2009-Rapid_prototyping– a technology transfer approach for development of rapid tooling

Rapid prototyping–a technology transfer approach for development of rapid tooling

Dilip Sahebrao Ingole

Department of Mechanical Engineering,Prof.Ram Meghe Institute of Technology and Research,Badnera,India

Abhay Madhusudan Kuthe

Department of Mechanical Engineering,Visvesaraya National Institute of Technology,Nagpur,India

Shashank B.Thakare

Department of Mechanical Engineering,Prof.Ram Meghe Institute of Technology and Research,Badnera,India,and

Amol S.T alankar

Department of Mechanical Engineering,Gyan Ganga Institute of Technology and Sciences,Jabalpur,India

Abstract

Purpose–The purpose of this paper is to apply rapid prototyping(RP)philosophy as a technology transfer in industries to take its time and cost-effective advantages for development of rapid tooling(RT).

Design/methodology/approach–Experimentations are performed for development of RT for sand casting,investment casting and plastic moulding applications.

Findings–This paper reports the procedures developed for manufacture of production tooling using RP.A cost/bene?t model is developed to justify implementation of RP as a technology transfer in industries.

Research limitations/implications–The examples are limited to parts build by fused deposition modelling RP process.However,the concepts experimented may be applied for other RP processes.

Practical implications–RP has proved to be a cost-effective and time-ef?cient approach for development of RT,thereby ensuring possibility for technology transfer in casting as well as plastic industries.

Originality/value–This is the pioneer attempt towards quantifying RP bene?ts,in view of technology transfer.This paper presents original case studies and?ndings on the basis of experimentations performed in foundries.

Keywords Rapid prototyping,Machine tools,Cost-bene?t analysis

Paper type Case study

1.Introduction

Despite the substantial research in CAD/CAM technology, the gap between CAD and CAM have been identi?ed in two aspects:

1rapid creation of3D models and prototypes;and

2cost-effective production of tooling required for casting industry.

Rapid technologies(RTs)are the solutions for physical realization of products well before full-scale manufacturing (Y an and Gu,1996).Rapid manufacturing(RM),rapid tooling(RT),rapid prototyping(RP),virtual prototyping and reverse engineering are the range of technologies considered under RTs.The RP processes can be used for directly producing the casting patterns referred to as direct RT.Several researchers have explored rapid casting development using RP and RT(Chua et al.,1999;Pham and Gault,1998; Chakradeo and Kulkarni,2002;Rooks,2002;Pal et al.,2002; Rathore et al.,2002;Ingole et al.,2006).

Pattern development is the main bottleneck in terms of time and cost for manufacturing intricate castings in the foundries.T o substantially shorten the time for developing patterns,moulds and prototypes,RP is an ideal method for complex patterns making and component prototyping (Chakradeo and Kulkarni,2002;Rooks,2002).In particular,the use of RP processes has proved to be a cost-effective and time-ef?cient approach for producing patterns and core boxes for sand casting(Wang et al., 1999).Mueller(2005)reported that the RP patterns not only lowers cost and shortens lead times for low-volume casting jobs,but also it enables investment casting to compete with machining and weldments for very low-volume projects,even quantities of one.

There are two ways to realize the tooling using RP.The?rst is to obtain the mould cavity and deposit a layer of metal on

The current issue and full text archive of this journal is available at https://www.wendangku.net/doc/3d14330623.html,/1355-2546.htm

Rapid Prototyping Journal

15/4(2009)280–290

q Emerald Group Publishing Limited[ISSN1355-2546] [DOI10.1108/13552540910979794]Received:15August2008 Revised:14January2009 Accepted:12March2009

the mould obtained by RP.The metal layer forms the mould surface.The second is to use RP process to directly build pattern for investment casting process or sand casting process (Chua et al.,1999;Dickens et al.,1995;Pal et al.,2002;Pham and Gault,1998;Rathore et al.,2002).

The main aim of this paper is to report on the experimentation conducted for the rapid manufacture of production tooling required by casting as well as plastic moulding industries.It also aims to develop a cost/bene?t model to justify technology transfer of RP.

2.Need and scope for technology transfer in foundry industry

The idea of using RP machines for the manufacture of products in high or medium volumes seems unrealistic as the cycle times,material costs and capital equipment for processes such as injection moulding are far lower than RP. However,Hopkinson and Dickens(2001)appreciated the zero tool costs,reduced lead times and considerable gains in terms of freedom in product design and production schedules using RP.In metal casting processes,conventionally,the development of patterns and core boxes account for more than70per cent lead time and greatly in?uence cost and dimensional quality of the product.Lee et al.(2004) reported signi?cant amount of time savings(89per cent)in the lead times for the patterns produced with direct RP method as compared to sacri?cial patterns.Bernard et al. (2003)identi?ed that the layered manufacturing techniques are economically comparable with machining processes for the manufacturing of the core boxes.T o stay ahead in competition,the updated technology demands development of fast and accurate products of high standards.Study revealed that the sand cast components manufactured using RP patterns shown better results for dimensions and surface ?nish(Ingole et al.,2006).

These facts highlight the importance of developing a method for the RM of tooling.RP techniques involve no tooling or?xtures,resulting in simpler set-up,lower overhead cost and shorter production lead times.The parts that were previously impossible,extremely costly and time consuming can be built with an ease with RP.Karapatis et al.(1998) mentioned that,with an RT,the mass production tools such as moulds,dies,etc.can be made ready in very short times. The need for technology transfer for the development of tooling is due to following reasons:

.RP fabrication process is automated;

.fabricates intricate and small parts;

.substantial reduction in lead time;

.eliminates tooling;

.eliminates process planning;

.customized product;

.produces no scrap;and

.no assemblage of parts.

The following types of industries have the scope for technology transfer:

.sand casting;

.investment casting;and

.plastic moulding.3.Challenges in tooling development

Basically,the sand casting practice is not suitable for manufacturing small and intricate parts due to many reasons.The established tooling technologies require a great deal of time and expense.The challenges in established tooling development practices are summarized below:

.preparation of small-sized sand moulds are dif?cult with conventional patterns;

.perfection in producing contoured patterns is always the problem;

.wooden patterns are dimensionally unstable and metal patterns require more?nishing time and cost;

.accuracy is the major problem for parts produced with sand casting;

.parts produced with conventional patterns require further ?nishing;

.cores and core prints are required to be separately prepared and assembled;

.lead time for producing patterns is considerably large;and .metal patterns are heavy and wooden patterns being delicate,both required to be handled carefully.

4.Objectives and methodology

The objectives of the study are:

.to develop a model for faster and cheaper method for manufacturing of tooling;

.to verify the possibility for technology transfer from conventional to modern so as to take time and cost-effective advantage;and

.to quantify the magnitude of cost savings and other ef?ciencies that will result from technology transfer.

The following experimentations were conducted using RP: .development of RT with sand casting;

.development of RT with fused deposition modelling (FDM);and

.development of master patterns with RP patterns.

4.1Development of rapid tooling with sand casting There are various ways of obtaining the tooling using RP techniques.The?rst is to obtain the sand mould cavity using RP patterns and pouring metal into it.The obtained permanent mould can be used as a die after?nishing and surface treatment.The dies are used to produce wax patterns for investment casting.The dies produced with this method are also suitable to produce parts with plastic moulding process.Second,the acrylonitrile butadiene styrene(ABS) part cavities produced with RP process can be used as a die after metal coating/spraying.Third is to use the RP technique to directly fabricate a master pattern to produce other metal patterns.

The illustration is related to the method for rapid fabrication of cast iron small-sized dies,in considerably less time compared to the conventional die manufacturing techniques.The steps involved in development of the RT by using sand casting is shown in Figure1.The?rst step in development of RT consists3D solid model of a part as shown in Figure2.The standard tessellation language(STL)?le generated directly from solid model is used for part geometry recognition and preprocessing of physical prototype.The STL?le is utilized for physical realization of mould prototypes using FDM RP process as shown in

Figure 3.The cope and drag parts of the sand mould prepared using RP patterns are shown in Figure 4.The cast iron semi-?nished permanent moulds are shown in Figure 5.The permanent mould,called a die,is further heat treated,?nished and surface treated is shown in Figure 6.The plastic and wax components produced with ?nished die are shown in Figure 7.

The major advantages of the process are summarized below:

.produces accurate cast iron dies,since it uses accurately produced RP patterns;

.process is economical,manufacturing of patterns do not require tooling and process planning;

.intricate cast iron dies can be easily produced,since there is no limitation for shape of the required pattern;

.dies produced are suitable for investment casting,injection and blow moulding processes;and

.

dies are suitable for materials like wax,plastics and low melting point alloy parts.

4.2Development of rapid tooling with FDM

RP patterns can be used as substitutes for the traditional wax patterns employed in investment casting process.Figure 8represents a CAD model of a crankshaft and Figure 9shows the CAD model of split mould cavities of a crank part.Figure 2CAD models of split mould cavities

19

519

5105

24

Figure 3Split mould cavities of ABS produced with FDM

process

Figure 4Cope and drag parts of sand

moulds

Figure 5Semi-?nished cast iron

moulds

Figure 1Steps in RT development with sand casting

The plastic moulds are obtained with FDM RP process are shown in Figure 10.

4.2.1Development of tooling by plating on plastic

The metal plating on plastic carried out on ABS mould cavities is shown in Figure 11.The major bene?ts of metal plating on plastic are it:.

increases the thermal conductivity of the mould surface;.increases the life of the plastic mould acting as a die;and .

improves the surface ?nish of the RP mould.

4.2.2Observations during experimentation of plating on plastic .

During the electroplating of the plastic moulds,the surface treatment was carried out to make it conductive.The moulds were dipped into the solution for etching at 708C for 20min..

The moulds were fabricated in layers with the resolution of 0.3mm;due to its porous surfaces,the chemical percolated into pores..

The entrapped chemical could not be cleaned or taken out by any means.

Figure 6Surface-treated ?nished sand mould

dies Figure 7Plastic and wax components produced with sand cast

dies

Figure 8CAD model of a crank

part

Figure 9CAD models of split mould cavities of a crank

part

Figure 10Rapid prototyping models of split mould cavities with in-build

cores

.

As the surface could not be treated to make it conductive,the dies could not be metal plated.

Figures 12and 13represent the unsuccessful and partially successful attempts,respectively,of producing the wax patterns with ABS mould cavities as shown earlier in Figure 11.

In the next attempt,the two piece die was split into three pieces as shown in Figure 14.The transverse section of the die was taken to reduce height of the die.The additional vent was provided for removal of air.The die was held in vertical position and the molten wax at 788C temperature was injected into the die cavity at 248C (room temperature).The wax was allowed to cool and solidify for 20min.The wax patterns produced plastic die are shown in Figure 15and a wax pattern with gating and riser produced by RP plastic die is shown in Figure 16.

4.2.3Observations during production of wax patterns

Following are the observations during wax pouring process:.

Metal paint cannot cope with temperature above 808C but shows good thermal conductivity.It also improves the surface quality of tooling..

Metal paint is not peeled off when the wax pattern is removed..

Die half having the smaller depth can be separated easily and leaves the pattern,but the die half having larger depth needs ejectors to remove the pattern.4.3Development of master pattern from RP pattern In this case,a CAD model was prepared for the component using reverse engineering technique.The ABS pattern was developed using FDM RP process as shown in Figure 17(a).From this RP pattern,the aluminium master pattern was developed as shown in Figure 17(b).The resulted aluminium master pattern was used successfully to obtain the mould cavity and hundreds of sand casting components as shown in Figure 17(c).The components obtained shown better Figure 12Wax pattern produced after ?rst wax pouring –the unsuccessful

attempt

Figure 13Wax pattern produced after second wax pouring –partially successful

attempt

Figure 14Rapid prototyping models of metal coated mould cavities into three

splits

Figure 15Wax patterns produced by rapid prototyping split

mould

Figure 11Rapid prototyping models of split mould cavities with metal

coating

results including surface ?nish and dimensional accuracy.The features in ABS RP patterns were re?ected in the aluminium master pattern.These features were further transformed in the actual products.This ensures that one can successfully use RP patterns for getting the master patterns from metals.

4.4Rapid prototyping patterns for sand casting

RP patterns were used to obtain the sand mould cavities as shown in Figure 18.The resulted components shown better surface ?nish and dimensional accuracy as compared to the metal patterns.Various features like ?llets,chamfers,edges,etc.were prominently improved and closed tolerances were achieved.Figure 19shows drag part for the mould obtained from RP patterns.RP patterns can be removed very easily from green sand mould as compared to the wooden or metal patterns due to poor adhesive property of ABS plastic material.Figure 20shows actual sand cast components obtained from RP patterns.

4.5Cost and lead time comparison using different types of patterns

The comparison of cost and lead time is vital to the possibility of technology transfer in foundries.In order to determine the total cost of part preparation,the most in?uential parameters like model material,support material,man and machine hour rates,etc.were considered.The material cost was computed based on volume of material used and the unit price of material.The values of lead times for RP,wood and metal patterns are given in T able I.The values of percentage reduction in lead time as compared to RP patterns are given in T ables II and III represent comparative costs of patterns.T ables IV and V represent pattern unit costs and expected number of components produced using wood,ABS and metal patterns,respectively.T able VI gives the percentage savings in lead time compared to wood and metal patterns.

Figure 21shows the lead time comparison of producing RP,wood and metal patterns.The bar chart shows that the time required to produce RP pattern is minimum as compared to wood and metal patterns.The patterns produced with FDM RP process show 82-93per cent reduction in lead time compared to wood and metal patterns as shown in Figure 22.In RP,the lead time is drastically reduced because RP do not require special tooling,machine set-up and process planning before going for actual fabrication.

In order to determine the total cost of part preparation,the most in?uential parameters like model material,support material,man and machine hour rates,etc.were considered.

Figure 16Wax pattern with gating and riser produced by rapid prototyping split

mould

Figure 17Rapid prototyping pattern,brass master pattern and sand cast

product

(a) FDM RP pattern from ABS material (b) Aluminium master pattern (c) Sand cast product

The material cost was computed based on volume of material used and the unit price of material.Figure 23represents a comparison of costs for patterns produced with different methods.It has been observed that the cost of RP patterns is

Figure 18Rapid prototyping patterns for parts I and II produced with FDM

process

(a) Pattern for part-I (b) Pattern for part-II

Figure 19Drag part of green sand

mould

Figure 20Parts produced with sand casting

process

Table I Lead time comparison for producing different types of patterns

Time (h)

Type of pattern Pattern I Pattern II RP 138.5Wood 4848Metal

120

120

Table II Percentage reduction in lead time as compared to RP patterns

Pattern I

Pattern II

Metal Wood Metal Wood 89

82

93

82

Table III Comparative costs of patterns

Pattern I

Pattern II

Wood RP Metal Wood RP Metal Cost of pattern

1,700

9,458

9,673

950

5,428

6,208

Table IV Pattern cost per unit

Cost per unit

Type of patterns Pattern I Pattern II Metal

4.84 3.10RP 23.6513.57Wood

42.50

23.75

Table V Expected number of parts produced with different patterns

Patterns

Expected number of parts produced

Wood 40ABS 400Metal

2,000

lower than the patterns fabricated with CNC operation.But,the costs of RP patterns are found to be higher than the wood patterns.

Figure 24represents the per unit pattern cost comparison for patterns produced with the operations CNC,RP and woodworking.The bar chart indirectly shows that the unit cost of part produced with metal pattern is minimum,provided parts are produced in mass scale.For the small scale volume of production,the unit cost have been observed less in case of RP patterns.

Figure 25shows the expected number of parts that can be produced using wood,ABS and metal patterns.The expected number of parts produced using metal pattern is maximum,i.e.2,000and the number of parts produced using wood patterns is minimum,i.e.40.The RP patterns found to be useful for high-variety mid-volume type of production and RP patterns can generally produce about 400parts without any dif?culty.Figure 26shows the percentage savings in lead time Figure 21Lead time comparison for producing different types of patterns

20406080100120140Types of patterns

L e a d t i m e (h o u r s )

Figure 22Percentage reduction in lead time as compared to RP patterns

102030405060708090%

Figure 23

Comparative costs of patterns produced with different methods

2,000

4,0006,0008,00010,00012,000R S .

Figure 24Pattern cost per unit

51015202530354045Pattern - I Pattern - II

Types of patterns for part I and part II

P a t t e r n c o s t p e r u n i t (R s .)

Figure 25Expected number of parts produced with different patterns

3006009001,2001,5001,8002,100Wood

ABS

Metal

Types of patterns

Q u a n t i t y o f p a r t s

Figure 26Percentage savings in lead time compared to wood and

metal patterns

102030405060708090100% S a v i n g s i n l e a d t i m e

Table VI Percentage savings in lead time compared to wood and metal patterns

Percentage savings in lead time Patterns Pattern I Pattern II Wood 7382Metal

89

93

compared to wood and metal patterns.It has been observed that,the lead time was reduced by more than89-93per cent in comparison with metal patterns.The lead time of RP was reduced by73-82per cent in comparison with wood patterns.

5.1Development of“cost/bene?t”model

The costs incurred and cost saved in manufacturing processes can be easily quanti?ed.The quanti?ed cost helps a lot in making crucial?nancial decisions.But,it is very dif?cult to quantify the bene?ts like time,functionality,quality, satisfaction,manufacturability,customization,etc.in terms of cost.Attempts are made by the author to develop a“cost/ bene?t”model by quantifying the bene?ts of RP philosophy, in terms of costs savings,in order to justify RP’s implementation as a technology transfer in industries.

RP technology derives radical change by eliminating the costs in tooling,jigs and?xtures.It drastically reduces the cost of process planning.As a major change,the human cost is substantially reduced,since RP requires minimum human skill and attention.Finally,the signi?cant change occurs by materially reducing the cost of scrap,rework and assembly. The signi?cant costs incurred and costs saved in RP are identi?ed and conceptualized,respectively.The study revealed important information and the corresponding values of costs incurred and costs saved are represented in T able VII.The part design cost is more or less same in all the manufacturing processes.Hence,the cost of part design is not considered in the formulation of cost/bene?t model.The distinguished features and derived corresponding bene?ts of RP technology,along with their signi?cant impacts on costs are represented in Table VIII.Notations used in the formulation of“cost/bene?t”mathematical model are given in the respective tables.

5.2Signi?cance of complexity index

RP processes are in demand basically to manufacture complex geometry parts for single or low volume of production.Since RP is an automatic process,the number of parts produced of similar size and geometry show negligible variation.This causes dif?culty in comparing RP parameters to evaluate the performance.The mathematical model or generic form is necessary to correlate the costs and bene?ts in RP.The author has introduced a new term called“complexity index”in order to overcome above dif?culty and formed the basis to deal with variety of RP parts.The“complexity index”is computed from two parameters,i.e.total volume of material required to build the part and time elapsed and is represented by equation(1):

i?

em mts mT

t b

e1Twhere m m,s m and t b are the model material,support material and the build time,respectively.The values of build time are considered in minutes for the computation of complexity indices. The sample values of“complexity index”computed for various parts using the above formula are represented in T able IX.

The computed values of various bene?ts in terms of costs in RP are represented in T able X.

5.3Formulation of mathematical models for C o,C m,C L and C p

The following four mathematical models are formulated after identifying the dependent and independent parameters,for signi?cant costs and bene?ts in RP.The data are computed using dimensionally homogeneous equations(2-5),as given below:

Table VII Costs incurred and costs saved in RP

S.No.Costs incurred in RP Costs saved in RP(in terms of bene?ts)Range of savings(%)Average saving(%) 1Machine operation(C o)No process planning95-9896.5

2Material(C m)No tooling90-9592.5

3Operator(C L)No scrap or rework90-9894

4Pre-and post-processing(C p)No assembly100100

5–Operator80-9085

6–Machine setup90-9592.5

7–Total cycle time80-9587.5

8–Customized product80-9085

Table VIII Bene?ts affecting signi?cant costs in RP

Impact of bene?ts on signi?cant costs in RP S.No.Features of RP Bene?ts of RP C o C m C L C p 1Automated process Minimizes human cost(H m)A N A N 2Fabricate intricate and small parts Good manufacturability(M g)N N N N 3No tooling,jigs and?xtures Eliminates tooling cost(T c)A N A A 4Reduces process planning Reduces planning time(P p)N N A A 5Single unit or small batch Customized product(P c)A A A N 6Produces no scrap No disposal cost(D o)A A N A 7Better accuracy and?nish Assured quality(Q m)A A A A 8Integrated product manufacturing Eliminates assembly cost(A o)N N A A 9Requires no machine setup time Reduces total cycle time(M t)N N A A Note:A–affects,N–does not affect

C o?1:10136*

C o

P c

0:9705

e2T

C m?0:5821*

P2

c

*C m

D3

o

0:9875

e3T

C L?0:9283*eM t*C LT0:998e4T

C p?0:3942*

C p

t

1:022

e5T

The computed data are correlated with the data generated for fabricated RP parts.A good coef?cient of correlation(R2)is yielded using above equations for the observed and computed values.The“C”program is developed to inter-relate various in?uencing parameters and equations are solved by multiple regression analysis.

It is observed that the above equations are justi?able for the costs and bene?ts pertaining to RP.These equations may be used with con?dence for predicting the costs of various parts manufactured with RP.T able XI represents the observed and computed values of costs in RP.The effects of complexity index is studied for different costs mentioned earlier.It is observed that the complexity index in?uences most the operating cost as compared to the other three costs.Hence,the mathematical model represented by equation(2)was rearranged as follows:

C o?1:10136*

C o

P c

0:9705

ie6T

Equation(6)represents a re?ned model for computation of operating cost in RP.As far as the experience is concerned, author felts that the pre-and post-processing costs also should be in?uenced by complexity index.But the study of model suggests that it has the least effect on other three costs.The concept of complexity index hence proved to be very useful while designing the model equations for“cost/bene?t”in conjunction with RP.Equations(2-5)are justi?able by taking into consideration all of the observed values errors themselves.

Figures27-30represent the plots between observed and computed values from the model formulated to compute C o, C m,C L and C p values.It has been estimated that the simulation equations(2-5)predict the values of C o,C m,C L and C p with R2values0.9998,0.9729, 1.0and0.9805, respectively.

The formulated models therefore,may be used with con?dence for predicting the values of signi?cant costs C o, C m,C L and C p and considered as“cost/bene?t models”while dealing with RP.

6.Conclusions

RP have proved to be a cost-effective and time ef?cient approach for development of RT,thereby ensuring possibility for technology transfer in casting as well as plastic industries. The patterns produced with FDM RP process shown overall 82-93per cent reduction in lead time.The lead time observed to be reduced by89-93per cent in comparison with metal patterns.Similarly,the lead time of RP observed to be reduced by73-82per cent in comparison with wood patterns.The cost of RP patterns is lower than the patterns fabricated with CNC operation.But,the costs of RP patterns are found to be higher than the wood patterns.For the small scale volume of production,the unit cost have been observed less in case of RP patterns.The adopted methodologies provide cost and time saving approaches of manufacturing of small-sized cast iron dies.These dies are useful for producing wax,plastic or low melting point alloy components with investment casting, injection moulding and blow moulding processes.The total cycle time for manufacturing of small-sized dies drastically

Table IX“Complexity index”values for various parts

Part

Model

material,

m m(cm3)

Support

material,

s m(cm3)

Build

time,t b(hrs)

Complexity

index(i)

P1547.6444.1420.080.49

P2237.6514.6610.520.40

P3152.7517.577.80.36

P490.2913.68 4.010.43

P5109.5118.01 5.420.39

P6109.5118.01 5.420.39

P735.2878.95 3.760.51

Table X Bene?ts in terms of costs in RP

Part Complexity index(i)H m T c P p M t D o P c

P10.490.420.4540.470.450.460.42

P20.400.340.3700.390.370.380.34

P30.360.310.3370.350.340.340.31

P40.720.610.6640.690.660.670.61

P50.390.330.3630.380.360.370.33

P60.390.330.3630.380.360.370.33

P70.510.430.4680.490.470.480.43

Table XI Observed and computed values of costs incurred in RP

C o C m C L C p

Part Observed Computed Observed Computed Observed Computed Observed Computed P13,0122,9968,5556,6066026003028

P21,5781,5863,8023,6743163151314

P31,1701,1762,6542,840234233910

P41,0351,0752,0552,061207206159

P5*******,0552,06116316267

P6*******,8691,46716316267

P7564583––11311265

reduced because the manufacturing of patterns do not require special tooling and planning.Intricate cast iron dies can be easily produced,since there is no limitation for shape of the required pattern.The quanti?cation of bene?ts in terms of cost is very essential in order to evaluate the systems performance.The most signi?cant factors affecting decision criterion need to be identi?ed and analysed on common ground.The concept of complexity index taken into account for determining parameters to compare the performance proved to be very useful.The cost/bene?t model formulated to justify

implementation of RP as a technology transfer may be used with con?dence for predicting the values of signi?cant costs while dealing with RP .

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Corresponding author

Dilip Sahebrao Ingole can be contacted at:dsingole@https://www.wendangku.net/doc/3d14330623.html,

Figure 28Graph between observed and computed values of C

m

01,000

2,0003,0004,0005,0006,0007,0008,000Observed costs (C m )

C o m p u t e d c o s t s (C m )

Figure 29Graph between observed and computed values of C

L

0100200300400500600700Observed costs (C L )

C o m p u t e d c o s t s (C L )

Figure 30Graph between observed and computed values of C

p

010203040506070Observed costs (C p )

C o m p u t e d c o s t s (C p )

Figure 27Graph between observed and computed values of C

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05001,0001,5002,0002,5003,0003,500Observed costs (C o )

C o m p u t e d c o s t s (C o )

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