J. Barglik

3D modeling of induction hardening of gear wheels

Induction hardening of gear wheels is modeled. The model consists of two nonlinear partial differential equations describing the distributions of magnetic and temperature fields in the system. All material parameters are supposed to be functions of temperature. The model is then solved numerically in the 3D hard-coupled formulation using the professional code FLUX3D supplemented with a number of own scripts and procedures. The methodology is illustrated with a typical example whose results are discussed.

Higher‐order finite element modeling of rotational induction heating of nonferromagnetic cylindrical billets

Purpose – The purpose of this paper is to present a methodology of high‐precision finite element modeling of induction heating of rotating nonferromagnetic cylindrical billets in static magnetic field produced by appropriately arranged permanent magnets.Design/methodology/approach – The mathematical model consisting of two partial differential equations describing the distribution of the magnetic and temperature fields are solved by a fully adaptive higher‐order finite element method in the monolithic formulation and selected results are validated experimentally.Findings – The method of solution realized by own code is very fast, robust and exhibits much more powerful features when compared with classical low‐order numerical methods implemented in existing commercial codes.Research limitations/implications – For sufficiently long arrangements the method provides good results even for 2D model. The principal limitation consists in problems with determining correct boundary conditions for the temperature fi...

Modelling of continual induction hardening in quasi‐coupled formulation

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 nume...

Modelling of induction heating and consequent hardening of long prismatic bodies

The paper deals with the problem of induction hardening of long prismatic ferromagnetic bodies. The body is first heated to the austenitizing temperature typically in a cylindrical inductor fed from a source of harmonic current and then merged into a cooling medium. In specific cases, equalisation of temperatures within the body before its cooling may also be required. The mathematical model of the induction heating consists of two non‐linear second order differential equations of the parabolic type describing the distribution of the electromagnetic and non‐stationary temperature fields while the cooling is described by the heat equation and a theoretically empirical algorithm for mapping the process of hardening. The suggested methodology partially takes into account the temperature dependencies of all material parameters. The theoretical analysis is supplemented with an illustrative example and discussion of the results. Computations have been performed by means of professional codes and single‐purpose user programs developed by the authors.

Mathematical modeling of induction surface hardening

Purpose – As far as the author knows the modeling of induction surface hardening is still a challenge. The purpose of this paper is to present both mathematical models of continuous and simultaneous hardening processes and exemplary results of computations and measurements. The upper critical temperature Ac3 is determined from the Time Temperature Austenization diagram for investigated steel. Design/methodology/approach – Computation of coupled electromagnetic, thermal and hardness fields is based on the finite element methods, while the hardness distribution is determined by means of experimental dependence derived from the continuous cooling temperature diagram for investigated steel. Findings – The presented results may be used as a theoretical background for design of inductor-sprayer systems in continual and simultaneous arrangements and a proper selection of their electromagnetic and thermal parameters. Research limitations/implications – The both models reached a quite good accuracy validated by th...

Influence of the magnetic permeability on modeling of induction surface hardening

Purpose Modeling of induction surface hardening strongly depends on accuracy of material properties data and their temperature characteristics. However, it is especially complicated in case of the magnetic permeability dependent not only on temperature but also on the magnetic strength. This paper aims to estimate the influence of the magnetic permeability on modeling of coupled physical fields describing the process. Investigations are provided for the gear wheels made of the steel C45E. Design/methodology/approach Computation of coupled electromagnetic temperature and hardness fields is based on FEM methods. The Flux 3D software is applied for the numerical simulation of coupled electromagnetic and temperature fields. The QT Steel software is applied for a determination of the hardness and microstructure distributions. Findings Obtained results may be used as a kind of background for the design of induction surface hardening systems. Research limitations/implications The presented calculation model provided quite a good accuracy of hardness distribution validated by the experiments. Next work in the field should be aimed at taking into account a dependence of the magnetic permeability on the field current frequency. Originality/value Mathematical model of induction surface hardening with taking into account time dependence on the magnetic permeability on temperature and magnetic strength is elaborated. Experimental validation of hardness distribution is provided. A quite reasonable convergence between simulations and measurements was achieved.

Computer modelling and simulation of radiofrequency thermal ablation

Purpose – The purpose of this paper is to enable the correct selection of the radiofrequency thermal ablation (RFTA) process parameters for an individual patient by applying a computer modelling of RFTA.Design/methodology/approach – The model is based on the X‐ray computer tomography images of the primary and metastatic hepatic tumours. The authors used the professional package of FLUX3D to generate the geometric models, assign materials properties, assign boundary conditions, perform mesh, carry out coupled thermo‐electromagnetic analysis and for post processing. The distribution of temperature and electric potential in the tissues of tumour and liver had been obtained as main results of the calculations.Findings – The computational results show that the RFTA algorithm is effective in solving this practical problem. The computational results show that the selection of the type of electrodes used in the RFTA process is as important as the correct selection of the process parameters, i.e. voltage and frequ...

Induction surface hardening - comparison of different methods

The overview of the induction surface hardening methods were presented in the paper. Two examples are considered: continual hardening of cylinders made of steel 38Mn6 and dual frequency hardening of gear wheels made of steel 40 HNMA. Results of measurements provided at the experimental stand were presented. Acceptable accordance between measurements and numerical computations were obtained. Final conclusions were formulated. (Hartowanie indukcyjne powierzchniowe – porównanie różnych metod) Streszczenie. W pracy dokonano przeglądu metod hartowania indukcyjnego powierzchniowego elementów stalowych. Rozpatrzono dwa przypadki: hartowania przelotowego wałków ze stali 38Mn6 oraz hartowania dwuczęstotliwościowego kół zębatych ze stali 40HNMA. Przedstawiono wyniki pomiarów na stanowisku doświadczalnym. Uzyskano zadowalającą zbieżność między wynikami pomiarów i obliczeń numerycznych. Przegląd metod hartowania indukcyjnego powierzchniowego elementów stalowych

Induction hardening of steel elements with complex shapes

As an example of induction hardening of steel elements with complex shapes the induction contour hardening of gear wheels was selected. The model of the process was proposed and simulation results elaborated by means of professional computer software for coupled physical fields were presented. Quite reasonable accordance between computations and measurements was obtained. Streszczenie. Jako przykład hartowania indukcyjnego elementów stalowych o złożonych kształtach wybrano proces hartowania konturowego kół zębatych. Zaproponowano model procesu oraz przedstawiono wyniki symulacji z wykorzystaniem programów do obliczania sprzężonych pól fizycznych. Uzyskano zadowalającą zbieżność wyników pomiarów i obliczeń. (Hartowanie indukcyjne elementów stalowych o złożonych kształtach).

Mathematical Modeling of Induction Stirring of Liquid Metal in Crucible Furnace

Preheating of metals in induction crucible furnaces is often a long-term process characterized by a big energy consumption. Numerical simulation could be an useful tool for optimization of the process. The electromagnetic field distribution, time evolution of temperature field, velocity distribution and shape of free surface in a crucible of given geometry are affected by various parameters of the system. Quite reasonable results are obtained by means of simple two-dimensional numerical model validated by the experiments. Introduction Electromagnetic influence on liquid metal causes its movement due to Lorentz forces generated by electromagnetic induction. This idea could be applied in various metallurgical processes of liquid metals like: continual transportation, feeding, purification, stirring. For small distances electromagnetic kind of transportation realized by different types of magnetohydrodynamic pumps may replace classical ways of transportation. Electromagnetic feeders are more frequently applied mainly for aluminium or its alloys. Use of electromagnetic devices for purification (for instance for removal of non-metallic inclusions) was still applied rarely. One example of such an application was a reduction of oxides in aluminum during transportation in electromagnetic channel [1]. Induction stirring of liquid metals represents an advanced technology aiming at the improvement of their resultant structure and physical properties. We have at least three reasons for its application: degasification of melt, uniform distribution of all ingredients within the melt, its better nucleation. Liquid metals often contain certain amount of gases, for instance hydrogen, whose presence in the final product, is undesirable. During their processing in classical furnaces a part of gas bubbles gets out of the melt because of internal pressure in it. But due to viscosity a part of bubbles remains in its structure. And consequent induction stirring provided for instance in induction crucible furnaces may contribute to their removal. Until recently, the technology was used for amounts of metal not exceeding several tons placed in ceramic or special crucibles. Manufacturers search for possibilities that would allow processing much higher amounts of metal. 1. Mathematical Modelling Let us consider a continuous axi-symmetrical, two dimensional mathematical model of the induction stirring process taking place in a ceramic crucible of the induction furnace. The model corresponds to the real induction crucible furnace installed in the aluminium plant located in the southern Poland. The definition area for the case and its corresponding algorithm are presented in Fig. 1 and Fig. 2 respectively. 101 doi:10.22364/mmp2017.15