Automatic creation of exploded views for technical illustrations.
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Functions of Geometric Modelling • Manufacturing – Parts classification. – Process planning. – Numerical control data generation gen eration and verification. – Robot program generation. gene ration.
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Functions of Geometric Modelling • Production Engineering – – – –
Bill of materials. materials. Material requirement. requirement. Manufacturing resource resource requirement. Scheduling.
• Insp Inspec ecti tion on and and Qual Qualit ity y Cont Contro rol: l: – Program generation for inspection machines. machines. – Comparison of produced produced part with design. design. CAD/CAM Principles and
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Requ Requic icha ha and and Vo Voel elke kerr [1 [198 981] 1] spec specif ifie ied d the the foll follow owin ing g properties to be desired of in any geometric modelling (solids) system. •
The The confi configu gura ratio tion n of of soli solid d (ge (geom ometr etric ic mod model el)) mus mustt stay stay inv invar aria iant nt with regard to its location and orientation.
•
The The sol solid id must must have have an inte interi rior or and and mus mustt not not have have isol isolat ated ed parts.
•
The The soli solid d mus mustt be fini finite te and and occu occupy py only only a fini finite te shap shape. e.
•
The The app applilica cati tion on of a tran transfo sform rmati ation on or othe otherr ope opera ratio tion n that that add adds s or removes parts must produce another solid.
•
The The mod model el of the the solid solid in E3 (Eul (Euler er spac space) e) may may cont contai ain n inf infin inite ite number of points. However, it must have a finite number of surfaces, which can be described.
•
The The bou bound ndar ary y of of the the soli solid d mus mustt uni uniqu quel ely y ide identi ntify fy which which part part of the solid is exterior and which is interior. CAD/CAM Principles and
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4.2
Geometric Models
• Two-dimensional, an and • Three-dimensional. • The The thre three e pri princ ncip ipal al cla class ssif ific icat atio ions ns can can be – The line model, – The surface model, and – The solid or volume model CAD/CAM Principles and
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Fig. 4.2 3D geometric representation
techniques P2 P3
P1
S8
P10 S6
S5
P4 P9 P11
P12
S4 P5
P8
S3 S1
P6 S7
S2
P7 (a) LINE MODEL
(b) SURFACE MODEL
V1 V2
(c) VOLUME MODEL
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Fig. 4.3 A geometric model represented in
wire-frame model
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Fig. 4.4 Ambiguities present in the wire-frame
model
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Fig. 4.5 Impossible objects that can be
modelled using a wire-frame model
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Fig. 4.6 Generation of 3D geometry using
planar surfaces S5
S3 S6 S6
S5
S8
S8 S4
S3 S4
S1 S7
S2
S1
S2 S7
(b) SURFACE MODEL
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4.3 Geometric Construction Methods • The The thre threee-di dime mens nsio iona nall geom geomet etri ric c construction methods which extend from the 2D that is normally used are: – Linear extrusion or translational translational sweep, and – Rotational sweep.
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Fig. 4.8
Component model produced using
translational (linear) sweep (extrusion)
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Fig. 4.9
Component model produced using
translational (linear) sweep with taper in sweep direction
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Fig. 4.10
Component model produced using linear
sweep with the sweep direction along a 3D curve
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Fig. 4.11
Component model produced using
translational (linear) sweep with an overhanging edge
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Fig. 4.12 Component produced by the
rotational sweep technique
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Fig. 4.13 Various solid modelling primitives
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Fig. 4.14 The Boolean operators and their
effect on model construction
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Fig. 4.15 The Boolean operators and their
effect on model construction
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Fig. 4.16 Creating a solid with the 3D primitives in solid modelling
and the model shown in the form of Constructive Solid Geometry (CSG)
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Fig. 4.17 Model generated using the sculptured surfaces (Image appears with the permission of IBM World Trade Corporation/Dassault Systems Systems - Model generated generated using CATIA) CATIA)
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Fig. 4.18 The various types of surfaces used
in geometric modelling Classification of Surfaces
Planar surfaces Plane
Polygon Polyhedra
Curved surfaces
Free form surfaces
Single curved
Double curved
Cylinders Cones
Spheres Ellipsoids Paraboloid Torus
Ruled surfaces
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Coons surface
B-spline Bezier surface NURBS Fractals
Lofted surfaces
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Fig. 4.19
Ruled surface on the left is shown the curves
from which the ruled surface on the right is formed.
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Fig. 4.20 Coons surface generation
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The e Bézie Bézierr cu curve rve and and the the asso associa ciated ted Fig. 4.21 Th control polygon Y
Control Polygon
Control points
Curve
X
O CAD/CAM Principles and
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The e variou variouss examp examples les of of Bézie Bézierr cu curve rvess Fig. 4.22 Th depending on the associated control polygons p2
p2 p1 p3
p3 p0
p0
p1 p1
p3 p0 p2
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Fig. 4.23 The modification of Bezier curve by
tweaking the control points
Y
Control Polygon
Control points
Y
Curve
O
Control Polygon
Control points
Curve
X
X
O
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Fig. 4.24 The sp splilin ne curve
Y Control points
Control Polygon Curve
X
O CAD/CAM Principles and
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Fig. 4.25 The lofted surface
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Fig. 4.26 Example of filleting or blend method
for model generation
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Example of tweaking method for surface Fig. 4.27 modification ((Image appears with the permission of IBM World Trade Corporati Corporation/Da on/Dassault ssault Systems Systems - Model generated generated using CATIA)) CATIA))
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4.4 Constraint Based Modelling
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Fig. 4.28 Example of initial sketch without any
dimensions
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Fig. 4.29 The sketch shown above which is
fully constrained and dimensioned
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Fig. 4.30 The sketch in Fig. 4.29 when swept
along a linear path produces the solid
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Fig. 4.31 The sketch for the new feature (a
cut)
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Fig. 4.32 The solid after executing an
extruded cut of the geometry in Fig. 4.31
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Fig. 4.33 The final solid
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Fig. 4.34 The model tree of the part showing
the modelling process
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Fig. 4.35 A geometric model created following
the sequence of features as Box
→
Hole
→
Shell
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Fig. 4.36 A geometric model created following
the sequence of features as Box
→
Shell
→
Hole
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Fig. 4.37 Feature based model and its
modified form Slots - 2 Base feature Holes - 3
(A) Original model
Base feature
Slots - 2
Holes - 5
(B) Modified model CAD/CAM Principles and
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Fig. 4.38 Typical drawing for the variant
method of modelling
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Fig. 4.39 Part model produced using the
symbolic programming T C R G N COMPOSED PART
SYMBOL KEYS
C
G
C
KEY SEQUENCE
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Fig. 4.40 Examples of form elements used for
model generation in the case of axi-symmetric components Thread
Arc
Groove
Taper
Turn Fillet
Knurl Chamfer
Face
Blank
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Fig. 4.41 Examples of form features for modelling axi-symmetric
components with milled features
Taper
Turn
Chamfer
Groove
Face
Thread
Fillet
Knurl
Step
Axial hole
Keyway
Radial hole
Splines
Concentric slot
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Axial slot
Radial slot
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Fig. 4.42 Example component modelled using
the features shown in Fig. 4.41 A
3.2
All chamfers 1x45
0
Straight Knurl Pitch 1mm M36x1
1.6
45
90
60
42
-0.015 -0.040
0.01 A
R1.5
42
32 75
+
187 -
0.50 0.75
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Fig. 4.43 Example component modelled using
the features shown in Fig. 4.41 Chamfer 2X2 @45 10 dia 4 holes M8X1 LHT
2X2 Groove
12.5
75
50
Chamfer angle 45
25
2
12.5 25
4 holes on pcd 37.5
80
Sectional Elevation
End view CAD/CAM Principles and
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4.6 Curve representation • Implicit form, and • Parametric form. • In para arametr metric ic form form,, the the curv curve e is is represented as •
X = x(t)
•
Y = y(t)
•
Z = z(t) CAD/CAM Principles and
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Fig. 4.44 Circle Y
(X, Y) θ
X
O
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Fig. 4.45 Ellipse Y
x
2
a
2
+
y
2
b
2
=
1
(X, Y) b O
θ
a
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Fig. 4.46 Parametric curve representation in
Cartesian space p3 z p2
y u p1 x p0 CAD/CAM Principles and
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Fig. 4.47 Tw Two o cubic cubic Bé Bézie zierr cu curv rves es join joined ed at at p3 p2 p3
p1 u
p4
p0 z p5 y p6 x
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4.7 Surface Representation Methods
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Fig. 4.48 Typical surface display with the
parametric variables u and v
z
v u y
x CAD/CAM Principles and
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Fig. 4.49 A bi-cubic Bézier surface patch p(u,1), v=1 curve
p(0,v), u=0 curve
p23
p13
p24 p21
p12 p22
p44=p(1,1)
v p21
z p11=p(0,0)
p33
p14=p(0,1)
u
p32
p43
p31
y
p42
p(1,v), u=1 curve
p(u,0), v=0 curve
x
p41=p(1,0) CAD/CAM Principles and
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4.8 Modelling Facilities Desired • The geometric modelling features. • The The edi editi ting ng or mani manipu pula lati tion on feat featur ures es.. • The The dis disp play lay co contro ntroll fa facili ciliti tie es. • The The drafting features. • The The pr programmin ming fa facil cility. ty. • The The analysis sis features. • The The co connecti cting fe features. CAD/CAM Principles and
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Fig. 4.50 Elimination of hidden lines in display
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Fig. 4.51
Shaded image of a CAD geometric model ((Image
appears with with the permission permission of IBM World World Trade Corporation/Da Corporation/Dassault ssault Systems Model generated using CATIA))
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Fig. 4.52 Orthographic views from a geometric model (Image appears with with the permission permission of IBM World World Trade Corporation/Da Corporation/Dassault ssault Systems Model generated using CATIA)
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Fig. 4.53 Section view generation from a
geometric model
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Fig. 4.54 Exploded view and bill of materials
of an assembly modelled
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4.9 Rapid Prototyping (RP)
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Figure 4.55 Schematic of Stereolithography
device Scanning mirror Laser Cured resin (to form model) Liquid resin
Recoating bar
Platform
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Figure 4.56 Schematic of selective laser
sintering device Scanning mirror
Laser
Powder feed roller
Platform Build powder Sintered powder (to form parts)
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Figure 4.57 Schematic of Three-dimensional
printing device Binder solution Powder feed roller Printing head Nozzle Platform
Build powder Glued powder (to form parts)
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Fig. 4.58 Schematic of Fused deposition
modelling device Filament from a coil
Feeder
Melter
Extrusion nozzle
Solidified plaster (to form model)
Platform
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Fig. 4.59 Schematic of Laminated Object
Manufacturing device
Top view
Splits in excess material (for ease of removal)
Band of build material
Contour of actual cross section of the model
Laminating roller
Scanning mirror Laser
Band of build material
Laminate model
Laminating roller
Excess laminate material
Take-up roll
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Platform
Material supply roll
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Summary •
•
•
•
Infor Informa mati tion on ente entere red d thr throu ough gh geom geomet etri ric c mode modeliling ng is is util utiliz ized ed in a number of downstream applications such as drafting, manufacturing, inspection and planning. Geo Geometr metric ic mode models ls are are th three ree typ types es,, viz viz lin line mod model el,, sur surfa face ce mode modell and solid model. Line model though simple is rarely used because of the ambiguity present. Surface and solid models are extensively used in industrial applications. Amon Among g the the geom geomet etri ric c con constr struc uctio tion n met metho hods ds swee sweep p or or extr extrus usio ion n is most widely used, because of its simplicity and elegance in developing 3D models. Soli Solid d mod model elin ing g pro provi vide des s the the mos mostt una unamb mbig iguo uous us repr repres esen enta tati tion on of the solid model, but is more computing intensive. However to get the correct geometric model, it is essential to utilize solid modeling approach. CAD/CAM Principles and
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Summary •
•
• •
Surf Surfac aces es are are more more wide widely ly use used d and and it is is nec neces essa sary ry to use use different types of surfaces such as b-splines, Bezier, NURB, lofted, to get the user requirements fulfilled. Cons Constr trai aint nt or para parame metr tric ic bas based ed mode modeliling ng is the the main main methodology used by most of the 3D CAD systems. This system helps in grasping the designer’s intent and would greatly facilitate the modification and reuse of the existing designs. Some Some vari varian antt mod model elin ing g syst system ems s are are used used base based d on on tab tabul ular ar data data for specific applications. Form Form feat featur ures es is anot anothe herr for form m of of mod model elin ing g syst system em that that help helps s in in designing CAD systems with more intelligence built into the geometric entities that is possible by purely geometric systems discussed thus far.
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Summary •
• • •
The The math mathem emat atic ical al rep repre rese sent ntat atio ion n of of the the geo geome metr tric ic enti entiti ties es can can be in implicit or parametric form, the latter being the preferred method used in CAD systems because of its easier adaptation in software development. The The cur curve ve repr repres esen entat tatio ion n met metho hods ds can can be exte extend nded ed for for sur surfa face ce representations such as used in free form surfaces. A num numbe berr of of mod model elin ing g fac facili iliti ties es need need to be cons consid ider ered ed whil while e selecting a CAD/CAM system for any given application. Rapi Rapid d pro proto totyp typin ing g is is used used to gen gener erat ate e the the pro produ duct ct dir direc ectl tly y from from the 3D CAD model data. A number of different processes such as stereo lithography, selective laser sintering, 3D printing, fused deposition modeling, laminated object manufacturing, are used for this purpose.
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