OPTIMIZING THE MIXTURE OF FIBERS IN THE HEAT-RETAINING FABRIC BY THE METHOD OF MATHEMATICAL PLANNING

ABSTRACT

This article consists of the technological processes of the production of non-woven fabrics, the purposeful control of fabric composition by mathematical planning and obtaining mathematical models based on the research results, as well as studying modern methods of measuring the relevant parameters of the main technological processes.

АННОТАТЦИЯ

В данной статье рассматриваются технологические процесы производства нетканых материалов, целенаправленного управления составом ткани путем математического планирования и получения математических моделей по результатам исследований, а также изучение современных методов измерения соответствующих параметров основных технологических процессов.

Keywords: Content, property, optimal, planning, fiber, secondary resource fiber, canonical, polynomial

Ключевые слова: Содержание, свойство, оптимальное, планирование, волокно, вторичное ресурсное волокно, каноническое, полиномиальное

1. Introduction

The task of the textile industry is to increase the production of high-quality yarn by processing not only cotton fiber, but also wool fiber, and increase the production of fabric, knitted and carpet products, and non-woven fabrics. The uniqueness of the physical and mechanical properties of wool fiber complicates its processing. The properties of sheep's wool, even of one breed, depend on sex and age, feeding conditions and care, as well as other factors. In order to obtain yarn and wool products, it is necessary to achieve their uniformity, for this it is necessary to determine the geometric parameters of wool fibers as much as possible [1].

In the first sections, we considered that in the research conducted by our republican and foreign scientists, a lot of work was done on the processing of wool fibers obtained mainly from Khysori and Karakol sheep, and determination of their properties. Based on the purpose of the research, as one of the tasks defined, based on the improvement of the initial processing technology of local coarse and semi-coarse wool fibers, in order to expand the raw material base for textile products from wool fiber, the property indicators of local wool fibers were first studied.

There are many types of fabrics produced in the textile industry, and they are divided into groups of woven, knitted and non-woven fabrics. For the production of each type of fabric, raw materials with a certain appearance and properties are used. From this point of view, the non-woven fabric production technology differs from the previous ones. Usually, non-woven fabrics consist of fibers, yarns, woven fabrics or polymer layers, which are obtained by gluing them together or using special binders [2].

Therefore, fabrics made by connecting one or more types of textile products or non-textile materials with the help of connecting elements are called non-woven fabrics.

The production of non-woven products is considered a relatively new branch of the textile industry, and this type of products is characterized by low cost, originality of quality, and variety of production methods. Many types of fabrics are valuable in technology and medicine, and can be used instead of short-term gauzes.

The range and scope of the raw materials in the composition is very wide, according to the purpose of use, and the largest share (22% of the total volume) belongs to types used for medical and hygienic purposes. In addition, according to the total production volume, polymer coatings are used for various purposes in the fields of filtration, geotextile (road pavements, soil reinforcement), agrotechnical and construction (heating, roofing), light industry.

According to the accepted classification, the method of needle punching is one of the methods of non-woven fabric production by the method of non-woven fabric from fibers of mechanical technology. In such a fabric, the binding function is performed by the fibers themselves.

2. Materials and methods

In this way, filters are produced for technical purposes, for making spinning and wrapping products, floor coverings, blankets, and fabrics for making clothes.

If the structure of the fabric is analyzed, a small cylinder-shaped cavity is formed at the place where the needle is pierced. The fibers around this cylinder are entangled and connected to each other in different ways. In this case, we call one part of the fibers "active fibers", and the other part "participating" fibers. Active fibers have two or more attachment points. Participating fibers also participate in specific binding, but such binding is very loose.

In the process research of the textile industry, it is often necessary to mix components of different properties and sizes. In this case, one of the biggest problems is the issue of optimizing the proportions of constituent fibers [3].

Fiber is the main raw material in the production of non-woven fabrics. The choice of fiber and binder in the right proportion is important for the quality of the obtained product. In theory, all types of fibers can be used to make non-woven fabrics.

When determining the change in the value of all q-components included in the researched mixture, it was required to change the view of the working matrices.

In the optimization of the composition of the mixture, among the numerous matrices, the "Sheffe" matrix is widely used. The "Sheffe" matrix is used for the "Composition-property" mathematical models in obtaining the mathematical model of the regression relationship between the influence of the amount of wool, polyester and the amount of recovered fibers obtained from the processing of the used products on the heat storage property of the fabric. ” matrix used a simplex-lattice matrix (Table 1). Sheffe matrices and formulas for calculating regression coefficients of given polynomials are given.

Sheffe’s canonical polynomial was used to select the regression equation representing the composition of the three-component mixture.

When comparing mathematical models, the number of coefficients in the model that should be experimentally determined is 6.

A given polynomial of the second degree (n=2).

For this example, when the number of components is equal to q=3, the regression model looks like (1.), and its coefficients are determined from the following formula:

The model presented above can be obtained as a result of experiments conducted using this matrix.

Table 1.

“Contents” for mathematical models “Sheffe” matrix

The matrix experiments presented in Table 1 were carried out at 6 points in appropriate proportions.

The requirements for the physical properties of the fabric being prepared are determined by the function of the gauze and depend on their fiber composition, structure and finish. The composition of heat-retaining fabrics obtained by needle punching is mainly short staple fibers, cotton, wool industry waste, recycled fibers. The components that make up the mixture according to the order of composition of the matrix were defined as follows:

 - percentage of wool fiber;

 - percentage of polyester fiber;

 - share of secondary resource fibers.

Based on the research conducted to investigate the effect of the composition of the mixture on the heat retention properties of the fabric, the following parameters were obtained as output parameters:

Y- heat preservation feature of fabric % ;

A working matrix was created for conducting experiments (Table 2).

Table 2.

Working matrix for conducting experiments

With the help of this matrix, the third-order regression mathematical model of the following form is determined:

        (1.)

The values of the regression coefficients are determined as follows:

Taking into account the determined regression coefficients, we write a mathematical model that expresses the regression relationship between the composition of the fiber mixture and the heat retention property of the fabric:

By determining the output parameter determined by this model, i.e., the heat storage property of the non-woven fabric, placing them at the corresponding points of the simplex grid, the optimal proportions of the components included in the mixture are determined by combining the same values.

Figure 1. Experiment points in the simplex

4. Conclusions. In the analysis of the diagram, we can see the process of optimizing the influence of the change in the percentage of fibers in the wrong fabric on the heat storage properties of the fabric.

 Here, an increase in the share of secondary resource fiber means that the heat retention property of the fabric is low (experiment 3); increasing the percentage of wool fiber (experiment 1) makes the heat retention property of the fabric the highest; We can see that when 50% wool and 50% polyester make up the fibers (Experiment 4), average heat retention is achieved.

Due to the fact that wool fiber is naturally high in density, it was determined through theoretical and practical experiments to add up to 25-30% polyester and secondary resource fibers in order to reduce the compressibility of the fabric.

References:

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