Journal of Engineered Fibers and Fabrics 128 http://www.jeffjournal.org Volume 10, Issue 1 – 2015 Multi Response Optimization for Bursting Strength and Pill Density of Lacoste Fabrics Gulsah Pamuk, PhD Ege University, Bornova, Izmir TURKEY Correspondence to: Gulsah Pamuk email: [email protected]ABSTRACT Bursting strength and pilling tendency are two major quality characteristics of knitted fabrics. In this study, optimum yarn twist and loop length values that make bursting strength maximum and pilling performance minimum at the same time are calculated by using the desirability function technique, a kind of multi response optimization method. Good quality solutions were obtained with reduced number of experiments needed to provide sufficient information for statistically acceptable results. INTRODUCTION Among the various mechanical and physical properties of knitted fabrics, pilling performance and bursting strength are the most important. In the relevant literature, many factors affecting the pilling and bursting strength of knitted fabrics were investigated. Most of them focused on yarn properties [1,2,3,4,5]. On the other hand, artificial neural network [6,7], fuzzy logic theory [7] and Taguchi method [8] were employed to investigate the effect of process parameters on the pilling and bursting strength of knitted fabrics. Artificial neural networks deal with the estimation of a fitted response to a process [9]. Taguchi’s approximation aims to determine the optimum choice of levels of controllable factors in a process for the manufacturing of a product. The principle of choice of levels focuses on the minimization of variability around a pre-chosen target for the process response [11]. Beltran et al [6] investigated the application of artificial neural networks to model the relationship between fiber, yarn and fabric properties and the pilling propensity of single jersey and rib wool knitted fabrics. Ertugrul and Ucar [7], predicted bursting strength of cotton plain knitted fabrics by using fabric weight, yarn breaking strength and yarn breaking elongation parameters by neural network and Sugeno-Takagi fuzzy system. Apart from these studies, Mavruz and Ogulata [8], optimized the effects of yarn type, levels of relaxation treatment and loop length on the bursting strength of 1x1 rib structures by Taguchi design technique. Response surface (RS) is a method used for modeling the relationship between process inputs and output factors to predict responses and to optimize the process input factors [10]. In the current study the effect of yarn twist and loop length on the bursting strength and pill density for a single lacoste and a double lacoste fabric was examined by RS optimization procedure, and the desirability function technique employed to determine the optimum levels of yarn twist and loop length maximizing the bursting strength and minimizing the pill density. To the best of our knowledge this is the first study that maximizes the bursting strength and minimizes the pill density simultaneously by the using multi response optimization method. MATERIALS AND METHODS Materials Combed cotton, 30/1 Ne medium and high twisted yarns were used to manufacture fabrics. Two different fabric types, single lacoste and double lacoste, were knitted on 28E, 32’’ circular knitting machine equipped with positive feed system. Each fabric type was produced at three different loop length (0.26, 0.28 and 0.30cm). These lengths were selected in such a way that the knit loop length for all the fabric types remained the same. Therefore, 2 x 2 x 3 = 12 different samples were produced in total and they were laid on a flat surface in atmospheric condition for dry relaxation.
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Journal of Engineered Fibers and Fabrics 128 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
Multi Response Optimization for Bursting Strength and Pill Density of Lacoste Fabrics
Gulsah Pamuk, PhD
Ege University, Bornova, Izmir TURKEY
Correspondence to:
Gulsah Pamuk email: [email protected] ABSTRACT Bursting strength and pilling tendency are two major quality characteristics of knitted fabrics. In this study, optimum yarn twist and loop length values that make bursting strength maximum and pilling performance minimum at the same time are calculated by using the desirability function technique, a kind of multi response optimization method. Good quality solutions were obtained with reduced number of experiments needed to provide sufficient information for statistically acceptable results. INTRODUCTION Among the various mechanical and physical properties of knitted fabrics, pilling performance and bursting strength are the most important. In the relevant literature, many factors affecting the pilling and bursting strength of knitted fabrics were investigated. Most of them focused on yarn properties [1,2,3,4,5]. On the other hand, artificial neural network [6,7], fuzzy logic theory [7] and Taguchi method [8] were employed to investigate the effect of process parameters on the pilling and bursting strength of knitted fabrics. Artificial neural networks deal with the estimation of a fitted response to a process [9]. Taguchi’s approximation aims to determine the optimum choice of levels of controllable factors in a process for the manufacturing of a product. The principle of choice of levels focuses on the minimization of variability around a pre-chosen target for the process response [11]. Beltran et al [6] investigated the application of artificial neural networks to model the relationship between fiber, yarn and fabric properties and the pilling propensity of single jersey and rib wool knitted fabrics.
Ertugrul and Ucar [7], predicted bursting strength of cotton plain knitted fabrics by using fabric weight, yarn breaking strength and yarn breaking elongation parameters by neural network and Sugeno-Takagi fuzzy system. Apart from these studies, Mavruz and Ogulata [8], optimized the effects of yarn type, levels of relaxation treatment and loop length on the bursting strength of 1x1 rib structures by Taguchi design technique. Response surface (RS) is a method used for modeling the relationship between process inputs and output factors to predict responses and to optimize the process input factors [10]. In the current study the effect of yarn twist and loop length on the bursting strength and pill density for a single lacoste and a double lacoste fabric was examined by RS optimization procedure, and the desirability function technique employed to determine the optimum levels of yarn twist and loop length maximizing the bursting strength and minimizing the pill density. To the best of our knowledge this is the first study that maximizes the bursting strength and minimizes the pill density simultaneously by the using multi response optimization method. MATERIALS AND METHODS Materials Combed cotton, 30/1 Ne medium and high twisted yarns were used to manufacture fabrics. Two different fabric types, single lacoste and double lacoste, were knitted on 28E, 32’’ circular knitting machine equipped with positive feed system. Each fabric type was produced at three different loop length (0.26, 0.28 and 0.30cm). These lengths were selected in such a way that the knit loop length for all the fabric types remained the same. Therefore, 2 x 2 x 3 = 12 different samples were produced in total and they were laid on a flat surface in atmospheric condition for dry relaxation.
Journal of Engineered Fibers and Fabrics 129 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
Methods Tests, such as mass per unit area, pilling, and bursting strength, were performed on conditioned fabric samples under standard atmospheric conditions (20±2 ºC temperature and 65% ±2 relative humidity). The bursting strength was determined by a James Heal Pneumatic Bursting Strength Tester following ISO 13938-2 test standards. Six samples from each fabric type were tested. The device applies a pneumatic load under a rubber diaphragm of a specific area. The reading was noted in kPa. Pilling specimens were prepared and measured according to ISO 12945-2. For all samples, standard 2000 cycles were given. Pilled surfaces were evaluated by using an objective grading method SDL ATLAS PillGrade Automated Pilling Grading System. The PillGrade System is a 3D fabric scanning technology that objectively and repeatedly grades fabric. PillGrade outputs repeatable and objective 1.0-5.0 grade results, where 1=severe pilling, 2=distinct pilling, 3=moderate pilling, 4=slight pilling, and 5=no pilling. In this study, two and three levels were designated for these input parameters, respectively. In Table I, the levels are given.
TABLE I. The levels of yarn twist and loop length.
Factor Unit Level of Factor Yarn Twist (x1) Loop length (x2)
turn/m cm
600 900 0.26 0.28 0.30
The design matrix and the response values for bursting strength and pill density of single lacoste fabric and double lacoste fabric are given in Table II and Table III respectively.
TABLE II. Design matrix and responses for bursting strength and pill density of single lacoste fabric.
A BRIEF OVERVIEW OF MULTI-RESPONSE OPTIMIZATION IN RS METHODOLOGY Consider the second order RS model, given in Eq. (1).
(1)
where kxxx ,...,, 21 are input variables; 0β , iβ ,
iiβ , ijβ are unknown coefficients, and e is a random error term. The fitted form of dependent variable w to model in (1) can be represented in terms of the vector
, and matrix as in Eq. (2).
(2)
where is the estimated intercept term, and in
Eq. (3) contain the estimates of linear and second-order coefficients in Eq. (1).
(3)
Derringer and Suich [12], described a multi response optimization technique employing some composite functions which are called desirability functions. These functions are given in Eq. (4) – Eq. (6). If a particular fitted response w is to be maximized, minimized, or assigned a target value then the functions in (4), (5) and (6) are employed respectively.
ˆ0
ˆ ˆ
ˆ1
s
w A
w Ad A w BB A
w B
≤
− = < < − ≥
(4)
ˆ1
ˆ ˆ
ˆ0
t
w B
w Cd B w CB C
w C
≤
− = < < − ≥
(5)
ˆ0
ˆ ˆ
ˆ ˆ
ˆ0
s
t
w A
w A A w BB A
dw C B w CB C
w C
<
− ≤ ≤ − = − < ≤ −
>
(6)
In Eq. (4) - Eq. (6), it is obvious that d changes between zero and one. The exponents, s and t in Eq. (4) – Eq. (6) characterize the path for desirability values. The desirability functions show some lines if s and t take the value one. In Eq. (4), Eq. (5) and Eq. (6), the limit value B denotes the maximum, minimum and target values of some fitted responses since d takes the value one at this point.
Journal of Engineered Fibers and Fabrics 131 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
When responses 1 2ˆ ˆ ˆ, ,..., mw w w are simultaneously to be maximized, minimized, or assigned to a target value for the same or different objectivities, the overall desirability function of these responses which is given in Eq. (7) is employed [12].
(7) A multi response optimization problem with desirability function technique can be described as in Eq. (8) For
1 2ˆ ˆ ˆ, ,..., mw w w.
Maximum Subject to
(8) In Eq. (8), ( j = 1, 2, …, k) are the lower and upper bounds of process input variables [10]. ANALYSIS OF VARIANCE FOR BURSTING STRENGTH AND PILL DENSITY Single Lacoste Fabrics Table IV shows the analysis of variance for bursting strength data of single lacoste fabric given in Table II. The R2 = 0.903 and R2 (adj.) = 0.894 show that the second order response model in Eq. (1) adequately fits the data in Table II. In Eq. (9), the fitted response for bursting strength is given. As it can be seen from Table IV, both linear and square coefficients in fitted response are significant with P < 0.000 (linear) and P < 0.005 (square). In Table IV, the P value for lack of fit test indicates that there is no curvature for fitted response surface 1y , that is, there are no repeated observations for bursting strength for different values for yarn twist and loop length. TABLE IV. Analysis of variance for bursting strength of single lacoste fabric (y1).
R2 = 0.903 R2 (adj.) = 0.894
(9)
Figure 1 shows the response surface plots for bursting strength of single lacoste fabric as a function of yarn twist and loop length. As can be seen from Figure 1, the highest bursting strength occurred when yarn twist was 900 turns/m and loop length was 0.26 cm. It is obvious that the bursting strength slightly increases as yarn twist increases, but bursting strength strongly decreases as loop length increases.
0,30
y1(Bursting strength)
500 0,28
550
600
x2(Loop length)600 700 0,26800 900x1(Yarn twist)
FIGURE 1. Response surface plot showing the effect of yarn twist and loop length on bursting strength of single lacoste fabric.
In Table V, the ANOVA results for pill density data of single lacoste fabric in Table II are given. The
2y in Eq. (10) represents the fitted response of these data. Table V denotes that, the p value for linear, square and interaction terms are all significant. The interaction term in Eq. (10) indicates that the interaction between yarn twist and loop length reduces the pilling amount as the amount of yarn twist and loop length are simultaneously increased. Note that this interaction does not exist for bursting strength.
TABLE V. Analysis of variance for pill density of single lacoste fabric (y2).
R2 = 0.975 R2 (adj.) = 0.972
(10)
Journal of Engineered Fibers and Fabrics 132 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
In Figure 2, the effect of yarn twist and loop length on pill density of single lacoste fabric is illustrated as a graph. The graph indicates that as yarn twist increases the pill density decreases, but as loop length increases the pill density also increases.
0,30
y2(Pill desity)
1
0,28
2
3
x2(Loop length)600 700 0,26800 900x1(Yarn twist)
FIGURE 2. Response surface plot showing the effect of yarn twist and loop length on pill density of single lacoste fabric Double Lacoste Fabrics The design matrix and the response values for bursting strength and pill density of double lacoste fabric are given in Table III. Table VI and Table VII show the analysis of variance for the regression parameters of the predicted response. The model is surface quadratic for bursting strength and pill density of double lacoste fabric. As can be seen, both linear and square regression terms of fitted RS model are significant for bursting strength and pill density. TABLE VI. Analysis of variance for bursting strength of double lacoste fabric (z1).
R2 = 0.966 R2 (adj.) = 0.961
Based on Eq. (2), an empirical relationship between bursting strength and independent variables are expressed in Eq. (11).
(11)
Response surface plot (Figure 3), shows that maximum bursting strength is occurred for double lacoste fabric, when yarn twist and loop length are minimum. Bursting strength decreases as the yarn twist increases.
0,30
z1(Bursting strength)
5000,28
600
700
x2(Loop length)600 700 0,26800 900x1(Yarn twist)
FIGURE 3. Response surface plot showing the effect of yarn twist and loop length on bursting strength of double lacoste fabric.
TABLE VII. Analysis of variance for pill density of a double lacoste (z2).
R2 = 0.951 R2 (adj.) = 0.946
Based on Eq. (2), an empirical relationship between pill density and independent variables were expressed by the following Eq.
(12)
Response surface plot (Figure 4), indicates that minimum pill is obtained when yarn twist is maximum and loop length is minimum. Pill density increases as the yarn twist decreases.
Journal of Engineered Fibers and Fabrics 133 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
0,30
z2(Pill desity)
0,5
0,28
1,0
1,5
2,0
x2(Loop length)600 700 0,26800 900x1(Yarn twist)
FIGURE 4. Response surface plot showing the effect of yarn twist and loop length on pill density of double lacoste fabric. The determination of the optimum levels of yarn twist and optimum levels of loop length which simultaneously maximize the bursting strength and minimize the pill density of a single lacoste fabric and double lacoste fabric is an important problem. The quality characteristics (bursting strength and pill density), affected by yarn twist and loop length, were examined in terms of fitted response surfaces in Figures 1-4. By examining these figures, the optimum values of yarn twist and loop length that maximize the bursting strength and minimize the pill density simultaneously can be estimated to some degree. For instance, Figure 1 and Figure 2 indicate that the maximum bursting strength and minimum pill density of single lacoste fabric occurs for high levels of yarn twist and low level of loop length. But in Figure 3, the response surface has a saddle (minimax) system, thus the determinations of the optimum level of the yarn twist and loop length have some difficulties. These optimization problems can be solved by employing the desirability function technique. The Minitab Response Optimizer Software was employed for solution of this problem and the solution details are given in Tables VIII-XI. Table VIII and Table X denote the interval bounds for bursting strengths and pill densities. The weights in these tables indicate the exponents s and t of desirability functions in Eq. (4).and Eq. (5). respectively. Importance values denote equal weights of responses. The optimum levels of yarn twists and loop lengths for maximum bursting strength and minimum pill density of single lacoste fabrics are given in Table IX and Table XI.
TABLE VIII. Interval bounds for bursting strength and pill density of single lacoste fabrics.
TABLE IX. Optimum levels of yarn twist and loop length for maximum bursting strength and minimum pill density of single lacoste fabrics.
Yarn twist (x1)
Loop Length
(x2)
Predicted bursting strength
Predicted Pill
density
Composite Desirability
900 0.26 620.153 0.569 0.98 TABLE X. Response optimization for bursting strength and pill density of double lacoste fabrics.
TABLE XI. Optimum values of input variables for maximum bursting strength and minimum pill density of double lacoste fabrics.
Yarn twist (x1)
Loop Length
(x2)
Predicted bursting strength
Predicted Pill
density
Composite Desirability
600 0.26 725.224 0.533 0.99 CONCLUSION In this study, an empirical relationship between the response (bursting strength and pill density) and independent variables (yarn twist and loop length) were expressed by second order polynomial equations. Effects of input variables on bursting strength and pill density were assessed by response surface plots. Thanks to the desirability function technique a reduced number of experiments were needed in optimizing the input variables for simultaneously maximizing bursting strength and minimizing pill density of single and double lacoste fabrics. Optimum values were found to be 900 turns/m for yarn twist and 0.26 cm for loop length for single lacoste fabric and 600 turns/m for yarn twist and 0.26 cm for loop length for double lacoste fabrics.
Journal of Engineered Fibers and Fabrics 134 http://www.jeffjournal.org Volume 10, Issue 1 – 2015
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AUTHORS’ ADDRESSES Gulsah Pamuk, PhD Ege University Emel Akin Vocation School Bornova, Izmir 35100 TURKEY
