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Journal of Materials Processing Technology 184 (2007) 233–239

Surface roughness optimization in an end-milling operationusing the Taguchi design method

Julie Z. Zhang a,∗, Joseph C. Chen b, E. Daniel Kirby b

a Department of Industrial Technology, University of Northern Iowa, Iowa, USAb Department of Agricultural & Biosystems Engineering, Industrial Technology, Iowa State University, Iowa, USA

Received 27 January 2006; received in revised form 7 July 2006; accepted 27 September 2006

bstract

This paper presents a study of the Taguchi design application to optimize surface quality in a CNC face milling operation. Maintaining goodurface quality usually involves additional manufacturing cost or loss of productivity. The Taguchi design is an efficient and effective experimentalethod in which a response variable can be optimized, given various control and noise factors, using fewer resources than a factorial design. This

tudy included feed rate, spindle speed and depth of cut as control factors, and the noise factors were the operating chamber temperature and thesage of different tool inserts in the same specification, which introduced tool condition and dimensional variability. An orthogonal array of L (34)

9

as used; ANOVA analyses were carried out to identify the significant factors affecting surface roughness, and the optimal cutting combinationas determined by seeking the best surface roughness (response) and signal-to-noise ratio. Finally, confirmation tests verified that the Taguchiesign was successful in optimizing milling parameters for surface roughness. 2006 Elsevier B.V. All rights reserved.

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eywords: Taguchi design; Surface roughness; Milling operations

. Introduction

.1. Background

As a basic machining process, milling is one of the mostidely used metal removal processes in industry and milled sur-

aces are largely used to mate with other parts in die, aerospace,utomotive, and machinery design as well as in manufactur-ng industries [1,2]. Surface roughness is an important measuref the technological quality of a product and a factor thatreatly influences manufacturing cost. The mechanism behindhe formation of surface roughness is very dynamic, compli-ated, and process dependent; it is very difficult to calculate itsalue through theoretical analysis [3]. Therefore, machine oper-tors usually use “trial and error” approaches to set-up milling

achine cutting conditions in order to achieve the desired sur-

ace roughness. Obviously, the “trial and error” method is notffective and efficient and the achievement of a desirable value

∗ Corresponding author at: 37 ITC, Cedar Falls, IA 50613 0178, USA.el.: +1 319 273 2590; fax: +1 319 273 5818.

E-mail address: julie.zhang@uni.edu (J.Z. Zhang).

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924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2006.11.029

s a repetitive and empirical process that can be very time con-uming. The dynamic nature and widespread usage of millingperations in practice have raised a need for seeking a systematicpproach that can help to set-up milling operations in a timelyanner and also to help achieve the desired surface roughness

uality.

.2. Background of Taguchi design

One method presented in this study is an experimental designrocess called the Taguchi design method. Taguchi design,eveloped by Dr. Genichi Taguchi, is a set of methodologies byhich the inherent variability of materials and manufacturingrocesses has been taken into account at the design stage.he application of this technique had become widespread inany US and European industries after the 1980s. The beauty

f Taguchi design is that multiple factors can be consideredt once. Moreover, it seeks nominal design points that arensensitive to variations in production and user environments

o improve the yield in manufacturing and the reliability inerformance of a product [4]. Therefore, not only can controlledactors be considered, but also noise factors. Although similar toesign of experiment (DOE), the Taguchi design only conducts

234 J.Z. Zhang et al. / Journal of Materials Proce

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Fig. 1. Taguchi design procedure.

he balanced (orthogonal) experimental combinations, whichakes the Taguchi design even more effective than a fractional

actorial design. By using the Taguchi techniques, industriesre able to greatly reduce product development cycle timeor both design and production, therefore reducing costs andncreasing profit. Moreover, Taguchi design allows lookingnto the variability caused by noise factors, which are usuallygnored in the traditional DOE approach.

.3. Procedure of the Taguchi design method

To better understand Taguchi design, the procedure of theaguchi design is described in Fig. 1. The complete procedure inaguchi design method can be divided into three stages: systemesign, parameter design, and tolerance design (shown in Fig. 1).f the three design stages, the second stage – the parameteresign – is the most important stage [5]. It has been widelypplied in the US and Japan with great success for optimizingndustrial/production processes. The stage of Taguchi parameteresign requires that the factors affecting quality characteristicsn the manufacturing process have been determined. The majoroal of this stage is to identify the optimal cutting conditionshat yield the lowest surface roughness value (Ra).

The steps included in the Taguchi parameter design are:electing the proper orthogonal array (OA) according to the num-ers of controllable factors (parameters); running experimentsased on the OA; analyzing data; identifying the optimum con-ition; and conducting confirmation runs with the optimal levelsf all the parameters. The details regarding these steps will beescribed in the section of experimental design.

.4. Application of the Taguchi parameter design in milling

perations

As applying Taguchi parameter design requires the identifica-ion of factors affecting targeted quality characteristics, relevant

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ssing Technology 184 (2007) 233–239

iterature must be reviewed to screen the most important amongnumber of factors or conditions affecting surface roughness

f milled surface. As a multi-point machining process, moreotential variability makes it even harder to obtain a surfaceoughness model in milling operations compared with singleoint machining [3]. Tsai et al. [3] stated that the possible fac-ors affecting surface finish were found to be feed rate, cuttingpeed, depth of cut, cutter geometry, cutter runout, tool wear, andhe cutter force and vibration under dynamic cutting conditions.sing Taguchi design, Fuh and Wu [6] included cutting speed,

eed rate, depth of cut, tool nose radius, and flank as controlactors for the creation of a statistical model to predict surfaceoughness for aluminum parts in end milling operations. Ghanit al., [7] conducted a study to optimize cutting conditions forardened steel under semi-finish and finish conditions. Apply-ng cutting speed, feed rate, and depth as control factors, theysed measured responses (i.e., surface roughness and resultantutting force) and their calculated signal-to-noise ratio to deter-ine the optimal cutting condition. Bouzid et al. [8] did research

o obtain optimal cutting parameters such as cutting speed, feeder tooth, and cutting depth for surface roughness in down faceilling operations by using duplex (ferritic/austenitic) stainless

teel and carbon steel compositions as samples. Also applyinghese three cutting parameters as control factors, Lin [9] stud-ed multiple characteristics including removed volume, surfaceoughness, and burr height, and in this research a weighted valueas used to optimize the cutting condition for face milling oper-

tions. The studies reviewed above indicated although applied inarious working conditions for solving different, specific prob-ems, they all selected the three commonly applied machiningarameters – feed rate, cutting speed, and depth of cut – as con-rol factors. These studies indicated that the technique of Taguchiarameter design worked well in optimizing cutting parameterso achieve the surface finish result.

Following the review above, this study included feed rate,pindle speed, and depth of cut as control variables. Since sur-ace cutting speed (in feet per minute) is linearly correlated toeed rate (in inches per tooth or inches per revolution), the con-rol variable of cutting speed was specified as spindle speedin revolutions per minute) in this study. Tool wear is anothermportant factor impacting the surface quality of parts in millingperation [10]. It is hard to categorize the degree of tool wearn machining practices. Therefore, tool wear is considered aoise factor by applying a set of brand new tool inserts and aet of tool inserts in the same geometric specification but withlight wear in a face mill cutter. In addition, another possibleariable is the machining environmental temperature, and it haseen suggested that the surrounding temperature is an influen-ial factor in analysis of the thermal machining dynamics [11].dding temperature as a noise factor enables this study to sim-late the impacts that a harsh machining temperature such ason-air conditioned shops will have on surface finish. Coolants often used in machining processes not only to reduce heat from

he tool and the workpiece, but also to lubricate the machinedurface. Due to the constraints of the lab condition, the impactf coolants to surface roughness was not included in this study.research proposal has been submitted regarding the bio-based

J.Z. Zhang et al. / Journal of Materials Pro

Table 1The basic Taguchi L9(34) orthogonal array

Run Control factors and levels

A B C D

1 1 1 1 12 1 2 2 23 1 3 3 34 2 1 2 35 2 2 3 16 2 3 1 27 3 1 3 289

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utting fluids, and related research may be conducted in theuture.

. Purpose of study

The Taguchi parameter design stage is the primary designpplied in the study, and the purpose of this study is to effi-iently determine the optimal face milling parameters to achievehe smallest surface roughness value for aluminum parts underarying conditions. The questions that this study will addressnclude the following:

What are the relationships between the controllable factors(in the study: spindle speed, feed rate, and depth of cut) andthe response factor (surface roughness)?How do the noise factors (temperature and tool wear) affectthe response factor?What are the optimal conditions of the milling parameters forsurface roughness?What are the optimal conditions for the two noise factors?

. Experimental design

.1. Orthogonal array and experimental factors

Following the procedure described in Fig. 1, the first step in the Taguchi

ethod is to select a proper orthogonal array. The standardized Taguchi-based

xperimental design, a L9(34) orthogonal array described in Peace [4], was usedn this study and is shown in Table 1. This basic design makes use of up to fourontrol factors, with three levels each. A total of nine experimental runs muste conducted, using the combination of levels for each control factor (A–D)

•

•

able 2arameters, codes, and level values used for orthogonal array

arameter Code Level 1

ontrol factorsSpindle speed, rpm A 1500Feed rate, ipm (mmpm) B 20 (508)Depth of cut, in (mm) C 0.060 (1.5

oise factorsTool wear X NoneTemperature range, ◦F (◦C) Y 65–75 (18

esponse variableSurface roughness, Ra (�in.) – –

cessing Technology 184 (2007) 233–239 235

s indicated in Table 1. The addition of noise factors is optional, and requireshat each run should be conducted once for each combination of noise factors.owever, this study did not use all the array cells for four factors, becausenly three factors were considered (spindle speed, feed rate, and depth of cut).herefore, the last column (for the fourth factor) in the L9(34) orthogonal array

s left empty for this specific study.The selected parameters, as discussed in the introduction, are listed in Table 2

long with their applicable codes and values for use in the Taguchi parameteresign study. The control and noise factors are independent variables, and theesponse variable is the dependent variable.

The control factors are the basic controlled parameters used in a milling oper-tion. The spindle speeds and depth of cut were selected from within the rangef parameters for finishing and semi-finishing milling of aluminum. The feedates were slightly lower than normally used for milling aluminum workpieces,n consideration of safety concerns.

The noise factors listed in Table 2 are variables often uncontrolled in machinehops, which may affect the surface roughness of a milling operation mentionedarlier. The temperature ranges included both a normal (65–75 ◦F/18.3–23.9 ◦C)nd a high (95–100 ◦F/35–37.8 ◦C) shop temperature range. The normal rangencludes a range of common temperatures based on what heating and air con-itioning systems are usually set for, or normal room temperature. The highemperature range is what a machine shop without air conditioning in somereas would expect during the summer. The second noise factor is the use ofither good inserts or inserts with light tool wear, which introduces a variableommon to all machine shops. The light tool wear on the inserts was createdy lightly grinding the cutting edge with a small abrasive grinder. The lightool wear here means no crater wear on the insert surfaces, some friction marksndicating slight flank wear.

A modified orthogonal array in Table 3 was created using the basic Taguchirthogonal array and the selected parameters from Table 2. In this array, theasic array with the control factors are shown as the inner control factor array,nd the added noise factors are shown in the outer noise array. Since all nineutting conditions specified in the array come with four combinations of noiseactors (normal temperature with no tool wear, normal temperature with lightool wear, high temperature with no tool wear, and high temperature with lightool wear), it brings the total number of runs to 36 for the experiment.

.2. Experimental set-up and procedure

After the orthogonal array has been selected, the second step in Taguchiarameter design (see Fig. 1) is running the experiment. This experiment wasonducted using the hardware listed as follows:

CNC Mill: Fadal VMC-40 vertical machining center.Surface roughness measurement device: Federal Pocketsurf Stylus Profilome-ter (measures Ra in �in.; stylus travel 0.1 in./2.54 mm).Space heater: 1500 W Honeywell Quick Heat Ceramic Heater (small forced-

air space heater with thermostat with thermal protection devices for safety).Thermometer: Taylor digital thermometer #1420 (digital thermometer withprobe, range includes 50–120 ◦F/10–48.9 ◦C) (Taylor Instruments).Cutting tool inserts: APKT 160408R coated carbide inserts (Ingersoll CuttingTools).

Level 2 Level 3

2500 350030 (762) 40 (1016)

2) 0.080 (2.03) 0.100 (2.54)

Light wear –.3–23.9) 95–100 (35–37.8) –

– –

236 J.Z. Zhang et al. / Journal of Materials Processing Technology 184 (2007) 233–239

Table 3Completed orthogonal array

Outer noise array

X 1 1 2 2Y 1 2 1 2

Run Inner control factor array N1 N2 N3 N4 R̄a s s2 η

A B C

1 1 1 1 35.5 47 71.5 58.5 53.13 15.43 238.23 −34.772 1 2 2 59.5 58.5 51 69 59.50 7.38 54.50 −35.543 1 3 3 68.5 56.5 96.5 133 88.63 34.00 1156.06 −39.414 2 1 2 26 23.5 82.5 53.6 46.40 27.66 765.21 −34.365 2 2 3 31 40 56 26 38.25 13.18 173.58 −32.026 2 3 1 45 41 58.5 49 48.38 7.50 56.23 −33.777 3 1 3 23.5 26.5 76.5 30.5 39.25 25.00 624.92 −33.038 3 2 1 24.5 22.5 51 56.5 38.63 17.63 310.73 −32.379 3 3 2 31.5 38 82 48 49.88 22.47 504.73 −34.57

A B C

R̄a effectsLevel 1 67.08 46.26 46.71Level 2 44.34 45.46 51.93Level 3 42.58 62.29 55.38

A B C

� effectsLevel 1 −36.57 −34.05 −33.64

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vsurements, which are used to verify the performance of thecalculated S/N ratio. This type of experiment, in which a smallerresponse variable is desirable, should produce S/N ratios thatincrease as the variance and means decrease.

Level 2 −33.38Level 3 −33.32

Tool holder: Fadal VNE90-1250C 3-insert mill with 1.25 in. (31.75 mm) cutdiameter (for above inserts).Surface table: polished granite surface for more stable and accurate surfaceroughness measurements.Microsoft Excel and JMP software packages for charting data and statisticalanalysis.

The 36 experiments were cut in a random sequence to better eliminate anyther invisible factors that might also contribute to the surface roughness. Theigh temperature was created through heating up the air inside the machinehamber by the heater to the defined temperature and maintaining the tempera-ure 5 min. The light tool wear on the inserts was created by lightly grinding theutting edge with a small abrasive grinder. It is hard to control the degree of toolear when grinding the inserts. A microscope was used to observe and measure

he flank wears on the inserts to control the wear situation of the three insertss similar as possible. Because the difficulty still existed due to the researchers’nability to reproduce the exactly same tool wear situation, tool wear was con-idered a noise factor in this study. A simple NC program was written withifferent cutting conditions specified to have the Fadal machine face mill the topurface of 3/4 × 1 1/2 × 3 in. (19.1 × 38.1 × 76.2 mm) aluminum blocks. Afterach cut, the surface roughness was measured on the surface table with the stylusrofilometer. Three fixed spots on each milled surface, one in the middle andhe other two on the edge, were used to measure the surface roughness of theut, and the mean of the three readings was recorded in the orthogonal array. Aiagram of measurement points were shown in Fig. 2.

. Results and analysis

The procedures after the experimental runs are analyzingata and identifying the optimal levels for all the control factorssee Fig. 1). The results of the surface roughness measurementsnd their average value (�in. R̄a) of each sample are shown in

−33.31 −34.82−35.92 −34.82

able 3, along with the additional parameters of the expandedrthogonal array. The individual surface roughness measure-ents are noted as N1–N4 for each run in the array. A final

olumn has been added to this array, to indicate the signal-to-oise (S/N) ratio, which is calculated as follows:

= −10 log

[1

n(∑

y2i )

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here η is the S/N ratio, yi the individual surface roughnesseasurements in columns N1–N4, n the number of combined

oise factors; in this case, n = 4.Also added to this array are the standard deviation (s),

ariance (s2), and the mean (R̄a) of the surface roughness mea-

Fig. 2. Three spots for taking surface roughness measurements.

J.Z. Zhang et al. / Journal of Materials Processing Technology 184 (2007) 233–239 237

Table 4T-test for effect on surface roughness of alternating between two sets of insertswith different wear

No wear Light wear

Mean 38.80556 63.86667Variance 206.0629 611.4612Observations 18 18d.f. 17t stat −4.51184tP

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Table 6ANOVA analysis for the effect of feed rate on surface finish

Source d.f. Sum of square Mean square F ratio Prob > b

Sp 2 2169.367 1084.68 2.0575 0.1439Error 33 17397.155 527.19Cumulative total 35 19566.522

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critical one-tail 1.739607(T ≤ t) one-tail 0.000154

A visual examination found that the noise factors may affecturface roughness because of the rather large standard deviationscross each row of the experimental runs. The changing trendf surface roughness brought by different inserts sets with andithout tool wear (coded as outer noise array factor X1 and X2)

s consistent from experimental run #1 through #9. No matter inhat cutting parameter condition, the samples cut by the insertsith wear always result in larger surface roughness values. On

he other hand, no such a consistent trend was found amonghe samples collected by varying machine chamber temperature,hich is coded as outer noise array factor Y1 and Y2. In order toresent a more rigorous analysis, two comparison t-tests wereade to see if the differences associated with the two noise

actors were significant.The t-test for the effect of tool wear on surface roughness

n Table 4 shows that tool wear, as would be expected, hasignificantly reduced the quality of the milled surface fromhe mean surface roughness of 38.8 �in. (0.99 �m) to 63.9�in. 1.62 �m) (p < .001). As shown in Table 5, the differ-nce between surface roughness in high temperature (mean8.8 �in./1.24 �m) compared to the one in normal temperaturemean 53.9 �in./1.37 �m) was not significant (p > .05). There-ore, it cannot be concluded from this experiment that theemperature significantly affects the quality of the finished sur-ace. In this study, only 5 min was maintained for keeping theigh temperature, and more time may need to be maintained foruture study to investigate the impact of environmental temper-ture.

A non-formal examination of the effects introduced by theontrol factors found that the mean surface roughness reducedreatly when feed rate was set from level 3 to level 2, how-ver, the surface roughness almost did not change when feed

able 5-test for effect on surface roughness of normal (70 ± 5 ◦F) and high (95–100 ◦F)oom temperature

Normal temperature(65–75 ◦F)

High temperature(95–100 ◦F)

ean 53.91667 48.75556ariance 502.3897 633.5344bservations 18 18.f. 17stat 1.086147critical one-tail 1.739607(T ≤ t) one-tail 0.146288

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Fig. 3. Pair means comparisons for feed rate.

ate was set from level 1 to level 2. The ANOVA analysis illus-rated in Table 6 and pair means comparisons in Fig. 3 for feedate shows that surface roughness difference caused by varyingeed rate was not significant as the other studies found [12].his would seem to imply that the noise factors could possiblydd uncertain interactions by varying the tool wear factor. Aomplete study including the interaction effects among factorsould open another research agenda with more experimental

uns. But this is beyond the scope of the current research set-upnd research purpose.

As for the effect of spindle speed and depth of cut on surfaceoughness, there is not a completely consistent conclusion inrevious studies. For example, Ghani et al. [6] found that highutting speed and low depth of cut in addition to the main fac-or of low feed rate would improve surface finish for machiningardened steel (AISI H13) with a TiN coated P10 carbide insert.ouzid et al. [7] found a high value of cutting speed used withsmall value of feed rate would improve the roughness of theachined Duplex stainless steel surface. They also found that an

ptimal value of depth of cut was more dependent on the mate-ial characteristics and the machine dynamics. For this study,he ANOVA analysis shown in Table 7 and pair means compar-sons in Fig. 4 for spindle speed shows that spindle speed was a

ignificant factor affecting surface roughness, and the setting ofpindle speed at 3500 rpm produced the smallest surface rough-ess value. The pair means comparison in Fig. 5 for depth of cut

able 7NOVA analysis for the effect of spindle speed on surface finish

ource d.f. Sum of square Mean square F ratio Prob > b

p 2 4466.367 2233.18 4.8804 0.0139rror 33 15100.155 457.58umulative total 35 19566.522

238 J.Z. Zhang et al. / Journal of Materials Proce

Fig. 4. Pair means comparisons for spindle levels.

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Fig. 5. Pair means comparisons for depth levels.

learly shows that depth of cut was not a significant factor in thistudy; however, the milling operations at low depth of cut consis-

ently provided a low surface roughness during this study. Theurface roughness changing trend revealed in the experimen-al data provides a direction to determine the optimum cuttingondition.

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Fig. 6. R̄a and S/N ratio effect

ssing Technology 184 (2007) 233–239

. Determination of the optimum cutting condition

The (mean response variable) effect table under the array inable 3 indicates the mean of the response variable means forach level of each control factor. This specifies the mean surfaceoughness value that each level of each control factor produceduring this experiment. The S/N ratio effect table under the arrayn Table 3 indicates the mean of the S/N ratio values for eachevel of each control factor. Fig. 6 shows the surface roughnessRa) and S/N ratio effects from Table 3.

In this study, it is the-smaller-the-better case, which meanshe smallest surface roughness would be the ideal situation. Alsohe largest S/N ratio, reflecting the best response given the noisen the machine set-up system, would be the ideal situation. Thiss the criteria employed in this study to determine the optimalutting condition.

By following the criteria of smaller surface roughness andarger S/N ratio, the graphs in Fig. 6 was used to determinehe optimal set of parameters from this experimental design.he control factor of spindle speed (A) at level 3 (3500 rpm)rovided the best result. Similarly, the control factor of feedate (B) at level 2 (30 ipm) provided the best result. Althoughepth of cut (C) was not a significant factor impacting surfaceoughness result, of the three set-up conditions, depth of cut atevel 1 provided the lowest surface roughness and highest S/Natio. Therefore depth of cut at level 1 (0.06 in./1.52 mm) waselected for the optimal cutting condition. The criteria of theowest response and highest S/N ratio were followed and therere no conflicts in this study in determining the optimal spin-le speed, feed rate, and depth of cut. Therefore, the optimizedombination of levels for the three control factors from the anal-sis so far was A3-B2-C1. In addition, this study supports the

ontention that the insert without wear (X1) will generate a bet-er surface finish. The statistical analysis indicated that thereas no significant difference when temperature was set as nor-al or high level, thus, temperature set-up would not matter in

s for each control factor.

J.Z. Zhang et al. / Journal of Materials Pro

Table 8The results of the confirmation run

Sample # Ra (�in.)

1 24.02 25.03 24.54 22.05 23.06 25.57 19.08 25.59 18.510 20.511 23.012 22.013 25.014 25.51

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he confirmation run. For the researchers’ convenience, in theonfirmation run temperature was set-up as normal temperatureY1). The optimized levels of the three parameters A3-B2-C1X1, Y1) were included in the confirmation run.

. Confirmation run

After the optimal levels of all the control factors were identi-ed, the last step in Taguchi parameter design is conducting theonfirmation run (see Fig. 1). The combination of the optimalevels of all the factors should produce the optimal magnitudef surface roughness (the smallest Ra). This conclusion must beurther supported through the confirmation runs. Fifteen samplesere cut under the optimal parameter set-up in the study for theurpose of confirmation run. The optimal levels for the control-able factors were spindle speed 3500 rpm, feed rate 30 in./min762 mm/min), depth of cut 0.06 in (1.52 mm). In terms of thexperimental result, the optimal levels for the noise factors inonfirmation run were no tool wear condition and normal tem-erature range. Table 8 shows the results of the confirmation run.

Compared with the experiment results in Table 3, theean surface roughness of the 15 confirmation samples

2.9 �in. (0.58 �m), which was very close to the smallest value23.5 �in./0.60 �m) of surface roughness in Table 3. Therefore,he confirmation run indicated that the selection of the optimalevels for all the parameters produced the best surface roughness.

. Conclusions

In this study the optimal cutting condition for face millingas selected by varying cutting parameters through the Taguchi

[

cessing Technology 184 (2007) 233–239 239

arameter design method. With the L9(34) orthogonal array, aotal of 36 experimental runs, covering three main factors eacht three levels and two noise factors each at two levels, indi-ated that the Taguchi parameter design was an efficient way ofetermining the optimal cutting parameters for surface finish.he experimental results indicate that in this study the effects ofpindle speed and feed rate on surface were larger than depth ofut for milling operation. In addition, one of the noise factors,ool wear, was found to be statistically significant. The surfacenish achievement of the confirmation runs under the optimalutting parameters indicated that of the parameter settings usedn this study, those identified as optimal through Taguchi param-ter design were able to produce the best surface roughness inhis milling operation. This was accomplished with a relativelymall number of experimental runs, given the number of controlnd noise factors, suggesting that Taguchi parameter design is anfficient and effective method for optimizing surface roughnessn a milling operation.

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[3] Y.H. Tsai, J.C. Chen, S.J. Lou, In-process surface recognition system basedon neural networks in end milling cutting operations, Int. J. Mach. ToolManuf. 39 (4) (1999) 583–605.

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[5] G. Taguchi, M. El Sayed, C. Hsaing, Quality Engineering and QualitySystems, McGraw-Hill, NY, 1989.

[6] K.H. Fuh, C.F. Wu, A proposed statistical model for surface quality pre-diction in end-milling of Al alloy, Int. J. Mach. Tool Manuf. 35 (8) (1995)1187–1200.

[7] J.A. Ghani, I.A. Choudhury, H.H. Hassan, Application of Taguchi methodin the optimization of end milling, J. Mater. Process. Tech. 145 (1) (2004)84–92.

[8] W. Bouzid, A. Zghal, L. Sai, Taguchi method for design optimiza-tion of milled surface roughness, Mater. Technol. 19 (3) (2004) 159–162.

[9] T.R. Lin, Optimization technique for face milling stainless steel with mul-tiple performance characteristics, Int. J. Adv. Manuf. Tech. 19 (5) (2002)330–335.

10] F. Ismail, M.A. Elbestawi, R. Du, K. Urbasik, Generation of milled surfacesincluding tool dynamics and wear, J. Eng. Ind. T. ASME 115 (3) (1993)245–252.

11] Y. Huang, S.Y. Liang, Cutting forces modeling considering the effect of

12] D.K. Baek, T.J. Ko, H.S. Kim, Optimization of feed rate in a face millingoperation using surface roughness model, Int. J. Mach. Tool Manuf. 41 (3)(2001) 451–462.