Research ArticlePerformance Optimization Prediction and Adequacy byResponse Surfaces Methodology with Allusion to DRF Technique

Lokesh Shukla1 and Anita Nishkam2

1 Government Central Textile Institute Kanpur India2 Apollo Institute of Engineering and Technology Kanpur India

Correspondence should be addressed to Lokesh Shukla drshukla kanpurrediffmailcom

Received 14 September 2013 Accepted 20 November 2013 Published 4 March 2014

Academic Editors L Andronic and W Xu

Copyright copy 2014 L Shukla and A Nishkam This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The RSM introduces statistically designed experiments for the purpose of making inferences from data The second-order modelis the most frequently used approximating polynomial model in RSM The most common designs for the second-order model arethe 3119896 factorial Doehlert Box-Behnken and CCD In this Box and Behnken design of three variables is selected as a representativeof RSM and 70 30 polyester-wool DRF yarn knitted fabrics samples as a process representative The survey reveals that second-order model is the most frequently used approximating polynomial model in RSMThe Box-Behnken is the most suited design foroptimization and prediction of data in textile manufacturing and this model is well-suited for DRF technique yarn knitted fabricThe trend was as higher wool fiber length shows higher fabric weight abrasion and bursting strength correlation of TM was notvisible however role of strands spacing is found dominant in comparison to other variables at 14mm spacing it shows optimumbehaviors The optimum values were weight (gmsmt2) 206 at length 75mm TM 25 and 14mm spacing abrasion (cycles) 1325 atlength 70mm TM 225 and 14mm spacing bursting (kgcm2) 1435 at length 70mm and TM 200 and 18mm spacing A selectedvariables fiber length TM and strand spacing have substantial influence The adequacies of response surface equations are veryhigh The line trends of knitted fabric basic characteristics were almost the same for actual and predicted models The difference() was in range of 121 to minus145 201 to minus726 and 1784 to minus661 the accuracy () was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and the Discrepancy Factor (119877-Factor) was noted to be 0016 0002 and 0229 for weight abrasion and burstingrespectively between actual and predicted data The 119871-estimation factors for actual and predicted data were that (i) the ratio werein range of 101 to 099 102 to 093 and 122 to 094 for weight abrasion and bursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was in range of 122 to 092 and (iv) the toting ratio was in range of 102 to 094

1 Introduction

The response surface methodology (RSM) introduces sta-tistically designed experiments for the purpose of makinginferences from data To achieve this goal statistical consid-erations for preliminary planning of experiments standardstatistical designs for experiments and underlying logic forusing these designs are emphasized It is a common butmajor error to view statistics as a tool to be used onlyafter the experiments are completed Even using their mostsophisticated tools researchers receiving data from improp-erly designed experiments can make only indistinct andapproximate inferences Therefore it is unfortunate because

experimental data represent an expenditure of both time andmoney [1]

In general the theoretical model that relates some con-trollable variables to a response either is not available or isvery complex Identifying and fitting from experimental dataan appropriate response surface model requires some useof statistical experimental design fundamentals regressionmodeling techniques and optimization methods As animportant subject in the statistical design of experimentsRSM introduced by Box and Wilson [2] comprises a groupof mathematical and statistical techniques that is useful forempirical model building and analysis of problems in whicha response of interest is influenced by several variables [3]

Hindawi Publishing CorporationISRN TextilesVolume 2014 Article ID 634041 12 pageshttpdxdoiorg1011552014634041

2 ISRN Textiles

It is important to fit a mathematical model equation inorder to approximate a relationship between response andindependent variables and determine the optimum settingsof these variables that result in the maximum response

The two important models that are commonly usedin RSM including the first-order model and second-ordermodel [4] are as follows

119884 = 1205730

119896

sum

119894=1

120573119894119883119894+ 120576 (1)

119884 = 1205730

119896

sum

119894=1

120573119894119883119894+

119896

sum

119894=1

1205731198941198941198832

119894+

119896

sum

119894=1

119896

sum

119894 = 119895=1

120573119894119895119883119894119883119895+ 120576 (2)

where 119884 is the response 1205730is the constant 120573

119894is the slope

or linear effect of the factor 119883119894 120573119894119894is the quadratic effect of

the factor 119883119894 120573119894119895is the interaction effect between the input

factors 119883119894and 119883

119895 and 120576 is the residual term The first-order

models are inadequate to represent true functional relation-ships with independent variables The second-order model ismost suitable highly structured flexible and diversified inorder to locate the optimum point

11 Designs for Fitting the Second-Order Model The second-order model is the most frequently used approximatingpolynomial model in RSM The most common designs forthe second-order model are the 3119896 factorial Doehlert Box-Behnken and central composite designs (CCDs) [5 6]Thesesymmetrical designs differ from one another with respect totheir selection of experimental points number of levels forvariables and number of runs and blocks

12 3119896 Factorial Design The 3119896 factorial design consists ofall the combinations of the levels of the control variableswith three levels each low medium or centre and high[4] The number of experimental runs (119873) required for thisdesign is defined as 119873 = 3119896 where 119896 is the number offactors The 3119896 factorial design needs a large number ofexperimental runs for large 119896 which loses its efficiency inthe modeling of quadratic functionsTherefore a 3119896 factorialdesign is more appropriate having factors numbering lessthan five Due to its requirement for more experimental runsit can usually be accommodated in practice designs thatpresent a smaller number of experimental points such asDoehlert Box-Behnken and CCDs aremore often usedTheapplication of 3119896 factorial design is not frequent and theuse of this design has been limited to the optimization oftwo variables because its efficiency is very low for a highernumber of variables

13 Doehlert Design The Doehlert (or uniform shell) designhas been developed by Doehlert [7] The Doehlert designis for heterogeneous levels of variables This property isimportant when some variables are subject to restrictionssuch as cost andor instrumental constraints or when it isimportant to study a variable at major or minor levels Theintervals between each variable level must have a uniformdistribution [6]The number of experiments required (119873) for

theDoehlert design is defined as119873 = 1198962+119896+119862

0 where 119896 is the

number of factors and 1198620is the number of centre points For

two variables a central point surrounded by six points from aregular hexagon represents this design For three variables itis represented by a geometrical solid called a cub octahedronand depending on how this solid is projected in the plane itcan generate some different experimental matrices Althoughits matrices are neither orthogonal nor rotatable it presentssome advantages such as requiring few experimental pointsfor its application and high efficiency [8]

14 Box-Behnken Design This design was developed by Boxand Behnken [9] The Box-Behnken design provides threelevels (minus1 0 +1) for each variable which are equally spacedThe number of experiments required (119873) is given by 119873 =2119896(119896 minus 1) + 119862

0 where 119896 is the number of variables and 119862

0

is the number of central points The design is representedas a cube and all points lie on a sphere of radius radic2 Inaddition this design does not contain any points at thevertices of the cubic region created by the upper and lowerlimits for each variable [10] The Box-Behnken design forthree variables takes optimization with its 13 experimentalpoints This design is more economical and efficient in termsof the number of required runs than their corresponding 3119896designs with 27 experiments Therefore this design is usefulin avoiding experiments that would be performed underextreme conditions for which unsatisfactory results mightoccur However it is ineffective for situations in which wewould like to know the responses at extremes

The Box-Behnken design has been used for finding theoptimum experimental conditions leading to an optimalefficiency of different processes

15 Central Composite Design The CCD presented by Boxand Wilson in 1951 [2] is the design most commonly usedfor fitting second-order models and it has been subjected tomuch attention in the theoretical development of its proper-ties as in its practical use [10] This design combines a two-level full or fractional factorial design with additional startpoints and at least one point at the centre of the experimentalregion The CCD is widely used for the optimization ofthree variables This design requires an experiment numberaccording to119873 = 2119896+2119896+119862

0 where 119896 is the number of factors

and 1198620is the number of central points In CCD all factors

are studied in five levels This119873 experiment is distributed asfollows [4 10]

(1) Full (or fractional) 2119896 factorial experiments whosefactors levels are coded as minus1 +1 these experimentsare the only points that contribute to the estimationof the two-factor interactions

(2) Axial (or star) 2119896 experiments with coordinates(plusmn120572 0 0) (0 plusmn120572 0) (0 0 plusmn120572) thecodified value of 120572 is defined as 120572 = (2119896)14 Theaxial points do not contribute to the estimation ofinteraction terms If curvature is found in the systemthe addition of axial points allows for efficientestimation of the pure quadratic terms

ISRN Textiles 3

(3) 1198620central points at (0 0 0) these experiments

provide an estimation of pure error and contributeto the estimation of quadratic terms The CCD is arotatable and orthogonal design A design is rotatableif the precision of the response estimation in alldirections is equal and the orthogonality of the designmeans that different variable effects can be estimatedindependently This design has been widely used forthe optimization of several processes [11]

16 Optimization by Response Surface Methodology In mostproduction processes the theoretical model that relatessome controllable variables (factors) to a response eitheris not available or is very complex In conventional meth-ods used to determine this relationship experiments arecarried out varying systematically the studied parameterand keeping the others constant This should be repeatedfor all the influencing parameters resulting in an unreli-able number of experiments In addition this exhaustiveprocedure is not able to find the combined effect of theeffective parameters In this way the information about therelation between factors and response should be obtainedin an empirical way [10 12] Using RSM it is possibleto estimate linear interaction and quadratic effects of thefactors and to provide a prediction model for the response[13]

The textile industry is one of the largest and oldestindustries worldwide and yarn manufacturing is the keyprocess of it The efficiency of yarn manufacturing dependson a number of factors which are governed by the per-formance of fiber yarn and fabric initial characteristicsand processing parameters of the experimental setup andalso multiple pathways Due to the complexity and varietyof influencing factors it is difficult to evaluate the relativesignificance of several affecting factors especially in thepresence of complex interactions [14] In the day by dayinnovations and introduction of latest technologies in yarnand fabric manufacturing large numbers of textile scientistsare developing somany advancesThe development of doubleroving feed (DRF) techniques is one of them and widelyaccepted by the textile producers The DRF yarn uses areincreasing in the entire field including the knit-wears

In the recent studies only traditional one-factor-at-a-time experiments were tested for evaluating the influence ofoperating factors on the DRF technique efficiency howeververy few researchers also used RSM The DRF technique isnot only time and work demanding but also completely lacksrepresentation of the effect of interaction between differentvariables or factors RSM allows an appropriate design ofthe experiments which helps to decrease the number ofruns In addition the modeling of the system facilitates theinterpretation ofmultivariate phenomena and is valuable toolfor scaling up [15]

Thepresent endeavors reviewed the RSM techniques usedfor process optimization The Box and Behnken design ofthree variables is selected as a representative of RSM TheDRF yarn knitted fabric production is chosen as a process forwhich the adequacy of the RSM is evaluated

2 Material and Methods

21 Materials The fibers specifications are given in Table 1

22 Methods

221 Sample Preparation and Sequence of Operations Thesequence of operations for production of yarns and fabricssamples was as follows

(1) blending of polyester andwool in 70 30 (five passagesin gill boxes) by weight

(2) combing (French combing)(3) gilling (three passages in gill boxes)(4) top formation(5) gilling (four passages in gill boxes)(6) roving formation (simplex frame)(7) DRF yarn production (modified ring frame)(8) fabric production (knitted)

222 Attachments to Produce DRF Yarn The followingattachments are fitted in the conventional ring frame for theproduction of yarns by DRF technique

(1) rear roving guide(2) double roving feeding attachments in drafting zone

223 Spinning Parameters The finisher sliver was processedin aforesaid sequence of operations to produce 24s worstedcount yarn at blend ratio 70 30 polyester wools by thefollowing roving parameters

(1) roving wrapping 050 grams per meter(2) delivery speed 45 meters per minute(3) roving TPM 2400(4) roving CV () 610

224 Knitted Fabric Production Details Knitted fabric pro-duction details are as follows

(a) machine details

(1) knitting machine Black Burn UK(2) feeder 8 (two yarns per feed)(3) gauge 10 Needlesinch(4) speed (rpm) 22

(b) particular of fabrics

(1) design single jersey plain knit(2) yarn tension (gramtex) 170(3) tube diameter (inches) 1900

4 ISRN Textiles

Table 1 Fiber specifications

Fiber used 64S Australian Merino wool Long staple (varying cut length) polyester1 2 3

1 Longest (mm) staple length 160 165 170 1502 Uniform (mm) staple length 115 119 124 1303 Average (mm) staple length 65 70 75 894 Shortest (mm) staple length 15 15 15 355 Average micron (120583) 225 225 225 mdash6 Moisture regain () 163 163 163 mdash7 Bundle strength (gramTex) 12 12 12 1448 Residual grease () 05 05 05 mdash9 Alkali solubility 105 105 105 mdash10 Urea bisulphite solubility () 42 42 42 mdash11 Fineness (denier) mdash mdash mdash 25

Table 2 Actual and coded values for independent variables and experimental design

Sample codeLevels of variables

1198831Wool fibre length (mm) 119883

2Twist multiplier 119883

3Strand spacing (mm)

Coded Actual Coded Actual Coded Actual1 minus1 65 minus1 200 0 142 1 75 minus1 200 0 143 minus1 65 1 250 0 144 +1 75 1 250 0 145 0 70 0 225 0 146 minus1 65 0 225 minus1 107 +1 75 0 225 minus1 108 minus1 65 0 225 +1 189 +1 75 0 225 +1 1810 0 70 0 225 0 1411 0 70 minus1 200 minus1 1012 0 70 1 250 minus1 1013 0 70 minus1 200 +1 1814 0 70 +1 250 +1 1815 0 70 0 225 0 14

225 Experimental Design To study the individual andinteractive effects of variables Box and Behnken factorialdesign was used for three variablesThe following parametersare selected as prototype variables

(1) fiber length (1198831)

(2) twist multiplier (1198832)

(3) strand spacing (1198833)

Table 2 shows the coded and actual values of threeparameters considered and fifteen sets of experimental com-binations by DRF yarn and fabrics are knitted

226 Measurement of Fabric Properties There are numbersof fabric properties that can be optimized by using this exper-imental approach however three fundamental properties are

measured The fabric weight per square meter (gmsmt2)(weight) was evaluated by ASTM D-3776-79 method taking10 times 10 cm sample from different places of knitted fabricThe abrasion cycle (abrasion) was measured by ASTM D-1966method usingmartindale abrasion testerThe specimenswere mounted on rectangular blocks of 15 times 25 incheswith abrading material which was itself fabric and thena number of rubs were counted by noting the number ofcycles from counter in abrasion cycles The bursting strength(bursting) is determined by ASTM D-3886-80 method usingdiaphragm type tester operated by hydrostatic pressure Thefabric samples are clamped by means of metal rings ofinternal diameter 30 plusmn 5mm in the tester by screwing theclamping ring too tight over the test piece Thus pressurewas increased on the diaphragm until the test piece burst inbetween 7 and 20 seconds to increase pressure from zero tobursting point and then readings ware noted from the dial

ISRN Textiles 5

227 Development of Statistical Model To correlate theeffects of variables and the response the following second-order standard polynomial was considered [16]

119884 = 1198870+ 11988711198831+ 11988721198832+ 11988731198833+ 119887111198832

1+ 119887221198832

2

+ 119887331198832

3+ 1198871211988311198832+ 1198871311988311198833+ 1198872311988321198833

(3)

where 119884 represents the responses and 1198870 1198871 1198872 119887

23are

the coefficients of the model The coefficients of main andinteraction effects were determined by using the standardmethod The response surface equations are calculated forprediction of responses

228 Optimization of Fabric Properties The optimum fabricperformance was predicted by using equations at all levels ofvariables drawing contours

229 Adequacy ofModels The followings termswere studiedfor the adequacies of the models

(a) Difference () is calculated by using the followingequation

Difference () = (PredictedValue minus Actual Value) times 100Actual Value

(4)

(b) Accuracy () is calculated by using the followingequation

Accuracy () = Actual Value times 100PredictedValue

(5)

(c) Discrepancy Factor (119877-Factor) is calculated [17] byusing the following equation

119877 = radic(sum119875119886minus 119875119901)2

sum(119875119886)2 (6)

where119877 =Discrepancy Factor119875119886= actual values and

119875119901= predicted values

(d) 119871-estimation is calculated by using the followingequation

Ratio = Actual ValuePredictedValue

Multiple Ratio = 1198771times 1198772times 1198773

(7)

where1198771 1198772 1198773 are ratios of parameters 1 2 3

and we have

Ratio Product =1198601times 1198602times 1198603times sdot sdot sdot

1198751times 1198752times 1198753times sdot sdot sdot

Toting Ratio =1198601+ 1198602+ 1198603+ sdot sdot sdot

1198751+ 1198752+ 1198753+ sdot sdot sdot

(8)

where 1198601 1198602 1198603 are actual performances of

parameters 1 2 3 1198751 1198752 1198753 are predicted per-

formances of parameters 1 2 3

3 Results and Discussions

The actual observations predicted values and different cal-culated parameters for adequacy response surface equationsand coefficient of correlation values are given in Table 3 Therespective contours at different levels of variables were con-structed and are given in Figures 1(a) to 1(c) The discussionsare as follows

31 Weight at Different Levels of Variables From Figure 1(a)as depicted in (1)(A) TM decreases from 225 and spacingincreases as the weight reduces The trend is miscellaneous(B) The trend is miscellaneous TM and spacing increase astheweight decreases consistently (C)Up to 14mmspacing asTMdecreases from 225 weight decreases however at slightlyabove 225 TM spacing increases as the weight also increases

As depicted in (2)(A) two trends were found firstincreasing weight as spacing increases in fiber length abovecoded level + 05 and second decreasing weight as lengthdecreases from 70mm (B) As length decreases from 70mmand spacing increases to 18mm weight decreases In lengthabove 70mm as spacing increases weight increases andbelow reverse trend is visible (C) In 70 to 75mm in length asspacing increases weight is reduced however when length isfrom 65 to 70mm weight increases

As depicted in (3)(A) TM decreases and length increasesup to 70mm while weight decreases however in furtherincreases in length weight increases (B) As TM decreasesand length is up to 70mm weight decreases however infurther increases in length weight increases (C) Optimumswere found at TM 225 and fiber length 70mm

32 Abrasion at Different Levels of Variables FromFigure 1(b) as depicted in (1)(A) the trends weremiscellaneous as at TM up to 225 and spacing near14mm the optimum is seen (B) As TM and spacing increasethe abrasion cycles are reduced to a certain limit At TM andspacing levels 0 the optimum is found (C) The trend wasalmost similar to (B)

As depicted in (2)(A) as length and spacing increaseabrasion increasesThe abrasion cycles are lowest at low fiberlength All parallel lines show similar trends in all spacings(B) The parallel horizontal lines show that optimum couldnot be found in the range and the fiber length increases atall spacings as abrasion increases (C) The trend is almostsimilar to (A) as length decreases and spacing increases fromthe decrease of the abrasion cycles All lines are parallel andshowing the same relationship at each spacing and length

As depicted in (3)(A) as TM increases and lengthdecreases the tendency of reduction in abrasion cycles isnoted (B) As length decreases and TM is below 225 theabrasion reduces After TM is 225 as length increases abra-sion decreases (C)As the length decreases TM increases andabrasion reduces the trend is miscellaneous

33 Bursting atDifferent Levels of Variables FromFigure 1(c)as depicted in (1)(A) as spacing and TM increase up toa certain TM bursting increases (B) As TM increases and

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 ISRN Textiles

It is important to fit a mathematical model equation inorder to approximate a relationship between response andindependent variables and determine the optimum settingsof these variables that result in the maximum response

The two important models that are commonly usedin RSM including the first-order model and second-ordermodel [4] are as follows

119884 = 1205730

119896

sum

119894=1

120573119894119883119894+ 120576 (1)

119884 = 1205730

119896

sum

119894=1

120573119894119883119894+

119896

sum

119894=1

1205731198941198941198832

119894+

119896

sum

119894=1

119896

sum

119894 = 119895=1

120573119894119895119883119894119883119895+ 120576 (2)

where 119884 is the response 1205730is the constant 120573

119894is the slope

or linear effect of the factor 119883119894 120573119894119894is the quadratic effect of

the factor 119883119894 120573119894119895is the interaction effect between the input

factors 119883119894and 119883

119895 and 120576 is the residual term The first-order

models are inadequate to represent true functional relation-ships with independent variables The second-order model ismost suitable highly structured flexible and diversified inorder to locate the optimum point

11 Designs for Fitting the Second-Order Model The second-order model is the most frequently used approximatingpolynomial model in RSM The most common designs forthe second-order model are the 3119896 factorial Doehlert Box-Behnken and central composite designs (CCDs) [5 6]Thesesymmetrical designs differ from one another with respect totheir selection of experimental points number of levels forvariables and number of runs and blocks

12 3119896 Factorial Design The 3119896 factorial design consists ofall the combinations of the levels of the control variableswith three levels each low medium or centre and high[4] The number of experimental runs (119873) required for thisdesign is defined as 119873 = 3119896 where 119896 is the number offactors The 3119896 factorial design needs a large number ofexperimental runs for large 119896 which loses its efficiency inthe modeling of quadratic functionsTherefore a 3119896 factorialdesign is more appropriate having factors numbering lessthan five Due to its requirement for more experimental runsit can usually be accommodated in practice designs thatpresent a smaller number of experimental points such asDoehlert Box-Behnken and CCDs aremore often usedTheapplication of 3119896 factorial design is not frequent and theuse of this design has been limited to the optimization oftwo variables because its efficiency is very low for a highernumber of variables

13 Doehlert Design The Doehlert (or uniform shell) designhas been developed by Doehlert [7] The Doehlert designis for heterogeneous levels of variables This property isimportant when some variables are subject to restrictionssuch as cost andor instrumental constraints or when it isimportant to study a variable at major or minor levels Theintervals between each variable level must have a uniformdistribution [6]The number of experiments required (119873) for

theDoehlert design is defined as119873 = 1198962+119896+119862

0 where 119896 is the

number of factors and 1198620is the number of centre points For

two variables a central point surrounded by six points from aregular hexagon represents this design For three variables itis represented by a geometrical solid called a cub octahedronand depending on how this solid is projected in the plane itcan generate some different experimental matrices Althoughits matrices are neither orthogonal nor rotatable it presentssome advantages such as requiring few experimental pointsfor its application and high efficiency [8]

14 Box-Behnken Design This design was developed by Boxand Behnken [9] The Box-Behnken design provides threelevels (minus1 0 +1) for each variable which are equally spacedThe number of experiments required (119873) is given by 119873 =2119896(119896 minus 1) + 119862

0 where 119896 is the number of variables and 119862

0

is the number of central points The design is representedas a cube and all points lie on a sphere of radius radic2 Inaddition this design does not contain any points at thevertices of the cubic region created by the upper and lowerlimits for each variable [10] The Box-Behnken design forthree variables takes optimization with its 13 experimentalpoints This design is more economical and efficient in termsof the number of required runs than their corresponding 3119896designs with 27 experiments Therefore this design is usefulin avoiding experiments that would be performed underextreme conditions for which unsatisfactory results mightoccur However it is ineffective for situations in which wewould like to know the responses at extremes

The Box-Behnken design has been used for finding theoptimum experimental conditions leading to an optimalefficiency of different processes

15 Central Composite Design The CCD presented by Boxand Wilson in 1951 [2] is the design most commonly usedfor fitting second-order models and it has been subjected tomuch attention in the theoretical development of its proper-ties as in its practical use [10] This design combines a two-level full or fractional factorial design with additional startpoints and at least one point at the centre of the experimentalregion The CCD is widely used for the optimization ofthree variables This design requires an experiment numberaccording to119873 = 2119896+2119896+119862

0 where 119896 is the number of factors

and 1198620is the number of central points In CCD all factors

are studied in five levels This119873 experiment is distributed asfollows [4 10]

(1) Full (or fractional) 2119896 factorial experiments whosefactors levels are coded as minus1 +1 these experimentsare the only points that contribute to the estimationof the two-factor interactions

(2) Axial (or star) 2119896 experiments with coordinates(plusmn120572 0 0) (0 plusmn120572 0) (0 0 plusmn120572) thecodified value of 120572 is defined as 120572 = (2119896)14 Theaxial points do not contribute to the estimation ofinteraction terms If curvature is found in the systemthe addition of axial points allows for efficientestimation of the pure quadratic terms

ISRN Textiles 3

(3) 1198620central points at (0 0 0) these experiments

provide an estimation of pure error and contributeto the estimation of quadratic terms The CCD is arotatable and orthogonal design A design is rotatableif the precision of the response estimation in alldirections is equal and the orthogonality of the designmeans that different variable effects can be estimatedindependently This design has been widely used forthe optimization of several processes [11]

16 Optimization by Response Surface Methodology In mostproduction processes the theoretical model that relatessome controllable variables (factors) to a response eitheris not available or is very complex In conventional meth-ods used to determine this relationship experiments arecarried out varying systematically the studied parameterand keeping the others constant This should be repeatedfor all the influencing parameters resulting in an unreli-able number of experiments In addition this exhaustiveprocedure is not able to find the combined effect of theeffective parameters In this way the information about therelation between factors and response should be obtainedin an empirical way [10 12] Using RSM it is possibleto estimate linear interaction and quadratic effects of thefactors and to provide a prediction model for the response[13]

The textile industry is one of the largest and oldestindustries worldwide and yarn manufacturing is the keyprocess of it The efficiency of yarn manufacturing dependson a number of factors which are governed by the per-formance of fiber yarn and fabric initial characteristicsand processing parameters of the experimental setup andalso multiple pathways Due to the complexity and varietyof influencing factors it is difficult to evaluate the relativesignificance of several affecting factors especially in thepresence of complex interactions [14] In the day by dayinnovations and introduction of latest technologies in yarnand fabric manufacturing large numbers of textile scientistsare developing somany advancesThe development of doubleroving feed (DRF) techniques is one of them and widelyaccepted by the textile producers The DRF yarn uses areincreasing in the entire field including the knit-wears

In the recent studies only traditional one-factor-at-a-time experiments were tested for evaluating the influence ofoperating factors on the DRF technique efficiency howeververy few researchers also used RSM The DRF technique isnot only time and work demanding but also completely lacksrepresentation of the effect of interaction between differentvariables or factors RSM allows an appropriate design ofthe experiments which helps to decrease the number ofruns In addition the modeling of the system facilitates theinterpretation ofmultivariate phenomena and is valuable toolfor scaling up [15]

Thepresent endeavors reviewed the RSM techniques usedfor process optimization The Box and Behnken design ofthree variables is selected as a representative of RSM TheDRF yarn knitted fabric production is chosen as a process forwhich the adequacy of the RSM is evaluated

2 Material and Methods

21 Materials The fibers specifications are given in Table 1

22 Methods

221 Sample Preparation and Sequence of Operations Thesequence of operations for production of yarns and fabricssamples was as follows

(1) blending of polyester andwool in 70 30 (five passagesin gill boxes) by weight

(2) combing (French combing)(3) gilling (three passages in gill boxes)(4) top formation(5) gilling (four passages in gill boxes)(6) roving formation (simplex frame)(7) DRF yarn production (modified ring frame)(8) fabric production (knitted)

222 Attachments to Produce DRF Yarn The followingattachments are fitted in the conventional ring frame for theproduction of yarns by DRF technique

(1) rear roving guide(2) double roving feeding attachments in drafting zone

223 Spinning Parameters The finisher sliver was processedin aforesaid sequence of operations to produce 24s worstedcount yarn at blend ratio 70 30 polyester wools by thefollowing roving parameters

(1) roving wrapping 050 grams per meter(2) delivery speed 45 meters per minute(3) roving TPM 2400(4) roving CV () 610

224 Knitted Fabric Production Details Knitted fabric pro-duction details are as follows

(a) machine details

(1) knitting machine Black Burn UK(2) feeder 8 (two yarns per feed)(3) gauge 10 Needlesinch(4) speed (rpm) 22

(b) particular of fabrics

(1) design single jersey plain knit(2) yarn tension (gramtex) 170(3) tube diameter (inches) 1900

4 ISRN Textiles

Table 1 Fiber specifications

Fiber used 64S Australian Merino wool Long staple (varying cut length) polyester1 2 3

1 Longest (mm) staple length 160 165 170 1502 Uniform (mm) staple length 115 119 124 1303 Average (mm) staple length 65 70 75 894 Shortest (mm) staple length 15 15 15 355 Average micron (120583) 225 225 225 mdash6 Moisture regain () 163 163 163 mdash7 Bundle strength (gramTex) 12 12 12 1448 Residual grease () 05 05 05 mdash9 Alkali solubility 105 105 105 mdash10 Urea bisulphite solubility () 42 42 42 mdash11 Fineness (denier) mdash mdash mdash 25

Table 2 Actual and coded values for independent variables and experimental design

Sample codeLevels of variables

1198831Wool fibre length (mm) 119883

2Twist multiplier 119883

3Strand spacing (mm)

Coded Actual Coded Actual Coded Actual1 minus1 65 minus1 200 0 142 1 75 minus1 200 0 143 minus1 65 1 250 0 144 +1 75 1 250 0 145 0 70 0 225 0 146 minus1 65 0 225 minus1 107 +1 75 0 225 minus1 108 minus1 65 0 225 +1 189 +1 75 0 225 +1 1810 0 70 0 225 0 1411 0 70 minus1 200 minus1 1012 0 70 1 250 minus1 1013 0 70 minus1 200 +1 1814 0 70 +1 250 +1 1815 0 70 0 225 0 14

225 Experimental Design To study the individual andinteractive effects of variables Box and Behnken factorialdesign was used for three variablesThe following parametersare selected as prototype variables

(1) fiber length (1198831)

(2) twist multiplier (1198832)

(3) strand spacing (1198833)

Table 2 shows the coded and actual values of threeparameters considered and fifteen sets of experimental com-binations by DRF yarn and fabrics are knitted

226 Measurement of Fabric Properties There are numbersof fabric properties that can be optimized by using this exper-imental approach however three fundamental properties are

measured The fabric weight per square meter (gmsmt2)(weight) was evaluated by ASTM D-3776-79 method taking10 times 10 cm sample from different places of knitted fabricThe abrasion cycle (abrasion) was measured by ASTM D-1966method usingmartindale abrasion testerThe specimenswere mounted on rectangular blocks of 15 times 25 incheswith abrading material which was itself fabric and thena number of rubs were counted by noting the number ofcycles from counter in abrasion cycles The bursting strength(bursting) is determined by ASTM D-3886-80 method usingdiaphragm type tester operated by hydrostatic pressure Thefabric samples are clamped by means of metal rings ofinternal diameter 30 plusmn 5mm in the tester by screwing theclamping ring too tight over the test piece Thus pressurewas increased on the diaphragm until the test piece burst inbetween 7 and 20 seconds to increase pressure from zero tobursting point and then readings ware noted from the dial

ISRN Textiles 5

227 Development of Statistical Model To correlate theeffects of variables and the response the following second-order standard polynomial was considered [16]

119884 = 1198870+ 11988711198831+ 11988721198832+ 11988731198833+ 119887111198832

1+ 119887221198832

2

+ 119887331198832

3+ 1198871211988311198832+ 1198871311988311198833+ 1198872311988321198833

(3)

where 119884 represents the responses and 1198870 1198871 1198872 119887

23are

the coefficients of the model The coefficients of main andinteraction effects were determined by using the standardmethod The response surface equations are calculated forprediction of responses

228 Optimization of Fabric Properties The optimum fabricperformance was predicted by using equations at all levels ofvariables drawing contours

229 Adequacy ofModels The followings termswere studiedfor the adequacies of the models

(a) Difference () is calculated by using the followingequation

Difference () = (PredictedValue minus Actual Value) times 100Actual Value

(4)

(b) Accuracy () is calculated by using the followingequation

Accuracy () = Actual Value times 100PredictedValue

(5)

(c) Discrepancy Factor (119877-Factor) is calculated [17] byusing the following equation

119877 = radic(sum119875119886minus 119875119901)2

sum(119875119886)2 (6)

where119877 =Discrepancy Factor119875119886= actual values and

119875119901= predicted values

(d) 119871-estimation is calculated by using the followingequation

Ratio = Actual ValuePredictedValue

Multiple Ratio = 1198771times 1198772times 1198773

(7)

where1198771 1198772 1198773 are ratios of parameters 1 2 3

and we have

Ratio Product =1198601times 1198602times 1198603times sdot sdot sdot

1198751times 1198752times 1198753times sdot sdot sdot

Toting Ratio =1198601+ 1198602+ 1198603+ sdot sdot sdot

1198751+ 1198752+ 1198753+ sdot sdot sdot

(8)

where 1198601 1198602 1198603 are actual performances of

parameters 1 2 3 1198751 1198752 1198753 are predicted per-

formances of parameters 1 2 3

3 Results and Discussions

The actual observations predicted values and different cal-culated parameters for adequacy response surface equationsand coefficient of correlation values are given in Table 3 Therespective contours at different levels of variables were con-structed and are given in Figures 1(a) to 1(c) The discussionsare as follows

31 Weight at Different Levels of Variables From Figure 1(a)as depicted in (1)(A) TM decreases from 225 and spacingincreases as the weight reduces The trend is miscellaneous(B) The trend is miscellaneous TM and spacing increase astheweight decreases consistently (C)Up to 14mmspacing asTMdecreases from 225 weight decreases however at slightlyabove 225 TM spacing increases as the weight also increases

As depicted in (2)(A) two trends were found firstincreasing weight as spacing increases in fiber length abovecoded level + 05 and second decreasing weight as lengthdecreases from 70mm (B) As length decreases from 70mmand spacing increases to 18mm weight decreases In lengthabove 70mm as spacing increases weight increases andbelow reverse trend is visible (C) In 70 to 75mm in length asspacing increases weight is reduced however when length isfrom 65 to 70mm weight increases

As depicted in (3)(A) TM decreases and length increasesup to 70mm while weight decreases however in furtherincreases in length weight increases (B) As TM decreasesand length is up to 70mm weight decreases however infurther increases in length weight increases (C) Optimumswere found at TM 225 and fiber length 70mm

32 Abrasion at Different Levels of Variables FromFigure 1(b) as depicted in (1)(A) the trends weremiscellaneous as at TM up to 225 and spacing near14mm the optimum is seen (B) As TM and spacing increasethe abrasion cycles are reduced to a certain limit At TM andspacing levels 0 the optimum is found (C) The trend wasalmost similar to (B)

As depicted in (2)(A) as length and spacing increaseabrasion increasesThe abrasion cycles are lowest at low fiberlength All parallel lines show similar trends in all spacings(B) The parallel horizontal lines show that optimum couldnot be found in the range and the fiber length increases atall spacings as abrasion increases (C) The trend is almostsimilar to (A) as length decreases and spacing increases fromthe decrease of the abrasion cycles All lines are parallel andshowing the same relationship at each spacing and length

As depicted in (3)(A) as TM increases and lengthdecreases the tendency of reduction in abrasion cycles isnoted (B) As length decreases and TM is below 225 theabrasion reduces After TM is 225 as length increases abra-sion decreases (C)As the length decreases TM increases andabrasion reduces the trend is miscellaneous

33 Bursting atDifferent Levels of Variables FromFigure 1(c)as depicted in (1)(A) as spacing and TM increase up toa certain TM bursting increases (B) As TM increases and

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Textiles 3

(3) 1198620central points at (0 0 0) these experiments

provide an estimation of pure error and contributeto the estimation of quadratic terms The CCD is arotatable and orthogonal design A design is rotatableif the precision of the response estimation in alldirections is equal and the orthogonality of the designmeans that different variable effects can be estimatedindependently This design has been widely used forthe optimization of several processes [11]

16 Optimization by Response Surface Methodology In mostproduction processes the theoretical model that relatessome controllable variables (factors) to a response eitheris not available or is very complex In conventional meth-ods used to determine this relationship experiments arecarried out varying systematically the studied parameterand keeping the others constant This should be repeatedfor all the influencing parameters resulting in an unreli-able number of experiments In addition this exhaustiveprocedure is not able to find the combined effect of theeffective parameters In this way the information about therelation between factors and response should be obtainedin an empirical way [10 12] Using RSM it is possibleto estimate linear interaction and quadratic effects of thefactors and to provide a prediction model for the response[13]

The textile industry is one of the largest and oldestindustries worldwide and yarn manufacturing is the keyprocess of it The efficiency of yarn manufacturing dependson a number of factors which are governed by the per-formance of fiber yarn and fabric initial characteristicsand processing parameters of the experimental setup andalso multiple pathways Due to the complexity and varietyof influencing factors it is difficult to evaluate the relativesignificance of several affecting factors especially in thepresence of complex interactions [14] In the day by dayinnovations and introduction of latest technologies in yarnand fabric manufacturing large numbers of textile scientistsare developing somany advancesThe development of doubleroving feed (DRF) techniques is one of them and widelyaccepted by the textile producers The DRF yarn uses areincreasing in the entire field including the knit-wears

In the recent studies only traditional one-factor-at-a-time experiments were tested for evaluating the influence ofoperating factors on the DRF technique efficiency howeververy few researchers also used RSM The DRF technique isnot only time and work demanding but also completely lacksrepresentation of the effect of interaction between differentvariables or factors RSM allows an appropriate design ofthe experiments which helps to decrease the number ofruns In addition the modeling of the system facilitates theinterpretation ofmultivariate phenomena and is valuable toolfor scaling up [15]

Thepresent endeavors reviewed the RSM techniques usedfor process optimization The Box and Behnken design ofthree variables is selected as a representative of RSM TheDRF yarn knitted fabric production is chosen as a process forwhich the adequacy of the RSM is evaluated

2 Material and Methods

21 Materials The fibers specifications are given in Table 1

22 Methods

221 Sample Preparation and Sequence of Operations Thesequence of operations for production of yarns and fabricssamples was as follows

(1) blending of polyester andwool in 70 30 (five passagesin gill boxes) by weight

(2) combing (French combing)(3) gilling (three passages in gill boxes)(4) top formation(5) gilling (four passages in gill boxes)(6) roving formation (simplex frame)(7) DRF yarn production (modified ring frame)(8) fabric production (knitted)

222 Attachments to Produce DRF Yarn The followingattachments are fitted in the conventional ring frame for theproduction of yarns by DRF technique

(1) rear roving guide(2) double roving feeding attachments in drafting zone

223 Spinning Parameters The finisher sliver was processedin aforesaid sequence of operations to produce 24s worstedcount yarn at blend ratio 70 30 polyester wools by thefollowing roving parameters

(1) roving wrapping 050 grams per meter(2) delivery speed 45 meters per minute(3) roving TPM 2400(4) roving CV () 610

224 Knitted Fabric Production Details Knitted fabric pro-duction details are as follows

(a) machine details

(1) knitting machine Black Burn UK(2) feeder 8 (two yarns per feed)(3) gauge 10 Needlesinch(4) speed (rpm) 22

(b) particular of fabrics

(1) design single jersey plain knit(2) yarn tension (gramtex) 170(3) tube diameter (inches) 1900

4 ISRN Textiles

Table 1 Fiber specifications

Fiber used 64S Australian Merino wool Long staple (varying cut length) polyester1 2 3

1 Longest (mm) staple length 160 165 170 1502 Uniform (mm) staple length 115 119 124 1303 Average (mm) staple length 65 70 75 894 Shortest (mm) staple length 15 15 15 355 Average micron (120583) 225 225 225 mdash6 Moisture regain () 163 163 163 mdash7 Bundle strength (gramTex) 12 12 12 1448 Residual grease () 05 05 05 mdash9 Alkali solubility 105 105 105 mdash10 Urea bisulphite solubility () 42 42 42 mdash11 Fineness (denier) mdash mdash mdash 25

Table 2 Actual and coded values for independent variables and experimental design

Sample codeLevels of variables

1198831Wool fibre length (mm) 119883

2Twist multiplier 119883

3Strand spacing (mm)

Coded Actual Coded Actual Coded Actual1 minus1 65 minus1 200 0 142 1 75 minus1 200 0 143 minus1 65 1 250 0 144 +1 75 1 250 0 145 0 70 0 225 0 146 minus1 65 0 225 minus1 107 +1 75 0 225 minus1 108 minus1 65 0 225 +1 189 +1 75 0 225 +1 1810 0 70 0 225 0 1411 0 70 minus1 200 minus1 1012 0 70 1 250 minus1 1013 0 70 minus1 200 +1 1814 0 70 +1 250 +1 1815 0 70 0 225 0 14

225 Experimental Design To study the individual andinteractive effects of variables Box and Behnken factorialdesign was used for three variablesThe following parametersare selected as prototype variables

(1) fiber length (1198831)

(2) twist multiplier (1198832)

(3) strand spacing (1198833)

Table 2 shows the coded and actual values of threeparameters considered and fifteen sets of experimental com-binations by DRF yarn and fabrics are knitted

226 Measurement of Fabric Properties There are numbersof fabric properties that can be optimized by using this exper-imental approach however three fundamental properties are

measured The fabric weight per square meter (gmsmt2)(weight) was evaluated by ASTM D-3776-79 method taking10 times 10 cm sample from different places of knitted fabricThe abrasion cycle (abrasion) was measured by ASTM D-1966method usingmartindale abrasion testerThe specimenswere mounted on rectangular blocks of 15 times 25 incheswith abrading material which was itself fabric and thena number of rubs were counted by noting the number ofcycles from counter in abrasion cycles The bursting strength(bursting) is determined by ASTM D-3886-80 method usingdiaphragm type tester operated by hydrostatic pressure Thefabric samples are clamped by means of metal rings ofinternal diameter 30 plusmn 5mm in the tester by screwing theclamping ring too tight over the test piece Thus pressurewas increased on the diaphragm until the test piece burst inbetween 7 and 20 seconds to increase pressure from zero tobursting point and then readings ware noted from the dial

ISRN Textiles 5

227 Development of Statistical Model To correlate theeffects of variables and the response the following second-order standard polynomial was considered [16]

119884 = 1198870+ 11988711198831+ 11988721198832+ 11988731198833+ 119887111198832

1+ 119887221198832

2

+ 119887331198832

3+ 1198871211988311198832+ 1198871311988311198833+ 1198872311988321198833

(3)

where 119884 represents the responses and 1198870 1198871 1198872 119887

23are

the coefficients of the model The coefficients of main andinteraction effects were determined by using the standardmethod The response surface equations are calculated forprediction of responses

228 Optimization of Fabric Properties The optimum fabricperformance was predicted by using equations at all levels ofvariables drawing contours

229 Adequacy ofModels The followings termswere studiedfor the adequacies of the models

(a) Difference () is calculated by using the followingequation

Difference () = (PredictedValue minus Actual Value) times 100Actual Value

(4)

(b) Accuracy () is calculated by using the followingequation

Accuracy () = Actual Value times 100PredictedValue

(5)

(c) Discrepancy Factor (119877-Factor) is calculated [17] byusing the following equation

119877 = radic(sum119875119886minus 119875119901)2

sum(119875119886)2 (6)

where119877 =Discrepancy Factor119875119886= actual values and

119875119901= predicted values

(d) 119871-estimation is calculated by using the followingequation

Ratio = Actual ValuePredictedValue

Multiple Ratio = 1198771times 1198772times 1198773

(7)

where1198771 1198772 1198773 are ratios of parameters 1 2 3

and we have

Ratio Product =1198601times 1198602times 1198603times sdot sdot sdot

1198751times 1198752times 1198753times sdot sdot sdot

Toting Ratio =1198601+ 1198602+ 1198603+ sdot sdot sdot

1198751+ 1198752+ 1198753+ sdot sdot sdot

(8)

where 1198601 1198602 1198603 are actual performances of

parameters 1 2 3 1198751 1198752 1198753 are predicted per-

formances of parameters 1 2 3

3 Results and Discussions

The actual observations predicted values and different cal-culated parameters for adequacy response surface equationsand coefficient of correlation values are given in Table 3 Therespective contours at different levels of variables were con-structed and are given in Figures 1(a) to 1(c) The discussionsare as follows

31 Weight at Different Levels of Variables From Figure 1(a)as depicted in (1)(A) TM decreases from 225 and spacingincreases as the weight reduces The trend is miscellaneous(B) The trend is miscellaneous TM and spacing increase astheweight decreases consistently (C)Up to 14mmspacing asTMdecreases from 225 weight decreases however at slightlyabove 225 TM spacing increases as the weight also increases

As depicted in (2)(A) two trends were found firstincreasing weight as spacing increases in fiber length abovecoded level + 05 and second decreasing weight as lengthdecreases from 70mm (B) As length decreases from 70mmand spacing increases to 18mm weight decreases In lengthabove 70mm as spacing increases weight increases andbelow reverse trend is visible (C) In 70 to 75mm in length asspacing increases weight is reduced however when length isfrom 65 to 70mm weight increases

As depicted in (3)(A) TM decreases and length increasesup to 70mm while weight decreases however in furtherincreases in length weight increases (B) As TM decreasesand length is up to 70mm weight decreases however infurther increases in length weight increases (C) Optimumswere found at TM 225 and fiber length 70mm

32 Abrasion at Different Levels of Variables FromFigure 1(b) as depicted in (1)(A) the trends weremiscellaneous as at TM up to 225 and spacing near14mm the optimum is seen (B) As TM and spacing increasethe abrasion cycles are reduced to a certain limit At TM andspacing levels 0 the optimum is found (C) The trend wasalmost similar to (B)

As depicted in (2)(A) as length and spacing increaseabrasion increasesThe abrasion cycles are lowest at low fiberlength All parallel lines show similar trends in all spacings(B) The parallel horizontal lines show that optimum couldnot be found in the range and the fiber length increases atall spacings as abrasion increases (C) The trend is almostsimilar to (A) as length decreases and spacing increases fromthe decrease of the abrasion cycles All lines are parallel andshowing the same relationship at each spacing and length

As depicted in (3)(A) as TM increases and lengthdecreases the tendency of reduction in abrasion cycles isnoted (B) As length decreases and TM is below 225 theabrasion reduces After TM is 225 as length increases abra-sion decreases (C)As the length decreases TM increases andabrasion reduces the trend is miscellaneous

33 Bursting atDifferent Levels of Variables FromFigure 1(c)as depicted in (1)(A) as spacing and TM increase up toa certain TM bursting increases (B) As TM increases and

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

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International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 ISRN Textiles

Table 1 Fiber specifications

Fiber used 64S Australian Merino wool Long staple (varying cut length) polyester1 2 3

1 Longest (mm) staple length 160 165 170 1502 Uniform (mm) staple length 115 119 124 1303 Average (mm) staple length 65 70 75 894 Shortest (mm) staple length 15 15 15 355 Average micron (120583) 225 225 225 mdash6 Moisture regain () 163 163 163 mdash7 Bundle strength (gramTex) 12 12 12 1448 Residual grease () 05 05 05 mdash9 Alkali solubility 105 105 105 mdash10 Urea bisulphite solubility () 42 42 42 mdash11 Fineness (denier) mdash mdash mdash 25

Table 2 Actual and coded values for independent variables and experimental design

Sample codeLevels of variables

1198831Wool fibre length (mm) 119883

2Twist multiplier 119883

3Strand spacing (mm)

Coded Actual Coded Actual Coded Actual1 minus1 65 minus1 200 0 142 1 75 minus1 200 0 143 minus1 65 1 250 0 144 +1 75 1 250 0 145 0 70 0 225 0 146 minus1 65 0 225 minus1 107 +1 75 0 225 minus1 108 minus1 65 0 225 +1 189 +1 75 0 225 +1 1810 0 70 0 225 0 1411 0 70 minus1 200 minus1 1012 0 70 1 250 minus1 1013 0 70 minus1 200 +1 1814 0 70 +1 250 +1 1815 0 70 0 225 0 14

225 Experimental Design To study the individual andinteractive effects of variables Box and Behnken factorialdesign was used for three variablesThe following parametersare selected as prototype variables

(1) fiber length (1198831)

(2) twist multiplier (1198832)

(3) strand spacing (1198833)

Table 2 shows the coded and actual values of threeparameters considered and fifteen sets of experimental com-binations by DRF yarn and fabrics are knitted

226 Measurement of Fabric Properties There are numbersof fabric properties that can be optimized by using this exper-imental approach however three fundamental properties are

measured The fabric weight per square meter (gmsmt2)(weight) was evaluated by ASTM D-3776-79 method taking10 times 10 cm sample from different places of knitted fabricThe abrasion cycle (abrasion) was measured by ASTM D-1966method usingmartindale abrasion testerThe specimenswere mounted on rectangular blocks of 15 times 25 incheswith abrading material which was itself fabric and thena number of rubs were counted by noting the number ofcycles from counter in abrasion cycles The bursting strength(bursting) is determined by ASTM D-3886-80 method usingdiaphragm type tester operated by hydrostatic pressure Thefabric samples are clamped by means of metal rings ofinternal diameter 30 plusmn 5mm in the tester by screwing theclamping ring too tight over the test piece Thus pressurewas increased on the diaphragm until the test piece burst inbetween 7 and 20 seconds to increase pressure from zero tobursting point and then readings ware noted from the dial

ISRN Textiles 5

227 Development of Statistical Model To correlate theeffects of variables and the response the following second-order standard polynomial was considered [16]

119884 = 1198870+ 11988711198831+ 11988721198832+ 11988731198833+ 119887111198832

1+ 119887221198832

2

+ 119887331198832

3+ 1198871211988311198832+ 1198871311988311198833+ 1198872311988321198833

(3)

where 119884 represents the responses and 1198870 1198871 1198872 119887

23are

the coefficients of the model The coefficients of main andinteraction effects were determined by using the standardmethod The response surface equations are calculated forprediction of responses

228 Optimization of Fabric Properties The optimum fabricperformance was predicted by using equations at all levels ofvariables drawing contours

229 Adequacy ofModels The followings termswere studiedfor the adequacies of the models

(a) Difference () is calculated by using the followingequation

Difference () = (PredictedValue minus Actual Value) times 100Actual Value

(4)

(b) Accuracy () is calculated by using the followingequation

Accuracy () = Actual Value times 100PredictedValue

(5)

(c) Discrepancy Factor (119877-Factor) is calculated [17] byusing the following equation

119877 = radic(sum119875119886minus 119875119901)2

sum(119875119886)2 (6)

where119877 =Discrepancy Factor119875119886= actual values and

119875119901= predicted values

(d) 119871-estimation is calculated by using the followingequation

Ratio = Actual ValuePredictedValue

Multiple Ratio = 1198771times 1198772times 1198773

(7)

where1198771 1198772 1198773 are ratios of parameters 1 2 3

and we have

Ratio Product =1198601times 1198602times 1198603times sdot sdot sdot

1198751times 1198752times 1198753times sdot sdot sdot

Toting Ratio =1198601+ 1198602+ 1198603+ sdot sdot sdot

1198751+ 1198752+ 1198753+ sdot sdot sdot

(8)

where 1198601 1198602 1198603 are actual performances of

parameters 1 2 3 1198751 1198752 1198753 are predicted per-

formances of parameters 1 2 3

3 Results and Discussions

The actual observations predicted values and different cal-culated parameters for adequacy response surface equationsand coefficient of correlation values are given in Table 3 Therespective contours at different levels of variables were con-structed and are given in Figures 1(a) to 1(c) The discussionsare as follows

31 Weight at Different Levels of Variables From Figure 1(a)as depicted in (1)(A) TM decreases from 225 and spacingincreases as the weight reduces The trend is miscellaneous(B) The trend is miscellaneous TM and spacing increase astheweight decreases consistently (C)Up to 14mmspacing asTMdecreases from 225 weight decreases however at slightlyabove 225 TM spacing increases as the weight also increases

As depicted in (2)(A) two trends were found firstincreasing weight as spacing increases in fiber length abovecoded level + 05 and second decreasing weight as lengthdecreases from 70mm (B) As length decreases from 70mmand spacing increases to 18mm weight decreases In lengthabove 70mm as spacing increases weight increases andbelow reverse trend is visible (C) In 70 to 75mm in length asspacing increases weight is reduced however when length isfrom 65 to 70mm weight increases

As depicted in (3)(A) TM decreases and length increasesup to 70mm while weight decreases however in furtherincreases in length weight increases (B) As TM decreasesand length is up to 70mm weight decreases however infurther increases in length weight increases (C) Optimumswere found at TM 225 and fiber length 70mm

32 Abrasion at Different Levels of Variables FromFigure 1(b) as depicted in (1)(A) the trends weremiscellaneous as at TM up to 225 and spacing near14mm the optimum is seen (B) As TM and spacing increasethe abrasion cycles are reduced to a certain limit At TM andspacing levels 0 the optimum is found (C) The trend wasalmost similar to (B)

As depicted in (2)(A) as length and spacing increaseabrasion increasesThe abrasion cycles are lowest at low fiberlength All parallel lines show similar trends in all spacings(B) The parallel horizontal lines show that optimum couldnot be found in the range and the fiber length increases atall spacings as abrasion increases (C) The trend is almostsimilar to (A) as length decreases and spacing increases fromthe decrease of the abrasion cycles All lines are parallel andshowing the same relationship at each spacing and length

As depicted in (3)(A) as TM increases and lengthdecreases the tendency of reduction in abrasion cycles isnoted (B) As length decreases and TM is below 225 theabrasion reduces After TM is 225 as length increases abra-sion decreases (C)As the length decreases TM increases andabrasion reduces the trend is miscellaneous

33 Bursting atDifferent Levels of Variables FromFigure 1(c)as depicted in (1)(A) as spacing and TM increase up toa certain TM bursting increases (B) As TM increases and

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CompositesJournal of

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Biomaterials

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Textiles 5

227 Development of Statistical Model To correlate theeffects of variables and the response the following second-order standard polynomial was considered [16]

119884 = 1198870+ 11988711198831+ 11988721198832+ 11988731198833+ 119887111198832

1+ 119887221198832

2

+ 119887331198832

3+ 1198871211988311198832+ 1198871311988311198833+ 1198872311988321198833

(3)

where 119884 represents the responses and 1198870 1198871 1198872 119887

23are

the coefficients of the model The coefficients of main andinteraction effects were determined by using the standardmethod The response surface equations are calculated forprediction of responses

228 Optimization of Fabric Properties The optimum fabricperformance was predicted by using equations at all levels ofvariables drawing contours

229 Adequacy ofModels The followings termswere studiedfor the adequacies of the models

(a) Difference () is calculated by using the followingequation

Difference () = (PredictedValue minus Actual Value) times 100Actual Value

(4)

(b) Accuracy () is calculated by using the followingequation

Accuracy () = Actual Value times 100PredictedValue

(5)

(c) Discrepancy Factor (119877-Factor) is calculated [17] byusing the following equation

119877 = radic(sum119875119886minus 119875119901)2

sum(119875119886)2 (6)

where119877 =Discrepancy Factor119875119886= actual values and

119875119901= predicted values

(d) 119871-estimation is calculated by using the followingequation

Ratio = Actual ValuePredictedValue

Multiple Ratio = 1198771times 1198772times 1198773

(7)

where1198771 1198772 1198773 are ratios of parameters 1 2 3

and we have

Ratio Product =1198601times 1198602times 1198603times sdot sdot sdot

1198751times 1198752times 1198753times sdot sdot sdot

Toting Ratio =1198601+ 1198602+ 1198603+ sdot sdot sdot

1198751+ 1198752+ 1198753+ sdot sdot sdot

(8)

where 1198601 1198602 1198603 are actual performances of

parameters 1 2 3 1198751 1198752 1198753 are predicted per-

formances of parameters 1 2 3

3 Results and Discussions

The actual observations predicted values and different cal-culated parameters for adequacy response surface equationsand coefficient of correlation values are given in Table 3 Therespective contours at different levels of variables were con-structed and are given in Figures 1(a) to 1(c) The discussionsare as follows

31 Weight at Different Levels of Variables From Figure 1(a)as depicted in (1)(A) TM decreases from 225 and spacingincreases as the weight reduces The trend is miscellaneous(B) The trend is miscellaneous TM and spacing increase astheweight decreases consistently (C)Up to 14mmspacing asTMdecreases from 225 weight decreases however at slightlyabove 225 TM spacing increases as the weight also increases

As depicted in (2)(A) two trends were found firstincreasing weight as spacing increases in fiber length abovecoded level + 05 and second decreasing weight as lengthdecreases from 70mm (B) As length decreases from 70mmand spacing increases to 18mm weight decreases In lengthabove 70mm as spacing increases weight increases andbelow reverse trend is visible (C) In 70 to 75mm in length asspacing increases weight is reduced however when length isfrom 65 to 70mm weight increases

As depicted in (3)(A) TM decreases and length increasesup to 70mm while weight decreases however in furtherincreases in length weight increases (B) As TM decreasesand length is up to 70mm weight decreases however infurther increases in length weight increases (C) Optimumswere found at TM 225 and fiber length 70mm

32 Abrasion at Different Levels of Variables FromFigure 1(b) as depicted in (1)(A) the trends weremiscellaneous as at TM up to 225 and spacing near14mm the optimum is seen (B) As TM and spacing increasethe abrasion cycles are reduced to a certain limit At TM andspacing levels 0 the optimum is found (C) The trend wasalmost similar to (B)

As depicted in (2)(A) as length and spacing increaseabrasion increasesThe abrasion cycles are lowest at low fiberlength All parallel lines show similar trends in all spacings(B) The parallel horizontal lines show that optimum couldnot be found in the range and the fiber length increases atall spacings as abrasion increases (C) The trend is almostsimilar to (A) as length decreases and spacing increases fromthe decrease of the abrasion cycles All lines are parallel andshowing the same relationship at each spacing and length

As depicted in (3)(A) as TM increases and lengthdecreases the tendency of reduction in abrasion cycles isnoted (B) As length decreases and TM is below 225 theabrasion reduces After TM is 225 as length increases abra-sion decreases (C)As the length decreases TM increases andabrasion reduces the trend is miscellaneous

33 Bursting atDifferent Levels of Variables FromFigure 1(c)as depicted in (1)(A) as spacing and TM increase up toa certain TM bursting increases (B) As TM increases and

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 ISRN Textiles

Table3Com

paris

onof

actualandpredictedvalues

(a)

Refn

oWeightp

ersquare

meter

Abrasio

ncycle

sBu

rstin

gstreng

th(kgcm

2 )119871-estim

ation

12

34

51

23

45

12

34

56

78

910

1201

20350minus12

41012

4099

117000

123354minus543

10543

095

1200

1174

217

9783

102

096

096

138300

144878

095

2192

19400minus10

41010

4099

123000

123354minus029

10029

100

1300

1280

154

9846

102

100

100

143500

1440

34

100

3196

19400

102

9898

101

120000

123354minus280

10280

097

1210

1290minus661

10661

094

092

092

140810

1440

44

098

4206

20350

121

9879

101

115000

123354minus72

61072

6093

1305

1256

375

9625

104

098

098

136905

144960

094

5186

18633minus018

10018

100

127000

129833minus223

10223

098

1320

1250

530

9470

106

103

103

146920

149716

098

6197

19579

061

9939

101

119500

128145minus72

31072

3093

1220

1138

672

9328

107

101

101

140420

148862

094

7193

19579minus14

51014

5099

122000

128145minus504

10504

095

1350

1174

1304

8696

115

108

108

142650

148898

096

8189

1912

9minus12

11012

1099

126000

131521minus438

10438

096

1400

1184

1543

8457

118

112

112

146300

151834

096

9190

1912

9minus068

10068

099

1240

00

131521minus607

10607

094

1285

1220

506

9494

105

099

099

144285

151870

095

10188

18633

089

9911

101

132500

129833

201

9799

102

1305

1250

421

9579

104

107

107

152605

149716

102

11197

19854minus078

10078

099

119000

116916

175

9825

102

1220

1133

713

9287

108

109

109

139920

137903

101

12187

18904minus10

91010

9099

128000

1264

1612

49876

101

1405

1179

1609

8391

119

119

119

148105

1464

99

101

13184

18454minus029

10029

100

131000

129792

092

9908

101

1435

1179

1784

8216

122

122

122

150835

149425

101

14193

19404minus054

10054

099

121000

120292

059

9941

101

1370

1225

1058

8942

112

112

112

141670

140921

101

15185

18633minus072

10072

099

130000

129833

013

9987

100

1310

1250

458

9542

105

104

104

149810

149716

100

Average

19227

19295minus037

10037

100

123667

126378minus227

10227

098

1309

1212

712

9288

108

106

105

098

Max

206

20350

121

1014

510

11325

131521

201

1072

710

21435

1290

1784

10661

122

122

126

102

Min

184

18454minus14

59879

099

1150

116916minus72

69799

093

1200

1133minus661

8216

094

092

086

094

119877-Factor

0016

0002

0229

(b)

Respon

sesurfa

ceequatio

ns(1198772)

1119884(w

eight)=18633minus2251198833+7211198832 1+5211198832 2+47511988311198832+47511988321198833

096

2119884(Ab

rasio

n)=129833+16881198833minus64791198832 2minus275011988311198832minus475011988321198833

071

3119884(Bursting

)=1250+0181198831+0231198832+0231198833minus0711198832 3minus03511988311198832

086

1actualvalue2predictedvalue3difference(

)4accuracy

()5actualvaluespredicted

values6

produ

ctof

1(allparameters)produ

ctof

2(allparameters)7

produ

ctof

5(all

parameters)8

sum

ofallactual

values

ofparameters

9sum

ofallpredictedvalues

ofparameters10produ

ct(8lowast9)

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Textiles 7

195

195

200205

185

190

190

195

minus10 -05 00 05 10minus10

minus05

00

05

10

190

195

200

190

200

190

185

190

195 200

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus10minus10

minus10minus10

minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

190

200

185

190

190

190

195

195

200

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

minus10 -05 00 05 10

minus05

00

05

10

X3

X1

(1) Weight at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Weight at TM (A) 200 (B) 225 and (C) 250

(3) Weight at spacing (mm) (A) 10 (B) 14 and (C) 18

(A) (B) (C)

(A) (B) (C)

(A) (B) (C)

(a) Weight at different levels of variables

Figure 1 Continued

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 ISRN Textiles

1200

1250

13001300

1250

1250

1300

1300

1200

12501300 1200

1250

1200

1250

1300

1240

1240

1260

1260

1280

1280

1300

1300

12501300

1300

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X2

(B) (C)

(A) (B) (C)

(A) (B) (C)

1300

1310

1290

(3) Abrasion at spacing (mm) (A) 10 (B) 14 and (C) 18

(2) Abrasion at TM (A) 200 (B) 225 and (C) 250

(1) Abrasion at fiber length (mm) (A) 65 (B) 70 and (C) 75

(b) Abrasion at different levels of variables

Figure 1 Continued

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Textiles 9

12

13

14

135140

140

145

13

14

14

13

14

15

13

13

13

14

12

31

14

125 13

0

130

135

135

135

140

145

150

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X3

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X3

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(A)

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

X2

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

minus10 -05 00 05 10minus10

minus05

00

05

10

X1

(B) (C)

(1) Bursting at fiber length (mm) (A) 65 (B) 70 and (C) 75

(2) Bursting at TM (A) 200 (B) 225 and (C) 250

(3) Bursting at spacing (mm) (A) 10 (B) 14 and (C) 18

(c) Bursting at different levels of variables

Figure 1 Fabric performances

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 ISRN Textiles

spacing decreases at a certain point bursting is optimumThen with further increase in TM and decrease in spacingbursting decreased (C) As TM from 225 and spacing from14mm increase bursting increases

As depicted in (2)(A) as spacing increases below 70mmin length decreasing trend is observed however at above14mm spacing trend was reversed (B) As length and spacingincrease the bursting decreases up to 70mm in length (C)The miscellaneous trends were noted after 70mm of lengthand spacing increased the bursting increases also as lengthincreases while from 70mm as spacing increases burstingdecreases

As depicted in (3)(A) as TM decreases and fiber lengthincreases up to 70mm bursting decreases however from 70to 75mmof length as TMdecreases from225 to 250 burstingalso decreases (B) As TM decreases up to 225 and fiberlength increases up to 70mm bursting increases and withfurther decreases in TM bursting decreases (C) As lengthincreases and TM decreases bursting increases first up to acertain length then it decreases

The fabric performance is proportional to the character-istics of fiber yarn and knit structures In the study selectedvariables mainly have an impact on yarns and yarns areassociated with knitted fabric

In DRF spinning as fiber length increases more lengthtraps in drafting results a more compact yarn At optimumTM the emerging fibers from front roller nip are trapped athigher binding force and gain better packing density becausethe packing density weight per unit length of yarn is higher

In higher spacing convergence angle is greater whichgenerates higher false twist as strand results in more compacttrapping of surface fibers and ultimately more compact yarnstructure In DRF production after optimum TM there iscomparatively loosely packed yarn which shows less weightper unit length of fabric Also after or before optimumspacing between strands the trapping of fiber reduces causingloose structure of yarn and ultimately as fiber length increasesthe weight of fabric decreases also the abrasion and burstingstrength are reduced With the increase of TM and strandspacing up to a certain limit (optimum condition of spin-ning) weight abrasion and bursting strength increase how-ever after or before optimum condition adverse behaviors areseenThe probable reasonmay be that up to a certain limit ithelps in better insertion of twist in single strand which causesbetter trapping of fibers in the yarn periphery and therebyimprovement in various properties of yarn and respectivefabrics

In other studies almost similar findings were reportedby Ghasemi and other workers that woolpolyester blendedworsted yarn is successfully produced by feeding two rovingin spinning system and that yarnsrsquo specifications such astensile strength elongation and abrasion resistance remainalmost unchanged [18]

The literature reveals that as fiber length TM or strandspacing reaches the optimum value the yarns produced aremore compact due to better binding The numbers of fibersin unit length are higher The numbers of fibers present inthe yarn structure are directly proportional to the ultimateproduct that is knitted fabric The weight of unit area

also increases or decreases respectively [19] due to fibertrappings Similar results are admitted by other researchersthat in samemanufacturing conditions the breaking strengthtearing strength abrasion resistance and crease recoveryproperties of fabric are improved in case of DRF yarn thanplies yarn [20]

34 Adequacy of Models The comparative analysis betweenactual and predicted performances ofDRF yarn knitted fabricis shown by line diagram as given in Figures 2(a) to 2(c) Thediscussions are as follows

Figure 2(a) depicts that trend is almost similar in actualand predicted weight per square meterThe actual weight persquare meter was maximum at 206 minimum at 184 andaverage at 19227 however predicted weight per squaremeterwas maximum at 20350 minimum at 18454 and average at19295 respectively

Figure 2(b) depicts that abrasion cycles trend of predictedvalues is different from the actual values up to maximumvalues therefore it remains almost the same The actualabrasion cycles were maximum at 1325 minimum at 1150and average at 123667 however predicted actual cycles weremaximum at 131521 minimum at 116916 and average at126378 respectively

Figure 2(c) depicts that bursting strength trend of pre-dicted values is different from the actual values The actualbursting strength values were maximum at 1435 minimumat 1200 and average at 1309 however predicted burstingstrength values were maximum at 1290 minimum at 1133and average at 1212 respectively

The coefficients of correlation (1198772) between observed andpredicted valueswere 096 071 and 086 forweight abrasionand bursting respectively which shows significant influence

The difference () was maximum at 121 201 and 1784minimum at minus145 minus726 and minus661 and average at minus037minus227 and 712 forweight abrasion and bursting respectively

The accuracy () was maximum at 10145 10727 and10661 minimum at 9879 9799 and 8216 and average at10037 10227 and 9288 for weight abrasion and burstingrespectively

The Discrepancy Factor (119877-Factor) was noted to be0016 0002 and 0229 for weight abrasion and burstingrespectively

The values under 119871-estimation are as followsThe values of ratio were maximum at 101 102 and 122

minimum at 099 093 and 094 and average at 100 098and 108 for weight abrasion and bursting respectively

The multiple-ratios were calculated maximum at 126minimum at 086 and average at 105

The values of ratio products were calculated maximum at122 minimum at 092 and average at 106

The values of toting ratio were calculated maximum at102 minimum at 094 and average at 098

4 Conclusions

(1) The second-order model is the most frequentlyused approximating polynomial model in RSM The

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Textiles 11

205

200

195

190

185

180

Wei

ght s

quar

e met

er

Actual weight per square meterPredicted weight per square meter

Weight per square meterActual versus predicted

(a) Weight per square meter

Actual abrasionPredicted abrasion

Abrasion resistanceActual versus predicted

1325

1275

1225

1175

1125

Abra

sion

resis

tanc

e

(b) Abrasion resistance

Burs

ting s

treng

th

Actual versus predicted

Actual burstingPredicted bursting

Bursting strength

1450

1400

1350

1300

1250

1200

1150

1100

(c) Bursting strength

Figure 2 Comparative analysis actual versus predicted performances

Box-Behnken is the most suited design for optimiza-tion and prediction of data in textile manufacturingand this model is well-suited for DRF technique yarnknitted fabric

(2) The higher wool fiber length shows higher fabricweight abrasion and bursting strength

(3) The correlation of TM is not visible

(4) The role of strands spacing is dominant in comparisonto other variables at 14mmspacing it shows optimumbehaviors

(5) The optimum were weight (gmsmt2) 206 at length75mm TM 25 and 14mm spacing abrasion (cycles)1325 at length 70mm TM 225 and 14mm spacingbursting (kgcm2) 1435 at length 70mm andTM200and 18mm spacing

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 ISRN Textiles

(6) The variables have substantial influence

(7) The adequacies of response surface equations are veryhigh

(8) The line trends of knitted fabric basic characteristicswere almost the same for actual and predictedmodels

(9) The difference () was in range of 121 to minus145201 to minus726 and 1784 to minus661 the accuracy ()was in range of 10145 to 9879 10727 to 9799 and10661 to 8216 and theDiscrepancy Factor (119877-Factor)was noted to be 0016 0002 and 0229 for weightabrasion and bursting respectively between actualand predicted data

(10) The 119871-estimation factors for actual and predicted datawere that (i) ratio was in range of 101 to 099 102to 093 and 122 to 094 for weight abrasion andbursting respectively (ii) the multiple-ratio was inrange of 126 to 086 (iii) the ratio product was inrange of 122 to 092 and (iv) the toting ratio was inrange of 102 to 094

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] D M Wardrop and R H Myers ldquoSome response surfacedesigns for finding optimal conditionsrdquo Journal of StatisticalPlanning and Inference vol 25 no 1 pp 7ndash28 1990

[2] G E P Box and K BWilson ldquoOn the experimental attainmentof optimum conditionsrdquo Journal of the Royal Statistical SocietyB vol 13 pp 1ndash14 1951

[3] D C Montgomery Design and Analysis of ExperimentsResponse Surface Method and Designs JohnWiley amp Sons NewYork NY USA 2005

[4] A I Khuri and S Mukhopadhyay ldquoResponse surface method-ologyrdquoWiley Interdisciplinary Reviews vol 2 no 2 pp 128ndash1492010

[5] V A Sakkas M A Islam C Stalikas and T A AlbanisldquoPhotocatalytic degradation using design of experiments areview and example of the Congo red degradationrdquo Journal ofHazardous Materials vol 175 no 1-3 pp 33ndash44 2010

[6] M A Bezerra R E Santelli E P Oliveira L S Villar and L AEscaleira ldquoResponse surface methodology (RSM) as a tool foroptimization in analytical chemistryrdquo Talanta vol 76 no 5 pp965ndash977 2008

[7] D H Doehlert ldquoUniform shell designsrdquo Journals of the RoyalStatistical Society C vol 19 pp 231ndash239 1970

[8] C R T Tarley G Silveira W N L dos Santos et alldquoChemometric tools in electroanalytical chemistry methodsfor optimization based on factorial design and response surfacemethodologyrdquo Microchemical Journal vol 92 no 1 pp 58ndash672009

[9] G E P Box and DW Behnken ldquoSome new three-level designsfor the study of quantitative variablesrdquo Technometrics vol 2 no4 pp 455ndash475 1960

[10] S Brown R Tauler andRWalczak ldquoResponse surfacemethod-ologyrdquo in Comprehensive Chemometrics vol 1 pp 345ndash390Elsevier Amsterdam The Netherlands 2009

[11] F Oughlis-Hammache N Hamaidi-Maouche F Aissani-Benissad and S Bourouina-Bacha ldquoCentral composite designfor the modeling of the phenol adsorption process in a fixed-bed reactorrdquo Journal of Chemical and Engineering Data vol 55no 7 pp 2489ndash2494 2010

[12] R H Myers and D C Montgomery Response Surface Method-ology Process and Product Optimization Using Designed Experi-ments John Wiley amp Sons New York NY USA 2002

[13] A T Hoke ldquoEconomical second-order designs based on irreg-ular fractions of the 3k factorialrdquo Technometrics vol 16 no 3pp 375ndash384 1974

[14] M J Box and N R Draper ldquoFactorial designs themdashX1015840Xmdashcriterion and some related mattersrdquo Technometrics vol 13 pp731ndash742 1971

[15] K G Roquemore ldquoHybrid designs for quadratic responsesurfacesrdquo Technometrics vol 18 pp 419ndash423 1976

[16] W G Cochran and G M Cox Experimental Design AsiaPublishing House Delhi India 1963

[17] J Skilling and R K Bryan ldquoMaximum entropy imagereconstructionmdashgeneral algorithmrdquo Royal Astronomical Soci-ety vol 211 pp 111ndash124 1984

[18] R Ghasemi RMozafari-Dana SM Etrati and S ShaikhzadehNajar ldquoComparing the physical properties of producedsirospun and new hybrid solo-siro spun blend woolpolyesterworsted yarnsrdquo Fibres and Textiles in Eastern Europe vol 16no 1 p 66 2008

[19] D GericheThe Indian Textile Journal pp 102ndash111 1995[20] S Bhatnagar K R Salotra and R C D Kaushik The Indian

Textile Journal pp 52ndash53 1994

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials