Modelling of continual induction hardening in quasi‐coupled formulation

Abstract

Purpose -As far as the authors know, no sufficiently complete model of continual induction hardening was developed and solved so far. The paper presents both mathematical model of the process and algorithm of its solution in the quasi-coupled formulation. Design/methodology/approach -Computation of electromagnetic and temperature fields is based on the finite element method, while time variable boundary conditions are determined by means of an original theoretically-empirical procedure. Findings -Substantial are backgrounds for design of the inductor and parameters of the field current as well as parameters of the cooling medium. Research/limitations/implications -The model reached a good level of accuracy validated by suitable experiments. Nevertheless, next work in the field will also have to respect history of the heating before cooling itself (the austenitizing temperature is a function of the velocity of heating). Very important is also appropriate meshing of the investigated region to suppress numerical instabilities appearing during the computation process. Finally, acceleration of numerical schemes is a must, because modelling of one common task (on very fast PCs) takes about 4 h. Practical implications -The results and conclusions may be used for designing devices for continual induction hardening of axisymmetric bodies. Originality/value -Complete mathematical and computer model of the process, original methodology for finding the coefficient of convective heat transfer from the cooled part of the heated workpiece to ambient water spray.

A–ϕ formulation of a mathematical model for the induction hardening process with a nonlinear law for the magnetic field

“…Some of them provide various numerical schemes e.g. [1][2][3][4][5][6]. But they omit mathematical or numerical analysis of their models and numerical schemes.…”

Continual induction hardening of steel bodies

“…The problem is, moreover, nonlinear (the relative magnetic permeability is a function of magnetic field and temperature) and nonstationary, and the value of the austenitization temperature may depend on the history of heating. Papers that are aimed at the simulation of the process are relatively rare [4,1,3,6]. Despite a lot of work in the domain, the methodology still suffers from various simplifications enforced by lack of experimental data and capabilities of available software.…”

Fully discrete T‐ψ finite element method to solve a nonlinear induction hardening problem

“…In the case of linear constitutive relation in Maxwell's equations, there exist a lot of works devoted to induction hardening so far. Some papers present various numerical schemes for computation [1,4,6,12,30]. Other papers study the well-posedness of the problem and give theoretical results [7,14,17,18,[33][34][35].…”