c© ARISER Vol. 4 No. 2 (2008) 61-75Engineering: Indu

Arab Research Institute in Sciences & Engineeringhttp://www.arabrise.org

Online Publishing Group ISSN 1994-3253

Optimization of Process Parameters in Vertical CNC Mill Machines UsingTaguchi’s Design of Experiments

Dalgobind MAHTO and Anjani KUMAR

Department of Production & Industrial Engineering, National Institute of Technology, Jamshedpur, INDIAmahto123@rediffmail.com; anj kumar2001@yahoo.co.in

Received 10 April 2008; Accepted 08 May 2008

With the more precise demands of modern engineering products, the control of surface texture togetherwith dimensional accuracy has become more important. This paper outlines the Taguchi optimizationmethodology, which is applied to optimize cutting parameters in end milling operation. The study wasconducted in machining operation in hardened steel DIN GX40CRMOV5-1. The processing of the jobwas done by TiN coated carbide inserted end-mill tool under semi-finishing and finishing conditions ofhigh-speed cutting. The milling parameters evaluated were cutting speed, feed rate and depth of cut. Theexperiments were conducted by using L-27 (313) orthogonal array as suggested by Taguchi. Signal-to-Noise (S/N) ratio and Pareto Analysis of Variance (ANOVA) are employed to analyze the effect of millingparameters on surface roughness. Main effects of process parameters on the quality characteristics havebeen analyzed. The results show that the optimum parameters of machining by CNC Milling Machine forspecified hardened steel material DIN GX40CRMOV5-1 is obtained at a cutting speed of 355m/min, feedrate 0.1mm per tooth and depth of cut 0.5mm.

Keywords: Surface Roughness, Design of Experiment, ANOVA and Signal-to-Noise Ratio.

Contents1 Introduction . . . . . . . . . . . . . . . . . 612 Taguchi’s View on Quality . . . . . . . . . 62

2.1 Factors Affecting Surface Roughness . 622.2 Aims and Objectives . . . . . . . . . 62

3 Literature Review . . . . . . . . . . . . . . 624 Taguchi’s design of experiment . . . . . . 64

4.1 Taguchi methods . . . . . . . . . . . 644.2 Achieving variability reduction: qual-

ity by design . . . . . . . . . . . . . . 64

4.3 Problem Formulation . . . . . . . . . 665 Plan of experiments . . . . . . . . . . . . . 66

5.1 Experimental setup, cutting conditionsand procedure adopted . . . . . . . . 66

5.2 Selection of levels for process variables 685.3 Measuring instruments used . . . . . 68

6 Experimental Results . . . . . . . . . . . . 686.1 Analysis of data and discussion . . . . 68

7 Conclusions . . . . . . . . . . . . . . . . . 69

1 Introduction

With the more precise demands of modern engineering products, the control of surface texture together with di-mensional accuracy has become more important. It has been investigated that surface texture greatly influencesthe functioning of the machined parts. Manufacturing involves various processes to turn raw materials to finishedproducts to be used for a variety of purposes. Whatever may be the manufacturing process used, it is not possibleto produce perfectly smooth surface. Hence, the improved qualities of product and the economics of the manufac-turing operation are very important consideration to produce product having the functional and visual appeal.

Although the aims of all the processes are to obtain the desired shape, size and finish. The selection of a par-ticular process depends on several factors, which includes the shape and size of the finished component, precisionrequired in the volume of production, cost of material and process and its availability. The commonly used methodfor obtaining the desired shape, size and finish is machining, which involves removal of excess material in theform of chips. Machining is one of the most versatile manufacturing processes. Popularity of milling for machin-ing application is increasing mainly due to the introduction of High Speed Machining (HSM), made possible byimprovements in the design and operation of milling machines and tools. Most frequently, milling involves the

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generation of flat faces and slots. However, its application for contour milling is growing with the availability ofCNC milling machines.

With the introduction of high speed machining (HSM), the scope of application of milling is continuouslyexpanding.

2 Taguchi’s View on Quality

Taguchi proposes a holistic view of quality, which relates quality to cost, not just to the manufacturer at the timeof production, but to the customer and society as a whole. Taguchi defines quality as, “The quality of a productis the (minimum) loss imparted by the product to the society from the time product is shipped” {Bryne [4]}. Thiseconomic loss is associated with losses due to rework, waste of resources during manufacture, warranty costs,customer complaints and dissatisfaction, time and money spent by customers on failing products, and eventual lossof market share.

2.1 Factors Affecting Surface Roughness

The variables that influence the economics of machining operations are numerous. Some of the important onesare machine tool capacity, work piece material and its geometry, tool geometry, vibrations, cutting parameterssuch as speed, feed, depth of cut and types of coolant used etc. The cutting parameters affect the production rate.The surface roughness, surface texture and dimensional deviations are also affected by the cutting conditions.Ultimately, it has overall impact on the product quality as well as the unit cost of component and productivity.

The principal reasons for controlling the surface roughness is essential to enhance the service life of the com-ponents, as it improves the fatigue resistance; and reduces corrosion and initial wear due to lack of irregularitiesand closer dimensional tolerances.

The economic selection of cutting conditions requires knowledge of technical aspects and cost aspects, whichare not easily available in many cases. Surface roughness (Ra) in machining is a measure of micro-geometricaltechnological quality errors occurred in a product and a factor that greatly influences manufacturing cost. It de-scribes the geometry of the machined surface texture, which is entirely process dependent. The prescribed samplinglength as per IS: 2073 150 is 0.8mm for majority of the machining processes and in case of milling operation theRoughness value is 0.32µ to 25µ. Therefore, this may be the basis of optimizing the operational characteristic ofthe processes.

2.2 Aims and Objectives

The principle aim and objective of the present study is to minimize the variation level within the specified targetvalue and to obtain a better surface finish, for better product quality and productivity. The conceptual Signal toNoise Ratio and Pareto ANOVA approaches with Taguchi’s design methodology, in the metal cutting operation,has been used in the present analysis.

3 Literature Review

Taguchi methods, developed by Dr. Genichi Taguchi, refer to techniques of quality engineering that embody bothstatistical process control (SPC) and new quality related management techniques. Most of the attention and discus-sion on Taguchi methods has been focused on the statistical aspects of the procedure; it is the conceptual frameworkof a methodology for quality improvement and process robustness that needs to be emphasized. The entire conceptcan be described in two basic ideas:

1. Quality should be measured by the deviation from a specified target value, rather than by conformance topreset tolerance limits.

2. Quality cannot be ensured through inspection and rework, but must be built in through the appropriate designof the process and product

Through the proper design of a system, the process can be made in sensitive to variations, thus avoiding thecostly eventualities of rejection and/or rework. In order to determine and subsequently minimize the effect offactors that cause variation, the design cycle is divided into three phases of System Design, Parameter Design, andTolerance Design.

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 63

The Taguchi Method was developed 50 years ago and has been used with great success to optimize automobileand other product manufacturing. More recently, The Taguchi Method was applied to direct mail and web applica-tions. The Taguchi Method takes a number of elements on a page with one or more alternatives for each element anddictates exact combinations that will allow estimating the positive or negative effect of each element/alternative.

Taguchi tests have been run on email, PPC ads and Landing Pages with great success. Where an AB Split Testmight create a 5− 10% improvement, a Taguchi test cycle will regularly return 25− 45% improvement and hasbeen known to improve results by 100% or more.

The operational steps as found from the reviews of literatures recommended to State problem and objective first,then to list responses, control parameters, and sources of noise. In the same way thereafter plan the experiment,run experiment and predict improved parameter settings and finally run confirmatory experiment. If the objectiveis not met, then it’s back to step (2). Otherwise, improved design can be adopted.{Aggarwal et al. [1]} have worked on the interaction graphs for a two-level combined array experiment design.

Their conclusion is that quality can be obtained by robust design.{Benardos & Vosniakos [2]} have presented the Prediction of surface roughness in CNC face milling using

neural networks and Taguchi’s design of experiments. They predicted that surface roughness is influenced by feed,speed and depth of cut.

Determination of the chip geometry, cutting force and roughness in free form surfaces finishing milling, withball end tools is the study by {Bouzakis et al. [3]}. Bryne’s {Bryne [4]} study on Taguchi’s approach to parametersdesign signifies the methodologies adopted in the study. {Dae et al. [5]} has studied the issue of optimization in aface milling operation.

Taguchi methods, developed by Dr. Genichi Taguchi, refer to techniques of quality engineering that embodyboth statistical process control (SPC) and new quality related management techniques. Most of the attention anddiscussion on Taguchi methods has been focused on the statistical aspects of the procedure; it is the conceptualframework of a methodology for quality improvement and process robustness that needs to be emphasized. Thearticle by {David et al [6]} has presented a statistical approach to Taguchi Method. {Henri et al. [7]} studiedsurface shape prediction in high speed milling.

The studies by {Jiju & Frenin [8]} on Taguchi’s design of experiment for engineers is how to select the problemand implement it using the methodologies to enhance quality, reduce process variability and wastages of time awell as other factors.

Surface roughness performance was studied by {John et al. [9]}. Their study is how to identify and decideoptimum parameters in End-Milling operations

Similarly, {Kishawy & Elbestawi [10]} have presented case studies on the effects of process parameters onmaterial side flow during hard turning. They concluded that through the proper design of a system, the processcould be made insensitive to variations, thus avoiding the costly eventualities of rejection and/or rework. In orderto determine and subsequently minimize the effect of factors that cause variation, the design cycle is divided intothree phases of System Design, Parameter Design, and Tolerance Design. The similar views has been expressed by{Mandara & Joseph [11]} in their research work entitled multiple regression-based multilevel in-process surfaceroughness recognition system in milling operation{Wang & Chang [12]} have done experimental study of surface roughness in slot end milling. They advocate

that the optimization of process parameter can greatly enhance surface roughness.According to {Resit et al. [?]}, Quality and cost are the main ingredients in Taguchi’s approach to design

optimization.A case study by {Robert et al. [14]} on tool path feed rate optimization suggests that quality and cost as well as

other variations can be minimized. The area of product development, although a “soft” area in terms of technology(especially in a field such as composites), is however perhaps all the more important due to the changes in paradigmnecessary for a successful completion of the product realization process. Not only does the development effort needan integrated team, but it also depends heavily on team dynamics, procedures, and even intangibles such as trustand team loyalty suggests {Ryan [15]}. {Thomson et al. [?]} have analyzed the effectiveness of DOE on injectionmolding operation by Taguchi Methods. The conclusion emphasizes that the approaches would find successfulapplicability in regions where the culture and people are in many cases asymmetrically aligned with the needs andproductivity demands.

A methodology of decision support system was given by {Vidal et al. [17]} for optimizing the selection ofparameters when planning milling operations.

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{Warner & Connor [18]} have found that through application of Taguchi’s design of experiment the productquality and productivity have improved as optimization of the process parameter played a crucial role in moldingprocess.

4 Taguchi’s design of experiment

4.1 Taguchi methods

The quality engineering methods of Dr. Taguchi, employing design of experiments (DOE), is one of the mostimportant statistical tools of TQM for designing high quality systems at reduced cost. Taguchi methods providean efficient and systematic way to optimize designs for performance, quality, and cost. Fundamentally, traditionalexperimental design procedures are too complicated and not easy to use. A large number of experimental workshave to be carried out when the number of the process parameters increases. To solve this problem, the Taguchimethod has used a special design of orthogonal arrays to study the entire parameter space with only a small numberof experiments. Taguchi is the developer of the Taguchi method. Taguchi methods has been widely utilized inengineering analysis and consists of a plan of experiments with the objective of acquiring data in a controlled wayand in order to obtain information about the behavior of a given process. The greatest advantage of this methodis to save the effort in conducting experiments. Therefore, it reduces the experimental time as well as the cost byfinding out significant factors fast.

4.2 Achieving variability reduction: quality by design

Product / process design has a great impact on life cycle cost and quality. Taguchi emphasizes pushing qualityback to the design stage since inspection and statistical quality control can never fully compensate for a baddesign. The quality engineering methods of Dr. Taguchi seek to design a product / process, which is insensitive orrobust to causes of quality problems. The three steps of quality by design are system design, parameter design, andtolerance design. System design involves the development of a system to function under an initial set of nominalconditions. System design requires technical knowledge from science and engineering. In the parameter designstep, the specific values for system parameters are determined. Tolerance design is used to determine the besttolerances for the parameters.

4.2.1 Steps applied in Taguchi methods Taguchi proposed a standard procedure for applying his method foroptimizing any process. The steps suggested by Taguchi are:

– Determine the quality characteristic to be optimizedThe first step in the Taguchi method is to determine the quality characteristic to be optimized. The qualitycharacteristic is a parameter whose variation has a critical effect on product quality. It is the output or theresponse variable to be observed.

– Identify the noise factors and test conditionsThe next step is to identify the noise factors that can have a negative impact on system performance and quality.Noise factors are those parameters which are either uncontrollable or are too expensive to control. Noisefactors include variations in environmental operating conditions, deterioration of components with usage, andvariation in response between products of same design with the same input.

– Identify the control parameters and their alternative levelsThe third step is to identify the control parameters thought to have significant effects n the quality character-istic. Control (test) parameters are those design factors that can be set and maintained. The levels (test values)for each test parameter must be chosen at this point. The number of levels, with associated test values, for eachtest parameter defines the experimental region.

– Design the matrix experiment and define the data analysis procedureThe next step is to design the matrix experiment and define the data analysis procedure. First, the appropriateorthogonal arrays for the noise and control parameters to fit a specific study are selected. Taguchi providesmany standard orthogonal arrays and corresponding linear graphs for this purpose.After selecting the appropriate orthogonal arrays, a procedure to simulate the variation in the quality charac-teristic due to the noise factors needs to be defined. A common approach is the use of Monte Carlo simulation.However, for an accurate estimation of the mean and variance, Monte Carlo simulation requires a large num-ber of testing conditions which can be expensive and time consuming. As an alternative, Taguchi proposes

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 65

orthogonal array based simulation to evaluate the mean and the variance of a product’s response resulting fromvariations in noise factors.

– Conduct the matrix experimentThe next step is to conduct the matrix experiment and record the results. The Taguchi method can be usedin any situation where there is a controllable process. The controllable process can be an actual hardwareexperiment, systems of mathematical equations, or computer models that can adequately model the responseof many products and processes.

– Analyze the data and determine the optimum levels for control factorsAfter the experiments have been conducted, the optimal test parameter configuration within the experiment-design must be determined. To analyze the results, the Taguchi method uses a statistical measure of perfor-mance called signal to noise (S/N) ratio borrowed from electrical control theory.

– Predict the performance at these levelsUsing the Taguchi method for parameter design, the predicted optimum setting need not correspond to one ofthe rows of the matrix experiment. This is often the case when highly fractioned designs are used. Therefore, asthe final step, an experimental confirmation is run using the predicted optimum levels for the control parametersbeing studied.

The summary of steps applied for Taguchi optimization in the present study is presented in Fig.1.

4.2.2 Signal to noise ratio and Pareto ANOVA approaches The S/N ratio developed by Dr. Taguchi is a per-formance measure to choose control levels that best cope with noise. The S/N ratio takes both the mean and thevariability into account. In its simplest form, the S/N ratio is the ratio of the mean (signal) to the standard devia-tion (noise). The S/N equation depends on the criterion for the quality characteristic to be optimized. While thereare many different possible S/N ratios, three of them are considered standard and are generally applicable in thesituations below;

– Biggest-is-best quality characteristic (strength, yield),– Smallest-is-best quality characteristic (contamination),– Nominal-is-best quality characteristic (dimension).

In addition to the Signal to Noise Ratio (S/N ratio), the obtained results have been tested using statistical Analy-sis of Variance (ANOVA) with Pareto chart to indicate the impact of process parameters on surface roughness.

1. Determine quality characteristics to be optimized

2. Identify the noise factors and test conditions

3. Identify the control factors and their alternative levels

4. Design the matrix experiment and define the data analysis procedure

5. Conduct the matrix experiment

6. Analyze the data and determine optimum levels for control factors

7. Predict the performance at these levels

FIG. 1: Steps applied in Taguchi optimization method.

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The reason of combining Pareto chart with Analysis of Variance was to detect causes applying the principlethat 80 percent of the problems usually stem from 20 percent of the causes.

Pareto ANOVA technique of analysis has been used in this experimentation to analyze data for process opti-mization in past research also . Pareto ANOVA is a simplified ANOVA method, which uses Pareto principle. It is aquick and easy method to analyze result of parameters design. It does not require an ANOVA table and therefore,does not use F-test. The calculations of these tables are done by the use of standard orthogonal arrays.

4.3 Problem Formulation

There are two objectives of this research. The first is to demonstrate a systematic procedure for using Taguchidesign methodology in process control of a milling machine. The second is to demonstrate the use of this method-ology in identifying the values of controlling parameters namely speed, feed and depth of cut, to obtain the optimumsurface roughness; and to meet the required performance criteria.

5 Plan of experiments

Taguchi methods combine the experiment design theory and the quality loss function concept; and are used indeveloping robust designs of products and processes in solving some confusing problems of manufacturing. Theselected orthogonal array was L 27 (3 13), which has 27 rows corresponding to the number of tests with threecolumns at three levels, as shown in Tab. 1. The factors and the interactions are assigned to the columns. Theoutputs studied were surface roughness (Ra) and cutting forces. For the purpose of observing the effect of cuttingconditions say, cutting speed, feed rate and depth of cut on the finished product in face milling, three factors, eachat three levels, are taken into account, as shown in Tab. 2. The depth of cut in axial direction has been kept constantand equal to 2 mm.

Axial depth of cut has been kept constant, 2mm.

5.1 Experimental setup, cutting conditions and procedure adopted

Experimentation was conducted on a 3-axis Vertical CNC Milling Machine fitted with high-speed motorized spin-dle, which can rotate up to 400 rpm. Dry condition has been recommended for the experimental work. A four-fluteTitanium Nitride coated insert end mill cutter was used. The diameter of the end mill cutter is 100 mm, helix angleis 300 and radial rack angle is 2◦C. The photograph of the experimental set-up is shown in Fig. 2.

FIG. 2: Experimental set-up.

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 67

TAB. 1: L 27(313) Standard orthogonal array table with factor A, B and C aranged in 2, 5 and 6 respectively.

Run 1 2 3 4 5 6 7 8 9 10 11 12 131 0 0 0 0 0 0 0 0 0 0 0 0 02 0 0 0 0 1 1 1 1 1 1 1 1 13 0 0 0 0 2 2 2 2 2 2 2 2 24 0 1 1 1 0 0 0 1 1 1 2 2 25 0 1 1 1 1 1 1 2 2 2 0 0 06 0 1 1 1 2 2 2 0 0 0 1 1 17 0 2 2 2 0 0 0 2 2 2 1 1 18 0 2 2 2 1 1 1 0 0 0 2 2 29 0 2 2 2 2 2 2 1 1 1 0 0 0

10 1 0 1 2 0 1 2 0 1 2 0 1 211 1 0 1 2 1 2 0 1 2 0 1 2 012 1 0 1 2 2 0 1 2 0 1 2 0 113 1 1 2 0 0 1 2 1 2 0 2 0 114 1 1 2 0 1 2 0 2 0 1 0 1 215 1 1 2 0 2 0 1 0 1 2 1 2 016 1 2 0 1 0 1 2 2 0 1 1 2 017 1 2 0 1 1 2 0 0 1 2 2 0 118 1 2 0 1 2 0 1 1 2 0 0 1 219 2 0 2 1 0 2 1 0 2 1 0 2 120 2 0 2 1 1 0 2 1 0 2 1 0 221 2 0 2 1 2 1 0 2 1 0 2 1 022 2 1 0 2 0 2 1 1 0 2 2 1 023 2 1 0 2 1 0 2 2 1 0 0 2 124 2 1 0 2 2 1 0 0 2 1 1 0 225 2 2 1 0 0 2 1 2 1 0 1 0 226 2 2 1 0 1 0 2 0 2 1 2 1 027 2 2 1 0 2 1 0 1 0 2 0 2 1

B×C A B C B×C A×B A×C A×B A×C

TAB. 2: Factor and level used in experiment.

Process parameters Parameter designation Levels0 1 2

Speed (m/min) A 224 280 355Feed (mm/tooth) B 0.1 0.16 0.25Depth of cut (mm) C 0.3 0.5 0.8

The selection of proper cutter for doing a job in is very important in milling operation. For this the work piecematerial was properly identified. The chemical investigation of the work piece was done. The details of chemicalcomposition have been tabulated in Tab. 3. According to chemical composition the work material was ChromeAlloy Steel.

Depending upon the cutter and the work piece, suitable speed and feed were set on the machine. Depth of cutdepends on the amount of material to be removed. However, it was predetermined to keep the depth of cuts as0.10mm, 0.16mm and 0.25mm. The axial depth of cut was kept constant as 2mm (as specified in Table2).

– Setting procedure of machine

For setting up the machine, the knee locking clamp and the cross slide lock were loosened. The spindle wasturned on and its rotation was checked. The table was positioned so that the work piece is under the cutter. Theknee was raised slowly by turning the vertical head feed crank until the cutter just touched the work piece. The

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TAB. 3: Chemical composition of work material DIN GX40CRMOV5-1.

Element % By weightC 0.39Si 0.95

Mn 0.47P 0.012S 0.018Ni 0.06Cr 5.28Cu 0.39Mo 1.23V 0.99

micrometer dial on the feed screw was then set on zero. The table was then lowered slightly down (by half revo-lution of hand feed crank to clear the work slightly from the cutter) and the table was moved longitudinally untilthe cutter is clear of the work piece. The knee was again raised to zero mark. The knee lock and the cross slidelock were tightened. The machine was then ready to cut. The table was slowly moved into the revolving cutteruntil the full depth of cut was obtained before engaging the power feed. When the cut was completed, the powerfeed was disengaged. The same sequence of operation was repeated for 27 times on different sample pieces withcombination of Speed, Feed and Depth of cut. The machine was the CNC machine. It had a provision to operate iteither locally or through CNC System.

5.2 Selection of levels for process variables

The process parameters and their levels have been decided on the basis of experimental results available in IS: 2073and Hinman. According to them, the selection of cutting speed depends on the sturdy of work piece and rigidityof the milling cutter. The limitations imposed by the machine are also considered during the parameter and levelselection.

The cutting speed has to be lowered when the chips section is increased. In the case of materials, which are nothomogenous, and also in the case of the hardest material in each category, the lowest values should be used first.Hence, for the material DIN GX40CRMOV5-1 the speed was selected as 224m/min and accordingly as per planof experiment it was increased to 280m/min and 355m/min. The combination of feed rate (mm/min) and Depth ofcut (mm) are tabulated in Tab. 4.

5.3 Measuring instruments used

The following instruments and equipment have been used to measure the pertaining data obtained in the study.

– A Kilster Dynamometer (Model 9275 Piezo-Electric 3-component type) has been used for measuring theforces.

– Teknonix oscilloscope has been used for recording forces. It has been measured in unit Newton (N).– The surface roughness has been measured using Keane Tator Surface Roughness (Ra) Tester. The roughness

value has been measured in µm.

6 Experimental Results

The experimental data have been optimized with Taguchi’s design of experiment. For the analysis of these dataMinitab 14 software has been used. The results obtained by the above software are presented in Figs. 3 to 9 andtabulated in Table 5 to 12.

6.1 Analysis of data and discussion

The data obtained from the experiments has been analyzed in a series of standard steps as discussed in section4, when they change from one level to another level are calculated and plotted as response curves. The response

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 69

curves are the average value of the characteristic and average S/N values versus level of process parameters. Theresponse curves are used as an aid to visualize the parametric effect on selected quality characteristics. The ANOVAidentifies the significant parameters and quantifies their effect on the selected quality characteristics. Associatedwith each response curve is the S/N response curve, which is used to keep in the selection of optimal level ofresponse process parameters for individual quality characteristics.

All these information were stored in the computer automatically with the help of software installed. The para-meters like roughness and force were measured. The obtained experimental data were gathered and presented inTable 4 for further analysis.

The next step was to identify the noise factors that could have a negative impact on system performance andquality. Noise factors were those parameters which were either uncontrollable or were too expensive to control.Noise factors included variations in environmental operating conditions, deterioration of components with usage,and variation in response between products of same design with the same input. The noise factors were identifiedand recorded. The experimental results for surface roughness and cutting force with their corresponding signal tonoise ratio has been presented in Tab. 5.

7 Conclusions

An overview of the Taguchi method has been presented and the steps involved in the method were briefly described.Overall, the Taguchi method is a powerful tool, which can offer simultaneous improvements in quality and cost.Furthermore, the method can aid in integrating cost and engineering functions through the concurrent engineer-ing approach required to evaluate cost over the experimental design. The Taguchi method emphasizes pushingquality back to the design stage, seeking to design a product/process, which is insensitive or robust to causes ofquality problems. It is a systematic and efficient approach for determining the optimum experimental configu-ration of design parameters for performance, quality, and cost. Principal benefits include considerable time andresource savings; determination of important factors affecting operation, performance and cost; and quantitativerecommendations for design parameters, which achieve lowest cost, high quality solutions.

It can be concluded that better optimization of cutting parameters are necessary in order to obtain a good finish.It was observed in the experiment that the use of S/N ratio requires low feed rate for obtaining the best surface finish(Ra). It has been observed that smaller angle of tool angular position is obtained at lower depth of cut. Therefore,it is preferable to set the depth of cut at low value. Therefore, one can say that the set values of for level 1 aresuitable to obtain good quality of surface finish. From the result, the interaction of factor B and factor C is moreimportant than the effect of individual factors. In other words, in order to get the best result it requires experienceto combine these two factors to achieve a suitable combination of feed rate and depth of cut. Moreover, the S/Nratio has suggested that the cutting force depends on feed rate and depth of cut. Both the feed rate and depth of cutwas found the best combination at level ‘0’ to obtain low value of cutting force. Also, the required force to formthe chips was dependent on the shear yield strength of the work material and under cutting conditions and on thearea of the chip section zone.

From the analysis of the result in end milling using conceptual S/N ratio and Pareto ANOVA approaches, thefollowing conclusions can be drawn from the present study:

1. Taguchi’s robust design method is suitable to analyze the metal cutting problem as described in the presentwork.

2. Conceptual S/N ratio and Pareto ANOVA approaches for data analysis draw similar conclusion.3. In end milling, use of high cutting speed (355m/min.), low feed rate (0.1mm per tooth) and low depth of cut

(0.5mm) are recommended to obtained better surface finish for the specific test range in a specified material.Similar experiments can be conducted to choose the best combination of speed, feed and depth of cut in orderto improve product quality and productivity.

4. Low feed rate (0.1mm per tooth) and low depth of cut (0.3mm) lead to smaller value of resultant cutting forcefor the specific test range.

5. The use of high cutting speed, low feed rate and low depth of cut leads to better surface finish (or low surfaceroughness) and application of low cutting force.

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speed feed

depth

Main Effects Plot (data means) for SN ratios

Signal-to-noise: Smaller is better

FIG. 3: Variation of means of main effect plot (data means) for signal to noise ratio with speed, feed and depth of cut.

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 71

TAB. 4: Experimental results for surface roughness and cutting force.

Parameters Measured ParameterSpeed (m/min) Feed Rate (mm/Tooth) Depth of Cut (mm) Roughness (Ra) in (µm) Force (N)

224 0.1 0.3 0.207 469224 0.1 0.5 0.231 1229224 0.1 0.8 1.045 1085224 0.16 0.3 0.756 949224 0.16 0.5 0.169 1277224 0.16 0.8 0.448 1746224 0.25 0.3 0.418 1563224 0.25 0.5 0.872 1736224 0.25 0.8 0.513 2175280 0.1 0.3 0.245 503280 0.1 0.5 0.203 1125280 0.1 0.8 1.424 1203280 0.16 0.3 0.872 1179280 0.16 0.5 0.252 1167280 0.16 0.8 0.671 1716280 0.25 0.3 0.234 1446280 0.25 0.5 0.888 1944280 0.25 0.8 0.27 2144355 0.1 0.3 0.531 649355 0.1 0.5 0.263 1225355 0.1 0.8 1.392 1761355 0.16 0.3 1.024 1270355 0.16 0.5 0.579 736355 0.16 0.8 0.608 1334355 0.25 0.3 0.657 1208355 0.25 0.5 1.202 1826355 0.25 0.8 0.615 1831

Mea

n of

SN

rati

os

355280224

5

4

3

2

0.250.160.10

0.80.50.3

5

4

3

2

speed feed

depth

Main Effects Plot (data means) for SN ratios

Signal-to-noise: Smaller is better

FIG. 4: Variation of mean of means for main effect plot (data means) with speed, feed and depth of cut .

72 N. Nasser

TAB. 5: The experimental results for surface roughness and cutting force and their corresponding S/N ratio..

meters Calculated S/N ratioSpeed (m/min) Feed rate

(mm/Tooth)Depth of cut(mm) S/N ratio for Sur-

face RoughnessS/N ratio for Force

230 0.1 0.3 1.368 −5.342230 0.1 0.5 1.273 −6.179230 0.1 0.8 −0.038 −6.071230 0.16 0.3 0.243 −5.955230 0.16 0.5 1.544 −6.212230 0.16 0.8 0.697 −6.484230 0.25 0.3 0.758 −6.388230 0.25 0.5 0.119 −6.479230 0.25 0.8 0.58 −6.675285 0.1 0.3 1.222 −5.403285 0.1 0.5 1.385 −6.102285 0.1 0.8 −0.307 −6.161285 0.16 0.3 0.119 −6.143285 0.16 0.5 1.197 −6.134285 0.16 0.8 0.347 −6.469285 0.25 0.3 1.262 −6.32285 0.25 0.5 0.103 −6.577285 0.25 0.8 1.137 −6.662357 0.1 0.3 0.55 −5.624357 0.1 0.5 1.16 −6.176357 0.1 0.8 −0.287 −6.492357 0.16 0.3 −0.021 −6.208357 0.16 0.5 0.475 −5.734357 0.16 0.8 0.432 −6.25357 0.25 0.3 0.365 −6.164357 0.25 0.5 −0.16 −6.523357 0.25 0.8 0.422 −6.525

TAB. 6: Response table for S/N ratio for surface roughness and significant interaction.

Parameters Designation Parameters Average Value of Surface roughness Main EffectsLevel 0 Level 1 Level 2 Lmax−Lmin.

A Speed 0.727 0.718 0.326 0.490B Feed 0.707 0.559 0.509 0.198C Depth 0.651 0.788 0.331 0.457

A×B Interaction 0.665 0.601 0.504 0.161B×C Interaction 0.943 0.853 −0.025 0.968A×C Interaction 0.557 0.678 0.535 0.143

TAB. 7: Two-way table for cutting force.

B0 B1 B2 TotalC0 −5.34 − 5.40 −

5.62 =−16.36−5.95 − 6.14 −6.20 =−18.29

−6.38 − 6.32 −6.14 =−18.84

−53.49

C1 −6.17 − 6.10 −6.17 =−18.44

−6.21 − 6.13 −5.74 =−18.07

−6.47 − 6.57 −6.52 =−19.56

−56.07

C2 −6.07 − 6.16 −6.49 =−18.72

−6.48 − 6.46 −6.25 =−19.19

−6.67 − 6.66 −6.52 =−19.85

−57.76

Total −53.52 −55.55 −58.25 −167.32

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 73

TAB. 8: Two way table for surface roughness.

B0 B1 B2 TotalC0 1.368 + 1.222 +

0.55 = 3.1400.243 + 0.119 −.021 = 0.341

0.758 + 1.262 +0.365 = 2.385

5.866

C1 1.273 + 1.358 +1.160 = 3.791

1.544 + 1.197 +0.475 = 3.216

0.119 + 0.103 −0.160 = 0.062

5.069

C2 −0.138 −0.287 − 0.307 =−.732

0.432 + 0.347 +0.697 = 1.476

0.580 + 1.137 +0.422 = 2.139

2.883

Total 6.199 5.033 4.586 15.818

TAB. 9: Pareto ANOVA for factors and their interactions.Factor and Interaction

A B C A×B B×C A×C A×B B×C A×C0 6.544 6.326 5.866 5.991 8.495 5.021 4.893 4.676 5.6211 6.465 5.033 7.096 5.411 7.679 6.106 6.409 4.969 5.0072 2.936 4.586 2.983 4.543 −.229 4.818 4.643 6.298 5.317

Mea

n of

SN

rati

os

355280224

-60.0

-61.2

-62.4

-63.6

-64.8

0.250.160.10

0.80.50.3

-60.0

-61.2

-62.4

-63.6

-64.8

speed feed

depth

Main Effects Plot (data means) for SN ratios

Signal-to-noise: Smaller is better

FIG. 5: Variation of means of main effect plot (data means) for signal to noise ratio with speed, feed and depth of cut.

roug

hnes

s

depthspeed

0.80.50.3355280224355280224355280224

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Individual Value Plot of roughness vs depth, speed

FIG. 6: Variation of surface roughness with speed and depth of cut for constant values of feed (feed: o.10, 0.16, 0.25 mm/tooth) at three levels.

74 N. Nasser

forc

e

speeddepth

3552802240.80.50.30.80.50.30.80.50.3

2250

2000

1750

1500

1250

1000

750

500

Individual Value Plot of force vs speed, depth

FIG. 7: Variation of force with speed and depth of cut for constant values of feed (feed: o.10, 0.16, 0.25 mm/ tooth) at threelevels.

forc

e

feeddepth

0.250.160.100.80.50.30.80.50.30.80.50.3

2250

2000

1750

1500

1250

1000

750

500

Individual Value Plot of force vs feed, depth

FIG. 8: Variation of force with depth of cut and feed for constant values of speed (speed: 224,280and 355 m / min) at threelevels.

Mea

n of

Mea

ns

355280224

1800

1600

1400

1200

10000.250.160.10

0.80.50.3

1800

1600

1400

1200

1000

speed feed

depth

Main Effects Plot (data means) for Means

FIG. 9: Variation of mean of means of main effect plot (data means) of force with speed, feed and depth of cut.

Optimization of Process Parameters in Vertical CNC Mill Machines Using Taguchi’s Design of Experiments 75

TAB. 10: Pareto ANOVA analysis for sum of square of difference, contribution ratio cumulative contribution and their factorsand interaction.

Factor and InteractionSSD A B C A×B B×C A×C A×B B×C A×C

25.477 4.899 26.741 3.182 139.310 2.877 5.479 4.482 0.565CR 11.96 2.299 11.553 1.493 65.253 1.350 2.572 2.104 0.265CC 11.96 14.259 26.812 28.305 93.558 94.908 97.48 99.584 99.894

TAB. 11: Statistical calculations for level of parameters and their interaction.

Sum at level Parameters and InteractionSSD A B C A×B B×C A×C A×B B×C A×C

−55.78 −53.55 −53.54 −55.34 −54.31 −55.41 −55.55 −54.71 −55.76CR −55.97 −55.58 −56.11 −55.52 −56.53 −56.00 −56.50 −55.67 −56.15CC −55.69 −58.31 −57.78 −56.58 −56.60 −56.04 −55.40 −56.62 −55.52

TAB. 12: Pareto table for sum of square of difference, contribution ratio cumulative contribution and their parameters andinteraction.

Parameters and InteractionSSD A B C A×B B×C A×C A×B B×C A×C

0.118 34.263 27.393 2.677 10.219 0.749 2.143 5.483 0.605CR 0.141 41.05 32.746 3.201 12.23 0.91 2.562 6.561 0.725CC 0.141 41.11 73.93 77.13 89.36 90.27 92.84 99.40 100

Where, SSD = Sum of Square of Difference, CR = Contribution Ratio (%) and CC = Cumulative Contribution.

Where, SSD = Sum of Square of Difference, CR = Contribution Ratio (%), CC = Cumulative Contribution.