Математичне моделювання процесів охолодження трубних заготовок із полімерів

Abstract

There are many works about producing of polymer tubes. But less attention is paid to the process of chilling of polymer products. The chilling of polymer tube billets, as most polymer processing processes, is a non-isothermal process. This means that it is necessary to solve the heat problem. Accurate calculation of the heat balance is one of the main components for the final result of the extrusion process. The mathematical model had been created for process of chilling of polymer tube billets after extrusion in this work. Several mathematical models of heating process for heat and power equipment have been created. Different calculation schemes, methods and equations for its solution are suggested. The mathematical model for process of chilling of polymer tube billets after it extrusion can be considered an expansion of research. The mathematical model is based on cylindrical coordinate system with assumption of axisymmetric along angular coordinate. The initial problem statement considered non-stationary process. A transition was made to the differential equation in partial derivatives along two linear coordinates. Solution of this equation was found using the operation method (Laplace integral transform method). The final solution of the problem (after direct and reverse Laplace transform) was obtained from the Bessel function. It was calculated in MathCAD with the help of built-in functions and computing modules. The mathematical model was created for modeling and optimization of process of chilling of polymer tube billets. The results of calculation were presented as graphs that make it possible to characterize the adequacy of the materials. Keywords: mathematical model, balance equation, Laplace transform, program block.