Mathematical Modeling of the Process of a Non-Contact Surface Pyrography on the Shoe Nonwoven Materials

Aesthetic indicators occupy a special place in assessing the quality of shoes. Aesthetic properties are especially relevant for the youth assortment, as they help in popularizing the consumption of items with certain, given parameters. Expanding the range of felt shoes based on the development of technology for decorating upper parts with non-contact pyrography while improving its aesthetics is certainly an urgent task. The object of the study is the technological process of non-contact laser pyrography of felt shoe upper parts. The subjects of the study are finished shoes and outer details of the uppers made of felt. Three main degrees of impact are considered: surface, volume and through. A hypothesis has been put forward that the degree of laser impact on the material, in particular on the details of the upper of shoes made of felt, can be much greater. To assess the thermal conductivity and thermal resistance, we used the installation and methodology for studying the thermal properties of flat bodies, developed at the Russian State University. A. N. Kosygin. The least squares method was used to estimate the coefficients of the regression model. The significance of the coefficient estimates was checked using the standard method of linear multivariate regression analysis. The adequacy of the model was checked by the square of the coefficient of determination. The conducted studies and calculations have proved that contour burning should be used in felt shoes, since a complex pattern will be used to decorate it, which is created using special software. The elements of the main drawing should be combined with each other so that the composition as a whole look harmonious and combines with the main idea of the drawing itself. In order to optimize the technological parameters and study the process of decorating the details of the uppers of shoes made of felt by pyrography, the methods of graphic and mathematical modeling were applied in the work, which makes it possible to appropriately approach the process of predicting the properties of shoes with felt uppers during their manufacture and operation.