Chapter 4 Geometric Modelling

CAD/CAM Principles and Applications Ch 4 Geometric Modelling

CAD/CAM Principles and

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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


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


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


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


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


X

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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


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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Chapter 4 Geometric Modelling

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