Математическая модель процесса экструзии вязко-пластичной углеродной массы

Abstract

Рассмотрен процесс формования углеродных изделий из коксопекового композита. Разработано математическую и численную модели прессового инструмента для экструзии электродных заготовок с использованием приближения жидкости Bingham-Papanastasiou для описания поведения углеродной массы. Проведена верификация разработанной численной модели по данным экспериментальных исследований и определенно, что разница между расчётными и экспериментально измеренными значениями температуры мундштука пресса не превышает 4–6 %.Manufacturing of large-size carbon products such as electrodes and carbon blocks requires multistage production cycle, special equipment and significant resources and energy consumption. The article is devoted to the technological stage of carbon products forming with the usage of extrusion method. On this stage carbon blanks are shaped and sized and also their physical properties start to be formed. It is necessary to use effective operating regimes in order to get a high quality and defectless products. The development of mathematical model of carbon materials extrusion process is an important task in numerical modeling since it enables us to estimate effective process parameters. Coke/pitch composition exhibits viscoplastic properties. It behaves as a rigid body at the low stress but flows as a viscous fluid at high stress. We propose mathematical model of carbon mass extrusion process with the usage of viscoplastic Bingham-Papanastasiou viscosity model. The model is based on transient nonlinear system of partial differential equation. It consists of continuity equation, motion equation and energy equation for laminar incompressible Bingham-Papanastasiou fluid flow and energy equation with additional heat source for solid parts of pressing equipment. The dynamically changeable initial and boundary conditions are used for the description of different stages of extrusion process. We performed verification and validation of the developed mathematical and numerical models of thermohydrodynamic state of extrusion equipment. Results of numerical analyses are presented in the article in the form of temperature plots and fields. The comparison of numerical and experiment data shows good agreement and the average difference is 4–6 %. This confirms model capability to solve engineering and manufacturing problems related to carbon mass extrusion process.