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The purpose of this paper is to present a model of induction heating of aluminium billets rotating in a static magnetic field generated by permanent magnets. The model is solved by the authors' own software and the results are verified experimentally.

The mathematical model of the problem given by two partial differential equations describing the distribution of the magnetic and temperature fields in the system is solved by a fully adaptive higher‐order finite element method in the hard‐coupled formulation. All material nonlinearities are taken into account.

The method of solution realized by the code is reliable and works faster in comparison with the existing low‐order finite element codes.

The method works for 2D arrangements with an extremely high accuracy. Its limitations consist mainly in problems of determining the coefficients of convection and radiation for temperature field in the system (respecting both temperature and revolutions).

The methodology can successfully be used for design of devices for induction heating of cylindrical nonmagnetic bodies by rotation and anticipation of their operation parameters.

The paper presents a fully adaptive higher‐order finite element and its utilization for a hard‐coupled numerical solution of the problem of induction heating.

The paper seeks to present a methodology of computer simulation of coupled magneto‐thermo‐mechanical processes in various electrical engineering devices. The methodology allows determining their parameters, characteristics and behaviour in various operation regimes.

The mathematical model consisting of three equations describing magnetic field, temperature field and field of mechanical strains and stresses (or thermoelastic displacements) is solved numerically, partially in the hard‐coupled formulation.

The methodology seems to be sufficiently robust, reliable and applicable to a wide spectrum of devices.

At this stage of research, the hard‐coupled formulation of thermo‐mechanical (or thermoelastic) problems is still possible only in 2D.

The methodology can successfully be used for design of numerous machines, apparatus and devices from the area of low‐frequency electrical engineering ranging from small actuators to large synchronous generators.

Complete numerical analysis of coupled magneto‐thermo‐mechanical phenomena in electrical devices.

The purpose of this paper is to investigate the parameters and operation characteristics of an actuator working on the principle of thermoelasticity whose structure was designed by the authors.

The mathematical model of the system describes the effects of three physical fields (electromagnetic field, temperature field, and field of mechanical strains and stresses due to thermoelasticity). While the electromagnetic field was solved independently, the thermomechanical task in common with the contact problem was solved in the hard‐coupled formulation. The computations were mostly carried out by own codes.

This type of actuator is characterized by extremely high forces acting in its dilatation element.

The parameters of the system may still be improved using a longer field coil and dilatation element. Attention has to be paid, however to the mechanical stability of the system. Another improvement could be achieved by suitably designed cooling of the coil that would allow increasing parameters of the field current (its frequency or amplitude).

The device is promising for various fixing tasks in the industrial environment.

Although the methods of numerical processing of particular fields are known, the paper provides an algorithm for their simultaneous solution while respecting the temperature dependencies of the material properties and continuous change of the contact surfaces.

The purpose of this paper is to propose and analyze a combined heat treatment of metal materials, consisting in classic induction pre-heating and/or post-heating and full heating by laser beam. This technology is prospective for some kinds of surface hardening and welding because its application leads to lowering of temperature gradients at the heated spots, which substantially reduces local residual mechanical strains and stresses.

The task was solved like the 3D hard-coupled problem for electromagnetic field, temperature field and field of displacements. It was solved numerically using the techniques based on the FEM. For solution was used commercial software COMSOL Multiphysics, some parts were solved using own scripts in the software Agros.

In the paper are shown results of the numerical solution and experimental measured data. Due the work the authors found that the influence of the pre-heating and post-heating really leads to limit the temperature gradients and from other measurements is clear that also to improving of the welding.

The paper presents fully 3D nonlinear and nonstationary mathematical model of hybrid laser welding, its numerical solution experimental verification.

The paper aims to describe the modeling of the induction-assisted laser welding process taking into account the keyhole effect and phase changes in the material.

A sophisticated mathematical model of the above heat treatment process is presented, taking into account the above phenomena and all available nonlinearities of the material. Its numerical solution is carried out using the finite element method incorporating algorithms for the deformation of geometry and solution of the flow field.

Unlike various simplified models solved in the past, this approach incorporating a sophisticated model of heat transfer and flow of melt is able to reach a very accurate solution, differing only by a small error (not more than 8 per cent) from the experiment.

The presented model does not consider several subtle phenomena related to the evaporation of metal after irradiation of the material by a laser beam. In fact, at the heated spot, all three phases of the material coexist. The evaporated metal forms a capillary leak off and forms a cloud above the spot of irradiation. Due to the absorption of laser power in this cloud, the process of heating decelerates, which leads to a decrease in the process efficiency.

The presented model and methodology of its solution may represent a basis for design of the process of laser welding.

The main value is the proposal of numerical model for solution a complex multiphysical model with respecting several physical phenomena whose results are available in a short time and still with a good agreement with the experimental verification.

This paper aims to present a three-dimensional (3D) model of hybrid laser welding of a steel plate. Before welding, the plate is pre- and/or post-heated by induction to avoid mechanical stresses in material due to high gradients of temperature. Welding itself is realized by laser beam without welding rod. The model takes into account existence of both solid and liquid phases in the weld.

Presented is the complete mathematical model of the above heat treatment process, taking into account all relevant nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). Its numerical solution is realized by the finite element method. Some important results are compared with experimental data.

In comparison with the former model developed by the authors that did not take into account the phase change, the results are more realistic and exhibit a better accordance with measurements. On the other hand, they strongly depend on sufficiently accurate knowledge of material parameters in both solid and liquid levels (that represent the input data).

The quality of calculated results strongly depends on the material properties and their temperature dependencies. In case of alloys (whose chemical composition may vary in some range), such data are often unavailable and must be estimated on the basis of experiments. Another quantity that has to be calibrated is the time dependence of power delivered by the laser beam, which is due to the production of a plasma cloud above the exposed spot.

The presented model and methodology of its solution may represent a basis for design of the complete technology of laser welding with induction pre-heating and/or post-heating.

Fully 3D model of hybrid laser welding (supplemented with pre- and/or post-heating by magnetic induction) taking into account both solid and liquid phases of welded metal and influence of the plasma cloud is presented.

A model of hybrid fillet welding is built and solved. No additional material (welding rod, etc.) is used. Heating of the welded parts is realized by laser beam with induction preheating and/or postheating. The purpose of these operations is to reduce the temperature gradient in welded parts in the course of both heating and cooling, which reduces the resultant hardness of the weld and its neighborhood and also reduces undesirable internal mechanical strains and stresses in material.

The complete mathematical model of the combined welding process is presented, taking into account all relevant nonlinearities. The model is then solved numerically by the finite element method. The methodology is illustrated with an example, the results of which are compared with experiment.

The proposed model provided satisfactory results even when some subtle phenomena were not taken into account (flow of melt in the pool after irradiation of the laser beam driven by the buoyancy and gravitational forces and evaporation of molten metal and influence of plasma cloud above the irradiated spot).

Accuracy of the results depends on the accuracy of physical parameters of materials entering the model and their temperature dependencies. These quantities are functions of chemical composition of the materials used, and may more or less differ from the values delivered by manufacturers. Also, the above subtle physical phenomena exhibit stochastic character and their modeling may be accompanied by non-negligible uncertainties.

The presented model and methodology of its solution may represent a basis for design of welding processes in various branches of industry.

The model of a complex multiphysics problem (induction-assisted laser welding) provides reasonable results confirmed by experiments.

This paper aims to propose a number of approaches to reduce the temperature gradient of titanium billets in the heat treatment process.

Modeling physical processes in the induction unit is calculated by the finite element method. Required power was calculated based on the fact that all the induced power is allocated in a certain layer and there are loss flows and heating flows. Also, an opportunity is offered to reduce temperature difference using numerical optimization, control system based on proportional-integral regulator and ballast blank.

The asymmetry of the magnetic field at the ends of the inductor significantly affects the temperature uniformity along the length of the workpiece. Increasing the length of the workpiece by adding ballast blanks reduces the temperature drop. Also, increasing the non-magnetic gap in some cases it is possible to improve the quality of through heating.

The results of this study are verified only for a number of titanium alloys. Therefore, this knowledge is appropriate to apply for this type of materials. In future studies, it is possible to expand the possibilities of the considered approaches for other types of materials.

Part of the study will be used to industrial plant for purpose of heat treatment of titanium alloys workpiece. Especially, control system will be basically made based on the model.

A novel methodology of induction heating of titanium alloy Ti6Al4V in the form of cylindrical billets is presented that simplifies the process and improves temperature uniformity along the radius and length of the billet by optimizing the shape of the inductor and selecting suitable power modes.

The paper aims to deal with shape optimization of a novel thermoelastic clutch working on the principle of induction heating. The clutch consists of a driving part, with a ferromagnetic ring, and a driven part. The driving part rotates in a static field produced by appropriately arranged static permanent magnet. Currents induced in the rotating ferromagnetic ring cause its temperature to rise and increase its internal and external radii. As soon as its external diameter reaches the diameter of head of the driven part, it starts also rotating because of mechanical friction between both parts.

Presented is the complete mathematical model of the device, taking into account all relevant nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). The forward solution is realized by the finite element method, and the shape optimization is solved using heuristic algorithms.

The clutch was found to be fully functional and may be used in applications with limited access into the device.

The coefficient of expansion of material of the driven part must be substantially lower than the same coefficient of the driving part to keep the necessary friction torque. The clutch can be only used in applications where higher temperatures (such as 300°C) are not dangerous to the environment.

The presented model and methodology of its solution may represent a basis for design of devices for transfer of generally mechanical forces and torques.

This paper presents an idea of induction-produced thermoelastic connection of two parts capable of transferring mechanical forces and torques.

Impedance of long direct massive conductors carrying time‐variable currents is a complex function of time. Its evolution is affected not only by the skin effect but also by the temperature rise. This paper presents a numerical method that allows one to compute the resistance and internal inductance of a non‐ferromagnetic conductor of any cross‐section from values of the total Joule losses and magnetic energy within the conductor, and also illustrates the theoretical analysis based on the field approach on a typical example and discusses the results.