Multiple response optimization of sizing machine settings and sized yarn tensile properties using advanced method of experimental design

On a loom, the warp yarns experience exceptionally high mechanical stresses and strains, as well as significant abrasion from friction. As a result, significant yarn breakages cause loom stoppages and, hence, production and quality interruptions. To mitigate this problem, the warp yarns should be treated with a thin, strong film of an appropriate adhesive. The aim of this study is therefore, to investigate the effect of sizing machine parameters on tensile properties of the yarn and to optimize the sized yarn tensile properties. Design expert 11 software with Box-Behnken design has been employed to design the research, analyze the results of experiments, and optimize the responses. In this research, three factors, each at three levels (wet zone yarn tension (A) (340, 380, and 420 N), squeezing roller pressure (B) (13, 15, and 17 N), and sizing machine speed (C) (30, 49, and 68 m/min), as well as three response variables (gain strength, loss elongation, and stretch), are considered. 15 samples of sized yarn have been produced with various combinations of the given factors, and the values of the response variables are measured for each sample. It has been observed that wet zone yarn tension and squeezing roller pressure have a significant effect on gain strength, stretch, and loss elongation. According to the regression analysis, gain strength has a negative relationship with wet zone yarn tension and a positive relationship with squeezing roller pressure. In the other case, both wet-zone yarn tension and squeezing roller pressure have a positive and significant effect on loss elongation and yarn stretch. At 340 N wet zone yarn tension, 13 N squeezing roller pressure, and 51 m/min sizing machine speed, the optimum values of gain strength (32.7 cN/tex), loss elongation (18.5%), and stretch (1.4%) were obtained. The methodologies employed in this study revealed the empirical relationship between the factors and the responses, the interaction effects of the factors on the responses, and multiple response optimizations. The optimized result of this study can be applied to the warp yarn sizing and can improve the tensile properties of the yarn and the loom’s efficiency significantly.


Introduction
The most traditional and aristocratic way to dress is with woven fabrics.It is one of the oldest methods of fabric manufacturing and is made by the interlacement of warp and weft threads. 1 In the weaving process, the warp yarns on a loom undergo extreme mechanical actions of frequent strains and stresses as well as considerable abrasion due to friction. 2Consequently, the raw yarn would develop a substantial amount of protrude fibers on its surface, which hinders fabric formation due to the creation of balls in dense warps, lint generation, inter-yarn entanglements, and inter-fiber clinging.As a result, there are excessive yarn breakages and, hence, loss of production and quality deterioration of fabric.To reduce these problems, a strong warp yarn shall be provided for weaving.The warp yarns shall always be treated with a thin, strong film of an appropriate adhesive."This process of coating the warp yarns is called sizing." 3 The old saying that the core of weaving is sizing still holds true.This assertion is even more vital in the current situation, because loom speeds are 10 times faster than shuttle looms. 4As a result, it is a very crucial and significant step in warp yarn preparation.The yarn is sized before being utilized for weaving using a sizing machine.The beam creel, size box, drying chamber, and winding head are the four main parts of a sizing machine.The warp sheet is submerged in the adhesive and binder paste during this procedure, and then the warp is appropriately squeezed to remove the surplus glue.The warp is then dried and wound on the weaver beam.After sizing, warp yarn tensile strength increases, and the yarn's hairiness also reduces significantly. 5Properly sizing also improved abrasion resistance with a minimal loss of the warp yarn extensibility. 6 variety of sizing machine parameters are responsible for the correct preservation of sized yarn quality.Different yarn tension zones, sizing machine speed, squeezing roller pressure, saw box temperature, and size paste viscosity are some of the crucial characteristics that must be regulated during sizing. 2,6o prevent slackness in the warp yarn, a sufficient amount of tension is required.When yarn is processed on a sizing machine, the yarns must be under moderate tension.The excessive tension applied to the warp yarn during sizing results in a permanent stretch in the yarn.This permanent stretch causes a reduction in elongation at break of sized yarn and this elongation is known as stretch.If the extensibility of the sized yarn is below a certain level, the yarns are likely vulnerable to breaking during weaving. 1,7ive zones of tension are available in the sizing machine that can affect the stretch of the sized yarn.These are demonstrated in Figure 1 as: (1) from the first squeezing roller (1) to the final warper beam (2), (2) from the first to the second squeezing roller (2-3) and up to the first drying cylinder (3-4), (3) from the first to the last drying cylinder (4-5), (4) from the last drying cylinder to the drag roll (5-6), and (5) in the winding zone (6-7). 7The wet (sizing) zone yarn tension has a very prominent effect on the stretch of the yarn because, as it is in the wet state, its extensibility is extremely high upon application of tension.
The other factor affecting the yarn's property is squeezing roller pressure.The extent of size paste penetration in the yarn and the amount of sizing material absorbed by the yarn depend on the squeeze roller pressure. 1High squeezing pressure increases fiber-to-fiber and fiber-to-size attachment, packing density, and size penetration, resulting in improved surface quality, breaking strength, and weaving efficiency. 8,9On the other hand, excessive pressure can flatten the yarn and increase size penetration, which can have an impact on the yarn's look and next operations.The density of the sheet and the material being sized determine how much pressure should be used. 10ia and Zhang 11 indicated the effect of sizing machine speed on the coating and penetration rate of the size material on the yarn.According to the study, the coating rate of the sizing solution on the yarn has a direct relation with the speed of the sizing machine and an inverse relation with the squeezing roller pressure."As a result, when the sizing machine speed is fast, the penetration rate will be low and the coating rate will be high; on the contrary, the result will be an opponent."The study by Sabır and Sarpkaya 12 also revealed that sizing machine speed is the most dominant parameter that determines the strength of sized yarn and loom efficiency.
Many studies have been conducted to examine how different sizing machine settings affect the yarn's tensile properties.However, the methodologies employed in the earlier study did not reveal the empirical relationship between the factors and the responses, and the interaction effects of the factors on the responses have not been studied.In addition, the simultaneous optimization of the sizing machine settings that leads to the optimal mechanical properties of sized yarn has never been studied.In a practical situation, when two sizing machine parameters increase or decrease at the same time, the mechanical properties of the warp yarns are significantly affected.To the best of our knowledge, this kind of research has not yet been done.
In this research, the effects of squeezing roller pressure, wet zone yarn tension, and speed of the sizing machine on the gain strength, stretch, and loss elongation of sized yarn have been investigated using advanced methods of analysis.Design expert 11 software programs with a Box-Behnken design have been employed to design the experiment and examine the results of the experiment extensively.

Materials
The gray yarn samples were obtained from Bahir Dar Textile Share Company, with the properties explained in Table 1.The yarn samples have been produced by a rotor spinning machine (R923).

Methods
In this research, the effects of squeezing roller pressure, wet zone yarn tension, and speed of the sizing machine on the tensile properties of sized yarn were studied.The samples of sized yarn have been produced with a Rotal-Karl Mayer sizing machine model (SRL-SMR-SP).Other sizing machine and size box variables like size liquor concentration, viscosity, temperature, and R.F.% have been kept constant.
Experimental design.In this research, the effects of squeezing roller pressure, wet zone yarn tension, and speed of sizing machine on the gain strength, stretch, and loss elongation of sized yarn have been investigated using advanced methods of analysis.Design expert 11 software with a Box-Behnken design have been employed to design the experiment and examine the results of the experiment extensively.ANOVA, regression analysis, 3D plots (to examine the interaction effects of two factors on the response variables), and each factor's effect on the response/dependent variable were used in the analysis.The designated factors and levels of the factors are shown in Table 2. Fifteen experimental runs have been formed by the design expert 11 software randomly as indicated in Table 3 and 15 samples of sized yarn have been produced.

Characterization of responses variables
Gain strength and loss of elongation.The tensile strength and elongation properties of sized and unsized yarn were measured by a universal tensile strength tester (STATIMAT ME + tensile tester) according to ISO 2062. 13Five replicates have been taken for each test, and the average value was taken for analysis.The formulas used to calculate the amount of gain strength and loss elongation due to the sizing process are shown in equations (1) and (2). 14 Stretch.In this research, the stretch of the warp yarn is obtained from the sizing machine.In the Karl Mayer-Rotal sizing machines, the value of stretch is clearly shown on the machine control panel; therefore, the average value of sized yarn stretch is directly obtained from the control panel of sizing machine after 200 m of yarn have been sized for each sample.

Result and discussion
A 95% confidence level was used to examine the variation in the tensile properties of the sized warp yarn caused by changes in the sizing machine process parameters.If the p-value is less than 0.05, the factors affects the response significantly; if the p-value is higher than 0.05, the factor has no significant impact on the response. 15,16The effects of each factor on gain strength, loss elongation, and stretch are explained very well in the following sections.

Effect of wet zone yarn tension, squeezing roller pressure, and sizing machine speed on gain strength of warp yarn
In the sizing process, the gain strength of the yarn is affected by the sizing machine parameters like tension, squeezing roller pressure, and speed.For better quality sized yarn, uniform tension and optimum squeezing roller pressure are required. 10In this section, the effect of these factors on the gain strength of sized yarn has been investigated.Fifteen samples of fabric have been produced according to the design of the experiment, as demonstrated in Table 3.
As illustrated in Table 4, the wet zone yarn tension and squeezing roller pressure have a significant impact on the gain strength of the yarn.Not only the main effect but also the interactions between wet zone yarn tension and squeezing pressure, squeezing pressure and sizing machine speed, and quadratic terms (A 2 , B 2 , and C 2 ) have also had significant effects on the average sized yarn strength.The wet zone yarn tension has the most significant influence on the strength of sized yarn with p < 0.0001.
Table 5 shows the predicted R 2 -value (0.9152) is in reasonable agreement with the adjusted R²-value of (0.9800) and the difference is less than 0.2, which means no overfitting and a regression model can properly predict the responses for new observation.Figure 2 also shows, there is a linear correlation between the predicted and experimental values which suggests that the regression model is appropriate and all the actual and predicted values are fitted to straight line showing that the errors are very less.Equation (3) represents regression equations produced by the design expert program in terms of coded parameters for significant factors.The quantitative relationships between variables A, B, and C and their interactions with the response values are described by the regression model equations.It demonstrates a negative relation between the strength of the sized yarn and the wet zone yarn tension, interactions between BC, and the quadratic terms A 2 and C 2 .Nonetheless, there is a positive association between the sized yarn strength and the squeezing roller pressure as well as the interactions between AB and the quadratic term B 2 .
The effects of various sizing machine parameters (wet zone yarn tension, squeezing pressure, and sizing machine speed) on average sized yarn strength are demonstrated in Figure 3. Generally, the tensile strength of the yarn is influenced to a greater extent by the wet zonal yarn tension of the sizing machine.The reason is that, in the wet state (sizing zone), the warp yarn is stretched quickly when tension is applied.According to Salama et al. 17 report, 66.7% of the stretch in the sizing process occurs in the wet tension region of the sizing machine.This results in a reduction in gain strength and an increase in loss elongation.As shown in Figure 3(a), the tensile strength of the sized yarn is influenced by the wet zone tension.As the wet zone yarn tension increases, the yarn strength first increases to some extent and then decreases rapidly.The generation of fiber slippage in the yarn structure, which takes place under high wet tension, is the primary cause of the reduction in sized yarn strength.Since the fiber uniformity ratio in the polyester cotton blend yarn is low, fiber-to-fiber friction decreases as tension increases, which results in poor resistance of the yarn to the applied load.This is also in agreement with. 18Figure 3(b) shows a direct correlation between the strength of the sized yarn and the squeezing pressure.This is because higher squeezing pressures allow the size material to penetrate the yarn core more deeply, enhancing inter-fiber binding and the packing density or compactness of the yarn, which is also in agreement with Hari et al. 9 and Patil et al. 19 A high packing density increases fiber cohesion and reduces inter-fiber slippage, which helps increase the strength of the sized yarn, which is also supported by Maatoug et al. 16 The interaction effects of the factors (wet zone yarn tension, squeezing pressure, and sizing machine speed) on average sized yarn strength are demonstrated in Figure 4 using a 3D plot.As indicated in Figure 4(a), the wet zone yarn tension and squeezing roller pressure effects on the strength of the yarn are opposite (i.e.strength increases as squeezing roller pressure increases and decreases as wet zone yarn tension increase).Figure 4(b) shows the interaction of BC has the most significant effect on the yarn strength.At squeezing roller pressure of 17 kN, sizing machine speed of 30 m/min, and constant wet zone tension of 380 N, the gain strength reached a maximum level.That means when the sizing machine speed is at its lowest level, the squeezing pressure should be at its highest level to obtain the maximum gain strength of the yarn.This is because at low speed, the yarn waiting time in the sizing box is greater, and there is enough time for the size material to penetrate into the core of the yarn and higher pressure also assist the penetration of size material in to the core of the yarn.

Effect of wet zone yarn tension, squeezing roller pressure, and sizing machine speed on loss elongation of warp yarn
Elongation refers to the yarn's change in length at breaking force.It is one of the most essential yarn quantitative characters as it has an influence on how woven materials are produced and used. 20,21In the sizing process, this change can occur for several reasons.The tension of the sizing machine, the squeezing roller pressure, and the speed of the sizing machine are among the factors dealt with in this research.Table 6 revealed that the linear variables (wet zone yarn tension and squeezing roller pressure), the interaction variables AC and BC, and the quadratic variables A 2 and C 2 have a significant effect on the elongation loss of the yarn.The wet zone yarn tension has the lowest p-value of <0.0001, which implies that it has the most significant influence on the loss of elongation of sized yarn compared to sizing machine speed and squeezing roller pressure.
The regression model depicted in equation ( 4) show the quantitative effect of significant factors A and B, their interactions and quadratic terms A 2 and C 2 with the response variable values.It shows that wet zone yarn tension, squeezing roller pressure, and interactions between squeezing roller pressure and sizing machine speed have a positive correlation with the elongation loss of the sized yarn.However, the quadratic terms A 2 and C 2 have a negative correlation with the elongation loss of sized yarn.( )− ( ) ( ) Table 5 shows that the values of adjusted R 2 and predicted R 2 for loss of elongation are found to be 0.9635 and 0.8455, respectively.This indicated a high degree of correlation between the actual and predicted values.Similarly, the difference between the adjusted R 2 and predicted R 2 is less than 0.2, which means there is no over-fitting and a regression model can properly predict the responses.In addition, as indicated in Figure 5 there is a linear correlation between the predicted and experimental values, which suggests that the regression model is appropriate for the data.
Figure 6 show that sizing machine speed has no noticeable impact on the elongation loss percentage.However, the wet zone yarn tension and squeezing pressure have a significant effect on the loss of elongation.
Figure 6(a) shows that as wet zone yarn tension increase, the sized yarn loss elongation increases significantly.The loss of elongation is directly related to the degree of stretch and the elasticity of the yarn, which is in agreement with the previous studies. 2,7,17As the yarn tension in the wet state increases, the stretch on the yarn increases, and consequently, it will loss its elongation properties.This is because, in the wet state, the yarn is easily stretchable on application of tension due to the low sliding resistance of the fibers in the yarn in the wet state.This is also in agreement with previous studies. 2,7s stated in Figure 6(b), when the squeezing roller pressure increases, the loss of elongation of the sized yarn increases.The reason is that as the squeezing roller pressure increases, the packing density of the yarn and fiber-tofiber attachment increase, resulting in an interruption in fiber mobility.As a result of this, the yarn's elasticity properties are reduced significantly.Increasing or decreasing the speed of the sizing machine (Figure 6(c)) does not have a significant effect on the loss of elongation; however, it has a significant effect when it interacts with both wet zone  yarn tension and squeezing roller pressure, as indicated in Figure 7(a) and (b).Moreover, 3D plots were constructed to visualize the interaction effect of two independent variables on the loss elongation of the sized yarn.Figure 7(a) and Table 6 with a p-value of 0.0001 show that the interaction effect of sizing machine speed and wet zone yarn tension on the loss of elongation is more significant than the other interaction.When factor A is 340 N and factor C is 30 m/min, the loss elongation reached a minimum level of 13.22% at a constant squeezing pressure of 15 kN.As shown in Figure 7(b) the interaction effect of squeezing roller pressure and sizing machine speed is also significant.

Effect of wet zone yarn tension, squeezing roller pressure, and sizing machine speed on yarn stretch of warp yarn
The yarns are stretched as the yarns move from the creel to the size box, the size box to the drying cylinders, the drying cylinders to the draw rolls, and the draw rolls to the final beam.Depending on the type of yarn being sized, the net stretch must be kept under control to preserve the elasticity of the sized yarn. 10The yarn's extensibility is quite high when tension is applied in the wet zone, and it is the most crucial factor that influences the degree to which the yarn stretches.An analysis is done on the impact of wet zone yarn tension, squeezing pressure, and size machine speed on stretch in this part.
From Table 7, it is observed that the wet zone yarn tension with a p-value of 0.0004 has the largest effect on the yarn stretch, followed by the interactive effect between wet zone yarn tension and sizing machine speed with a p-value of 0.0021 and squeezing pressure with a p-value of 0.0244.
As shown in Table 6, the values of adjusted R 2 and predicted R 2 for stretch are found to be 0.8146 and 0.6377, respectively.This indicates a high degree of correlation between the actual and predicted values.Figure 8 signifies that the actual and predicted values of stretch are close to the straight-line curve, which indicates that the actual and predicted values are nearly equal and the error is very small.
As shown in Figure 9, the sizing machine speed has no noticeable impact on the stretch percentage.However, wet zone yarn tension and squeezing roller pressure have a significant effect on sized yarn stretch.The stretch of the yarn is observed to increase significantly as the wet zone yarn tension (sizing zone) increases as shown in Figure 9(a).The reason for this is that in the wet state, the yarn is easily stretchable by the applied tension, and after stretching the  yarn in the wet zone, the yarn gets less time to return to its original length before drying.According to Salama et al., 17 reports, 66.7% of the stretch in the sizing process occurs in the wet tension region of the sizing machine.Figure 9(b) also shows that the stretch percentage of the sized yarn increases as the squeezing roller pressure increase.
According to the regression equation, sized yarn stretching has a positive relationship with both wet zone yarn tension and squeezing roller pressure.But the interaction effect between wet zone yarn tension and sizing machine speed shows a negative correlation with the stretch of sized yarn as stated in equation (5).
To demonstrate the interaction effect of independent variables on the stretch percentage of the sized yarn, 3D plots are used.Figure 10 show the interaction effect of wet zone yarn tension and sizing machine speed on sized yarn stretch.It revealed that while both wet zone yarn tension and sizing machine speed decreased simultaneously, the stretch percentage of the yarn decreased significantly.When the wet zone yarn is high at higher speed of sizing machine the yarn get short time to return to its original length before drying resulting in permanent stretch.

Response optimization
The optimization technique is an influential tool used to find the required design parameters and the best set of operating conditions.It refers to finding the values of decision variables that correspond to and provide the maximum or minimum of one or more desired objectives.The formulation of objective functions and the selected optimization technique determine the predictability of optimal solutions. 22o find the optimum response values, multiple response optimization approaches were used and Design-Expert (version 11) statistical software was applied to obtain the best compromise of response.A multiple response  approach is adopted from Derringer and Suich. 23ccordingly, the optimization of the response variables and factors is stated in Table 8.As shown in Table 8, the optimum values of gain strength (32.7 cN/tex), loss in elongation (18.5%), and stretch (1.4%) were obtained at 340 N wet zone yarn tension, 13 N squeezing roller pressure, and 51 m/min sizing machine speed.

Conclusion
In this research, the impact of sizing machine tension, squeezing roller pressure, and sizing machine speed on the tensile properties of the yarn was examined.The method applied revealed the mathematical correlation between dependent and independent variables, the interaction effects of independent variables on dependent variables, and multiple response optimizations.In general, the machine parameters involved in the sizing process, such as wet zone yarn tension, squeezing roller pressure, and sizing machine speed, affect the tensile properties of the yarn significantly.The quality of the sized yarn is determined by these factors, and for maximum weaving effectiveness, a good sizing process is crucial.
According to the study's findings, the average sized yarn strength is significantly influenced by wet zone yarn tension, squeezing roller pressure, and sizing machine speed.The squeezing roller pressure has a positive association with the strength of the sized yarn; however, the wet zone yarn tension has a negative correlation with it.In comparison to sizing machine speed and squeezing roller pressure, the wet zone yarn tension has significantly greatest impact on the loss of elongation of sized yarn with p-value of less than 0.0001, and as wet zone yarn tension increase the loss in elongation also increase (i.e. the yarn stretched too much). .
In addition, the findings of this study also revealed that wet zone yarn tension and, squeezing roller pressure significantly affect the average sized yarn strength with p-values of 0.0001 and 0.0052 respectively.From the regression equation, it can be seen that the squeezing roller pressure has a positive association with the strength of the sized yarn, whereas, the wet zone yarn tension has a negative correlation.Compared to sizing machine speed and squeezing roller pressure, wet zone yarn tension has the greatest impact on the loss of elongation of sized yarn, and their correlation with loss of elongation is negative.The optimum values of the responses of gain strength, loss elongation and stretch are 32.7 cN/tex, 17.5% and 1.4% respectively at 340 N wet zone yarn tension, 13 N squeezing roller pressure, and 51 m/min sizing machine speed.The method employed in this research provides comprehensive information on the tensile properties of sized yarn.The upcoming effort will use a screening experiment to thoroughly identify the important parameters among all those involved in the sizing process that affect the tensile properties of the sized yarn.

Figure 2 .
Figure 2. Actual versus predicted values of sized yarn gain strength.

Figure 3 .
Figure 3.Effect of wet zone yarn tension (a), squeezing roller pressure (b) and sizing machine speed (c) of sizing machine on sized yarn gain strength.

Figure 4 .
Figure 4. 3D plot showing interaction effect of squeezing pressure and wet zone yarn tension (a), and squeezing pressure and sizing machine speed (b) on the sized yarn gain strength.

Figure 5 .
Figure 5. Actual versus predicted values of sized yarn loss elongation.

Figure 6 .
Figure 6.Effect of wet zone yarn tension (a), squeezing pressure (b) and sizing machine speed (c) on the loss elongation of sized yarn.

Figure 7 .
Figure 7. 3D plots showing interaction effect wet zone yarn tension and sizing machine speed (a), and squeezing pressure and sizing machine speed (b) on elongation loss of sized yarn.

Figure 8 .
Figure 8. Actual versus predicted values of sized yarn stretch.

Figure 9 .
Figure 9.Effect of wet zone yarn tension (a), squeezing pressure (b) and sizing machine speed (c) on sized yarn stretch.

Figure 10 .Table 8 .
Figure 10.3D plot indicating interaction effect of sizing machine speed and wet zone yarn tension on stretch percentage of sized yarn.

Table 1 .
Unsized yarn properties and sizing conditions.

Table 2 .
Identified factor with their actual levels.

Table 3 .
Average test results of sized yarn response values with different combinations of factors.

Table 4 .
Analysis of variance (ANOVA) results for gain strength percentage of sized yarn.

Table 5 .
Coefficients of determination values for gain strength, loss elongation, and stretch of sized yarn.

Table 6 .
Analysis of variance (ANOVA) results for loss elongation percentage of sized yarn.

Table 7 .
ANOVA results for sized yarn stretch.