Задачі нестаціонарної теплопроводності електропровідних тіл у електромагнітному полі

Abstract

У статті розглядається аналіз нестаціонарного температурного поля, яке виникає у циліндричному тілі при його індукційному нагріванні за допомогою зовнішнього спірального багатовиткового індуктора. Представлені результати аналітичного розв’язання за допомогою методу перетворення за Лапласом та чисельного розв’язання методом скінчених елементів.The article deals with issues related to the analysis of transient propagation ofthe temperature field in electrically conductive bodies under the influence of an electromagnetic field. The action of the electromagnetic field on electrically conductive bodies is manifested in two versions: the possible movement of the body and a change inits temperature in accordance with the Joule-Lenz law. The energy of the electromagnetic field is used in various technological operations, including in the sense of changing the temperature of the processed objects. The use of the temperature effect of an electromagnetic field is typical, for example, for technological operations such as induction heating. A calculated study of the unsteady temperature field inthis case allows us to select rational structural and operational parameters of the technological operation. In addition, it is known that a change in body temperature leads to the appearance of thermal deformations, which makes a certain contribution to the stress-strain state and can affect the working life anddurability of technological equipment. Thus, the topic of the article isrelevant in practical and scientific aspects. In the analysisof real structures, the features of their geometry and operating conditions require the use of numerical analysismethods. Analytical calculation methods, which most often allow obtaining approximate results, can be used as evaluative for simplified calculation models. In technological operations of induction heating of massive cylindrical billets, a spiral multicoil inductor is very often used. The article considers the task of analyzing the spatiotemporal distribution of temperature in a cylindrical billet, which is heated by an external multiturn inductor. The problem is considered in an axisymmetric formulation. The spatial-temporal distribution of the basic characteristics of the electromagnetic field is preliminarily determined. An analytical solution to the problem is presented, which was obtained by the Laplace transform method, under the assumption of unlimited workpiece, itsideal electrical conductivity, as well as neglecting the real heat transfer conditions at its boundary. The numerical solution of the problem is obtained by the finite element method and is devoid of these simplifications. The analysis of the influence of the size of the inductor on the nature of the distribution ofthe temperature field in the workpiece is carried out.