Journal of Engineered Fibers and Fabrics 81 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

Grey Relational Analysis to Determine the Optimum Process Parameters for Open-End Spinning Yarns

Hossein Hasani, Somayeh Akhavan Tabatabaei, Ghafour Amiri

Isfahan University of Technology, Isfahan IRAN

Correspondence to:

Hossein Hasani email: h_hasani@cc.iut.ac.ir ABSTRACT This article focuses on an approach based on the Taguchi method with grey relational analysis for optimizing the process parameters for open-end spun yarns with multiple performance characteristics. A grey relational grade obtained from the grey relational analysis is used to optimize the process parameters. Optimal process parameters can then be determined by the Taguchi method using the grey relational grade as the performance index. CVm%, hair number per meter, and tenacity of yarn were selected as quality characteristics. Using these characteristics, the process parameters, including rotor speed, rotor diameter, opener speed, yarn linear density and navel type are optimized. The raw materials used in this investigation were cotton fibers (35%) and cotton waste (65%) collected from ginning machines. The Experimental results show parameter rotor speed has the most significant effect on the multiple performance characteristics. Keywords: Optimization, Grey relational analysis, Cotton wastes, Rotor spinning, Yarn quality INTRODUCTION In the rotor spinning system, yarn can be spun from cotton waste according to the desired end uses. No other spinning system exists enabling this economical application. The reuse of recovered fibers in the spinning process has been discussed by many researchers. [1, 2, 3] The results of several investigations [3, 4, 5, 6, 7] have revealed that machine parameters such as rotor diameter, rotor diameter opening covering type, and opening roller rotational speed significantly affect yarn physical and mechanical properties. Thus, the optimum machine parameters will be important to achieve the best desired yarn properties. Previously, the Taguchi Method was used to analyze optimal process parameters of a single quality characteristic. This method focused on optimizing a single quality response. [8] However, products in some processes have more than one quality response which should be considered. The Taguchi method

primarily uses engineering judgment to decide optimal factor levels for multi-responses, which increases uncertainty during the decision-making process. [9] This problem can be solved by the grey system theory introduced by Deng. [10] Chen et al. [11] proposed the integration of grey relational analysis and the Taguchi Method to resolve multiple quality characteristics. This method transforms multiple quality characteristics into single grey relational grades. By comparing the computed grey relational grades, the arrays of respective quality characteristics are obtained in accordance with response grades to select an optimal set of process parameters. In this paper, using the grey relational method, different process parameters of the rotor spinning system such as rotor diameter, rotor speed, yarn linear density, navel type, and opening roller speed were optimized to achieve the best multiple quality characteristics. EXPERIMENTAL The raw materials used in this investigation were cotton fibers and cotton waste collected from ginning machines. Fiber properties of cotton and wastes were measured by the Spinlab 900 according to ASTM D4605. A summary of raw fiber properties is included in Table I. The blending of cotton fibers (35%) and waste (65%) was carried out at the first passage in the drawing frame. A second passage was used to improve the homogeneity of the blending. Slivers were used to produce yarns with three different linear densities Ne 12, Ne 16 and Ne 20 on an Elitex rotor-spinning machine. Taguchi’s experimental design was used to produce the yarn samples and analyze the effect of each of the controllable factors on multiple responses. The controllable factors which considered in this research were rotor diameter and speed, opening roller speed, navel type and yarn linear density. The different levels of these factors are shown in Table II. The orthogonal array L27 Table III was used because it

Journal of Engineered Fibers and Fabrics 82 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

requires only twenty-seven runs for combinations of five controllable factors varied at three levels. Samples were kept in standard testing condition for 24 hours prior to testing. The yarn hairiness, tenacity and evenness were the responses in this study. For each sample, a 500 meter length of yarn was tested on a Zweigle G 566 hairiness tester at a yarn speed of 50 m/min to obtain the number of hairs per meter. The number of hairs exceeding 3 mm was measured. Thirty tests were necessary to obtain average yarn hairiness values. Standard method ASTM D2256 was used to determine single yam strength (cN/tex) by the Instron. The testing speed was 60 mm/min, pretension force was 15cN, and the gauge length was 500 mm. For each yarns sample, ten samples were taken to obtain an average value. Yarn unevenness was measured with reference to ASTMD 1425, by the Uster Tester 3 at 100 m/min for 5 minutes. TABLE I. Fiber properties summary.

TABLE II. Parameters and their levels.

Grey Relational Analysis Method In the grey relational analysis, experimental results (CVm%, tenacity and number of hair per meter) were first normalized and then the grey relational coefficient was calculated from the normalized experimental data to express the relationship between the desired and actual experimental data. Then, the

grey relational grade was computed by averaging the grey relational coefficient corresponding to each process response (3 responses). The overall evaluation of the multiple process responses is based on the grey relational grade.

TABLE III. Experimental design (L27).

As a result, optimization of the complicated multiple process responses can be converted into optimization of a single grey relational grade. In other words, the grey relational grade can be treated as the overall evaluation of experimental data for the multi response process. Optimization of a factor is the level with the highest grey relational grade. [9] Data Pre-Processing is normally required, since the range and unit in one data sequence may differ from others. It is also necessary when the sequence scatter

Journal of Engineered Fibers and Fabrics 83 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

range is too large, or when the directions of the target in the sequences are different. [9] In the study, a linear data preprocessing method for the yarn tenacity is the higher-the-better and is expressed as:

(1)

Yarn unevenness indexes (CVm%) and hair number of yarn per meter, which are the lower-the-better can be expressed as:

(2)

where xi (k) is the value after the grey relational generation, min yi (k) is the smallest value of yi (k) for the kth response, and max yi(k) is the largest value of yi(k) for the kth response. An ideal sequence is x0(k) (k=1, 2, 3) for three responses. The definition of the grey relational grade in the grey relational analysis is to show the relational degree between the twenty-seven sequences (x0(k) and xi(k), i=1, 2, . . . , 27; k=1, 2, 3). The grey relational coefficient ξi(k) can be calculated as:

(3)

Where is the difference of

absolute value between x0(k) and xi(k); ϛ = distinguishing coefficient (0_1); ∆min, smallest value of ∆0i; and ∆max, largest value of ∆0i.. After averaging the grey relational coefficients, the grey relational grade Ύi can be obtained as:

(4)

where n is the number of process responses. The higher value of the grey relational grade represents the stronger relational degree between the reference sequence x0(k) and the given sequence xi(k). As mentioned before, the reference sequence x0(k) is the best process response in the experimental layout. The higher value of the grey relational grade means that the corresponding cutting parameter is closer to optimal. [9] In other words, optimization of the complicated multiple process responses is converted into optimization of a single grey relational grade. [8]

RESULTS AND DISCUSSIONS A level average analysis was adopted to interpret the results. This analysis is based on combining the data associated with each level for each factor. The difference in the average results for the highest and lowest average response is the measure of the effect of that factor. The greatest value of this difference is related to the largest effects of that particular factor. Data preprocessing of each performance characteristic and the experimental results for the grey relational according to formulas (3) and (4) are given in Table IV and V. TABLE IV. Data preprocessing of each performance characteristic.

Journal of Engineered Fibers and Fabrics 84 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

TABLE V. Grey relational coefficient (ξi) of each performance characteristic and Grey relational grade (ɣ) calculated from them.

RUN

1 0.409 0.633 0.496 0.513

2 0.545 0.471 0.424 0.48

3 0.461 0.749 0.354 0.521

4 1 0.651 0.517 0.723

5 0.855 0.333 0.482 0.557

6 0.897 0.662 0.428 0.663

7 0.336 1 0.361 0.566

8 0.333 0.826 0.428 0.529

9 0.335 0.861 0.401 0.533

10 0.475 0.913 0.342 0.577

11 0.438 0.905 0.354 0.566

12 0.42 1 0.405 0.608

13 0.566 0.522 1 0.696

14 0.537 0.913 0.546 0.665

15 0.468 0.827 0.549 0.615

16 0.914 0.703 0.523 0.714

17 0.783 0.688 0.519 0.664

18 0.765 0.725 0.598 0.696

19 0.603 0.714 0.344 0.554

20 0.579 0.657 0.403 0.546

21 0.658263 0.474664 0.335004 0.489

22 0.570388 0.812389 0.383147 0.589

23 0.554245 0.842202 0.333333 0.577

24 0.550351 0.991361 0.419899 0.654

25 0.560859 0.880998 0.35025 0.597

26 0.54023 0.69863 0.506963 0.582

27 0.729814 0.978678 0.355813 0.688

According to the Taguchi method, the statistic delta defined as the difference between the high and the low effect of each factor, was used. A classification can be done to determine the most influent factor. When so done, the multiple objective optimization problems are transformed into a single equivalent objective function optimization problem. The higher grey relational grade will be close to the optimal condition. Using the grey relational grade value, the mean of the grey relational grade for each level of different factors, and the total mean of the grey relational grade is summarized in Table VI. Then a response graph of the grey relational analysis is obtained by main effect analytic computation, as shown in Figure 1. The response graph indicates the

optimal factorial sets: A2, B2, C2, D3 and E1., i.e. a yarn linear density of 16 Ne, a rotor speed of 48,000 r.p.m., an opener speed of 8400 r.p.m., a rotor diameter of 66 mm, and a navel without flute. TABLE VI. Response table for GRG values.

Grey

rel

atio

nal g

rade

201612

0.650

0.625

0.600

0.575

0.550

530004800041000 970084007350

665448

0.650

0.625

0.600

0.575

0.550

321

Yarn linear density Rotor speed Opener speed

Rotor diameter Navel type

Response graph for mean grey relational grades

 FIGURE 1. Response graph for mean grey relational grades.

According to the results presented in Table VI, for cotton-waste (35/65) spun yarns, rotor speed has the largest effect on the multiple yarn quality indexes. Factor yarn linear density is second and is followed by factor rotor diameter, factor opener speed and factor navel type. Considering this principle, the recommended levels are summarized in Table VII. The empirical relationships between yarn quality and the five controllable factors were analyzed using MINITAB software. The optimum conditions for process factors have been represented in Table VII. TABLE VII. Optimum conditions of different factors.

Journal of Engineered Fibers and Fabrics 85 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

Analysis of Variance The purpose of the ANOVA is to investigate which factors significantly affect the performance characteristic. This is accomplished by separating the total variability of the grey relational grades, which is measured by the sum of the squared deviations from the total mean of the grey relational grade, into contributions by each machining parameter and the error. [9] The percentage contribution by each factor to the total sum of the squared deviations SST can be used to evaluate the importance of the cutting parameter change on the performance characteristic. In addition, the F test can also be used to determine which factor has a significant effect on the performance characteristic. Usually, the change of a determined factor has a significant effect on the performance characteristic when the F value is large. Results of the ANOVA Table VIII indicate that rotor speed is the most significant factor for affecting the multiple performance characteristics. Based on the previous discussion, the optimal factors are rotor speed at level 2, Yarn linear density at level 2, and rotor diameter at level 2 and opener speed at level 2. The results show that the navel type has no significant effect on the multiple performance characteristics. TABLE VIII. Analysis of variance table of process factors.

Prediction and Validation of the Grey Relational Grade of Optimum Result After the optimal level of the different factors is selected, the final step is to predict the performance characteristic using the optimal level of factors.

(5)

The estimated grey relational grade using the optimal level of process factors can be calculated as where total mean of the grey relational grade, mean of the grey relational grade at the optimal level,

and q number of process factors that significantly affect the multiple performance characteristics. Based on Eq. (5), the estimated grey relational grade using the optimal process parameters can then be obtained. Table IX shows the results of the confirmation experiment using optimal factors. As shown in Table IX, Yarn tenacity increased from 8.74 cN/tex to 10.94 cN/tex, hair per meter of yarn is reduced from 4.8 to 4.1, and yarn CVm% is improved from 17.29 to 16.29. Through this study, it is clearly shown that the multiple performance characteristics are improved. TABLE IX. Results of yarn quality using the initial and optimal process factors.

CONCLUSION A grey relational grade obtained from the grey relational analysis was used to optimize the process parameters of open-end spinning system with multiple performance characteristics (CVm%, hair number per meter, and tenacity of yarn). The experimental results show that parameter rotor speed has the most significant effect on the multiple performance characteristics. Factor yarn linear density is second and is followed by factor rotor diameter, factor rotor opener speed, and factor navel type. The result of the confirmation tests yielded an improvement of 0.278 in grey relational grade, after validation. Therefore, the integration of grey relational analysis and the Taguchi Method can be applicable for the optimization of process parameters and help to improve process efficiency.

Journal of Engineered Fibers and Fabrics 86 http://www.jeffjournal.org Volume 7, Issue 2 – 2012

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Indian Textile Journal, April, 1997, pp. 16-18.

[2] M. Taher Halimi; M. Ben Hassen; B. Azzouz; F. Sakli, Effect of cotton waste and spinning parameters on rotor yarn quality, Journal of the Textile Institute, 2007, Vol. 98 No. 5, pp. 437–442.

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[6] A. Barella; A. M. Manich, The Influence of the Spinning Process, Yarn Linear Density, and Fiber Properties on the Hairiness of Ring-spun and Rotor- spun Cotton Yarns, Journal of the Textile Institute, Volume 79, Issue 2, 1988, pp. 189 – 197.

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AUTHORS’ ADDRESSES Hossein Hasani Somayeh Akhavan Tabatabaei Ghafour Amiri Isfahan University of Technology Textile Engineering Department Isfahan 84156-83111 IRAN