Mathematical model of selective infrared heating application in the manufacture of glass-plastic products

Abstract

Today's information resources offer a variety of rational composite structures hardening methods and equipment design for these processes. In parallel, there is literature that offers the mathematical modeling of the hardening process of polymer composite materials. Due to the complexity and long duration of the structures polymerization process, there is a need to create a mathematical model for polymerization results predicting, using different temperatures and infrared radiation (including selective) time. Performed the comparative analysis of different mathematical models based on the Navier-Stokes equation. Owing to the development of numerical methods, such as the finite difference method and the finite element method (MCR and FEM), new opportunities have opened up for a more complete physical features calculations of the studied processes. The polymerization process of the composite in time can be represented by the state function s (t), which is equal to one at the beginning of the process at t = 0, and zero at the end. The hardening process is characterized by a certain polymerization rate v, which shows which part of the composite is synthesized per unit time. A mechanism explaining the kinetics of the reaction rate v1 was proposed by Arrhenius. Accordingly, for any chemical reaction or any change in the physical state of the body, the molecules must overcome the energy barrier, which is called the activation energy. After analyzing the classical equations, a mathematical model was proposed, which describes the process of hardening the composite material under the combined action of heat flux and infrared radiation. A method for determining the parameters of a mathematical model based on the results of experimental research is proposed. A method of accounting for the parameters of infrared radiation in the presented mathematical model, which can be used for the selected spectrum of the radiation and the filters was used. Based on the Arrhenius Equation, a mathematical model was developed that describes the process of changing the physical and mechanical characteristics of composites during hardening. Having determined the constants of the curing process a1, a2 and Ea - the activation energy of the polymerization reaction, it is possible to estimate the degree of hardening of the composite at any time.