Utility Concept and Taguchi

7/29/2019 Utility Concept and Taguchi

http://slidepdf.com/reader/full/utility-concept-and-taguchi 1/7

9

International Journal of Mechanical and Materials Engineering (IJMME), Vol. 7 (2012), No. 1, 9 – 15.

ANALYSIS AND PARAMETRIC OPTIMIZATION OF ABRASIVE HOT AIR JET

MACHINING FOR GLASS USING TAGUCHI METHOD AND UTILITY CONCEPT

N. Jagannatha

1*

, S.S. Hiremath

2

and K. Sadashivappa

3

1Department of Industrial & Production Engineering, SJM Institute of Technology, Chitradurga 577502, India

2Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India

3Department of Industrial & Production Engineering, Bapuji Institute of Engineering and Technology,

Davangere 577004, India

*Corresponding author’s E-mail: [email protected]

Received 26 July 2011, Accepted 11 January 2012

ABSTRACT

Carrier media plays a major role in removal of material

in Abrasive Jet Machining (AJM). In this paper, an

attempt has been made to use hot air as carrier media in

AJM. Modified Taguchi robust design analysis isemployed to determine optimal combination of process

parameters. The Analysis Of Variance (ANOVA) is also

applied to identify the most significant factor. It can be

found that the air temperature is the most significant

factor on Material Removal Rate (MRR) and Roughness

of machined surface (R a). It has been observed that there

is good agreement between the predicted values and

experimental values of optimization. The influence of

temperature on MRR and R a has been discussed. It can be

found that at high temperature, there is a sufficientevidence of more plastic deformation accompanied by

brittle fracture failure which results in increase of MRR

and reduction of roughness.

Keywords: Abrasive hot air jet, Material Removal Rate

(MRR), Roughness, ANOVA, Multi-response S/N ratio.

1. INTRODUCTION

The glass and other brittle materials can be machined by

non-conventional processes such as Ultrasonic

Machining (USM), Abrasive Jet Machining (AJM),

Electrical Discharge Machining (EDM), ElectrochemicalMachining (ECM), Laser Beam Machining (LBM) and

Plasma Arc Machining (PAM). Abrasive Jet Machining

has high degree of flexibility, and hence it is typically

used for machining of glass and ceramic materials.Manufacturers are trying to reduce the operation cost andincrease the quality of products. The surface roughness

and MRR are significant characteristics in machining of

glass using AJM. There is a need to optimize the process

parameters in a systematic way to achieve the output

characteristics /responses by using experimental methods

and statistical models. Taguchi’s robust design method issuitable to solve the metal cutting problem like milling

with minimum number of trials as compared with a full

factorial design and one factor at a time method (Ghani et

al., 2004). Tasirin et al. (2007) reported that Taguchi

method can also be applied for food drying problems to

optimize process parameters.

The approach adopted by design of experiment through

the Taguchi orthogonal array is very popular for solving

optimization problems in manufacturing engineering

(Vijian and Arunachalam, 2006; Chen and Chen, 2007;

Zhang et al., 2007; Mahapatra and Chaturvedi, 2009;

Basavarajappa et al., 2009; Bushroa et al., 2011; Nor et

al., 2011; Ng et al., 2011) and ANOVA has been usedsuccessfully in process optimization.

Utility concept is a simple, useful and provides an

appropriate solution for multi-response optimization

problems. It is found that a little work has been reported

(Kaladhar et al., 2011) on multi-response optimization

in machining to determine the best combination of the

process parameters. Recently Grey relational analysis is

successfully employed in conjunction with Taguchi

design of experiments to optimize the multiple response problems (Sathia and Jaleel, 2010; Das and Sahoo,

2011). The process parameters which affect the shape of

the surface machined by AJM using Design of experiment and ANOVA were analyzed

(Balasubramaniam et al., 1999). The design of nozzle

and variable parameters like pressure of carrier media,abrasive types and size, abrasive flow rate and stand-off

distance have effects on MRR and it has been discussed

by experimental investigations. Drilling of glass sheets

with different thicknesses have been carried out by AJM

in order to determine its machinability under different

controlling parameters (El-Domiaty et al., 2009). Anintermittent jet mechanism to increase the efficiency of

jet in micro-grooving and also developed statistical

models for the prediction and process optimization of

micro abrasive intermittent jet machining (Zhang et al.,2005). Enough research work has not been carried out onhot air jet machining. It has been proved that the cutting

of glass material can also be performed using only hot air

jet (Muralidhar et al., 1982). A compact portable hot air

jet gun has been developed for thermal cutting of glass

plate and the effect of various parameters on cutting rate

has been discussed (Prakash et al., 2001).

From the above literature survey, it has been found that

the existing research works on AJM have not focused on

carrier media. In this paper, an attempt has been made to

use hot air as carrier media in AJM. In this consideration,

an abrasive hot air jet machine has been developed. It can be applied for various operations such as drilling, surface

etching, engraving and micro finishing on the glass and

its composites. The multi characteristics optimization



10

model based on Taguchi method and Utility concept has

been employed to determine the optimal combination of the machining parameters to attain the minimum surface

roughness and maximum MRR simultaneously. The

confirmation test is also conducted to verify the results.

The effect of air temperature (hot air) on MRR and

surface roughness is also discussed in this paper.

2. MATERIALS & METHODS

2.1 Experimentation

The schematic diagram of experimental set up is shown

in Figure1. It consist of portable Abrasive chamber,

Heating chamber with controller, Mixing head, Nozzle

and Three axes table with CNC controller. A part of air

flows through the abrasive chamber and the feeding of

abrasive particles take place due to the pressure

difference in the abrasive chamber and main flow.

Abrasive particles are mixed with air and then they enter

into the mixing head where the hot air is mixed with

abrasives and then passed through the nozzle as shown inFigure 2. The abrasive hot jet is available at the tip of

nozzle striking on the target. The flow of abrasive is

controlled by a valve below the chamber. The nozzles are

usually made up of Sapphire / Tungsten carbide material

of hardness 50-60 HRC. As the Tungsten carbidematerial is of high cost, in this research work, alloy steel

(EN38) heat treated of hardness 50 HRC was used for

nozzles. The temperature of air at the exit of nozzle is

measured using sensors (Thermocouples).

Figure 1 Schematic of Abrasive hot air jet process

2.2 MaterialsIn the present work, Soda-lime glass was used as the

work material. The suitable size of specimen was used

for grooving processes. The specimens were washed and

weighed before machining. The maskants were stuck onthe surface of specimen to protect the un machined part

of work material.

Figure 2 Abrasive hot air jet striking on surface of glass

plate

The material used for the maskants were steel or bronze

as they resist the high temperature of abrasive hot air jet.

After the test, the samples were cleaned with pressurized

air and final weight was measured using a digital

electronic balance (BSA224S-CW SARTORIOUS,

GERMANY) with resolution of 0.1mg. Four

measurements for each sample were taken and the

average value was the final reading. The weight loss per

unit time for each specimen is calculated and considered

as material removal rate. Similarly the roughness of

machined part was measured using a surface roughnesstester (Surf Test SJ201P, Mitutuyo, Japan). The average

Roughness value R a of the machined part was recorded at

four different locations and the mean value was

considered as a roughness of surface.

Table 1 Process parameters and their levels

Parameter Level

1

Level

2

Level

3

A SOD (mm) 4 8 12

B Feed rate (mm/min) 20 30 40

C Air temperature (oC) 27 200 320



11

Table 2 Orthogonal array and Experimental Results with S/N Ratios

Sl.

No.

FactorsMRR

(g/min)

R a (µm)S/N ratio

MRR

η1 (dB)

S/N ratio

R aη1 (dB)

S/N ratioMulti-

response

η (dB)A B C

1 4 20 27 0.089 2.54 -21.012 -8.096 -14.5542 4 30 200 0.130 1.74 -17.721 -4.810 -11.265

3 4 40 320 0.171 1.37 -15.340 -2.734 -9.037

4 8 20 200 0.102 2.01 -19.827 -6.063 -12.945

5 8 30 320 0.140 1.45 -17.077 -3.227 -10.152

6 8 40 27 0.062 2.84 -24.152 -9.066 -16.609

7 12 20 320 0.135 1.47 -17.393 -3.346 -10.369

8 12 30 27 0.050 3.05 -26.020 -9.685 -17.852

9 12 40 200 0.051 2.92 -25.848 -9.307 -17.577

2.3 Parameters and DesignIn this process, a large number of variables are involved

and all these variables affect the machining results

directly or indirectly. For the purpose of presentinvestigation, only major and easy to control variables

like stand-off distance, feed rate and air temperature wereconsidered in this experiment. The other experimental

parameters were kept constant throughout the machining

as shown in Table 1. In order to obtain high efficiency in

the planning and analysis of experimental data, the

Taguchi parameter design was applied. Taguchi method

uses a statistical measure of performance called Signal-to-Noise(S/N) ratio. The ratio depends on the quality

characteristics of the product/process to be optimized.

The standard S/N ratios generally used are as follows: -

Nominal-is-best, Smaller-the-better and Larger-the-

Better. The optimal setting is the parameter combination,which has the highest S/N ratio, (Taguchi, 1986;

Mahapatra and Chaturvedi, 2009). One of the important

steps involved in Taguchi’s technique is selection of

orthogonal array. An orthogonal array is a small set from

all possibilities which helps to determine least number of

experiments. Which will further help to determine the

optimum level for each process parameters and establish

the relative importance of individual process parameters.

In this work, the orthogonal array L9 was selected.

The multi-response methodology based on Taguchi’s

robust design technique and Utility concept was used for

optimizing the multi-responses like MRR and R a.Taguchi’s standard S /N ratios were selected to obtain the

optimum parameters combination (Ross, 1996). They

were, Larger the better type S/N ratio for MRR and

Smaller the better type S/N ratio for R a as calculated by

Eqs. (1) and (2) respectively.

(1)

[] (2)

2.4 Utility Concept

Utility can be defined as the usefulness of a product or a process in reference to the levels of expectations to the

consumers (Kumar et al., 2010). The overall usefulnessof a process /product can be represented by a unified

index termed as utility which is the summation of the

individual utilities of various quality characteristics. It isdifficult to obtain the best combination of process

parameters, when there are multi-responses to beoptimized. The adoption of weights in the utility concept

helps in this difficult situations by differentiating the

relative importance of various responses. If xi represents

the measure of effectiveness of i th process response

characteristic and n represents number of responses,

then the overall utility function can be written as (Bunn,1982)

( ) [ () () ()] (3)

where U(x1 , x2 , x3 ... xn ) is the overall utility of n processresponse characteristics and U i(xi ) is utility of i th

response characteristic. Assignment of weights is based

on the requirements and priorities among the various

responses. Therefore the general form or weighted from

of Eq. (3) can be expressed as

( ) () (4)

where ∑

where W i is the weight assigned to the i th response

characteristic. The utility concept employs the weighingfactors to each of S/N ratio of the responses to obtain a

multi response S/N ratio for each trial of the orthogonal

array. The multi-response S/N ratio is calculated by the

equation.

(5)

where w1 and w2 are the weighing factors associated with

the S/N ratio of MRR and R a respectively. These

weighing factors were decided based on the priorities

among the various responses to be simultaneously

optimized. In the present work, weighing factors of 0.5

for MRR and 0.5 for R a are assumed. This gives

priorities to all responses for simultaneous minimizationand maximization. The overall mean of η associated with

k number of trials is computed as;



12

∑

(6)

3. RESULTS AND DISSCUSSION

3.1 Analysis of single response Experiments were conducted on soda lime glass plate to

study the performance of grooving process using

orthogonal array L9. The values of Single-response S/Nratios MRR ( η1) and R a (η2) are calculated using Eqs.

(1) and (2) respectively. The combined multi-response

S/N ratio is calculated using Eq. (5) shown in Table 2.

The individual mean values of S/N ratios of responses of

MRR (η1) and surface roughness R a (η2) are shown in

Table 3 and Table 5 respectively. It can be found that the

optimal combination A1B1C3 is largest value of S/N

ratios of MRR and R a respectively. Therefore A1B1C3 is

the optimal combination of both responses MRR and R a.The main effect plots (Figure 3 and Figure 4) shows that

the optimum condition for MRR and R a are at level 1 (4

mm) of SOD, level 1 (20 mm/min) of Feed rate and

level 3 (320oC) of air temperature.

Table 3 Means of S/N ratio values of MRR

Parameter Level 1 Level 2 Level 3

ASOD

(mm)-18.024 -20.352 -23.087

BFeed rate

(mm/min)-19.410 -20.272 -21.780

CAir temperature(

oC)

-23.728 -21.132 -16.603

Table 4 Results of ANOVA for MRR

SourceD

FSeq SS Adj SS

Adj

MSF

Contri

bution

P (%)

A 2 38.529 38.529 19.26410.4

729.90

B 2 8.629 8.629 4.314 2.35 6.69

C 2 78.009 78.009 39.00421.2

360.54

Error 2 3.675 3.675 1.837 2.852

Total 8 128.841

Table 5 Means of S/N ratio values of R a

Parameter Level

1

Level

2

Level

3

A SOD (mm) -5.213 -6.135 -7.446

B Feed rate (mm/min) -5.835 -5.907 -7.035

C Air temperature (oC) -8.949 -6.726 -3.102

The statistical software with an analytical tool of ANOVA is used to determine which parameter

significantly affects the performance characteristics. The

results of ANOVA for the Single-response S/N ratios of

MRR (η1 ) and surface roughness R a (η2) are shown inTable 4 and Table 6.

Figure 3 Main effects plot based on the S/N ratio of MRR (η1)

Figure 4 Main effects plot based on the S/N ratio of R a(η2)

It can be seen that air temperature has the highest

contribution of about 60.54% for MRR and 80.99% for

R a, the other parameters have less contributions. It is

clear that the air temperature is one of the significant

factors that has more impact than any other factors on

MRR and R a.

Table 6 Results of ANOVA for Ra

Sourc

e

D

FSeq SS Adj SS

Adj

MSF

Contr

ibutio

n

P (%)A 2 7.566 7.566 3.783 3.82 11.72

B 2 2.720 2.720 1.360 1.37 4.21

C 2 52.258 52.258 26.129 26.40 80.99

Error 2 1.980 1.980 0.990 3.06

Total 8 64.524

3.2 Optimal parameter combination of Multi-

response The optimal combination of process parameters for

simultaneous optimization of MRR and R a is obtained

by the mean values of the multi-response S/N ratio of the

overall utility value as shown in Table 7.

The larger value of the multi-response S/N ratio means

the comparable sequence exhibiting a stronger



13

correlation with the reference sequence. Based on this

study, the combination A1B1C3 shows the largest value of the multi-response S/N ratio for the factors A, B, and C

respectively. Therefore, A1B1C3 is the optimal parameter

combination of the Abrasive hot air jet machining for

glass.

Table 7 Means of multi-response S/N Ratio

Parameter Level 1 Level 2 Level 3

A SOD (mm) -11.618 -13.235 -15.266

B Feed rate (mm/min) -12.622 -13.089 -14.407

C Air temperature (oC) -16.338 -13.935 -9.852

Table 8 ANOVA for the multi- response S/N ratio

SourceD

FSeq SS Adj SS

Adj

MSF

Contri

bution

P (%)

A 2 20.040 20.040 10.020 7.26 21.68B 2 5.141 5.141 2.571 1.86 5.56

C 2 64.485 64.485 32.243 23.35 69.76

Error 2 2.761 2.761 1.381 2.98

Total 8 92.428

The results of ANOVA for the Multi-response S/N ratios

as shown in Table 8. On the examining of the percentage

of contribution (P%) of the different factors, it can be

seen that air temperature has the highest contribution of

about 69.76% and the other parameters have less

contributions. It is clear that the air temperature is one of

the significant factors that have more impact than any

other factors. The main effect plots (Figure 5) shows thatthe optimum condition for Multiple response is at level 1

(4 mm) of SOD, level 1 (20 mm/min) of Feed rate and

level 3 (320oC) of air temperature.

3.3 Confirmation test After identifying the most influential parameters, the

final phase is to verify the experimental results (MRR

and R a) by conducting the confirmation test.

Figure 5 Main effects plot based on the multi- response

S/N ratio

The A1 B1 C3 is an optimal parameter combination of the

Abrasive hot air jet machining of single as well asmultiple responses. Therefore, the combination A1B1C3 is

treated as the confirmation test. The predicted optimal

value of response can be calculated using the equation.

∑ ( ( ) (7)

where m is the total mean of the response S/N ratio at

the optimal level and mi is the S/N ratio at optimal

parameter. The predicted optimal values for single-

response and multi-responses are listed in Table 9.

In order to validate, the experiment (four trials) is

conducted according to the optimal parameters levels

(A1B1C3) and the corresponding values of performance

measures are taken. Table 9 shows the predicted multi-response S/N ratio and multi-response S/N ratio obtained

from the experiment. It may be noted that there is good

agreement between the estimated value (-7.346) and theexperimental value (-8.216). Therefore, the condition A1

B1 C3 of the parameter combination of the Abrasive hot

air jet machining process is treated as optimal. Theoptimal combination A1 B1 C3 (4 mm, 20 mm/min and

320o

C) is also confirmed by ANOVA. It can be found

that the hot air is influencing on MRR and R a of Abrasive

Hot Air Jet Machining on glass.

4. INFLUENCE OF AIR TEMPERATURE ON MRR

and R aThe effect of air temperature on MRR and R a was studied

for grooving process using silicon carbide (SiC) of size

100µm as carrier media. The results are plotted as shownin Figure 6 and Figure 7. It can be noticed from Figure 6

that the air temperature has more significant effect onMRR at air temperature above 100

oC. It can be found

that MRR at higher temperature is more than that at low

(room) temperature. From Figure 7, it can be found that

the roughness of machined surface decreases as the

temperature of the air is increased. It is further observedthat the value of surface roughness is very less at higher

temperature and is more of at room temperature.

Figure 6 Effect of temperature on Material removal ratefor grooving



14

Table 9 Results of Confirmation Test

Performance

Characteristic

Optimal

setting

Predicted Optimal

S/N ratio

Experimental Optimal

S/N ratio

Single response

optimization MRR A1B1C3 -13.063 -14.154

R a A1B1C3 -1.632 -2.278

Multi response

optimizationMRR and R a A1B1C3 -7.346 -8.216

As hot air is supplied on the target, the temperature of

target is increased resulting in increasing the size of

radial crack initiated by impact of abrasive material. It

helps in removal of larger size of chips from the work material as indicated by an arrow mark in Figure 9.

Figure 7 Effect of temperature on Roughness for

grooving

Figure 8 Micrograph of machined surface at room

temperature (270C)

In agreement with this, our study reveals that the MRR of

material at high temperature is more as compared to that

of at low temperature. The removal of material in the

form of larger cracks creates a new smooth bottom of target and thus the roughness of the machined surface in

reduced. The morphology of eroded surface indicates thatat low temperature, there is an evidence of crack

initiation taking place by brittle nature. It can be

observed from Figure 9 that at high temperature, deep

chipping of material takes place due to more plastic

deformation. Hence,erosion rate increases and thus the

hot air has its influence in increasing MRR and reducing

roughness of machined surface.

Figure 9 Micrograph of machined surface at high

temperature (3200C)

5. CONCLUSION The optimization of process parameters of Abrasive hot

air jet machining using Taguchi orthogonal array with

multi-response analysis is discussed in this paper. From

the experimental investigation and analysis, the

following conclusions can be drawn

It has been found that the combination A1 B1C3

show the largest value of the Multi-response S/Nratio for the factors A, B, and C, respectively.

Therefore, A1 B1C3 is the optimal parameter

combination (Stand-off distance of 4 mm, the Feed

Brittle initiation of crack

Larger and deep chips



15

rate of 20 mm/min and the Air temperature of 320oC)

of the Abrasive hot air jet machining for glass.

Through ANOVA, the percentage of contribution to

the Air temperature is more as compared to other

parameters. Hence, the air temperature is the most

significant factor for the Abrasive Hot air jet

machining for the minimization of the roughness of machined surface and maximization of MRR.

It can be found that there is good agreement between

the estimated value (-7.346) and the experimental

value (-8.216). Therefore, the condition A1 B1 C3 of

the parameter combination of the Abrasive hot air jet

machining process was treated as optimal.

From the experimental results, it has been found thatthe air temperature has the greatest impact on MRR

and R a of grooved surface.

It can be observed from micrographs that at high

temperatures, there is sufficient evidence of more

plastic deformation accompanied by brittle fracture

failure which results in increase of MRR andreduction R a.

ACKNOWLEDGEMENTS The authors would like to thank the Visvesvaraya

Technological University (VTU), Karnataka, India for providing the financial support to carried out this

research work under VTU research grant scheme.

REFERENCES

Balasubramaniam, R., Krishnan, J. and Ramakrishnan N.

1999. An Experimental Study on the Abrasive Jet

Deburring of Cross-Drilled Holes, Journal of Material

Processing Technology 91: 178-182.Bunn, D.W. 1982. Analysis for optimal decisions, John

Wiley & Sons, New York.

Bushroa, A.R., Masjuki, H.H. and Muhamad, M.R. 2011.Parameter optimization of sputtered Ti interlayer

using Taguchi method, International Journal of

Mechanical and Materials Engineering 6 (2): 140-

146.

Chen, D.C. and Chen, C.F. 2007. Use of Taguchi

method to study a robust design for the sectioned beams curvature during rolling, Journal of Materials

Processing Technology 190: 130-137.

Das, S.K. and Saahoo, P. 2011. Tribological

characteristics of electro less Ni – B coating andoptimization of coating parameters using Taguchi

based grey relational analysis, Materials and Design

32: 2228 – 2238.

El-Domiaty, A., Abid El-, H.M. and Shaker, M.A. 2009.

Drilling of Glass Sheets by Abrasive Jet Machining,

World Academy of Science Engineering and

Technology 56: 61-67.Ghani, J.A., Choudhury, I.A. and Hassan, H.H. 2004.

Application of Taguchi method in the optimization of

end milling parameters, Journal of Materials

Processing Technology 145: 84 – 92.

Kaladhar, M., Subbaiah, K.V., Rao, C.S. and Rao, K.N.

2011. Application of Taguchi approach and Utility

Concept in solving the Multi- objective Problem

When Turning AISI 202Austenitic Stainless Steel,Journal of Engineering Science and Technology

Review 4 (1): 55-61.

Kumar, P., Barua, P.B. and Gaindhar, J.L. 2010. Quality

Optimization (Multi-characteristics) Through

Taguchi’s Technique and Utility Concept, Qualityand Reliability Engineering International 16: 475-485.

Mahapatra, S.S. and Chaturvedi, V. 2009. Modeling and

analysis of Abrasive wear performance of composites

using Taguchi approach, International Journal of

Engineering, Science and Technology 1: 123-135

Muralidhar, S., Pal, S., Mittal, R. and Kale, S.R. 1982. A

Study of thermal cutting of glass, Journal of

American Ceramic Society 82 (8): 2166-2176.

Ng, C.F., Kamaruddin, S., Siddiquee, A.N., Khan, Z.A.

2011. Experimental investigation on the recycled

hdpe and optimization of injection moulding process

parameters via Taguchi method, International Journalof Mechanical and Materials Engineering 6 (1): 81-

91.

Nor, N.H.M., Muhamad, N., Ibrahima, M.H.I., Ruzia,

and Jamaludin, K.R. 2011. Optimization of Injection

molding parameter of Ti-6Al-4V powder mix with palm stearin and polyethylene for the highest Green

strength by using Taguchi method, International

Journal of Mechanical and Materials Engineering 6

(1): 126-132.

Prakash, E.S. Sadashivappa, K. and Singaperumal, M.

2001. Non Conventional cutting of Plateglass usinghot air jet: Experimental studies, Mechatronics 11:

595-615.Ross, P.J. 1996. Taguchi Techniques for Quality

Engineering, McGraw-Hill Book Company,NewYork

Sathia, P. and Jaleel, M.Y.A. 2010. Gray based Taguchi

method for Optimization of Bead Geometry in Laser

Bead-on-Plate Welding, Advances in Production

Engineering and Management 4: 225-234.

Taguchi, G. 1986. Introduction to quality engineering,

Proceedings of Asian Productivity Organization,

UNIPUB, White Plains, NewYork Tasirin, S.M., Kamarudin, S.K., Ghani, J.A. and Lee,

K.F. 2007. Optimization of drying parameters of

bird’s eye chili in a fluidized bed dryer, Journal of

Food Engineering 80: 695 – 700Vijian, P. and Arunachalam, V.P. 2006. Optimization of

squeeze cast parameters of LM6aluminium alloy for surface roughness using Taguchi method, Journal of

Material Processing Technology 180: 161-166.

Zhang, J.Z., Chen, J.C. and Kirby, E.D. 2007. Surface

roughness optimization in a end – milling operation

using the Taguchi design method, Journal of Material

Processing Technology 184: 233-239.Zhang, L., Kuriyagawa, T., Yasutomi, Y. and Zhao, J.

2005. Investigation into micro Abrasive intermittent

jet machining, International Journal of Machine Tools

& Manufacture 45: 873 – 879.

Utility Concept and Taguchi

Documents

Transcript of Utility Concept and Taguchi