CAM system integration

ARTICLE IN PRESS

Robotics and Computer-Integrated Manufacturing 20 (2004) 457–467

Mathematical representation of feature conversion for CAD/CAM system integration Jian Gaoa,b,*, Detao Zhengb, Nabil Gindya a

School of Mechanical, Materials, Manufacturing Engineering and Management, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK b The Department of Mechanical Engineering and Electronic Engineering, Guangdong University of Technology, Guangzhou 510090, PR China

Abstract Automatic generation of machining information from a design system has been the research focus in feature-based CAD/CAPP/ CAM applications for many years. Design data from a CAD model cannot be directly used in a CAPP system due to the difficulties arising from different feature viewpoints in each application and in various feature representations. To create a process-planning model automatically using machine features, feature mapping or conversion is the key issue to solve this problem. This paper addresses the problem of how to convert the design feature representation into machining feature representation in a mathematical model. Design features in the design domain are represented by a set of faces of each feature geometry and a set of attributes such as dimensions and material feature. Machining features in the manufacturing domain are represented by a number of faces and relationships between these faces that are meaningful for the process/machining operations. Using a mathematical description of the feature mapping process, machining features can be deduced and formed by the Set Operation, and the difficult problem of feature interaction can be described mathematically and converted in theory. On the basis of feature representations in the design and manufacturing domains, the mathematical model of feature mapping is represented by a mapping function gd
m which is a synthesis function of the process mapping functions g1 and g2 : The first function, g1 ; extracts the topological elements of a feature from a design model, and forms its own face model which including an interactive feature topological elements. The second function, g2 ; groups these extracted elements into a machining feature according to the geometrical relationship between these elements and matches them with the pre-defined machining features. Examples are given in this paper to show the procedure of the feature mapping process. A feature-based CAD/CAPP/CAM integration system is described with the help of the formulation and representation of machining features. r 2004 Elsevier Ltd. All rights reserved. Keywords: CAD/CAPP/CAM integration; Feature-based modelling; Feature mapping/conversion; Feature interaction; Machining features; Set operation

1. Introduction In order to reduce product cost, rapid product development and improve product competition, agile manufacturing, concurrent engineering and information technology have been introduced into the manufacturing industry [1]. Nowadays, CAD/CAM systems are evolving rapidly, and a great variety of feature-based CAD/CAM software has been developed for product design, process planning and machining. These allow *Corresponding author. School of Mechanical, Materials, Manufacturing Engineering and Management, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Tel.:+44-115951-4116; fax: +44-115-951-3800. 0736-5845/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.rcim.2004.05.001

information transfer from design to manufacturing application. However, CAD design data cannot be directly used in CAM systems due to the variety of feature viewpoint and feature representation for each application. Feature is the medium of information transmission in the CAD/CAPP/CAM integration. It carries a mass of engineering information, both geometrical and nongeometrical, and organically links each system of CAD, CAPP and CAM. However, feature definitions depend on different application viewpoints. Design features are form features related to a component’s function, design intent, or model construction methodology. Machining features are form features associated with distinctive machining operations. In most feature-based systems,

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such as Pro/Engineer, a component is designed by starting with a simple extrusion or revolution operation (such as a cylinder or a protrusion base), and then modifying these by attaching features such as holes, ribs, slots, etc. to the component base. The designer specifies the position, size and orientation of these features [2]. Depending on the downstream machining application the necessary process converts design features into machining features through feature conversion or feature recognition. Feature recognition defines machining features from a geometry-based design model, whereas feature conversion converts machining features from a feature-based design model [3–7]. Automatic generation of machining information from a design feature model has been the main research focus in featurebased CAD/CAM applications [8]. As discussed in [9–12], the process of form feature mapping is a complex and difficult process, especially in the case of feature interaction. It is clearly important to further study the mechanism of feature mapping from the design domain to the manufacturing domain. This paper details a new approach to describing the process of feature conversion through mathematical set operations, which can represent more clearly the geometric changes before and after the feature mapping, thereby allowing one to understand the feature interaction process and so help to develop a feature conversion algorithm for the design and manufacturing system integration. Based on the feature description both in the design domain and manufacturing domain, this paper presents a mathematical model of form-feature mapping and also discusses the difficult problem of interactive features. Examples are given to show the deduction procedure of form feature mapping which includes the conversion of feature interaction. Finally, a general feature-based CAD/CAM integration system is described.

S as: Fdi ¼ pj¼1 fji ; (j ¼ 1; 2,y, p; face number); band Idi represents design intents, which including precision features Fpi (e.g. geometric dimensions and tolerances, and surface roughness), function features Ffi (such as centre line, symmetric axis, hole axis, etc.) and material features Fa : Thus, feature DF i in the design domain can be generally described as: DF i ¼ Fdi ,ðFpi 1 ,Fpi 2 ,?,Fpi s Þ,ðFfi1 ,Ffi2 ,?,Ffit Þ ! ! s t [ [ i i i ,Fa ¼ Fn , Fpl , Ffq ,Fa : ð2Þ q¼1

l¼1

Since design features are described on their composite faces, the relationship between these faces are uncertain for the determination of concrete geometry. Fig. 1 shows an example of this feature geometry uncertainty. Even though the three design features are all called ‘‘slot’’ features, they are distinct due to the different faces and geometries. A machining feature needs to describe the relationships between these feature faces. This, in part, explains why a process planning system cannot obtain machining information directly. 2.2. Features in machining domain In the machining domain, a machining feature is defined as an information-set with relatively fixed geometry, which is associated with a certain machining process intent. In the definition of the machining process intent, this includes machining operations and machining attributes; for instance, dimensions and tolerances, surface roughness and tool approach direction. According to this definition, the mathematical representation of machining feature can be written as ! ! p q [ [ i i i i i i MF ¼ Fm ,Ip ¼ Fm , Amu , Mmv ; ð3Þ u¼1

2. Feature representation 2.1. Features in design domain In the design domain, a design feature is an abstract geometry which can represent design intents and be used to construct the shape of a component. In other words, design features such as those shown in Table 1 can be defined as a combination of abstract form features (pure geometric features with no relations to other applications) and design intents. This can be described in a mathematical form as: DF i ¼ Fdi ,Idi ;

ð1Þ

where DF i represents the ith design feature; Fdi represents an abstract form feature in design domain, which is a composite of several faces and is represented

v¼1

where MF i represents the ith machining feature; Fmi represents form feature in machining domain; Ipi represents machining process intents; Aimu represents i machining attributes; and Mm represents machining v operations. The geometry of a machining feature Fmi can be represented as a union of the feature face set and their constraint relationships, that is Fmi ¼ ðf1i ,f2i ,?,fsi Þ,ðRi1 ,Ri2 ,?,Rit Þ ! ! s t [ [ fki , Ril ; ¼ k¼1

ð4Þ

l¼1

where fki denotes a set of composite faces of the ith feature, including planar face and cylinder face; Ril denotes a set of constraint relationships between feature

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Table 1 Classification of abstract form features Feature name

Geometrical shape

Protrusion

Slot

Hole

Rib

Cut

Round

Chamfer

Datum

datum2

datum1

datum3

f1

f7

f1 f1

f2

f3

slot = f1 ∪f2 ∪f3

f2

f3

slot = f1 ∪f2 ∪f3

f2

f3

f4

f5

f6

slot = f1 ∪f2 ∪f3 ∪f4 ∪f5 ∪f6 ∪f7

Fig. 1. The slot features defined by a number of faces are different in geometry.

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Table 2 Description of machining features Machining feature Fmi

Constraint relationship Ri

Geometric shape

Rperp ðf1 ; f2 Þ Radj ðf1 ; f2 Þ

Step

f1 f2

Fm
step ¼ ðf1 ,f2 Þ,ðRper ,Radj Þ Rperp ððf1 ; f2 Þ; ðf1 ; f3 Þ; ðf2; f3 ÞÞ Radj ðf1 ; f2 ; f3 Þ

Blindstep

f2

f1 f3

Fm
Blindstep ¼ ðf1 ,f2 ,f3 Þ,ðRper ,Radj Þ Slot

f1

Rperp ððf1 ; f2 Þ; ðf2 ; f3 ÞÞ Rpar ðf1 ; f3 Þ Radj ððf1 ; f2 Þ; ðf2 ; f3 ÞÞ

f3

f2 Fm
slot ¼ ðf1 ,f2 ,f3 Þ,ðRper ,Rpar ,Radj Þ Blindslot

f1

Rperp ððf1 ; f2 Þ; ðf1 ; f4 Þ; ðf2 ; f3 Þ;

f2

ðf2 ; f4 Þ; ðf3 ; f4 ÞÞ

f4

Rpar ðf1 ; f3 Þ Radj ððf1 ; f2 ; f4 Þ; ðf3 ; f2 ; f4 ÞÞ

f3 Fm
blindslot ¼ ðf1 ,f2 ,f3 ,f4 Þ ,ðRperp ,Rpar ,Radj Þ Pocket

f5

f2

f3

Rperp ððf1 ; f2 Þ; ðf1 ; f4 Þ; ðf1 ; f5 Þ;

f1

ðf2 ; f3 Þ; ðf2 ; f5 Þ; ðf3 ; f4 Þ; ðf3 ; f5 ÞÞ

Rpar ððf1 ; f3 Þ; ðf2 ; f4 ÞÞ

f4 Radj ððf1 ; f2 ; f4 ; f5 Þ; ðf3 ; f2 ; f4 ; f5 ÞÞ Fm
pocket ¼ ðf1 ,f2 ,f3 ,f4 ,f5 Þ ,ðRperp ,Rpar ,Radj Þ Hole

Axis

cylindface (cf1)

Z

Y X

cf2

Fm
hole ¼ cf1 ,cf2 ,Axis

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Table 2 (continued) Machining feature Fmi

Constraint relationship Ri

Geometric shape

Co-axis-hole

cf3

cf1

Z

Y

Axis

X cf2

cf4 Fm
co
axis
hole ¼ cf1 ,cf2 ,cf3 ,cf4 ,Axis

gm–d

1

Fd

g1

1

Fg 2 g

2

F

3

Fg .. .

Fd Fd .. . p

Fd

3

1

g2

Fm

1 4

2 3

3

Fm .. . q

p

Fm

Fg

Fig. 2. Mapping Function gd
m : Fd -Fm ( —one to one mapping,

gd–m = g2 o g1

2

Fm Fd

Fm

g1

g2 Fg

—one to two mapping, —multi to multi mapping, —two to one mapping).

  faces, Ril AR; R ¼ Rperp ; Rpar ; Rang ; Radj ; Rperp ; Rpar ; Rang and Radj means the perpendicular, parallel, angular, and adjacent relationships, respectively. According to the representation, a number of machining features are listed in Table 2. For example, the machining feature ‘‘slot ‘‘is described as Fm
slot ¼ ðf1 ,f2 ,f3 Þ,ðRperp ,Rpar ,Radj Þ:

3. Mathematical representation of feature conversion Suppose U is a set domain of abstract form features in the design domain, and V is a set domain of form features in the manufacturing domain, then PðUÞ and PðV Þ are the index set of the domain U and of the domain V : This means that PðUÞ and PðV Þ are the whole set of all subsets of U and V : Obviously, a feature set SFd in the design domain and a feature set SFm in the manufacturing domain should be a point set of U and V ; that is, SFd APðUÞ; SFm APðV Þ: If there is a rule, gd
m ; by which for every element (feature) xASFd an element (feature) yASFm can be

created correspondingly, then this rule gd
m is called a form feature mapping function from SFd in the design domain to SFm in the machining domain, and is denoted gd
m : SFd -SFm ; where SFd is called definition domain of gd
m ; and denoted by dom gd
m ¼ SFd ; SFm is called value domain of gd
m ; and denoted by val gd
m DSFm : If an element y is an image of an element x under the action of gd
m ; then as usual it is written y ¼ gd
m ðxÞ or gd
m : x-y; where x denotes the inverse image of the element y: In a word, the mathematical model of feature mapping from an abstract form feature set in the design domain to a machining feature set in the manufacturing domain can be denoted as: gd
m : SFd -SFm x/y ¼ gd
m ðxÞ:

ð5Þ

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3.1. The mapping function gd
m of form features The procedure of form feature mapping can be divided into two stages (shown in Fig. 2). The first stage is carried out through a process mapping function g1 from an abstract form feature Fd to a transition feature Fg : The second stage is carried out through a process mapping function g2 from the transition feature Fg to a manufacturing form feature Fm : For latter stage, there are four kinds of feature mapping involved: oneto-one mapping, one-to-two mapping, two-to-one mapping and multi-features to multi-features mapping. Consequently, the form-feature mapping function gd
m is a composition of the function g1 and g2 ; which can be represented as gd
m ¼ g2 3g1 : Fd -Fm ;

ð6Þ

where 3 is the symbol representing composition mapping by the function g1 and g2 :

where Fgi ¼ f1i ,f2i ,?,fsi is the compound of the faces of the ith feature Fdi ; and the formula f i -f j ¼ f ðiajÞ is true under no feature interaction. (2) when Fdi -Fdj af ðiajÞ; there are feature interactions between form features. The topological elements of the two interaction features Fdi and Fdj may be changed and result in the alternative of the original feature class and geometry. If the set operation of symmetric difference " is applied to these feature elements when two features Fdi and Fdj interact, the changes of the topological elements of Fdi and Fdj can be deduced through the process function S 1 mapping S 2 jg1 : Assume Fdi ¼ ls¼1 fsi ; Fdj ¼ lt¼1 ft ; and Fdi -Fdj a j i i j f ðiajÞ; fu AFd ; fv AFd ; if the two faces fui and fvj are interactive due to the interaction of the feature Fdi and Fdj ; and the other faces of the two interactive features remain unchanged. Then we obtain ! ! l1 l2 [ [ j j i i i j g1 ðFd ,Fd Þ ¼ fs ,ðfu "fv Þ, ft ; ð9Þ s¼1sau

3.2. Process mapping function g1

t¼1tav

fui "fvj

Let Fd ¼ fFdi ; i ¼ 1; 2; y; pg be an abstract form feature set, and Fg ¼ fFgi ; i ¼ 1; 2; y; pg be a face set corresponding to the elements of feature set Fd : If dom g1 ¼ Fd ; val g1 DFg ; then, g1 is a process mapping function from Fd to Fg ; which can be expressed as g1 : Fd -Fg x1 /y1 ¼ g1 ðxÞ;

ð7Þ

where, x1 AFd ; y1 AFg ; x1 is the inverse image of y1 ; and y1 is the image of x1 under the function g1 : The process mapping function g1 is used to extract the topological elements of a form-feature, such as faces, axes, loops, and edge elements. (1) When Fdi -Fdj ¼ f ðiajÞ; there is no interaction between form features, the process can be described as

represents the symmetric difference of where, two interactive faces fui and fvj ; the result of the symmetric difference " in set operation is analysed as follows: In Set Operations, we have the following rules: ð1Þ ðA"BÞ ¼ ðA,BÞ
ðA-BÞ ð2Þ ðA"BÞ ¼ ðA
BÞ,ðB
AÞ From these, the following operations can be derived: ðfui "fvj Þ

¼ ðfui ,fvj Þ
ðfui -fvj Þ;

ð10Þ

ðfui "fvj Þ ¼ ðfui
fvj Þ,ðfvj
fui Þ:

ð11Þ

Four situations for the feature interaction may be described as follow: (a) If fui Dfvj (shown in Fig. 3(a)), then fui "fvj in the set operation gives: fui ,fvj ¼ fvj ;

g1 ðFd Þ ¼ g1 ðFd1 ,Fd2 ,?,Fdp Þ

fui -fvj ¼ fui ;

fvj
fui ¼ fvj0

‘ fui "fvj ¼ ðfui ,fvj Þ
ðfui -fvj Þ ¼ fvj
fui ¼ fvj0 :

¼ ðf11 ,f21 ,?Þ,ðf12 ,f22 ,?Þ ,?,ðf1p ,f2p ,?,flp Þ

(b) If fui +fvj ; then we obtain:

¼ Fg1 ,Fg2 ,?,Fgp ;

ð8Þ

fui "fvj ¼ ðfui ,fvj Þ
ðfui -fvj Þ ¼ fui
fvj ¼ fui0 :

i

i

fu

fu j

fv j

fv j f v'

j

f v'

i

f u' i j f u ' = f iu − f v

j

i f u , f v — faces before interaction

j

i j j f v ' = f v − f u —faces after interaction

(a)

ð12Þ

f v ' = f vj − f iu j

( f v ' is the plane with twoout_loops) (b)

Fig. 3. Operation fui "fvj on the faces of interactive features.

ð13Þ

ARTICLE IN PRESS J. Gao et al. / Robotics and Computer-Integrated Manufacturing 20 (2004) 457–467

(c) If fui ¼ fvj ; then fui "fvj

¼

fui




fui

and

¼ f:

ð14Þ

(d) If fui gfvj (shown in Fig. 3(b)), we have fui
fvj ¼ fui0 ; fvj
fui ¼ fvj0 ‘ fui "fvj ¼ ðfui
fvj Þ,ðfvj
fui Þ ¼ fui ,fvj : In general, the difference operation expressed as: 8 > f; > > > > < f j0 ; v i j fu "fv ¼ > fui0 ; > > > > : f i0 ,f j0 ; u v

463

protrusion ¼ f1 ,f2 ,f3 ,f4 ,f5 ,f6 ; slot ¼ f11 ,f21 ,f31 ,f41 ,f51 ; cut ¼ f12 ,f22 :

ð15Þ

Because of the feature interaction between the feature 0 slot and the feature cut, the form feature set Fd corresponding to the modelling result is different from the original feature set Fd used. We have

application of the symmetric to the feature interaction can be fui ¼ fvj ;

0

Fd ¼ protrusion,blindslot,cut

fui Dfvj ; fui +fvj ;

ð16Þ

and

fui gfvj ;

blindslot ¼ f510 ,f210 ,f310 ,f410 ; cut ¼ f12 ,f220 :

where, fui and fvj represent the faces of the two features before their interaction, fui0 and fvj0 represent the faces of the two features after their interaction. Obviously, the process mapping function g1 could be used not only to extract the topological elements of the independence features, but also to identify the topological elements of the interactive features. The representation of form features in the design feature set can therefore be transformed to a face representation suitable for machining feature model. This face representation is a combination of a number of real faces existing on a component model. For instance, Fig. 4 illustrates the process of feature modelling and the result state of feature modelling for the component. In the design domain, the abstract form feature set Fd of the example component consist of protrusion, slot, and cut features, and the feature set, Fd ; is expressed as a union set of these features

Clearly, not only was the feature class in this example changed (from a slot feature to a blindslot feature), but also the composite faces of the features were altered. The deduction process from the process mapping function g1 can be expressed as: g1 ðFn Þ ¼ g1 ðprotrusion,slot,cutÞ ¼ ðf ,f2 ,f3 ,f4 ,f5 ,f6 Þ  ,ðf21 ,f31 ,f41 ,f51 ,ðf11 "f22 Þ,f12 Þ ¼ ðf1 ,f2 ,f3 ,f4 ,f5 ,f6 Þ  ,ðf210 ,f310 ,f410 ,f510 ,f220 ,f12 Þ; where f11 "f22 ¼ f220 ; since f11 Df22 : By means of the process mapping function g1 ; it is possible to determine the alternation of the features involved in feature interaction and obtain the correct representation of these features.

Fd ¼ protrusion,slot,cut

f3

protrusion f4 Fd

f1

=

1 f2

1

f6

1

f4

2

f1

∪ 1

f5 Design Process Record

f5

∪

f3'1

2

f2'1 f 5'1

f 2' ∪ 2

f1

f 14' protrusion

2

f2

1 f1

f3

∪

f2

Fd =

cut

slot

blindslot

cut Result in database

Fig. 4. Features used for component modelling process and features stored in database after modelling.

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3.3. The process mapping function g2 Let Fg ¼ fFgi ; i ¼ 1; 2; y; pg be a face set of form features obtained from the process mapping function g1 : Let Fm ¼ fFmj ; j ¼ 1; 2; y; qg be a set of machining features. If dom g2 ¼ Fg ; val g2 DFm ; then the function g2 is called the process mapping function from Fg to Fm ; and is written: g2 : Fg -Fm ; y1 /y2 ¼ g2 ðy1 Þ;

ð17Þ

where y1 AFg ; y2 AFm ; y1 is the inverse image of y2 ; y2 is the image under the function of g2 : On the basis of the composing faces of a form feature derived by the function g1 ; the process mapping function procedure is applied to search and deduce the hidden attributes of faces (such as their vectors and types), to identify the constraint relationship of faces (for example, perpendicular and parallelism), and to deduce the description of a form feature similar to that of the predefined features. In this way the form feature mapping from the design domain to the manufacturing domain can be finally achieved. Suppose that the function used to deduce the attributes and constraint relationship is called searching function and is represented by the symbol g21 : Suppose further that the function used to re-compose feature faces and inspect their relationship is called constraint function and represented by the symbol g22 : Then the process mapping function g2 is the synthesis of the searching function g21 and the constraint function g22 ; and is described as g2 ¼ g22 3g21 : Fg -Fm ; y1 /y2 ¼ g2 ðy1 Þ ¼ g22 ðg21 ðy1 ÞÞ;

ð18Þ

where represents synthesis of the two functions g21 and g22 : The result of the searching function g21 includes two items: the first is the description of a face set which contains the attributes of their vectors, loops and types. The other is the description of the constraint relationship between these faces of the feature. Let REL be the domain of constraint relationship, in other words, REL is a set of perpendicular ðRperp Þ; parallelism ðRpar Þ; angularity ðRang Þ; adjective ðRadj Þ and co face ðRcoface Þ relationships. It can be written as

feature. So, the function g21 can be expressed as ! p l [ [ 0 i fj ,PðRELÞ ; g21 ðy1 Þ ¼ i¼1

where i ¼ 1; 2,y, p, form features number involved in the design domain; j ¼ 1; 2,y, l, composed faces number corresponding to the form feature Fdi in the design domain. Substitute Formula (19) into Formula (18), the function g2 becomes g2 ðy1 Þ ¼ g22 ðg21 ðy1 ÞÞ ¼ g22

p l [ [

¼ g22

!! 0 fji ,PðRELÞ

j¼1

i¼1

l1 [

!

0 fj1 ,PðRELÞ

j¼1

,?,

lp [

,

!!

0

l2 [

! 0 fj2 ,PðRELÞ

j¼1

fjp ,PðRELÞ

j¼1 0 0 0 0 0 ¼ ðf11 ,f21 ,f31 ,Rper ,Rpar Þ,ðf12 ,f22 ,? 0 0 0 ,fl22 ,Rper ,Rpar ,R3 ,R4 Þ,?,ðf1q ,f2q 0 0 0 ,f3q ,f4q ,f5q ,R1 ,R2 ,R3 ,R4 ,R5 Þ

¼ Fm1 ,Fm2 ,?,Fmq q [ ¼ Fmi :

ð20Þ

i¼1

Formula (20) shows that the feature mapping process from Fg to Fm is realised through the process mapping function g2 by the synthesis of g21 and g22 : Combining the two process mapping functions g1 and g2 ; the mapping function gd
m of form features from the design domain to the manufacturing domain can be represented as: gd
m ¼ g2 3g1 : Fd -Fm y2 ¼ gd
m ðx1 Þ ¼ g2 ðg1 ðx1 ÞÞ ¼ g22 ðg21 ðg1 ðx1 ÞÞÞ:

ð21Þ

Thus, the result of the function gd
m can also be described as

gd
m

p [

! Fdi

¼ g22 g21 g1

i¼1

p [

!!! Fdi

i¼1

¼ g22 g21

p [ i¼1

REL ¼ fRperp ; Rpar ; Rang ; Radj ; Rcoface g PðRELÞ is an index set of REL, which includes all subsets except the empty set, namely, PðRELÞaf: Therefore, the result of the searching function g21 is a union of a face set and constraint relationships of the

ð19Þ

j¼1

¼ g22

p l [ [ i¼1

¼

q [ j¼1

Fmj :

l [

!!! fji

j¼1 0

!!

fji ,PðRELÞ

j¼1

ð22Þ

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slot

f6

f5 f1

f1′

f2

f3

′ f2-6

slot1

f7

f6′

465

f7′

f2′

gf f4

f5′

Fd = slot

slot2

f ′3 f4′

Fm′ = slot1 ∪ slot2 Fig. 5. Feature mapping of the form feature (slot). 1

f 2′

1 1

f

1

f2

f

2 1

f

1

f3

1

2 f2 → f

2 2′

→f

1

f

3′

f4′ 2 f2

1

f4

1

f

gf =

f5

Fd = slot ∪ cut

1 5′

2 2′′

2 2′′

2

f 1′

Fm = blindslot ∪ step

Fig. 6. Feature mapping when the slot feature and cut feature are interactive.

4. Examples Example 1: As shown in Fig. 5, a form feature slot is built on a solid block through an extruding modelling method. Machining features can be converted by means of the feature mapping function gd
m : The deduction procedure can be stated as gf ðslotÞ ¼ g2 ðg1 ðslotÞÞ ¼ g22 ðg21 ðg1 ðslotÞÞÞ ¼ g22 ðg21 ðf1 ,f2 ,f3 ,f4 ,f5 ,f6 ,f7 ÞÞ !! 7 [ fi ¼ g22 g21

gf ðslot,cutÞ ¼ g22 ðg21 ðg1 ðslot,cutÞÞÞ ¼ g22 ðg21 ðf21 ,f31 ,f41 ,f51 ,ðf11 "f22 Þ,f12 ÞÞ

i¼1

¼ g22

7 [

!

0

0

0

0

0

0

0

0

0

fi ,Rper ððf1 ; f2 Þ; ðf3 ; f4 Þ; ðf4 ; f5 Þ; ðf6 ; f7 Þ

i¼1 0

0

0

0

0

0

0

0

0

0

 ,Rpar ððf1 ; f7 Þ; ðf3 ; f5 Þ; ðf2 ; f6 ÞÞ,Rcoface ðf2 ; f6 Þ 0

 Radj ððf2 ; f1 ; f3 Þ; ðf5 ; f6 ; f4 Þ; ðf3 ; f2 ; f4 Þ; ðf6 ; f5 ; f7 ÞÞ 0

0

0

0

0

0

0

0

¼ ððf1 ,f2 ,f6 ,f7 Þ,ðRper ððf1 ; f2 Þ; ðf6 ; f7 ÞÞ 0

0

0

0

0

0

0

0

 ,Rpar ððf1 ; f7 Þ; ðf2 ; f6 ÞÞ,Rcoface ðf2 ; f6 ÞÞÞ 0

0

0

0

0

 ,ððf3 ,f4 ,f5 Þ,ðRper ððf3 ; f4 Þ; ðf4 ; f5 ÞÞ 0

0

0

0

0

 ,Rpar ðf3 ; f5 ÞÞÞ ¼ ðf1 ,f2
6 ,f7 ,Rper ,Rpar Þ 0

0

form feature slot through the proposed feature mapping function. Example 2: Fig. 6 shows an example of feature interaction by a slot feature and a cut feature in the design domain. The two design features are converted into two machining features blindslot and step through the form feature mapping function gd
m : The mapping procedure is expressed as

0

 ,ðf3 ,f4 ,f5 ,Rper ,Rpar Þ ¼ Fm
slot1 ,Fm
slot2 : The mapping result shows that the two machining features slot1 and slot2 have been transformed from the

¼ g22 ðg21 ðf21 ,f31 ,f41 ,f51 ,f220 ,f12 ÞÞ ¼ g22 ððf210 ,f310 ,f410 ,f510 ,f2200 ,f120 Þ,Rper ððf210 ; f310 Þ; ðf210 ; f510 Þ; ðf410 ; f310 Þ; ðf410 ; f510 Þ; ðf310 ; f510 Þ; ðf2200 ; f120 ÞÞ,Rpar ðf210 ; f410 Þ,Radj ððf210 ; f310 ; f510 Þ; ðf410 ; f310 ; f510 Þ; ðf2200 ; f120 ÞÞÞ ¼ ððf210 ,f310 ,f410 ,f510 Þ,Rper ððf210 ; f310 Þ; ðf210 ; f510 Þ; ðf410 ; f310 Þ; ðf410 ; f510 Þ; ðf310 ; f510 ÞÞ,Rpar ðf210 ; f410 Þ ,Radj ððf210 ; f310 ; f510 Þ; ðf410 ; f310 ; f510 ÞÞÞ,ððf2200 ; f120 Þ ,Rper ðf2200 ; f120 Þ,Radj ðf2200 ; f120 ÞÞ ¼ ðf210 ,f310 ,f410 ,f510 ,Rper ,Rpar ,Radj Þ ,ðf2200 ,f120 ,Rpar ,Radj Þ ¼ Fm
Blindslot ,Fm
step :

ARTICLE IN PRESS 466

J. Gao et al. / Robotics and Computer-Integrated Manufacturing 20 (2004) 457–467

Design Features

Feature Model of CAD System

Design Feature Database

Feature Extraction

Feature Conversion Module

Form Feature Mapping

Geometric Dimensions and Tolerances Mapping

Other Attributes Mapping such as surface finish.

Machining Features

Feature Mapping Postprocessor

Machining Feature-based Component Model

STEP file

Machining feature Knowledge Base Database

CAPP

Fig. 7. Schematic structure of the CAD/CAM integration system through feature mapping approach.

5. A proposed integration system through feature mapping Based on the mathematical representation of the feature mapping process, a CAD/CAM integration system through a feature conversion module was proposed and developed in [6,13]. Fig. 7 shows the framework of the feature mapping-based integration system. The system includes a part design module, a feature conversion module (including form feature conversion, geometric dimensions and tolerances conversion), a process planning model (based on the converted machining features) and a STEP file interface. The prototype system was developed for gearbox components used in machine tools through C++ and Pro/Develop tool.

6. Conclusions In this paper a mathematical model has been used to describe feature conversion process and is represented by two process mapping functions g1 and g2 : Function g1 is used to extract the information of topological elements of form feature, which includes the topological information of interactive features. Function g2 is used to define the mapped machining features through a searching function g21 and a constraint function g22 : The searching function fulfils the function of deducing the attributes and relationship of features, and the constraint function is used to reconstruct features and examines the relationship corresponding to the machining features. Through these functions, all relevant design feature information can be extracted and converted into machining features even though feature interaction is encountered in some cases. If a feature interacts with another feature, the original shape of the feature may be changed, and in general, becomes a different feature type. Through the analysis of the mathematic model this

alteration of form feature can be observed and machining features can be correctly generated. It is thus clear that the research presented in this paper could provide an important role for the analysis of feature representations and alterations in different applications. Based on the modelling analysis, especially in the case of feature interactions, the feature conversion algorithm can be developed robustly. A further development and implementation in CAD/CAM integration through the feature conversion module has been realised for gearbox components used in machine tools [13,14].

References [1] Yan X, Yamazaki K, Liu J. Recognition of machining features and feature topologies from NC programs. Computer-Aided Design 2000;32:605–16. [2] Trika SN, Banerjee P, Kashyap RL. Virtual reality interfaces for feature-based computer-aided design systems. Computer-Aided Design 1997;29(8):565–74. [3] Lee JY, Kim K. Generating alternative interpretation of machining features. Int J Adv Manufac Technol 1999;15: 38–48. [4] Regli WC. Geometric algorithms for recognition of features from solid models. Ph.D. Thesis, The University of Maryland, USA, 1995. [5] Han J. 3D geometric reasoning algorithms for feature recognition. Ph.D. Thesis, The University of Southern California, USA, 1996. [6] Zheng DT. The study on feature mapping for components from design domain to manufacturing domain. Ph.D. Thesis, Tsinghua University, China, 1997. [7] Gao J, Zheng DT. Representation on inverse image feature and image feature of feature mapping in the environment of integration. J Comput Integration Manufac System (Chinese) 1998;3:11–4. [8] Liu X. CFACA: component framework for feature-based design and processing planning. Computer-Aided Design 2000; 32:397–408. [9] Shah JJ, Mantyla M. Parametric and Feature based Cad/Cam: Concepts, Techniques, and Applications. New York: Wiley; 1995. [10] Fu Z, De PA, Saia A. Graph grammar approach to feature representation and transformation. Int J Comput Integrated Manufac 1995;6(1 and 2):137–51.

ARTICLE IN PRESS J. Gao et al. / Robotics and Computer-Integrated Manufacturing 20 (2004) 457–467 [11] Tsing Y-J, Joshi SB. Recognizing multiple interpretations of interacting machining features. Computer-Aided Design 1994;26(9):667–88. [12] Allada V, Anand S. Feature based modeling approaches for integrated manufacturing: state-of-the-art survey and future research directions. Int J Comput Integrated Manufac 1995; 8(6):411–40.

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[13] Gao J, Zheng DT, Gindy N. Automated dimension conversion of interactive features for CAD/CAPP integration. International conference of Manufacturing Automation, Guangzhou, China, June, 2000. [14] Gao J, Zheng DT, Gindy N. Extraction of Machining Features for CAD/CAM Integration. Int J Adv Manufac Technol, doi:10.1007/s00170-003-1882-9.