DOI 10.1007/s00170-004-2179-3

O R I G I N A L A R T I C L E

Int J Adv Manuf Technol (2006) 28: 262–271

Z. Bouaziz · J. Ben Younes · A. Zghal

Cost estimation system of dies manufacturingbased on the complex machining features

Received: 13 December 2003 / Accepted: 13 March 2004 / Published online: 25 January 2006© Springer-Verlag London Limited 2006

Abstract Part manufacturing estimation cost is a critical andimportant task for industrial firms. Price evaluation helps the en-terprise occupy a successful competitiveness in the market. Infact there are three main approaches for the manufacturing costevaluation the analytic approach, the analogic approach and theparametric approach.

This paper presents a cost estimation system of manufactur-ing dies based on a semi-analytic approach. The developed sys-tem uses a semi-analytic approach based on the principle of theanalogic approach and analytic approach. This principle has re-course to the analogic approach to search for analogies betweenthe shapes to be machined before grouping them into complexmachining features [1]. For each feature parameter the systemgenerates a process to be used as a sample and consequentlya model of machining time. In a second stage and by using theanalytic approach, the cutting time is determined either by re-moval rates of metal units for rough operation (cm3/min) or fromthe finishing operation surface (cm2/min) or by both productionways [1]. The after cutting return time is calculated through theequations developed for each machining type [2].

Keywords Cost estimate · Feature machining ·Process planning · Time

1 Introduction

In a competitive situation if a company’s estimate of its costs isunrealistically low (underestimate) then it may obtain an order

Z. Bouaziz (�)∗ · J. Ben Younes · A. ZghalLaboratory of mechanics, solids, structures and technological development,Ecole superieure des sciences et techniques,BP 56 Beb Mnara, 1008 Tunis, TunisiaE-mail: toubeir.bouaziz@enis.rnu.tnTel.: +216-74-274088Fax: +216-74-275595∗Department of Mechanical Engineering,Ecole Nationale d’Ingenieurs de Sfax,route de Sokra Km 3, BP. W 3038 Sfax Tunisia

but risks taking a financial loss. On the other hand, an over-estimate of costs will cause the company to lose orders. Theaccuracy of cost estimates is therefore very essential to the sur-vival of an organization. Good estimates are not only essentialfor external use but also for internal use. The relationships be-tween the over-and underestimates and the cost of products canbe represented by the Freiman curve shown in Fig. 1. The graphshows that:

• The greater the underestimate, the greater the actualexpenditure.

• The greater the overestimate the greater the actualexpenditure.

• The most realistic estimate results in the most economicalproject cost.

When costs are underestimated, initial plans for staffing,scheduling, machine processing, tooling, etc., are not achievable.Though plans are established to realize the underestimated cost,it becomes difficult for cost targets to be met as the project pro-gresses. In response, there is reorganization, replanning and pos-sibly the addition of personnel and equipment [4]. These tend toincur costs that were not originally budgeted for, resulting even-tually in an increase in costs. On the other hand, when costs are

Fig. 1. The Freiman curve [3]

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overestimated, rather than resulting in greater profits, the over-estimate reflects a Parkinson’s law application [3]: the moneyis available, it must be spent. Unless there is firm managementcontrol, there is a self-fulfilling prophesy and it will be virtuallyimpossible to reduce costs.

To resolve this problem several research works have de-veloped a realistic estimation. Wei and Egbelu [5] elaborateda framework to estimate the lowest product manufacturing costfrom the AND/OR tree representation of an alternative process.A major drawback of their framework was that it focused onlyon processing and material handling costs without consideringother direct product costs such as set-up, material, fixtures andlabour cost. Abdallah and Knight [6] developed an expert sys-tem for the concurrent product and process design of mechanicalparts. Their approach enabled designers to ensure that the prod-uct would be manufactured with existing manufacturing facilitiesto provide high quality and the lowest cost.

Rehman and Guenov [7] described a methodology for mod-elling manufacturing costs at the design phase of the life cycleof a product. In this system, the link between design knowledgeand manufacturing knowledge is achieved through an advancedartificial intelligent architecture, i.e. a backboard framework, forproblem solving.

It is clear that this model cannot be used to generate anaccurate manufacturing cost as it estimates the manufacturingcosts without consideration of process planning. Luong andSpedding [8] described the development and implementation ofa generic knowledge-based system for process planning and costestimation in the hole making process. A major feature of this sys-tem is that it unifies the process sequence, machinability and costestimates into an integrated system, which caters to the require-ments of small to medium sized companies, involved in batchproduction. Luong and Spedding’s system lacks an interface toa CAD system, and the capability of process plan optimization.

Shehab and Abdallah [9] developed a system that has the ca-pability of selecting a material, as well as machining process andparameters based on a set of design and production parametersand of estimating the product cost throughout the entire productdevelopment cycle including assembly cost.

Jung [10] developed a feature-based cost estimating systemfor machined parts. Cost estimate for all features in a categoryis based on manufacturing activities. Early cost estimates did notconsider the manufacturing activity, hence they were not accu-rate. Machining cost is proportional to machining time, whichincludes operational time and

non-operational time. Operation time includes the rough cut-ting time and finish cutting time. The tool approach time andnon-operation time are taken from past experience and approxi-mated for modification into mathematical forms.

Ben-Arieh [11] presents a hybrid cost estimate system for ra-tional parts that uses a combination of the variant approach andexplicit cost calculation. The variant approach is used to retrievemachining parameters from a database of past parameters. Theexplicit cost calculations are based on the part geometry, the cut-ting tools available and the machining parameters retrieved. Thesystem presented calculates the time that a part needs to stay

on the machine. This time, which includes processing, set-up aswell as tool changes, is used to find the machining cost.

In our research, we have worked with collaboration companymachining plastic injection moulds. The principle elements havebeen identified to define the needs relative to the methods rapidcost evaluation. Finally, we have elaborated a system of machin-ing cost evaluation, and its principal purpose is to help expertsin machining mould factories to rapidly evaluate the machiningcost of moulds. The objective is to:

• Decrease the time of machining cost estimation.• Improve the quality of cost figuring by diminishing the un-

certainty of different cost calculations.

In the first part of this paper, we present the general principleof the machining cost determination system. Later, we will ex-plain the modelling by complex machining feature used in thedeveloped system as well as a method of generating the process(used as a sample) and the models of machining time. Finally, wewill describe our approach for machining time calculation andthe developed information model.

2 The principle of the developed system

In order to estimate the machining cost, it is necessary to havea representation in the form of a produced model and not only ofa CAD model [12]. This produced model enables us to give thefeatures a semantic organized in three categories of information :geometric information, technologic information and informationconcerning the materials.

In short, to give the geometric model features a semantic, andto define the produced model, we have used parameterized fea-tures in our system. The principle consists of conceiving the diemodelling using the technological, dimensional and geometricalcharacteristics.

In the system presented in Fig. 2 we have developed two dif-ferent principles to determine the machining cost:

1. An algorithm generating a machining process. This processis selected from the data-base of the process (used as a pat-tern) and from the criteria proposed by the user.

2. A selecting process methodology among numerous onesfrom the data-base process.

Once the machining process is determined, the system gen-erates the parameters of the machining time model. The cuttingparameters are determined from a data-base which contains all thetechnological information. In the end, the system calculates thetime, and the total of machining cost. To determine this cost, wemultiply the total machining cost by the hourly production cost.

3 Machining cost estimate process

Based on the proposed structure, Fig. 3 shows the process organ-igram of machining cost analysis. This process can be presentedas follows:

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Fig. 2. Structure of developed system

Stage 1 Instead of having a global die evaluation, the estimateis done in a progressive way by searching for machin-ing solutions of each part. It is then interesting to de-compose the global problem into sub-problems [13]. Inthis first stage, each die is then decomposed into sev-eral cavities..

Stage 2 The second stage consists of generating the featuresfor each cavity. For this, we have defined four featuremodels. The purpose of this modelling is to formal-ize, on the one hand the industrial expertise, and onthe other hand the information linked to the realizationactivities.

Stage 3 For each feature model and starting from a knowledgebase, we generate in this stage a machining process.This generating takes into account the geometric andthe technological parameters and the machining mode.

Stage 4 In the first phase of this stage, the system generates themachining time model associated to each machiningprocess. Then, we calculate the model parameters start-ing from the feature technological attributes. Finally,the system can calculate the feature machining time.

Stage 5 In this stage, we can calculate the machining time ofeach cavity through the following expression:

ti =n∑

j=1

tj (1)

With: ti : machining time of each cavity (min) tj : ma-chining time of each feature (min).

Fig. 3. Algorithm of costanalysis process

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Stage 6 This stage enables us to calculate the machining timeof the die through the following expression:

tu =m∑

i=1

ti (2)

With: tu : the die machining time (min) ti : the machin-ing time of each cavity (min).

Stage 7 In this last stage the machining cost is calculated withthe following expression:

C = tu .Ch (3)

With: C: die machining cost ($) Ch : the hourly cost ofa machine ($/min).

4 Model of die definition

The model of die definition, which is of surface type, is based es-sentially on the notion of the machining feature. The approachby feature consists of describing the die not only as a geomet-ric object, but according to a certain number of characteristics.A machining feature is described therefore from four kinds ofinformation [1–14]:

1. The geometric data: allows the shape of the complex fea-ture to be represented. These data define the shape associatedwith the complex feature [15].

2. The technological attributes: they consist of parameters thatdescribe the die model (for example: roughness, material,etc.).

3. The shape attribute: it allows the specific kind of shape ofa complex feature related to the volume of material that de-fines the die to be realized. Two values of this attribute aredefined: hollow shape and in relief shape.

4. Processes especially adapted to machining the shape [16].

The evaluation of the die is established progressively insteadof a global evaluation. This is done by appreciating the solutionsfor machining of each part.

Fig. 5. Machining pocket feature

Fig. 4. Hierarchical structure of the die definition model

So, it is interesting to divide the whole problem into a numberof subproblems. Every die is decomposed in cavities that repre-sent a group of complex machining features, Fig. 4.

The definition of cavities is based on setting reference elem-ents. For a simple cavity, the element of reference is a complexfeature whose attribute of shape is the hollow type. The volumeof material to remove in this case is related to the theoreticalvolume permitting to define the attribute of shape. Establishingthe elements of reference for cavities consists of identifying ba-sic complex features. A bijection is thus created between thegroup of simple cavities and the other of basic features havingan attribute of shape. The identification of the reference elementsleads to the definition of the cavities.

The analysis of the shapes and the specification of the dies,achieved in the course of our trial of the construction of the ma-chining model, has lead us to settle four complex machiningfeatures [17]: the pocket, the arms, the revolution surface and thebump. Figure 5 defines the pocket feature with its attributes.

5 Generation of the process and the model ofmachining time

For each group of complex machining features, a knowledge-base composed of production rules helps to generate machiningpatterns process. The generating of the process, takes into ac-count the technological and geometrical feature parameters and

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the machining mode. A model of machining time calculation isattributed to each pattern process [1].

The first stage in the construction of data knowledge, consistsof acquiring the expertise linked to the machining process [17].This expertise is taken from die machining specialists of a col-laborating enterprise. We have tried to define all the machin-ing processes for a group of features. The selection of a pro-cess for a group of features is achieved according to the samecriteria.

We have preferred to represent this expertise in the form oforganigrams gathering in a global way, all of the possible pro-cesses taking into account the authorized values of all machiningfeatures parameters.

Fig. 6. Extract from the collection the expertiselinked to the machining feature(pocket of Fig. 5)

The table in Fig. 6 is an extract from a collection of pocketfeatures from Fig. 5. Where r is the ray of a cutting tool.

The use of production rules in a knowledge data systemseems to be the most direct means to represent the collected ex-pertise. Each machining feature is associated with a finished ofpossible machining processes. In each, the applied rules generateonly a process that is already known.

6 Method of determining the machining time

The expression of the model of machining time, in its generalshape, includes the time of cut, the extra time of machining and

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the time of machining correction. The latter can be expressed bythe following relation [18]:

ti = (1 +α)( tc + tcor) + tev (4)

Where α is an adjusting factor.

6.1 Calculation of cutting time

The proposed method searches quickly for the cutting time withmeaningful values, according to the drawing or size of the prod-uct and the cutting conditions.

The cutting time is determined from the drilling time tp,roughing time te, half-finishing time t f/2 and finishing time t f .The expression of the time can be written as follows:

tc = tp + te + t f/2 + t f (5)

The drilling time is determined from the hole depth L p andthe advance speed Vp. This time is expressed by the followingrelation:

tp = Lp

Vp(6)

In contrast, the cutting time in roughing is calculated with thevolume of material to remove and the volume rate. This one re-places the three cutting parameters utilized in the classic methodsfor calculating cutting time. Then, the cutting time can be writtenas:

te = V

Qv(7)

Q0 = l.a.Vf (8)

where V is the volume of material to remove in cm3, Qv is thevolume rate in cm3/min, l is the length of cut in cm, a is thedepth of passes in cm and Vf is the advance speed in cm/min.

In the same way, the cutting time in half-finishing and in fin-ishing is researched from the produced surfaces and from thesurface rate. The expression of the time is therefore:

tf = S

QS(9)

QS = p.Vf (10)

Fig. 7. Scallop height

where S is the produced surface in cm2, Q1 is the surface rate incm2/min, p is the tool-path interval in cm and Vf is the advancespeed of the tool in cm/min.

The value of the step (p) tool-path interval of the tool is esti-mated according to the scallop height, the geometric data and theshape of the surface.

The calculation of the tool-path interval for milling flatplanes is relatively simple. When the milling operation is com-pleted scallops remain on the finished surface as shown inFig. 7a. For a given allowable scallop height the tool-path inter-val can be obtained by using the Pythagoras theorem [19, 20].

P = 2√

r2 − (r−h)2 ≈ 2√

2 r h (11)

Where r denotes the radius of a ball-end cutter and h denotes theallowable scallop height.

In the case of a plane of inclination of an angle β, Fig. 7b,in proportion to the horizontal, the expression of the tool pathinterval between cuts becomes:

P = 2 cos β

√r2 − (r −h)2 ≈ 2 cos β

√2rh (12)

The calculation of the maximum allowable path interval fora general convex surface is more complicated than for a flat sur-face. A convex surface machined by a ball-end cutter is shownin Fig. 7c. The tool-path interval depends on the curvature of thesurface, the size of the cutter, and the allowable scallop heightremaining on the surface. The scallop height can be derived interms of the path interval, the cutter radius, and the local radiusof curvature of the convex surface [19, 20].

h = (R + r)

√

1−(

P

2R

)2

−√

r2−(

(R + r) P

2R

)2

− R (13)

Where R is the local radius of curvature of the convex surface.Since in practice R � h, Eq. 11, which yields the approxi-

mated solution of the tool-path interval:

P ≈√

8hrR

R + r(14)

The tool-path interval in machining of a concave surface canbe derived in a way similar to the convex case. The scallop height

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is given by:

h = (R + r)

√

1−(

P

2R

)2

−√

r2−(

(R + r) P

2R

)2

− R (15)

Since in practice R � h, Eq. 15, which yields the approxi-mated solution of the tool-path interval:

P ≈√

8hrR

R − r(16)

6.2 Determination of extra time of machining

The extra time of machining includes, times of return-length formovement of the tool in roughing cycle tev1, half-finishing cycletev2 and finishing cycle tev3 cycles. Then the time of extra ma-chining is written as follows:

tev = tev1 + tev2 + tev3 (17)

The determination of extra machining time of each cycle ismade by the analytical method. This time is calculated from therapid speed Vr and the total distance Ltr of rapid return of thecutting tool.

tev = Ltr

Vr(18)

To do this, we have developed expressions of the length ofrapid return for roughing, half-finishing and finishing cycles [2].

6.3 Determination of correction time

Sometimes, an excess of material may remain in the machining,due on one hand to the weak local curvature of the surface (rc),and on the other hand, to the radius of the cutting tool r > rc,Fig. 8a. This phenomenon generates a machining constraint [1].The excess of material left by the tool is equal to d. The value ofd is determined by the following equation:

d = (1− sin(θ/2))(r − rc)

sin(θ/2)(19)

After having finished the machining, it is necessary to cutagain the zone that contains the remaining material with a toolwhose radius is smaller than rc. The cycle used in this case iscalled the cycle of correction [21]. In this study, we show thatthe time of correction is not negligible and can reach 15% the offinishing time.

The value of time depends on the machining type. We distin-guish two cases:

1. Milling with the cutting tool extremity. The correction of sur-faces is made by passes with a spherical top tool following sev-eral levels, Fig. 8b, the number of slices is determined by thefollowing relation:

n = d

p′ (20)

Fig. 8. Examples of remaining material

In the same way, the total surface generated by the tool of correc-tion is equal to:

S = (r + rc)

2.πθ

360.L.n (21)

where L represents the whole length of correction.In this kind of work, the time is determined according to

surfaces calculated by Eq. 21 and expression 10 of the surfacerate.

2. Profile milling. The machining of the remaining material incorners is made according to parallel trajectories, Fig. 8c, andthrough several slices, Fig. 8d. The number of parallel trajecto-ries is determined by the following relation:

n1 = d

c(22)

On the other hand, the number of slices is found out by usingthis equation:

n2 = L

p′′ (23)

Consequently, the total length generated by the tool of cor-rection is determined by the following relation:

LT = (n1.n2)(r + rc)

2

πθ

360(24)

For the machining of corners, the time of correction is de-termined thanks to the length given by Eq. 24 and the advancespeed Vf .

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6.4 Considering of random errors

In the method of calculating the machining time proposed above,it is evident that the theoretical time of machining is differ-ent from the real time. This is due mainly, on the one handto errors of different methods of calculation, and on the otherhand to the defaults of CNC machines. Among these errors, onefinds:

1. Errors in calculating the volume of material to remove,2. Errors in calculating the surface to mill,3. Errors due to the speed of displacement of the tool (acceler-

ated speed, constant, decelerated).

To have more accurate values of machining time, we integratedin the expression of the time a coefficient of adjustment α asshown:

α = αm +αv +αs (25)

The value of the machine´s error coefficient αm is estab-lished by the statistical method [22]. The experiments provethat the cutting machines increase the cutting time by 2%.This value is generally constant and depends on the machineused.

On the other hand the values of errors coefficients αv and αs,vary according to the precision of the different calculations ofvolumes and surfaces. The same statistical method applied to theseveral shapes gives values of αv in the case of volume and of αs

in the case of surface [18].

7 Implementation

The developed system is to be used by experts in enterprise.We have had to choose an implementation environment whichis largely diffused. So we have opted for the use of object-orientation languages, which are variables on compatible com-puters (PC). Our choice concerns the Visual Basic languageunder windows exploitation systems.

A computer system has been developed in a first version withthe purpose to validate the model in the eyes of experts. We haveconfined its field of application to the machining time estimate ofa plastic blowing mould.

We have developed our system thanks to the database man-agement “ACESS”. It enables us to rapidly and efficiently defineimportant and strong data-bases.

The treatment of the die machining time requires a data-basemodel which is homogenous from the point of view of the ma-nipulated data of their binders. This modal is built from the twofollowing elementary models:

• The technological model has recourse to the technologicalattribute table of values, which characterize the die modelelements.

• The geometric model shows the geometric data structureswhich represent the base-elements (curve and surface).

The technological model tables are created and stored in the de-veloped data-base. On the contrary, the files of geometric models

are built progressively in parallel with the treatment of the ma-chining time by the developed system.

8 Example of machining die

Figure 8 shows the drawing of a die definition of a bottle madeof plastic. The shape shows that two different cavities exist. Cav-ity 1 is a pocket of length 220 mm and a width of 138 mm. Onthe contrary cavity 2 is a hollow cylinder of 20 mm of ray. Therough of the start is a prismatic part of 310×180×140 mm inaluminium with a resistance 100-150 HBN.

In this example we only treat the study of the generation ofcavity 1 machining cost.

The first step consists of parametrizing the form of cavity 1.The principal consists of introducing starting from an interfaceutilizer Fig. 10, the technological and geometric information.Then, we define the criteria of the choice of the machining pro-cess which are:

• The plunge of the roughing tool.• The roughing cycle of the pocket is conducted in zig-zag.• The finishing tool ray is equal to the connecting ray.

Starting from these criteria, the system selects a machining pro-cess. Figure 11a, which generates the model of machining timeFig. 11b.

In the roughing cycle, we utilize a two dimension counter-sink of a diameter of 8 mm and a number of teeth equal to four.The cut depth is chosen at 2 mm, as well as the distance betweentwo cuts which is calculated by the relation p = 0.875×d givinga value of 7 mm.

For the cycle 12 f and f we use a spheric end cutting tool of

a diameter of 8 mm. When we use Eq. 12, the tool path intervalbetween two cuts p is equal to 2.81 mm in half-finishing and of0.89 mm in finishing.

Due to the cut conditions of the data-base and from thetechnological information introduced by the utilizer, the systemgenerates the value of the volume rate for the roughing oper-ations equal to 66.84 cm3/min, the values of the surface rateequation to 44.72 cm2/min for the half-finishing operations and7.08 cm2/min for the finishing operations.

The volume and the surface of cavity 1 are calculated withthe precise method, which gives:

• The volume V = 1487.64 cm3.• The surface S = 645.49 cm2.• The adjustment coefficient α = 0.035.

The roughing time calculated by the system is equal to22.25 min, on the contrary, the time of half-finishing is about14.43 min. Finally, the finishing time calculated by the system isequal to 128.12 min.

In order to calculate the evolution time for each machiningcycle (extra time), it is necessary to calculate the return-lengthfor each cycle, with expressions developed in [2]. The numericcalculation gives a total return-length equal to 16 327.31 mm,and a time of 3.26 min. The total machining time, Fig. 12, for thecavity 1, is equal to 177.12 min equivalent to 2.95 h.

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Fig. 9. Example of die

Fig. 10. Interface window of a pocket feature

Fig. 11. Machining process type and model ofmachining time

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Fig. 12. Calculation window of total time machining

9 Conclusion

The research study presented in this paper is part of a develop-ment scheme of a system to elaborate the cost of plastic blowingmoulds.

This paper is intended to:

1. Propose a structure to help the conceptor analyze the die ma-chining cost during the phase of conception.

2. Propose a method for the cost evaluation, based on machin-ing complex features.

3. Obtain, with the system structure, a better homogeneity ofresults among the different conceptors.

With the structure of the developed approach, we have intro-duced some simplifications, namely at the level of cut parametersin such a way that the method remains easy for the majority ofindustries to apply.

The system uses a data-base which regroups the machiningparameters utilized by the manufacturers. This provides a betterevaluation of the parameters of the machining cost.

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