The paper discusses the optimization of the continuance of the Damp-Heating ... steaming iron press machine, and the preserving of the lustre of the fabrics.
Estimation and Optimization of the Parameters Preserving the Lustre of the Fabrics Krasimira Prodanova Technical University of Sofia, Faculty of Mathematics and Informatics Abstract. The paper discusses the optimization of the continuance of the Damp-Heating Process of a steaming iron press machine, and the preserving of the lustre of the fabrics. In order to be obtained high qualitative damp-heating processing, it is necessary to monitor parameters such as temperature, damp, and pressure during the process. The purpose of the present paper is a mathematical model to be constructed that adequately describes the technological process using multivariate data analysis. It was established that the full factorial design of type 2^ is not adequate. The research has proceeded with central rotatable design of experiment. The obtained model adequately describes the technological process of damp-heating treatment in the defined factor space. The present investigation is helpful to the technological improvement and modernization in sewing companies. Keywords: Design of Experiment, Multinomial optimization. Damp-heating process. Preserving of the lustre of the fabrics. PACS: 02.50.Sk
INTRODUCTION Experimental methods are finding increasing use in manufacturing to optimize the production process. Specifically, the goal of these methods is to identify the optimum settings for the different factors that affect the production process. Optimization of the continuance of the Damp-Heating Process (DHP) of a steaming iron press machine, and preserving of the lustre of the fabrics, is of great importance in the sewing industry. The problem was set by "Milena" Ltd, a Bulgarian company for clothes sewing, and the experiments were made with fabrics from "Nitex" Ltd, another Bulgarian company. High qualitative damp-heating processing requires monitoring of parameters such as temperature, damp, and pressure during the process. The problems, associated with estimation of the parameters of the equipment for the Damp-Heating Process with steam-electric presses, had been studied in different researches. However, the increase of the efficiency of the Damp-heating process of steam presses has not been investigated enough in the literature. There have been analyzed problems related to the transfer of mass and heat in the different stages of convective drying, with the cooling of the material. Thus, it can be summarized that attempts were made for analysis of some connections between the parameters of the process, but the full influence of the controlled factors, such that to be satisfied the optimal criteria for quality, have not been clarified enough in the literature. The purpose of the present paper is a mathematical model to be constructed which adequately describes the technological process using multivariate data analysis study. CPl 184, Applications of Mathematics itt Ettgitteerittg and Economics edited by G. Venkov, R. Kovacheva, and V. Pasheva © 2009 American Institute of Pliysics 978-0-7354-0750-3/09/$25.00
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Controlled factors during the experiment are as follows: Pressure in the running cylinder; Temperature of the steam; Quantity of the steam. It was established that the full factorial designs of type 2^ are not adequate. The research has proceeded with standard, three-variable, rotatable, central composite design. The obtained model adequately describes the technological process of dampheating treatment in the defined factor space. Statistical computations have been made with STATISTICA, and the optimal values of the parameters, have been found with GINO. The present investigation will be helpful to the technological improvement and modernization in sewing companies. • • •
The Model The investigation is of the continuance of the Damp-Heating Process and the preserving of the lustre of the fabrics. The experiments have been performed at a steam press of type HR-2A-04 HOFFMAN. The continuance of the DHP is measured in seconds. The three factors of interest in the study are the Pressure in the running cylinder, measured in kPa, the Temperature of the steam in °C, and the Quantity of the steam, in mm. The high and low levels of the factors are presented in Table 1. TABLE 1 . Levels of the factors. Factors Labels Pressure P Temperature T Steam S
Low (-1) 340 130 4
High (+1) 600 156 10
It was used standard coding for the levels of the factors. The performed design is full factorial design of type 2^ with one replication. The first dependent variable, continuance of the DHP, is denoted by Yi, and the second response variable, lustre of the fabrics, by Y2. The results of the experiments are in Table 2. The optimization criterion in the experiments in the case of continuance of the DHP (Yi) is minimization of the continuance, and in the case of lustre, is minimization of the lustre (Y2) of the fabrics. Both responses have to be non negative. Initially, it was performed full factorial design of type 2^. TABLE P
2. FiJl factorial design 2^. T S
Yj 1" trial 33 18 20 7 44 28 28 17
Y2 2-' trial 34 19 21 8 45 30 29 19
1" trial 0.88 1.54 1.55 2.09 0.49 1.11 1.08 1.80
2°' trial 0.90 1.55 1.56 2.11 0.51 1.09 1.1 1.78
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It was established that the obtained model is not adequate, in the sense of that after optimization, the optimal value for Yi, is not positive. For the lustre, Y2, the obtained model was assigned as inadequate under the Fcriterion for the lack of fit of the model. Designs with factors that are set at two levels implicitly assume that the effect of the factors on the dependent variable of interest is linear. It is impossible to test whether or not there is a non-linear (e.g., quadratic) component in the relationship between the factors and the dependent variable, if it is only evaluated at two points. Therefore a standard, three-variable, rotatable, central composite design with one replication of the experiments, and standard coding of the independent variables was used. The new levels of the factors are in Table 3.
TABLE 3 . Levels of the factors in the Central Composite Design Center High StarLow StarHigh (-1.68179) (1.68179) Factors Labels Low (0) (+1) Pressure P 340 470 600 251.3669 688.6331 Temperature T 130 143 156 121.1367 164.8633 Steam S 4 7 10 1.95462 12.04538
The designed experiment is in Table 4. TABLE 4. The Central Composite Design. p T S -1 -1 -1 -1 1 1 1 1 -1.68179 1.68179 0 0 0 0 0 0 0 0 0 0
-1 -1 1 1 -1 -1 1 1 0 0 -1.68179 1.68179 0 0 0 0 0 0 0 0
-1 1 -1 1 -1 1 -1 1 0 0 0 0 -1.68179 1.68179 0 0 0 0 0 0
Y 1" trial 33 44 20 28 18 28 8 19 39 17 39 16 8 26 21 20 19 21 22 21
YD
2"' trial 34 45 21 29 19 30 7 17 40 18 40 17 9 27 22 21 21 19 20 20
1" trial 0.88 0.49 1.55 1.08 1.54 1.11 2.09 1.80 1.19 2.37 0.57 1.58 1.41 0.60 1.11 1.1 1.08 1.16 1.14 1.10
2"' trial 0.90 0.51 1.56 1.1 1.55 1.09 2.11 1.78 1.23 2.39 0.60 1.60 1.45 0.90 1.03 1.03 1.05 1.13 1.10 1.03
The obtained effects of the independent variables in Yi and Y2, are shown in Table 5 and Table 6.
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TABLE 5. Effects for Yi. Factors Mean/Interc. (1) Pressure (L) Pressure (Q) (2) Temperature (L) Temperature (Q) (3) Steam (L) Steam (Q) (l)by(2) (l)by(3) (2) by (3)
TABLE 6. Effects for Y2. Factors Effects Mean/Interc. 1.083697 Pressure (L) 0.654279 Pressure (Q) 0.493680 Temperature (L) 0.613641 Steam (L) -0.403258
Effects 20.5806 -13.3266 5.6341 -13.1335 5.2805 10.2911 -2.1441 1.7500 0.5000 -0.7500
p-value 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000001 0.000773 0.284702 0.113552
p-value 0.000000 0.000000 0.000000 0.000000 0.000000
The adjusted coefficients of determination R^ for Yi and Y2 are 0.991 and 0.987 respectively. The p-values for the F-criterion for the lack of fit of the models, are 0.359 and 0.519, which indicates that both models are adequate. The model equations for Yi and Y2, are: Y^=20.580-6.663P+2.817P'-6.567T+2.640T'+5.146S-1.072S' +0.875PT+0.25PS-0.375TS Y2 =1.084+0.327P+0.247P' +0.307T-0.202S The optimal value for Yi is 1.896, and is obtained for P=1.015, T=1.076, and S=1.682, or in natural units, for P=601.95,T=156.988 and S=1.954. The optimal value for Y2 is 0.125, and it is obtained for P=-0.665, T=-1.682, and S=1.682, or in natural units, for P=383.55, T=121.34, and S=1.954. On Figure 1 and Figure 2, the surfaces of Yi and Y2 are depicted .
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FIGURE 1. The surface of Yi if T = 0 (Left), and if S = 0 (Right).
FIGURE 2. The surface of Y2 if T = 0.
CONCLUSION Both dependent variables, continuance of the Damp-Heating Process, and the preserving of the lustre of the fabrics, are presented as functions of the Pressure of the running cylinder. Temperature of the steam, and the Quantity of the steam of a steaming iron press machine. The constructed mathematical models adequately describe the variables in the defined factor space. The optimal values for the dependent variables, and the values of the factors, in which they are obtained, have been found. The present investigation will be helpful for the optimization, and the improvement of the Damp-Heating Process in the manufacturing in the sewing industry.
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ACKNOWLEDGMENTS This research is supported by Technical University of Sofia - grant No091NI00511/2009.
REFERENCES 1. Chechkin, A. et al. (1989) Design of the technological processes for the production of sewing products. Legprombitizdat, Moscow (in Russian). 2. Cochran, W.G., Cox, G.M. (1992). Experimental Designs. John Wiley & Sons, New York. Eisemberg, L. G. et al.(1990). Technological measurements and control-measurable devices in textile and light industry. Legprombitizdat, Moscow (in Russian). 3. Jobson, J.D. (1991). Applied Multivariate Data Analysis. Springer Verlag. 4. Sazhin, B. S. et al. (1999). Estimate of the effectiveness of the processes of contact and convective drying. Technology of textile industry, 4 (in Russian). 5. Sharov, V. (1983). Introduction to the technology of the sewing manufacture. Kiew. 6. Skiruta, M. A. (2002). Influence of the conditions of the Damp-Heating Process over the relaxation condition of the wool fabrics. Light industry, 5 (in Russian).
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