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Optimization of ring-spinning process parameters using response surface methodology a
a
a
Hasanuzzaman , Pranab K. Dan & Sanghita Basu a
Department of Industrial Engineering and Management, West Bengal University of Technology, Kolkata, India Published online: 03 Jul 2014.
To cite this article: Hasanuzzaman, Pranab K. Dan & Sanghita Basu (2014): Optimization of ring-spinning process parameters using response surface methodology, The Journal of The Textile Institute, DOI: 10.1080/00405000.2014.929250 To link to this article: http://dx.doi.org/10.1080/00405000.2014.929250
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The Journal of The Textile Institute, 2014 http://dx.doi.org/10.1080/00405000.2014.929250
Optimization of ring-spinning process parameters using response surface methodology Hasanuzzaman*, Pranab K. Dan and Sanghita Basu Department of Industrial Engineering and Management, West Bengal University of Technology, Kolkata, India
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(Received 19 March 2014; accepted 26 May 2014) Several processes are involved in textile industry for yarn production. Ring spinning is the most versatile machine for producing the spun yarn. It is necessary to optimize the ring-spinning process parameters in order to curtail cost and increase the production rate without affecting the yarn quality. In this study, the effects of spinning process parameters namely, spindle speed, roving twist multiplier (roving TM) and yarn TM are studied and have been optimized using three variable Box–Behnken design of Response Surface Methodology. It is determined that spindle speed of 17,000 rpm with 4.1 TM for yarn and 1.3 TM for roving results are the best optimal responses. Keywords: ring spinning; response surface methodology (RSM); spindle speed; yarn TM; roving TM
Introduction The competitive situation, globally, has forced the textile industry, involved largely in manufacturing yarn and fabric, to focus intensely on issues like productivity and cost reduction while maintaining the quality at high level. Yarn, which is produced through spinning, is the primary raw material in textile fabric manufacturing. The yarn is spun in roving frame and ring frame sequentially, and therefore for maximizing yarn productivity, increase in production rate of spinning in the aforementioned machines is necessary. The material produced in roving frame is fed into the ring frame. Generally, the ring frames deployed are much higher in number compared to roving frames in a textile plant as the out rate of the former is much less than that of the later and, therefore, the production rate in ring frame determines the fabric production output. Hence, the study focuses on the process parameters of ring frame and the corresponding output quality factors. Twist of roving frame is also considered as a design of experiment factor in ring frame. It may be noted that this factor namely twist in roving frame was not considered in earlier research. This work endeavours to optimize the factors namely spindle speed, yarn twist multiplier (yarn TM) and roving twist multiplier (roving TM) so that the maximum effective output is possible while maintaining the quality parameters or responses namely hairiness, irregularity, specific strength, imperfection, breakage rate and breaking extension. Although the above three factors namely spindle speed, yarn TM and roving TM are responsible for quality, the spindle speed ultimately determines the output rate, therefore, the objective of this work is to increase the output rate by way of setting the *Corresponding author. Email:
[email protected] © 2014 The Textile Institute
speed optimally while the quality is not compromised or other word to determine the speed of the spindle that maintains the output quality parameters within the acceptable and specified range. The effect of spinning process parameter in ring spinning had drawn the attention of researchers. Researchers are putting emphasis on maximizing production at each spinning sequence of machines and thus a detailed study on spinning process variables is required to find their effects on the yarn properties produced through ring spinning line (Ishtiaque, Kumar, & Salhotra, 2008). The aim of this paper is to study the effects of the three process parameters such as spindle speed, yarn TM and roving TM of ring spinning operations on six output responses namely yarn hairiness, irregularity, specific strength, imperfection, breakage rate and breaking extension and for this, Response Surface Methodology (RSM) (Feng, Xu, & Tao, 2012) with Box–Behnken design has been used. The amount of twist plays a vital role on physical and mechanical properties of low twist yarn bearing the properties: specific strength, breaking force, elongation, mass variation and hairiness (Abbasi, Peerzada, & Jhatial, 2012). The mathematical models so developed are analyzed and optimized to yield values of process parameters producing optimal values of output responses. Yarn tenacity or specific strength and irregularity in ring-spinning process are influenced by mechanical factors such as spindle speed, top roller pressure, twist multiplier and traveller numbers (Ahmad, Jamil, & Haider, 2002; Ishtiaque, Rengasamy, & Ghosh, 2004; Jackowski, Chylewska, & Cyniak, 2002; Mahmood, Jamil, Haq, & Javed, 2004). Yarn irregularity has a good correlation with fibre-related parameters
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like friction between them and also the roving parameters namely roving hank, twist multiplier, etc. So optimization of these parameters helps in improvement of imperfections of yarn (Chattopadhyay & Sinha, 2007; Das, Ishtiaque, & Kumar, 2004; Kumar & Nishkam, 2005; Mohamed & Veerasubramanian, 2009). Spinning process parameters such as speed of opening roller and linear density of yarn influence the strength characteristics of cotton yarns for rotor-spun yarn (Jackowski et al., 2002). The geometry of the spinning triangle influences the distribution of fibre tension within the yarn and, thus, affects the component of yarn torque. The spinning triangle or the dynamics of yarn formation has a significant and crucial effect on yarn properties (Feng, Xu, Tao, & Hua, 2010; Hua, Tao, Cheng, & Xu, 2007; Li, Xu, Tao, & Feng, 2011; Tang, Xu, & Tao, 2009). One basic way to increase profit and quality in the ring-spinning process is to keep the end breakage rate to a minimum level. Variation of yarn mass irregularity should be keep at a minimum and friction between fibres should be increased to minimize the end breakage rate that not only limits the maximum spindle speed but also deteriorates the quality (Ghosh, Ishtiaque, Rengasamy, & Patnaik, 2004). Increase of spindle speed causes increase in balloon diameter and therefore increases the spinning tension and ultimately increases the abrasion between yarn-lappet guide and yarn-ring traveller, and ultimately increases hairiness. The objective is to minimize hairiness output characteristics. Effect of roving count on the length of hairs is higher than that of the roving twist multiplier (Dhange, 2012). A study (Hossen & Saha, 2011) was reported in the contrast of selection of appropriate ring traveller number. An analytical model was developed for physical interpretation of yarn twist propagation in staple yarn spinning (Tang, Xu, & Tao, 2009). Study on the ringspinning process parameters and establishment of a linear relationship between spinning parameters such as roving hank (count), roving twist multiplier and break draft in ring frame for yarn properties has been conducted (Farooq & Shakir, 2011). In present study, carded cotton yarn is chosen for investigation and optimization of the process parameters namely spindle speed, yarn TM and roving TM using RSM. The software Design-Expert 8.0 has been used for computation involved in RSM.
correspondingly results in a set of output responses. The best method to explore the relationship between the input and output is the response surface methodology since it can determine the exact value within any given range of parameters value. The efficient RSM design, namely Box–Behnken design proposed by Box and Behnken in 1960, is considered here. This design is efficient because few runs are made in this design. RSM steps are shown in Figure 1. The software Design-Expert 8.0 has been used to calculate optimal result and also to find significance of each factor through Box–Behnken design. The design expert software is used to fit response surface model and to construct contour plot which helps to characterize the shape of the surface and locate the optimal value with reasonable tolerance. This software computes variance for first-order or other polynomial models. The R2 (coefficient of determination) indicates how well the data points fit the response surface and the lack-of-fit value determines whether the model is significant or not. The three factors spindle speed, yarn TM and roving TM have been chosen for this Box–Behnken experiment
Methodologies RSM method RSM is the collection of mathematical and statistical techniques that is useful for the modelling and analysis of problem in which a response of interest is influenced by several variables and the objective is to optimize this response. In the context of textile ring spinning, the process is influenced by several input parameters that
Figure 1.
RSM steps.
The Journal of The Textile Institute each with three levels and are coded as –1, 0 and +1 for low, intermediate and high values, respectively.
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xi x0 ; Xi ¼ Dx
(1)
where Xi is the coded value for independent variable, xi is the actual value for independent variable at level i, x0 is the actual value for independent variable at centred level value and Δx is the step change value for independent variable. The first step in RSM is to establish the relationship between the responses and the set of independent process variables. If the responses are well modelled by linear function of independent variables, the approximate function is given by the first-order linear regression equation:
3 di ¼
r
yL T L
;
(5)
provided, 0 ≤ di ≤ 1; di = 0 if response < low value; and di = 1 if response > high value. And, if the response is a minimum value, then is Desirability function, U y r d¼ ; (6) U T provided, 1 ≥ di ≥ 0; and di = 1; if response < low value; and di = if response > high value. where y = optimized response, L = lower limit of response, U = upper limit of response, T = target, for both Equations (5) and (6).
Testing methodologies y ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3 þ :
(2)
If there is a curvature in the system, then the approximate function is given by second-order multiple regression equation:
y ¼ b0 þ
3 X i¼1
bi xi þ
3 X i¼1
bii x2i þ
2 X 3 X
bij xi xj þ ; (3)
i¼1 j¼2
where y is the response, b0 model constant, bi xi linear term, bii x2i quadratic term, bij xi xj interaction term, error term. The method of least squares is used to estimate parameters in approximating the polynomial function. The response surface analysis is then performed using fitted surface. Design-Expert software uses simultaneous optimization technique popularized by Derringer and Suich in the year of 1980. The method makes use of an objective function, D(x), called the desirability function. It reflects the desirable ranges for each response (di). The desirable ranges are from zero to one (least to most desirable, respectively). The simultaneous objective function is a geometric mean of all transformed responses. The desirability functions are represented by Equation (4) through Equation (6) as below. Over all desirability function, 1
DðxÞ ¼ ðd 1 d 2 . . . d n Þn ;
(4)
where n = no. of responses and di = desirability function for each response. Now, if the response is a maximum value, then is Desirability function,
Testing of the samples, for measuring the value of the individual responses, is conducted at the standard atmospheric condition of humidity 65 ± 2% and temperature 20 ± 2 °C. Roving is prepared in the roving frame by varying the twist considering all the preparatory process parameters to be optimized, then set it to the ring frame machine as raw material and the desired responses are tested. During yarn preparation in the ring frame, the end breakages were counted, starting from the initial doff to the full doff, in an interval of 30 min and then the end breakages are calculated per 100 spindles per hour. Specific strength is the mass stress at breaking point also known as tenacity expressed as gm/tex. A measurement performed according the constant rate of extension principle with testing speed 5 m/min, specimen length 500 mm and pretension 0.5 cN/tex. For computation of specific strength, Equation (7) is used. Specific strength or tenacity ðgm=texÞ breaking load ðgmÞ ¼ : linear density ðtexÞ
(7)
Irregularity is the percentage mean deviation (PMD) for mass of unit length of yarn. This is caused by uneven fibre distribution along the length of the strand. The mass per unit length is measured first. Then the deviation from the mean is calculated, and PMD is derived and used as a measure of irregularity. Breaking extension is the increase in length produced by stretching a yarn to its breaking point expressed as the percentage of its initial length. The test is carried out on a dynamometer with a constant stretching speed
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under the gauge length of 500 mm, pretension 0.5 cN/tex and stretching speed 25 mm/min. Hairiness is a measure of the amount of fibres protruding from the structure of the yarn. The hairiness index corresponds to the total length of protruding fibres within the measurement field of 1 cm length of the yarn. Uster hairiness index is used to get the total length of hairs. Imperfection referred to the frequently occurring yarn faults comprises Thin places (diameter, ϕ – 50%), Thick places (ϕ + 50%) and Neps (ϕ + 200%). The yarn is prepared and the values of individual responses are derived according to the above methods and the required calculations are performed using the software Design-Expert 8.0.
Table 1. Process parameters with their actual values and coded levels. Coded levels Variables
−1
0
1
Spindle speed (A) Yarn TM (B) Roving TM (C)
15,000 3.7 1.1
17,000 3.9 1.3
19,000 4.1 1.5
different yarn characteristics are determined by conducting trials as shown in Table 2. Response surface equations for various responses along with the R2 and lack-of-fit F-value values are given in Table 3. The response surface equations given in Table 3 are derived using Equations (1)–(3).
Experimentation The experiments were performed in Jingwei JWF-1416 Roving Frame for preparation of roving with varying twists and the yarn prepared on Ring Frame EJM 138L1008. The carded cotton yarn samples were produced using all the combinations of three variable factorial design proposed by Box & Behnken. The actual levels of all three variables are taken within the industrially acceptable range. The atmospheric condition varies in the range during yarn preparation humidity in spinning room 45–63%, and temperature 30–35 °C. Results and discussions Coded levels with their respective values for the process parameters are shown in Table 1. Various responses of
Table 2. Run order
Experimental data for three variable Box and Behnken designs.
Box–Behnken design Spindle speed rpm (A)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Effect on end breakage rate Figures 2a and 2b displays the effect of spindle speed and yarn TM on end breakage rate. It is clear from the contour plot that with the increase in spindle speed end breakage rate also increases but breakage rate decreases with increase in yarn TM. It is observed from the experimental data that breakage rate decreases with increase in roving TM also. This can be explained due to the fact that as the spindle speed increases the spinning tension increases beyond the safe spinning tension, and therefore causes end breakages. When yarn twist increases, it reduces the spinning triangle which causes the better gripping of the fibre in the spinning zone and causes reduction in end breakages. Also, when roving TM increases, the
0 −1 1 1 1 0 0 −1 0 −1 0 −1 0 1 0
Yarn TM (B) 1 −1 0 1 0 0 1 0 0 0 −1 1 0 −1 −1
Responses (experimental result) Roving TM (C)
Breakage rate per 100 spindle per hour
Specific strength gm/tex
1 0 1 0 −1 0 −1 1 0 −1 1 0 0 0 −1
5.7 4.4 11.6 10.9 13.5 6.13 5.99 4.11 6.32 4.31 7.99 4.09 6.51 15.8 9.13
17.09 15.61 15.93 16.35 15.87 16.09 16.27 15.83 16.13 15.97 15.75 16.07 16.19 15.43 15.51
Breaking extension Irregularity % 8.31 9.11 8.39 8.93 9.25 8.63 8.91 8.57 8.69 9.09 8.47 8.79 8.61 8.87 9.03
3.53 3.97 3.3 3.59 4.19 3.67 4.39 3.41 3.71 4.43 3.49 4.19 3.81 3.47 4.41
Hairiness index
Imperfection per km
5.51 5.85 5.71 5.67 5.85 5.81 5.74 5.59 5.75 5.79 5.91 5.73 5.77 6.11 5.87
122 95 128 99 108 83 103 113 78 98 125 81 85 93 119
The Journal of The Textile Institute Table 3.
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Response surface equations, different responses and corresponding R2 value and lack-of-fit F-value.
Parameter
Response surface equation
Breakage rate Specific strength Irregularity Breaking extension Hairiness index Imperfection
6:46 þ 4:36A 1:33B 0:44C 1:15AB þ 1:81A þ 0:63B 16:15 þ 0:43B þ 0:12C 0:26A2 8:62 0:068B 0:32C þ 0:095AB 0:085AC þ 0:22A2 þ 0:071B2 3:72 0:18A þ 0:045B 0:46C þ 0:10B2 þ 0:13C 2 5:81 þ 0:047A 0:14B 0:066C 0:080AB 0:068BC 0:067C 2 83:38 þ 5:12A 3:38B þ 7:50C þ 5:00AB þ 7:58B2 þ 27:33C 2 2
2
R2 value
Lack-of-fit P-value (0.05) indicates that the lack-of-fit value is not significant relative to pure error which is desired.
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Effect on breaking extension Figures 5a and 5b represent the influence of spindle speed and roving TM on yarn breaking extension. It is
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observed from the contour plot that yarns’ breaking extension decreases with increase in spindle speed and roving TM. The effect of yarn TM is less compared to roving TM and spindle speed. This can be ascribed that as the roving twist increases, drafting force increases which causes straightening of fibres as they pass through the drafting zone thereby reducing the breaking extension of the yarn. When the spindle speed and yarn TM increase simultaneously the spinning tension increases which also causes the straightening of the fibres and therefore a reduction takes place in the value
Figure 6a.
Three-dimensional response surface showing hairiness index of yarn TM and roving TM.
Figure 6b.
Contour plot of response surface showing hairiness index of yarn TM and roving TM.
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of Breaking extension of the resulting yarn. From Table 3 it is shown that R2 value of the model is 0.9561 which is very close to 1. The meaning behind this is that 95.61% variation can be explained by this model and only 4.39% of total variation cannot be explained, which is an indication of good accuracy. A lack-of-fit value of 0.3050 (>0.05) indicates that the lack-of-fit value is not significant relative to pure error which is desired.
Effect on yarn hairiness index Figures 6a and 6b gives a clear idea about the effect of yarn TM and roving TM on yarn hairiness. It is clear from the contour diagram that yarn hairiness decreases with the increase in roving TM as well as the yarn TM. When both increase simultaneously then the yarn hairiness decreases. And it is found from the experimental result that the impact of spindle speed on
Figure 7a.
Three-dimensional response surface showing yarn imperfection of spindle speed and roving TM.
Figure 7b.
Contour plot of response surface showing yarn imperfection of spindle speed and roving TM.
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The Journal of The Textile Institute yarn hairiness is less compared to roving TM and yarn TM. This is due to the fact that when roving twist increases, the fibre becomes more compact and higher twist exerts greater control over the short fibre and reduces the amplitude of the drafting wave. On the other hand, when yarn TM increases the twist flow right up to the front roller nip that results in short spinning triangle. This causes better binding of edge fibres that consequently reduce yarn hairiness. Increases in the spindle speed means spinning balloon size also increases which increases the frictional contact between yarnballoon control ring and yarn-ring traveller. This may lead to more rubbing actions on the yarn surface thereby increases yarn hairiness. From Table 3 it is shown that R2 value of the model is 0.9506 which is very close to 1. This implies 95.06% variation can be explained by this model and only 4.94% of total variation cannot be explained, which is an indication of good accuracy. A lack-of-fit value of 0.3572 (>0.05) indicates that the lack-of-fit value is not significant relative to pure error which is desired. Effect on imperfection From Figures 7a and 7b it is clear that imperfection increases with increase in spindle speed. With increase in roving TM, imperfection decreases initially and again increases with increase in roving TM. It has been observed from the experimental data that effect of yarn TM on imperfection is not so significant. These results can be explained due to the fact that with the increase in roving twist, control over the fibre in the drafting zone increases which leads to better uniformity of the fibre distribution in the yarn. But when roving TM increases beyond the specific limit, roving becomes
Figure 8.
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more compact and causes uneven drafting of the roving which leads to an increase in imperfection in the yarn. As the spindle speed increases the drafting speed also increases. Therefore, the ratio of dynamic to static frictional force of the drafted ribbon increases. As a consequence, the floating fibres would like to take the intermediate speed and ensure shuffling of the fibres in the drafting zone. These factors may be responsible for the decrease in imperfections. But, at higher spindle speed, there will be more rubbing action between yarn surface and thread guide, balloon control ring and traveller. As a result, long hair may get rolled up and cause neps. This leads to more imperfections at higher spindle speed. From Table 3 it is shown that R2 value of the model is 0.9662 which is very close to 1. This indicates that 96.62% variation can be explained by this model and only 3.38% of total variation cannot be explained, which is an indication of good accuracy. A lack-of-fit value of 0.4852 (>0.05) indicates that the lack-of-fit value is not significant relative to pure error which is desired. Design-Expert software uses the simultaneous optimization technique that uses Desirability functions. The general approach for this is to convert each response into individual desirability function which ranges from 0 to 1. For this purpose, target for different responses are set according to their maximum or minimum properties. On the basis of this function, the optimum value of the spinning process parameters are spindle speed 17,020 rpm (0-level), yarn TM 4.1 (+1-level) and roving TM 1.3 (0-level). The optimal values of the input factors as well as the responses are presented through ramp diagram (Figure 8). Using this setting of process parameters, the predicted values for each individual response are derived as shown in Table 4.
Ramp diagram showing optimal results with desirability value.
12 Table 4.
Hasanuzzaman et al. Conformation report of responses at 95% confidence level (α = 0.05).
Response Breakage rate Specific strength Irregularity Breaking extension Hairiness Imperfection
Prediction
Std. Dev.
SE (n = 1)
95% PI low
95% PI high
6.46 16.15 8.62 3.72 5.81 83.38
0.4373 0.1870 0.0451 0.1082 0.0413 4.0457
0.4851 0.1999 0.0500 0.1200 0.0441 4.4883
5.34 15.71 8.51 3.44 5.71 73.03
7.58 16.59 8.74 3.99 5.91 93.73
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Conclusion There are many situations where quality engineers encounter several responses simultaneously. In such multiple response situations the optimization of parameters are accomplished through the mathematical modelling. In this research the experimental investigation demonstrates the effect of spinning parameters such as spindle speed, yarn TM and roving TM on the yarn properties like yarn hairiness, irregularity, specific strength, imperfection, breakage rate and breaking extension. The optimal values obtained from the analysis for the input variable i.e. spindle speed, yarn TM and roving TM are 17,000 (middle level) rpm, 4.1 (high level) and 1.3 (middle level), respectively. The high R2 (co-efficient of determination) value for all the responses indicate that there is high correlation between the input parameters and individual responses. This research shows that with increased spindle speed, the end breakage rate as well as the yarn imperfection increases and the yarn breaking extension decreases. Yarn specific strength and irregularity initially improved with increase in spindle speed but thereafter deteriorated with further increases in speed. The spindle speed, however, does not affect more on the yarn hairiness index compared to other factors. Most of the yarn-quality parameters are improved with increase in roving TM but yarn breaking extension decreases and yarn imperfection initially decreases with increase in roving TM but increases with further increase in roving TM. Yarn breakage rate, specific strength, irregularity and yarn hairiness index improved with increase in yarn TM but slightly improved the breaking extension and effect on yarn imperfection is not very significant as imperfection is mostly generated in drafting zone and there is no control of yarn TM on drafting zone. This work, based on the above, successfully brings out an insight about the type of relationship amongst the process variables affecting several qualitative output responses. References Abbasi, S. A., Peerzada, M. H., & Jhatial, R. A. (2012, July). Characterization of low twist yarn: Effect of twist on physical and mechanical properties. Mehran University
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on strength characteristics of cotton yarns. Fibres & Textiles in Eastern Europe, 116, 90–543. Kumar, A., & Nishkam, A. (2005, June). Effect of inter-fibre friction on yarn quality. Indian Journal of Fibre & Textile Research, 30, 148–152. Li, S. Y., Xu, B. G., Tao, X. M., & Feng, J. (2011, June). Numerical analysis of the mechanical behavior of a ringspinning triangle using the finite element method. Textile Research Journal, 81, 959–971.
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Mahmood, N., Jamil, N. A., Haq, A. U., & Javed, M. I. (2004, May). Effect of some mechanical variables in condensed spinning of cotton yarn. Pakistan Textile Journal, 5, 1–4. Mohamed, A. P., & Veerasubramanian, D. (2009, June). Roving twist and its significance. Indian Textile Journal, 119, 20. Tang, H. B., Xu, B. G., & Tao, X. M. (2009, September). A new analytical solution of the twist wave propagation equation with its application in a modified ring spinning system. Textile Research Journal, 80, 636–641.
