- Email: [email protected]
Cost evaluation in design with form features
Computer-Aided
PII: SOOlO-4485(96)00009-7
Cost evaluation form features Chang-Xue
(Jack) Feng, Andrew
c
in design with
Kusiak*t
and Chun-Che
Huang*
product, some metrics should of metrics of manufacturability in Shah et 01.‘I. namely:
Reducing the cost of a product at the design stage is more effective than at the manufacturing stage. In this paper, an attempt is presented to quantify the manufacturing cost in feature-based design. Machining form features are classified as simple and complex. The machining cost of a part depends not only on the type of form features, but also on the relationship among the features. This cost is calculated for four different cases: traditional machining, simultaneous machining, simultaneous set-up and changeover, and multiple machine tools. A manufacturing process is represented with a digraph. The
be specified. Four types and cost were presented
(a) total product cost, (b) feature-by-feature cost (in this paper called featurebased cost), (c) ‘good practice’ rules violation (GPRV) record, and (d) least cost processing opportunity (LCPO) record. As regards the feature-based cost evaluation, Shah cost et (II.” stated that by using the feature-by-feature evaluation method, ‘standards can be established for individual features for comparison in some sort of normalized fashion’. However, the disadvantage of this method is ‘costs associated with relationships between features cannot be represented. Also. a redesign strategy cannot be easily formulated’. To date, a comprehensive methodology for featurebased cost evaluation has not been developed. In this paper, an attempt is made to present a methodology for feature-based cost evaluation. The cost evaluation of machining form features is the main focus of this paper. A digraph representation is introduced to represent manufacturing operations and the corresponding time (cost). The feature-based cost evaluation problem is formulated as the shortest path problem (SPP), and a mathematical model as well as an algorithm is presented to determine the minimum cost design. The remainder of the paper is organized as follows. The next section categorizes the machining form features. The third section presents a quantitative basis for the cost evaluation of machining form features and the relationship among features. The fourth section discusses the formulation of the feature-based cost evaluation problem as the shortest path problem (SPP), and a mathematical model as well as an algorithm for determining the minimum cost design. Conclusions are drawn in the fifth section.
feature-based evaluation of manufacturing cost is formulated as the shortest path problem, and a mathematical model as well as an algorithm are presented to determine the minimum cost design alternative. Copyright 1’) 1996 Elsevier Science Ltd Keywords: feature-based
Desfgn. Vol 28, No 11. pp. 879-885. 1996 Copyr~ht 1996 Elseuer Science Ltd Pmted m Great Emtam All rights reserved OOIO-4485196 $15.00+0 00
design, design for machining, manufac-
turing cost evaluation
INTRODUCTION There are three major aspects in design for manufacturing (DFM): constraints, cost, and quality. The satisfaction of manufdcturing constraints ensures manufdcturdbility of a design’. The evaluation of manufacturing cost aims at minimizing the manufacturing cost of a design. The design for quality increases product quality and manufacturing yield at reduced cost’. This paper attempts to evaluate quantitatively machining cost of products. Some of the most important papers focusing on this issue are as follows. Chen et ~1.~ focused on a framework of feature-based design for manufacturing. Shaikh and Hansotia4, and Jha’ discussed different aspects of manufacturing cost. An extensive review of methods and tools for cost evaluation in design for manufacturing is provided by Thurston and Carnahan’, and Noble and Tanchoco7. The basic guidelines for cost estimation in manufacturing can be found in 0stwald8. Cunningham and Dixon’, and Chang” illustrated typical manufacturing form features. Before evaluating the manufacturing cost of a
CLASSIFICATION FEATURES
OF MACHINING
FORM
The number of features is not finite, however, they can be categorized into a finite number of classes. For each class, properties can be identified. and methodology can be developed to support each class of features rather than a specific feature. Classification of manufacturing form features are also found in References 9, 10 and 1214. These schemes cannot be used easily in the
Hit&z kianufacturing Technology Laboratory, Penn State University, Berks Campus, PO Box 7009, Reading, PA 19610-6009. USA * Intelligent Systems Laboratory, Department of Industrial Engineering, The University of Iowa, Iowa City, IA 52242-l 527, USA t To whom correspondence should be addressed Puper rrccid: 18 Mq 1995. Rrvisecl: 28 October 1995
879
Cost evaluation
in design
with form features:
Simple machining
C-X Feng
form features
- block - cylinder - flat surface - through hole - blind hole - round chamfer - lengthy chamfer - radial groove - keyway - block slot - v- slot - external thread
Typical Machining Form Features
Complex machining
form features
cost evaluation of feature-based designs. A scheme that appears to be appropriate in cost evaluation in a feature-based design is discussed next.
Simple machining form features In this paper, machining form features are classified as simple and complex features (set ~;~~ur~ I). Simple machining form features, c.g. a through hole. a chamfer, and so on, can be machined in a single operation and a single set-up using a non-shaped cutter. All the other machining form features could bc obtained in finite
Chamter 67
I 880
External thread
I
number of additions and subtraction to/from them. Typical simple machining form features are presented in 7ilhk~J I. In Tdh I, a cylinder and a hole are considered as two diRerent simple features, though they can be expressed in the same way (position, radius, and depth or height) from the design point of view. This is because they are obtained by performing different machining operations. A cylinder is obtained by an external turning operation while a hole by a drilling operation.
Complex machining form features
- face groove - T - slot - Y - slot - dovetail slot - internal spline - external spline - internal thread
quantitative classification quantitative environment
et al.
Before discussing the complex form features, two terms are defined. A set-up time is defined as the time used to relocate the part, while the change-over time refers to the time necessary to relocate or change the cutter. Complex machining form features can be derived from the simple form features. A complex feature. such as a Tslot. a Y-slot, cannot be obtained in a single machining operation and a single set-up and/or changeover but several operations and several set-ups and/or changeovers are required. Examples of complex machining form features are presented in Table 2. The formation of a complex feature from simple features is illustrated next. For example, the complex feature T-slot is obtained from the primitive feature block. First, a block slot and then another block slot is subtracted from the block by performing a milling operation. Similarly, a Y-slot is obtained by subtracting ;I V-slot, and a block slot from the primitive feature block. A feature extraction system should provide multiple interpretations of the features. Examples of the feature extraction approach include: Karinthi and Nau’“. who developed an algebraic approach to feature interaction; who presented an algorithm to Tseng and Joshi”. rccogniLe and interpret certain classes of interacting prismatic depression features, e.g. slots, blocks, and cylinders. The larger the number of operations needed to form u complex feature and the longer the set-up and changeover time. the longer the machining time and the higher the machining cost.
Cost evaluation
Table 3
Relationships
between
machining
form features
e,
in design
C-X Feng et a/.
with form features:
Table 4 Unit manufacturing among features
cost of form features and the relationship
Sit?7p/e ,fornlfi’LltLms n/a Block 0.1 Flat surface n/a Cylinder Round chamfer 0. I
Hole External thread V-slot Radial groove
0.1 0.4 0.3 0.2
Keyway Block slot Chamfer
0.3 0.1 0.1
(‘onlpil~.~ forrllfimws 0.5 T-slot 0.6 External spline
Y-slot Internal
0.6 0.5
Face groove Internal thread
0.7 0.6
0.5 0.6
5 6
0.7 1.7
Rclutionship.s
hrtnwn
I
fixtures
0.1 0.4
2 Note: n/a-
spline
not applicable
3 4 (this feature
is often a primitive
feature)
Relationships between machining form features Tub/e 3 interprets the relationships among machining form features at six levels using cylinders as an example. The easy/hard level of the relationship depends mainly on the nature of the set-up/change-over. The machining cost of a part is affected by the relationship among form features (RFF). Silva et ~1.‘~ referred to the RFF as a spatial relationship between features (SRF). They concluded that the spatial relationship includes the interacting and interfeature relationship. Using their point of view, each of the feature relationships 1-4 in T&de 3 is an interfeature relationship, since the features do not interact but there exist a spatial relationship between them. Relationships 5 and 6 in Tuhle J represent the interacting relationships as the features physically interact with each other. The machining time (cost) of a part depends on the time of performing operations and the change-over and set-up time. In general, the change-over and set-up time are the most significant components of machining time17, which implies that the shorter the change-over and the set-up times, the lower the machining cost. Also, the smaller the number of operations, the lower the machining cost. Hence, the number of change-overs and set-ups should be minimized at the early stages of design. The RFF has a significant impact on the machining cost imposed by change-o;;rs and set-ups. Lin and , and Kusiak” presented Wang ‘* . Hayes and Wright methods to minimize the number of change-overs and set-ups in machining. The ranking of machinability of typical RFFs is indicated in Table 3. For example, part 2 contains two holes with the same diameter. It is easier to machine than part 3 as a cutter does not have to be changed, although the relocation of the cutter is needed in both cases. Part 4 is more difficult to machine than parts 2 and 3 since it has to be relocated and an expensive fixture is needed to hold the part. The ranking scheme of machinability is further discussed in the next section. The analysis of types of form features and the RFFs provides a quantitative basis for evaluation of the machining cost. As a result, the unit machining cost and heuristics are developed to determine cost design.
depends on a specific manufacturing environment. The methodology for evaluation of the machining cost is based on the quantitative analysis in the cost of the form feature cost and the RFF cost in Table 4. For example, the complex feature T-slot is obtained from the primitive feature block. First, a block slot and then another block slot is subtracted from the block by performing a milling operation. The estimated cost is arbitrarily determined as 0.5. Similarly, a Y-slot is obtained by subtracting a V-slot, and a block slot from the primitive feature block. The estimated cost is determined on the comparative basis as 0.6. The cost of the Y slot is 0.1 higher than the cost of Y slot. The comparative cost of the relationships among features is based on the easy/hard level. rather than the form features themselves.
Traditional machining Based on the discussion in the second section, a unit manufacturing cost (UMC) is introduced for quantitative evaluation of manufacturing cost of form features and the RFFs (see Tub/e 4). The UMC is determined by two major factors: the type of activities and the time required to perform the activities, which is similar to the concept of activity-based-costing”. For example, the UMC of drilling one unit of a hole is 0.1 (see Table 4), and this value does not include the initial set-up cost of the part. Similarly, the unit cost of milling one unit of a chamfer is 0.1 as shown in Table 4, which provides the basis for calculating the machining cost of a part. The intention of this research is not to construct tables for industrial use but to present a research methodology for calculation of UMCs. Figure 2 shows the UMCs for two different part designs. A digraph is used to represent the manufacturing activities (operations), e.g. cutting, set-up, and tool change-over. Figure 3 presents a graph (the activity-on-
(b)
(4 UNIT
MANUFACTURING
COST
This section presents feature-based cost models for various manufacturing scenarios. The cost models presented here are not exhaustive as each model
I Figure 2 Two design alternatives of a relationship; (b) an orthogonal relationship
I part:
(a)
an
arbitrary
881
Cost evaluation
in design with form features:
C-X Feng et a/
(a) t setup/changeover
drdlmg f4
(b) drilling f4 Figure 3 alternative
A graph representing designs in t;ig~~ _’
the
manul;lcturmg
COSL ol’ the
arc (AOA) convention is used” representing the two designs in Figure 2. In the AOA convention. an arc represents an activity. a node represents an event (start. end), and an arrow represents the precedence among activities. Numerous graphical tools are available to generate process graphs, e.g. IDEF3”j, PERT/CPM’“.‘4. Numerous references on generating digraphs of manufacturing processes from computer-aided process planning are illustrated in the survey of Alting and Changls. only one manufacturing path is For simplicity, presented in Figurr 3 for each alternative design from all possible process plans Figuw 2. In practice. corresponding to the manufacturing environment should be considered. The path 0 - 1 - 2 - 3 -- 4 - 5 corresponds to the design in Figuw 2~. and path + 6 - 7 corresponds to Figzm 2h. In the first o-1 path, node 0 denotes the initial state, which is a block feature, node 5 denotes the terminal node shown in Figure 20. The arcs 0 - 1. 4 + 5. and 6 1 7 denote drilling operations (drilling feature fl, f3 and f4. respectively), arc 1 - 2 denotes a set-up [the set-up time is assumed to be longer than the changeover time, and since they occur simultaneously, only the set-up times 1 + 2 and 1 + 6 are considered (see Figure 3)]. The arc 2 - 3 in Figurr 3 denotes a milling operation (milling feature f2 in Figuw 2~). The manufacturing cost (c,) of a part can be calculated as follows: (1)
cp = (‘,,, + cc + (’h where L’,, = C:llI,,cc, --the
cost of machining
I, unit long
workpiece, where L’,,is the machining cost for unit length, and m is the number of machining operations; (‘c = C:‘!, C’C, the change-over cost of cutting tools, where cc, is the cost of change-over j, and n, is the total number of changeovers; and c\ = C;l’,c,,-the set-up cost of workpiece. where (‘,A is the cost of set-up k, and YI? is the total number of set-ups. Equation 1 assumes that the set-up and change-over tasks are performed sequentially, which applies to traditional machining. It also assumes that all operations are performed on one machine tool so that the transportation, storage, loading and unloading cost are not considered in the equation. Based on the graph in Figurr 3, Equation I is illuslrated next. Consider part 5 in Tub/e 3 (see also Figurc~ 2h). Assuming /,.i = 1, the unit cutting cost two holes, (‘11,= 0. I + 0.1 = 0.2 results from drilling where the value 0.1 is obtained from T&de I. Since the two holes cannot be drilled in one set-up, an additional set-up and change-over are needed. The change-over cost c’c= 0.2 refers to the cost of relocating the drill to the second hole. The set-up cost cs = 0.3 is based on the time used to relocate the part as the two holes are in different orientations. Thus the unit machining cost of this part is (’,, = 0.7 in Tub/e 4. Similarly, cp = 1.7 in Tub/c 4 for part 6 in T&e 3 (see also Figuw 2~).
Simultaneous machining There are situations were automatic and special purpose machine tools are employed. For example, to machine the part in Figure 4, a special machine tool can be used to drill the four satellite holes simultaneously. In this case, 1 in the machining cost ~4,~is calculated from Equation the same way as if the four operations were performed independently. In the graph representing this machining path, one operation occurs rather than four, however, the cost of this single operation equals to the total cost of the four operations (see Figure 4h). In Figzrrr 4h, the hole fl in the centre is drilled first. then the four satellite holes f2 arc drilled simultaneously. By simultaneous machining. one takes advantage of the economy of time as three tool changeovers are eliminated (see Figure 4h).
Q”
+
1 1
C
‘I-
-+A+? Qn bC
c-c
(b)
A-A (a)
changeover Figure 4
A
process graph
part with multiple
c-c 6)
drilling f2
operations:
(a) part: (b) machining
Figure 5 Two alternative part designs: (a) four small holes with different orientations than the large hole fl: (b) four small holes with the same orientation as the large hole fl
Cost evaluation
in design with form features:
C-X Feng et a/.
Multiple machine tools
Figure 6 alternative
The graph representing designs in Figum 5
Simultaneous
the manufacturing
process of two
Multiple machine tools are used when a part cannot be machined on a single machine. In this case, transportation, storage, and loading and unloading costs occur. It is more convenient to use time rather than cost to evaluate designs in this case. Let tLi, t,5,,tl,, and tui denote the transportation, storage, loadmg and unloading time, respectively, and (at,, cs,, cli, and cu, are their scaling factors, respectively. Then the manufacturing cost of the part is calculated as follows:
set-up and change-over (‘r =X:1, cmi + q=ot$k,
Simultaneous set-up and change-over occurs in machining when automatic machine tools are used. In this case, the set-up and the change-over costs cannot be calculated separately as expressed in Equation 1. Furthermore, the maximum of the set-up and change-over times is used rather than the cost (see Equation 2). cp = (‘,,, + C”,=otj”\ci
+ I&tsj$,j?
+ qlot,,,(.,J,
+ C;l”t,,3(.,,3
+ C:lq,)f”,&,,j‘l
(3)
where m and n are the total numbers of machining operations, and set-ups/change-overs, and n,, n2, n3, and n4 are the total numbers of transportation, storage, loading and unloading activities, respectively.
(2)
where c, is calculated as in Equation 1, t, is the maximum of set-up and change-over time, cscj is the scaling factor for transforming time into a cost. Equation 2 is illustrated next. Figure 5 presents two alternative part designs, while the graph in Figure 6 represents manufacturing cost of the two designs. Since a machine centre is used, machining, change-over and setup take place simultaneously. Consider case (a), the large hole is drilled first, then the two side holes are drilled simultaneously, and finally the remaining two side holes are drilled simultaneously. In this case, both the changeover from a large drill to a small drill and the set-up to reorient the part for drilling can be performed simultaneously. Let the maximum of the set-up and change-over time be 1 s. and the scaling factor be $0.3 per second, the cost of the simultaneous activity is $0.3 as indicated in Figure 6h. Accordingly, the total machining cost is the cost to drill the two side holes rather than the cost of drilling one side hole. Case (b) is illustrated in Figure 4h. The graph representing the manufacturing process is shown in Figure 6. For simplicity, only one manufacturing path is selected for each design alternative. Based on Figure 6. the manufacturing cost for design (a) is 1.5. while the manufacturing cost for design (b) is 0.7
THE MODEL EVAEUATION
OF FEATURE-BASED
COST
The shortest path model The problem of determining the minimum manufacturing cost can be formulated as the shortest path problem. Figure 7 illustrates four design alternatives of a part. A graph representing the RFFs of the part is presented in Figure 8a. The cost values c, -cl7 in Figure 8 corresponding to the manufacturing operations are listed in the Appendix. For simplicity, only one manufacturing path is presented in Figure 8a for each design in Figure 7. In practice, all alternative paths should be generated for each design so that the SPP algorithm selects the minimum manufacturing cost design alternative. Also, we assume the traditional machining process is used to manufacture this part (i.e. the case discussed in the previous section). Each design path ends with a feature and the corresponding operation. The latter implies that there may not be a common terminal node in the graph. The graph in Figure 8a is transformed into a network by adding a dummy node 29 and connecting it to the
-!
f,
D-D
(b)
E!E Cd)
Figure 7 The alternative part designs: (a) five holes with two orientations and two sizes: (b) five holes with one orientation and three different sizes; (c) three holes with two sizes and two threads with same size. and with holes and thread in the same orientation: (d) five holes in the same orientation and two different sizes
883
Cost evaluation
in design
with form features:
C-X Feng et al.
terminal node of each path with a dummy (zero cost) arc (see Figurr ah). Finding the minimum cost path in a network ~a11 be modelled as the network flow problem. In the solution. ;I unit flow is sent from the source to the sink at minimum cost. At the source, there is a net supply of one unit. While at the sink, there is a net demand of one unit. For all other nodes, there is no inflow or outflow.
arc, set u(.Y) = min[v(.\-), I/(P) + c,]. where (‘, is the cost of the arc,i from node p to node .Y. Step 3. [Fixing a value as permanent]. Of all nodes .Ywith associated temporary values. find node .I’ for which V(,I$) -_ min v(.Y). Label the value In as permanent and set 12= .I‘. Step 4. [Termination]. If the minimum cost from node ,\ to node I is considered, and if ,V= t,. then terminate the algorithm with v(t,) as the solution. Ifp # f,,, then return to Step 2. a11
The minimum cost algorithm For a large cost evaluation problem. an cfficicnt heuristic algorithm should be used rather than the standard approach for solving the minimum cost formulation. Since the feature-based evaluation problem is represented with a direct acyclic graph, the algorithm fol solving the cost evaluation problem, presented next, is essentially Dijkstra’s algorithm’“. The two algorithms differ in the termination condition. The cost evaluation algorithm terminates when a node I,,. denoting nodes preceding the terminal node I, 1s reached, while Dijkstra’s algorithm terminates when the terminal node t is reached.
The algorithm Denote the start node and the terminal node by .\ and /. respectively, and f, denotes nodes preceding the terminal node t. To each vertex .\- t X. a value I/(.\.) is assigned. which denotes the minimum cost from node .s e X to .\-. This value may be temporary or permanent. where temporary means that v(_x-) could still be reduced, and the permanent is the minimum cost. Step 1. [Initialization]. Set v(.c) = 0 and label this value as permanent. Set V(I) = x for all .\- t X and .\- # .s and label these values as temporary. Set 1’ z= ,Y. Step 2. [Updating the values]. For all nodes .\- with temporary values z~(_Y) and which are connected to 11by
Illustrative example For the network in Figwr Hh, the cost coefficients c, ii = I. .27) are assigned with the following values: (‘, ~- 0. I. (‘1 = 0.3. (‘3 = 0.3, CJ = 0.1, (‘5 = 0.2, C(,= 0.1 . (‘- ~=0.3. c\ = 0.2. (‘0 = 0.1. c,,, = 0.2, c,, = 0.1, (‘13 .= 0.3. (‘,I = 0.1. (‘13= 0.2, (‘,i =O.l. C’,h= 0.3, (‘17=O.l, (‘lh ~~ 0.2. c,<) = 0.1, (‘?,, = 0.3. c7, = 0.6, c2: = 0.2, (‘1: 0.6, (‘24= 0.2, (‘75= 0.1. (‘2(,= 0.2. (‘27= 0.1. In this example, node 1 is the start node s, node 29 is the terminal node t, and nodes 12, 20. 24, and 28 are the /,, nodes. Solving the minimum cost formulation with LINDO or applying the minimum cost algorithm. both results in the minimum cost nath (1 J (2) ~- (13) - (14) + (15) - (16) + (25)‘+ (2‘6j to design (/ in (27) --- (2X) - (29) corresponding Figuw 7.
CONCLUSlONS The methodology for classification and cost evaluation of machining form features and relationships among form features (RFFs) was proposed. The methodology is meaningful in feature-based design for manufacturing and benefits the establishment of standards for individual features. The unit manufacturing cost is determined by two major factors: the manuFacturing activities and the corresponding time required to perform these activities. Cost evaluation models for four typical machining cases were investigated. A design feature is checked and evaluated for manufacturability first, then the manufacturing cost is evaluated against the cost model. The impact of tolerances and the sequence of operations were not considered in the paper and should be studied separately.
ACKNOWLEDGMENT The research presented in this paper has been partially supported by research funds from the US Army (contract No DAAE07-93-C-R080) and the National Science Foundation (grant No DDM-9215259).
REFERENCES I
Figure 8
Representalion ol‘the feature-based cost c\;tluittion problem: (a) graph representing the generic relationship among fwm features. (b) directed acyclic network representing the relationship among form features
884
2
t cng. c‘ and Kusiak, A ‘C’onstralnt-based destgn 01’ parts’. ~‘1~lll~lrlr:Aicl~~~l I)L,.V.Vol ?X No 5 (19%) pp 343 352 I-‘cng.(’ and Kusink, A ‘Design of tolerances for quality’ 1,~Hight. 1 K and M&tree, F (Eds) IIc.Y&I 77~~~~ and Methoc/o/o~~~~ASME. New York (1994) pp 13 20
Cost evaluation
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IO II
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IX
I9
20 21 22 23
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26
Chen, 1’. Miller, R and Vemuri, K ‘On implementing an integrated design manufacturability assessment environment’ in Gupta. G and Shoup. T E (Eds) Computers in Enginrcring, ~roc. ASME Computws in Enginwring Cot?f: ASME. New York Vol I (1991) pp 407-413 Shaikh. M and Hansotia, B ‘Minimization of drilling costs: a closed-form solution ‘Comp~rtcx~ h&s/r. Engng Vol 23 No I ~4 ( 1992) pp 443 446 Jha. N ‘Stochastic mathematical modeling and manufacturing cost estimation in uncertain industrial environment’ Itilt. J. Prowl. Rcs. Vol 30 No I2 (1992) pp 2755m 2771 Thurston, D and Carnahan. J ‘Intelligent evaluation of designs for manufacturing cost‘ in Kusiak, A (Ed.) Conc~urr~nt Engineering: An/omtrtion. Tools. trnd Tcchniquc.s John Wiley, New York (1993)pp437~462 Noble, J and Tanchoco, J ‘Design for economics’ in Kusiak, A (Ed.) C’orrc~urrcnt Enginrcring: Automution. Tools, und Twhniyues John Wiley, New York (1993) pp 401-436 Ostwald. P AM Co.ri Estimutor (4th Ed.) McGraw-Hill, New York (1988) Cunningham, J and Dixon, J ‘Design with features: the origin of features’ irl Tipnis. V A and Patton, E M (Eds) C’orn/~uters in Enginowing ASME, New York Vol I (1988) pp 237-243 Chang, T C Ev/x,rt Procc.s.v Planning,for Munufircturing Addision Wesley, Reading, MA (I 990) Shah. J, Hsiao. D and Robinson. R ‘A framework for manufacturability evaluation in a feature-based (‘AI) system’ itt Prw NSF Dc,sign und Munqfucturing S~.vtm~ Cortf: Arizona State University, Tempe. AZ. ASME, New York (1990) pp 61 66 Pratt. M and Wilson, P ‘Requirements for support of form feature\ in a solid modeling systemtinal report’ CAM-l Rcporr. R-NS-ASPP-O/ Arlington, TX (1985) Shah, J ‘Features in design and manufacturing’ in Kusiak, A (Ed.) /ntc,/li,~cwr De.sisTn und Mtmufircturing John Wiley. New York (1992) Silva. R, Wood, K and Beaman, J, ‘Representing and manipulating interacting and interfeature relationships in engineering design for manufacture’ in Ravani, B (Ed.) Advunws in Design Auloma/ion. Proc. ASME Design Automcttion Conf: ASME, New York (1990) pp I-8 Karinthi, R R and Nau, D S ‘An algebraic approach to feature interactions’ fEEE Truns. PAMI Vol I4 No 4 (1992) pp 469% 484 Tseng. Y J and Joshi. S B ‘Recognizing multiple interpretations of interacting machining features’ Comput.-Aided Drs. Vol 26 No 9 ( 1994) pp 667m 688 Groocer. M Automation, Production S,~.v~em.s. und Compllrutw Intc,grutct/ Mtrnufuc~turing Prentice Hall, Englewood Cliffs. NJ (1987) Lin. c‘ and Wang, H ‘Optimal operational planning and sequencing: minimization of tool changeovers’ I/I/. J. Prod. Res. Vol 3 I No 2 (1993) pp 311~ 324 Hayes. C and Wright, P ‘Automatic process planning: using feature inleraction to guide search’ /. Mfi?a sysr. Vol 8 No I (1989) pp I- 15 Kusiak, A Intc~lligcwr Manufirc~twing .S~wcw~s Prentice Hall. Englewood Cliffs, NJ (I 990) Epstein, M (Ed.) Advancc.~ in Mnnug~mcnt Acwunting JAI Press. Greenwich, CT (1994) Elmaghraby. S Ac,tivit,v Network: Project Plunning und Control h? Network Models John Wiley. New York (1977) U S Air Force ‘Integrated computer aided manufacturing (ICAM) architecture Par II. volume IV-- Functional modeling manual (IDEFO)’ Wright-Patterson AFB, Ohio 45433: Air Force MateriaI5 Laboratory (1981) Steward, D Swrm Anul~sis and Managcmcwr: Strrrcrurc. Strutrg), und Design Petrocelli Books, New York (198 I) Altinp, L and Zhang. H ‘Computer aided process planning: the state-of-art survey’ In/. J. Prod. Rex. Vol 27 No 4 (1989) pp 553 585 Dijkstra, E ‘A note on two problems in connectlon with graphics’ N/ot~c~~r:cc/lc,Mufhcmutik Vol I No 3 (1959) pp 269-271
APPENDIX cost of drilling fl cost of repositioning
in design with form features:
C-X Feng et al.
cost of tool changeover cost of drilling feature f2 cost of repositioning the tool to f3 cost of drilling f3 cost of repositioning the workpiece cost of tool change-over cost of drilling f4 cost of repositioning the tool to f5 cost of drilling cost of tool change-over and repositioning workpiece cost of drilling f6 cost of repositioning the workpiece cost of drilling f8 cost of tool change-over and repositioning workpiece cost of drilling f7 cost of repositioning the workpiece cost of drilling f9 cost of tool change-over and repositioning workpiece cost of drilling and taping f10 cost of repositioning the workpiece cost of drilling and taping fl 1 cost of repositioning the workpiece cost of drilling f12 cost of repositioning the workpiece cost of drilling f13
the
the
the
Chang-Xue (Jack] Fang is tt.wistunt projtissor of’ Mcvhunicul Enginrering ut Penn Stutc Univwsit~, Bwks Cump~s. PA. He holds a BS dvgrw in mechunic~ul engineering, cm MS degree in munu.facturing enginaering. und u PhD degree in industrial engincrring. His wwurch interests ore in c~on~urrent enginwrirtg, quality mginwring. und ugile munu,facluring.
Andrew Kusiuk i.s pro/~ssor of’ Industriul Engineering ut the Univerxit~~ of’ lowu. IOMU Citjj. IA. He is intcws/ed in enginwring &sign. manufircturing. urtificial inlc~lligmcc~. trnd optin~i:trtion. Dr Kusiuk is The Editor-in-Chicjf of The
Journal
of Intelligent
Manufacturing.
Chun-Cite Huang is u PhD student in the Department of Industrial Enginrcring (II the Uniwrsity of lov~xt. Hr rcwived un MS degree in operutions wseurc,h ,fjw~~ Columbia Uniwr.sit~~ in 1992. His rrseurch intrrrsts ure in prodwt unti process design, kanhan .v~xtc~rn.s, umi scheduling.
the workpiece
885
PII: SOOlO-4485(96)00009-7
Cost evaluation form features Chang-Xue
(Jack) Feng, Andrew
c
in design with
Kusiak*t
and Chun-Che
Huang*
product, some metrics should of metrics of manufacturability in Shah et 01.‘I. namely:
Reducing the cost of a product at the design stage is more effective than at the manufacturing stage. In this paper, an attempt is presented to quantify the manufacturing cost in feature-based design. Machining form features are classified as simple and complex. The machining cost of a part depends not only on the type of form features, but also on the relationship among the features. This cost is calculated for four different cases: traditional machining, simultaneous machining, simultaneous set-up and changeover, and multiple machine tools. A manufacturing process is represented with a digraph. The
be specified. Four types and cost were presented
(a) total product cost, (b) feature-by-feature cost (in this paper called featurebased cost), (c) ‘good practice’ rules violation (GPRV) record, and (d) least cost processing opportunity (LCPO) record. As regards the feature-based cost evaluation, Shah cost et (II.” stated that by using the feature-by-feature evaluation method, ‘standards can be established for individual features for comparison in some sort of normalized fashion’. However, the disadvantage of this method is ‘costs associated with relationships between features cannot be represented. Also. a redesign strategy cannot be easily formulated’. To date, a comprehensive methodology for featurebased cost evaluation has not been developed. In this paper, an attempt is made to present a methodology for feature-based cost evaluation. The cost evaluation of machining form features is the main focus of this paper. A digraph representation is introduced to represent manufacturing operations and the corresponding time (cost). The feature-based cost evaluation problem is formulated as the shortest path problem (SPP), and a mathematical model as well as an algorithm is presented to determine the minimum cost design. The remainder of the paper is organized as follows. The next section categorizes the machining form features. The third section presents a quantitative basis for the cost evaluation of machining form features and the relationship among features. The fourth section discusses the formulation of the feature-based cost evaluation problem as the shortest path problem (SPP), and a mathematical model as well as an algorithm for determining the minimum cost design. Conclusions are drawn in the fifth section.
feature-based evaluation of manufacturing cost is formulated as the shortest path problem, and a mathematical model as well as an algorithm are presented to determine the minimum cost design alternative. Copyright 1’) 1996 Elsevier Science Ltd Keywords: feature-based
Desfgn. Vol 28, No 11. pp. 879-885. 1996 Copyr~ht 1996 Elseuer Science Ltd Pmted m Great Emtam All rights reserved OOIO-4485196 $15.00+0 00
design, design for machining, manufac-
turing cost evaluation
INTRODUCTION There are three major aspects in design for manufacturing (DFM): constraints, cost, and quality. The satisfaction of manufdcturing constraints ensures manufdcturdbility of a design’. The evaluation of manufacturing cost aims at minimizing the manufacturing cost of a design. The design for quality increases product quality and manufacturing yield at reduced cost’. This paper attempts to evaluate quantitatively machining cost of products. Some of the most important papers focusing on this issue are as follows. Chen et ~1.~ focused on a framework of feature-based design for manufacturing. Shaikh and Hansotia4, and Jha’ discussed different aspects of manufacturing cost. An extensive review of methods and tools for cost evaluation in design for manufacturing is provided by Thurston and Carnahan’, and Noble and Tanchoco7. The basic guidelines for cost estimation in manufacturing can be found in 0stwald8. Cunningham and Dixon’, and Chang” illustrated typical manufacturing form features. Before evaluating the manufacturing cost of a
CLASSIFICATION FEATURES
OF MACHINING
FORM
The number of features is not finite, however, they can be categorized into a finite number of classes. For each class, properties can be identified. and methodology can be developed to support each class of features rather than a specific feature. Classification of manufacturing form features are also found in References 9, 10 and 1214. These schemes cannot be used easily in the
Hit&z kianufacturing Technology Laboratory, Penn State University, Berks Campus, PO Box 7009, Reading, PA 19610-6009. USA * Intelligent Systems Laboratory, Department of Industrial Engineering, The University of Iowa, Iowa City, IA 52242-l 527, USA t To whom correspondence should be addressed Puper rrccid: 18 Mq 1995. Rrvisecl: 28 October 1995
879
Cost evaluation
in design
with form features:
Simple machining
C-X Feng
form features
- block - cylinder - flat surface - through hole - blind hole - round chamfer - lengthy chamfer - radial groove - keyway - block slot - v- slot - external thread
Typical Machining Form Features
Complex machining
form features
cost evaluation of feature-based designs. A scheme that appears to be appropriate in cost evaluation in a feature-based design is discussed next.
Simple machining form features In this paper, machining form features are classified as simple and complex features (set ~;~~ur~ I). Simple machining form features, c.g. a through hole. a chamfer, and so on, can be machined in a single operation and a single set-up using a non-shaped cutter. All the other machining form features could bc obtained in finite
Chamter 67
I 880
External thread
I
number of additions and subtraction to/from them. Typical simple machining form features are presented in 7ilhk~J I. In Tdh I, a cylinder and a hole are considered as two diRerent simple features, though they can be expressed in the same way (position, radius, and depth or height) from the design point of view. This is because they are obtained by performing different machining operations. A cylinder is obtained by an external turning operation while a hole by a drilling operation.
Complex machining form features
- face groove - T - slot - Y - slot - dovetail slot - internal spline - external spline - internal thread
quantitative classification quantitative environment
et al.
Before discussing the complex form features, two terms are defined. A set-up time is defined as the time used to relocate the part, while the change-over time refers to the time necessary to relocate or change the cutter. Complex machining form features can be derived from the simple form features. A complex feature. such as a Tslot. a Y-slot, cannot be obtained in a single machining operation and a single set-up and/or changeover but several operations and several set-ups and/or changeovers are required. Examples of complex machining form features are presented in Table 2. The formation of a complex feature from simple features is illustrated next. For example, the complex feature T-slot is obtained from the primitive feature block. First, a block slot and then another block slot is subtracted from the block by performing a milling operation. Similarly, a Y-slot is obtained by subtracting ;I V-slot, and a block slot from the primitive feature block. A feature extraction system should provide multiple interpretations of the features. Examples of the feature extraction approach include: Karinthi and Nau’“. who developed an algebraic approach to feature interaction; who presented an algorithm to Tseng and Joshi”. rccogniLe and interpret certain classes of interacting prismatic depression features, e.g. slots, blocks, and cylinders. The larger the number of operations needed to form u complex feature and the longer the set-up and changeover time. the longer the machining time and the higher the machining cost.
Cost evaluation
Table 3
Relationships
between
machining
form features
e,
in design
C-X Feng et a/.
with form features:
Table 4 Unit manufacturing among features
cost of form features and the relationship
Sit?7p/e ,fornlfi’LltLms n/a Block 0.1 Flat surface n/a Cylinder Round chamfer 0. I
Hole External thread V-slot Radial groove
0.1 0.4 0.3 0.2
Keyway Block slot Chamfer
0.3 0.1 0.1
(‘onlpil~.~ forrllfimws 0.5 T-slot 0.6 External spline
Y-slot Internal
0.6 0.5
Face groove Internal thread
0.7 0.6
0.5 0.6
5 6
0.7 1.7
Rclutionship.s
hrtnwn
I
fixtures
0.1 0.4
2 Note: n/a-
spline
not applicable
3 4 (this feature
is often a primitive
feature)
Relationships between machining form features Tub/e 3 interprets the relationships among machining form features at six levels using cylinders as an example. The easy/hard level of the relationship depends mainly on the nature of the set-up/change-over. The machining cost of a part is affected by the relationship among form features (RFF). Silva et ~1.‘~ referred to the RFF as a spatial relationship between features (SRF). They concluded that the spatial relationship includes the interacting and interfeature relationship. Using their point of view, each of the feature relationships 1-4 in T&de 3 is an interfeature relationship, since the features do not interact but there exist a spatial relationship between them. Relationships 5 and 6 in Tuhle J represent the interacting relationships as the features physically interact with each other. The machining time (cost) of a part depends on the time of performing operations and the change-over and set-up time. In general, the change-over and set-up time are the most significant components of machining time17, which implies that the shorter the change-over and the set-up times, the lower the machining cost. Also, the smaller the number of operations, the lower the machining cost. Hence, the number of change-overs and set-ups should be minimized at the early stages of design. The RFF has a significant impact on the machining cost imposed by change-o;;rs and set-ups. Lin and , and Kusiak” presented Wang ‘* . Hayes and Wright methods to minimize the number of change-overs and set-ups in machining. The ranking of machinability of typical RFFs is indicated in Table 3. For example, part 2 contains two holes with the same diameter. It is easier to machine than part 3 as a cutter does not have to be changed, although the relocation of the cutter is needed in both cases. Part 4 is more difficult to machine than parts 2 and 3 since it has to be relocated and an expensive fixture is needed to hold the part. The ranking scheme of machinability is further discussed in the next section. The analysis of types of form features and the RFFs provides a quantitative basis for evaluation of the machining cost. As a result, the unit machining cost and heuristics are developed to determine cost design.
depends on a specific manufacturing environment. The methodology for evaluation of the machining cost is based on the quantitative analysis in the cost of the form feature cost and the RFF cost in Table 4. For example, the complex feature T-slot is obtained from the primitive feature block. First, a block slot and then another block slot is subtracted from the block by performing a milling operation. The estimated cost is arbitrarily determined as 0.5. Similarly, a Y-slot is obtained by subtracting a V-slot, and a block slot from the primitive feature block. The estimated cost is determined on the comparative basis as 0.6. The cost of the Y slot is 0.1 higher than the cost of Y slot. The comparative cost of the relationships among features is based on the easy/hard level. rather than the form features themselves.
Traditional machining Based on the discussion in the second section, a unit manufacturing cost (UMC) is introduced for quantitative evaluation of manufacturing cost of form features and the RFFs (see Tub/e 4). The UMC is determined by two major factors: the type of activities and the time required to perform the activities, which is similar to the concept of activity-based-costing”. For example, the UMC of drilling one unit of a hole is 0.1 (see Table 4), and this value does not include the initial set-up cost of the part. Similarly, the unit cost of milling one unit of a chamfer is 0.1 as shown in Table 4, which provides the basis for calculating the machining cost of a part. The intention of this research is not to construct tables for industrial use but to present a research methodology for calculation of UMCs. Figure 2 shows the UMCs for two different part designs. A digraph is used to represent the manufacturing activities (operations), e.g. cutting, set-up, and tool change-over. Figure 3 presents a graph (the activity-on-
(b)
(4 UNIT
MANUFACTURING
COST
This section presents feature-based cost models for various manufacturing scenarios. The cost models presented here are not exhaustive as each model
I Figure 2 Two design alternatives of a relationship; (b) an orthogonal relationship
I part:
(a)
an
arbitrary
881
Cost evaluation
in design with form features:
C-X Feng et a/
(a) t setup/changeover
drdlmg f4
(b) drilling f4 Figure 3 alternative
A graph representing designs in t;ig~~ _’
the
manul;lcturmg
COSL ol’ the
arc (AOA) convention is used” representing the two designs in Figure 2. In the AOA convention. an arc represents an activity. a node represents an event (start. end), and an arrow represents the precedence among activities. Numerous graphical tools are available to generate process graphs, e.g. IDEF3”j, PERT/CPM’“.‘4. Numerous references on generating digraphs of manufacturing processes from computer-aided process planning are illustrated in the survey of Alting and Changls. only one manufacturing path is For simplicity, presented in Figurr 3 for each alternative design from all possible process plans Figuw 2. In practice. corresponding to the manufacturing environment should be considered. The path 0 - 1 - 2 - 3 -- 4 - 5 corresponds to the design in Figuw 2~. and path + 6 - 7 corresponds to Figzm 2h. In the first o-1 path, node 0 denotes the initial state, which is a block feature, node 5 denotes the terminal node shown in Figure 20. The arcs 0 - 1. 4 + 5. and 6 1 7 denote drilling operations (drilling feature fl, f3 and f4. respectively), arc 1 - 2 denotes a set-up [the set-up time is assumed to be longer than the changeover time, and since they occur simultaneously, only the set-up times 1 + 2 and 1 + 6 are considered (see Figure 3)]. The arc 2 - 3 in Figurr 3 denotes a milling operation (milling feature f2 in Figuw 2~). The manufacturing cost (c,) of a part can be calculated as follows: (1)
cp = (‘,,, + cc + (’h where L’,, = C:llI,,cc, --the
cost of machining
I, unit long
workpiece, where L’,,is the machining cost for unit length, and m is the number of machining operations; (‘c = C:‘!, C’C, the change-over cost of cutting tools, where cc, is the cost of change-over j, and n, is the total number of changeovers; and c\ = C;l’,c,,-the set-up cost of workpiece. where (‘,A is the cost of set-up k, and YI? is the total number of set-ups. Equation 1 assumes that the set-up and change-over tasks are performed sequentially, which applies to traditional machining. It also assumes that all operations are performed on one machine tool so that the transportation, storage, loading and unloading cost are not considered in the equation. Based on the graph in Figurr 3, Equation I is illuslrated next. Consider part 5 in Tub/e 3 (see also Figurc~ 2h). Assuming /,.i = 1, the unit cutting cost two holes, (‘11,= 0. I + 0.1 = 0.2 results from drilling where the value 0.1 is obtained from T&de I. Since the two holes cannot be drilled in one set-up, an additional set-up and change-over are needed. The change-over cost c’c= 0.2 refers to the cost of relocating the drill to the second hole. The set-up cost cs = 0.3 is based on the time used to relocate the part as the two holes are in different orientations. Thus the unit machining cost of this part is (’,, = 0.7 in Tub/e 4. Similarly, cp = 1.7 in Tub/c 4 for part 6 in T&e 3 (see also Figuw 2~).
Simultaneous machining There are situations were automatic and special purpose machine tools are employed. For example, to machine the part in Figure 4, a special machine tool can be used to drill the four satellite holes simultaneously. In this case, 1 in the machining cost ~4,~is calculated from Equation the same way as if the four operations were performed independently. In the graph representing this machining path, one operation occurs rather than four, however, the cost of this single operation equals to the total cost of the four operations (see Figure 4h). In Figzrrr 4h, the hole fl in the centre is drilled first. then the four satellite holes f2 arc drilled simultaneously. By simultaneous machining. one takes advantage of the economy of time as three tool changeovers are eliminated (see Figure 4h).
Q”
+
1 1
C
‘I-
-+A+? Qn bC
c-c
(b)
A-A (a)
changeover Figure 4
A
process graph
part with multiple
c-c 6)
drilling f2
operations:
(a) part: (b) machining
Figure 5 Two alternative part designs: (a) four small holes with different orientations than the large hole fl: (b) four small holes with the same orientation as the large hole fl
Cost evaluation
in design with form features:
C-X Feng et a/.
Multiple machine tools
Figure 6 alternative
The graph representing designs in Figum 5
Simultaneous
the manufacturing
process of two
Multiple machine tools are used when a part cannot be machined on a single machine. In this case, transportation, storage, and loading and unloading costs occur. It is more convenient to use time rather than cost to evaluate designs in this case. Let tLi, t,5,,tl,, and tui denote the transportation, storage, loadmg and unloading time, respectively, and (at,, cs,, cli, and cu, are their scaling factors, respectively. Then the manufacturing cost of the part is calculated as follows:
set-up and change-over (‘r =X:1, cmi + q=ot$k,
Simultaneous set-up and change-over occurs in machining when automatic machine tools are used. In this case, the set-up and the change-over costs cannot be calculated separately as expressed in Equation 1. Furthermore, the maximum of the set-up and change-over times is used rather than the cost (see Equation 2). cp = (‘,,, + C”,=otj”\ci
+ I&tsj$,j?
+ qlot,,,(.,J,
+ C;l”t,,3(.,,3
+ C:lq,)f”,&,,j‘l
(3)
where m and n are the total numbers of machining operations, and set-ups/change-overs, and n,, n2, n3, and n4 are the total numbers of transportation, storage, loading and unloading activities, respectively.
(2)
where c, is calculated as in Equation 1, t, is the maximum of set-up and change-over time, cscj is the scaling factor for transforming time into a cost. Equation 2 is illustrated next. Figure 5 presents two alternative part designs, while the graph in Figure 6 represents manufacturing cost of the two designs. Since a machine centre is used, machining, change-over and setup take place simultaneously. Consider case (a), the large hole is drilled first, then the two side holes are drilled simultaneously, and finally the remaining two side holes are drilled simultaneously. In this case, both the changeover from a large drill to a small drill and the set-up to reorient the part for drilling can be performed simultaneously. Let the maximum of the set-up and change-over time be 1 s. and the scaling factor be $0.3 per second, the cost of the simultaneous activity is $0.3 as indicated in Figure 6h. Accordingly, the total machining cost is the cost to drill the two side holes rather than the cost of drilling one side hole. Case (b) is illustrated in Figure 4h. The graph representing the manufacturing process is shown in Figure 6. For simplicity, only one manufacturing path is selected for each design alternative. Based on Figure 6. the manufacturing cost for design (a) is 1.5. while the manufacturing cost for design (b) is 0.7
THE MODEL EVAEUATION
OF FEATURE-BASED
COST
The shortest path model The problem of determining the minimum manufacturing cost can be formulated as the shortest path problem. Figure 7 illustrates four design alternatives of a part. A graph representing the RFFs of the part is presented in Figure 8a. The cost values c, -cl7 in Figure 8 corresponding to the manufacturing operations are listed in the Appendix. For simplicity, only one manufacturing path is presented in Figure 8a for each design in Figure 7. In practice, all alternative paths should be generated for each design so that the SPP algorithm selects the minimum manufacturing cost design alternative. Also, we assume the traditional machining process is used to manufacture this part (i.e. the case discussed in the previous section). Each design path ends with a feature and the corresponding operation. The latter implies that there may not be a common terminal node in the graph. The graph in Figure 8a is transformed into a network by adding a dummy node 29 and connecting it to the
-!
f,
D-D
(b)
E!E Cd)
Figure 7 The alternative part designs: (a) five holes with two orientations and two sizes: (b) five holes with one orientation and three different sizes; (c) three holes with two sizes and two threads with same size. and with holes and thread in the same orientation: (d) five holes in the same orientation and two different sizes
883
Cost evaluation
in design
with form features:
C-X Feng et al.
terminal node of each path with a dummy (zero cost) arc (see Figurr ah). Finding the minimum cost path in a network ~a11 be modelled as the network flow problem. In the solution. ;I unit flow is sent from the source to the sink at minimum cost. At the source, there is a net supply of one unit. While at the sink, there is a net demand of one unit. For all other nodes, there is no inflow or outflow.
arc, set u(.Y) = min[v(.\-), I/(P) + c,]. where (‘, is the cost of the arc,i from node p to node .Y. Step 3. [Fixing a value as permanent]. Of all nodes .Ywith associated temporary values. find node .I’ for which V(,I$) -_ min v(.Y). Label the value In as permanent and set 12= .I‘. Step 4. [Termination]. If the minimum cost from node ,\ to node I is considered, and if ,V= t,. then terminate the algorithm with v(t,) as the solution. Ifp # f,,, then return to Step 2. a11
The minimum cost algorithm For a large cost evaluation problem. an cfficicnt heuristic algorithm should be used rather than the standard approach for solving the minimum cost formulation. Since the feature-based evaluation problem is represented with a direct acyclic graph, the algorithm fol solving the cost evaluation problem, presented next, is essentially Dijkstra’s algorithm’“. The two algorithms differ in the termination condition. The cost evaluation algorithm terminates when a node I,,. denoting nodes preceding the terminal node I, 1s reached, while Dijkstra’s algorithm terminates when the terminal node t is reached.
The algorithm Denote the start node and the terminal node by .\ and /. respectively, and f, denotes nodes preceding the terminal node t. To each vertex .\- t X. a value I/(.\.) is assigned. which denotes the minimum cost from node .s e X to .\-. This value may be temporary or permanent. where temporary means that v(_x-) could still be reduced, and the permanent is the minimum cost. Step 1. [Initialization]. Set v(.c) = 0 and label this value as permanent. Set V(I) = x for all .\- t X and .\- # .s and label these values as temporary. Set 1’ z= ,Y. Step 2. [Updating the values]. For all nodes .\- with temporary values z~(_Y) and which are connected to 11by
Illustrative example For the network in Figwr Hh, the cost coefficients c, ii = I. .27) are assigned with the following values: (‘, ~- 0. I. (‘1 = 0.3. (‘3 = 0.3, CJ = 0.1, (‘5 = 0.2, C(,= 0.1 . (‘- ~=0.3. c\ = 0.2. (‘0 = 0.1. c,,, = 0.2, c,, = 0.1, (‘13 .= 0.3. (‘,I = 0.1. (‘13= 0.2, (‘,i =O.l. C’,h= 0.3, (‘17=O.l, (‘lh ~~ 0.2. c,<) = 0.1, (‘?,, = 0.3. c7, = 0.6, c2: = 0.2, (‘1: 0.6, (‘24= 0.2, (‘75= 0.1. (‘2(,= 0.2. (‘27= 0.1. In this example, node 1 is the start node s, node 29 is the terminal node t, and nodes 12, 20. 24, and 28 are the /,, nodes. Solving the minimum cost formulation with LINDO or applying the minimum cost algorithm. both results in the minimum cost nath (1 J (2) ~- (13) - (14) + (15) - (16) + (25)‘+ (2‘6j to design (/ in (27) --- (2X) - (29) corresponding Figuw 7.
CONCLUSlONS The methodology for classification and cost evaluation of machining form features and relationships among form features (RFFs) was proposed. The methodology is meaningful in feature-based design for manufacturing and benefits the establishment of standards for individual features. The unit manufacturing cost is determined by two major factors: the manuFacturing activities and the corresponding time required to perform these activities. Cost evaluation models for four typical machining cases were investigated. A design feature is checked and evaluated for manufacturability first, then the manufacturing cost is evaluated against the cost model. The impact of tolerances and the sequence of operations were not considered in the paper and should be studied separately.
ACKNOWLEDGMENT The research presented in this paper has been partially supported by research funds from the US Army (contract No DAAE07-93-C-R080) and the National Science Foundation (grant No DDM-9215259).
REFERENCES I
Figure 8
Representalion ol‘the feature-based cost c\;tluittion problem: (a) graph representing the generic relationship among fwm features. (b) directed acyclic network representing the relationship among form features
884
2
t cng. c‘ and Kusiak, A ‘C’onstralnt-based destgn 01’ parts’. ~‘1~lll~lrlr:Aicl~~~l I)L,.V.Vol ?X No 5 (19%) pp 343 352 I-‘cng.(’ and Kusink, A ‘Design of tolerances for quality’ 1,~Hight. 1 K and M&tree, F (Eds) IIc.Y&I 77~~~~ and Methoc/o/o~~~~ASME. New York (1994) pp 13 20
Cost evaluation
3
4
5
6
7
8 9
IO II
I2
13
I6
17
IX
I9
20 21 22 23
24 25
26
Chen, 1’. Miller, R and Vemuri, K ‘On implementing an integrated design manufacturability assessment environment’ in Gupta. G and Shoup. T E (Eds) Computers in Enginrcring, ~roc. ASME Computws in Enginwring Cot?f: ASME. New York Vol I (1991) pp 407-413 Shaikh. M and Hansotia, B ‘Minimization of drilling costs: a closed-form solution ‘Comp~rtcx~ h&s/r. Engng Vol 23 No I ~4 ( 1992) pp 443 446 Jha. N ‘Stochastic mathematical modeling and manufacturing cost estimation in uncertain industrial environment’ Itilt. J. Prowl. Rcs. Vol 30 No I2 (1992) pp 2755m 2771 Thurston, D and Carnahan. J ‘Intelligent evaluation of designs for manufacturing cost‘ in Kusiak, A (Ed.) Conc~urr~nt Engineering: An/omtrtion. Tools. trnd Tcchniquc.s John Wiley, New York (1993)pp437~462 Noble, J and Tanchoco, J ‘Design for economics’ in Kusiak, A (Ed.) C’orrc~urrcnt Enginrcring: Automution. Tools, und Twhniyues John Wiley, New York (1993) pp 401-436 Ostwald. P AM Co.ri Estimutor (4th Ed.) McGraw-Hill, New York (1988) Cunningham, J and Dixon, J ‘Design with features: the origin of features’ irl Tipnis. V A and Patton, E M (Eds) C’orn/~uters in Enginowing ASME, New York Vol I (1988) pp 237-243 Chang, T C Ev/x,rt Procc.s.v Planning,for Munufircturing Addision Wesley, Reading, MA (I 990) Shah. J, Hsiao. D and Robinson. R ‘A framework for manufacturability evaluation in a feature-based (‘AI) system’ itt Prw NSF Dc,sign und Munqfucturing S~.vtm~ Cortf: Arizona State University, Tempe. AZ. ASME, New York (1990) pp 61 66 Pratt. M and Wilson, P ‘Requirements for support of form feature\ in a solid modeling systemtinal report’ CAM-l Rcporr. R-NS-ASPP-O/ Arlington, TX (1985) Shah, J ‘Features in design and manufacturing’ in Kusiak, A (Ed.) /ntc,/li,~cwr De.sisTn und Mtmufircturing John Wiley. New York (1992) Silva. R, Wood, K and Beaman, J, ‘Representing and manipulating interacting and interfeature relationships in engineering design for manufacture’ in Ravani, B (Ed.) Advunws in Design Auloma/ion. Proc. ASME Design Automcttion Conf: ASME, New York (1990) pp I-8 Karinthi, R R and Nau, D S ‘An algebraic approach to feature interactions’ fEEE Truns. PAMI Vol I4 No 4 (1992) pp 469% 484 Tseng. Y J and Joshi. S B ‘Recognizing multiple interpretations of interacting machining features’ Comput.-Aided Drs. Vol 26 No 9 ( 1994) pp 667m 688 Groocer. M Automation, Production S,~.v~em.s. und Compllrutw Intc,grutct/ Mtrnufuc~turing Prentice Hall, Englewood Cliffs. NJ (1987) Lin. c‘ and Wang, H ‘Optimal operational planning and sequencing: minimization of tool changeovers’ I/I/. J. Prod. Res. Vol 3 I No 2 (1993) pp 311~ 324 Hayes. C and Wright, P ‘Automatic process planning: using feature inleraction to guide search’ /. Mfi?a sysr. Vol 8 No I (1989) pp I- 15 Kusiak, A Intc~lligcwr Manufirc~twing .S~wcw~s Prentice Hall. Englewood Cliffs, NJ (I 990) Epstein, M (Ed.) Advancc.~ in Mnnug~mcnt Acwunting JAI Press. Greenwich, CT (1994) Elmaghraby. S Ac,tivit,v Network: Project Plunning und Control h? Network Models John Wiley. New York (1977) U S Air Force ‘Integrated computer aided manufacturing (ICAM) architecture Par II. volume IV-- Functional modeling manual (IDEFO)’ Wright-Patterson AFB, Ohio 45433: Air Force MateriaI5 Laboratory (1981) Steward, D Swrm Anul~sis and Managcmcwr: Strrrcrurc. Strutrg), und Design Petrocelli Books, New York (198 I) Altinp, L and Zhang. H ‘Computer aided process planning: the state-of-art survey’ In/. J. Prod. Rex. Vol 27 No 4 (1989) pp 553 585 Dijkstra, E ‘A note on two problems in connectlon with graphics’ N/ot~c~~r:cc/lc,Mufhcmutik Vol I No 3 (1959) pp 269-271
APPENDIX cost of drilling fl cost of repositioning
in design with form features:
C-X Feng et al.
cost of tool changeover cost of drilling feature f2 cost of repositioning the tool to f3 cost of drilling f3 cost of repositioning the workpiece cost of tool change-over cost of drilling f4 cost of repositioning the tool to f5 cost of drilling cost of tool change-over and repositioning workpiece cost of drilling f6 cost of repositioning the workpiece cost of drilling f8 cost of tool change-over and repositioning workpiece cost of drilling f7 cost of repositioning the workpiece cost of drilling f9 cost of tool change-over and repositioning workpiece cost of drilling and taping f10 cost of repositioning the workpiece cost of drilling and taping fl 1 cost of repositioning the workpiece cost of drilling f12 cost of repositioning the workpiece cost of drilling f13
the
the
the
Chang-Xue (Jack] Fang is tt.wistunt projtissor of’ Mcvhunicul Enginrering ut Penn Stutc Univwsit~, Bwks Cump~s. PA. He holds a BS dvgrw in mechunic~ul engineering, cm MS degree in munu.facturing enginaering. und u PhD degree in industrial engincrring. His wwurch interests ore in c~on~urrent enginwrirtg, quality mginwring. und ugile munu,facluring.
Andrew Kusiuk i.s pro/~ssor of’ Industriul Engineering ut the Univerxit~~ of’ lowu. IOMU Citjj. IA. He is intcws/ed in enginwring &sign. manufircturing. urtificial inlc~lligmcc~. trnd optin~i:trtion. Dr Kusiuk is The Editor-in-Chicjf of The
Journal
of Intelligent
Manufacturing.
Chun-Cite Huang is u PhD student in the Department of Industrial Enginrcring (II the Uniwrsity of lov~xt. Hr rcwived un MS degree in operutions wseurc,h ,fjw~~ Columbia Uniwr.sit~~ in 1992. His rrseurch intrrrsts ure in prodwt unti process design, kanhan .v~xtc~rn.s, umi scheduling.
the workpiece
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