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The purpose of this paper is to present a new device (thermoelastic actuator) for accurate control of position whose principle is based on thermal dilatation of its working unit brought about by induction heating.

The device must satisfy the prescribed operation parameters (mainly the above thermal dilatation). The task to find them is a multiply coupled problem (interaction of electromagnetic field, temperature field and field of thermoelastic displacements) that is solved by the finite element method supplemented with a number of other procedures.

The control of position based on the described thermoelastic effect is very accurate and ranges from 1×10⁻⁶ to 1×10⁻³ m.

The device also contains two self‐locking friction clutches of conical shapes whose purpose is to fix the position of the plunger in the prescribed position. Further attention should be paid to their dynamic behaviour during the process of fixing.

The device can be used in various technical domains such as optics and laser or microscope techniques.

The principal part of the device contains no movable element, which is a substantial advantage in comparison to other systems based on mechanical, hydraulic or pneumatic principles working with movable elements or media.

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.

This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of measurement of the surface temperature of material during the process of heating and subsequent solution of the inverse problem using multi-parametric optimization.

The methodology is based on measurements and numerical solution of the forward and inverse problem, taking into account all involved nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). The inverse problem is solved by a genetic algorithm.

The suggested methodology was successfully verified on several metal materials whose temperature-dependent parameters are known. The calculated and measured results exhibit a very good accordance (the differences do not exceed about 10 per cent for room and higher temperatures).

At this moment, the methodology successfully works when the temperature dependence of just one material parameter is to be found (which means that the temperature dependencies of other parameters are known). The accuracy of results also depends on the correctness of other input data.

This paper provides a relatively easy possibility of finding the temperature dependencies of thermal conductivity or heat capacity of various alloys.

The paper proposes a methodology of finding the temperature dependence of a given material parameter that is not known in advance (which is of great importance in case of alloys).

A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing.

The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM.

The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability.

The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated.

The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials.

Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

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.

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.

Most eddy current problems are solved using numerical schemes based on the differential approach. Nevertheless, there exist several classes of tasks where use of this approach may be complicated (problems characterized by geometrical incommensurability of individual subdomains, motion, etc.). In such cases, application of the integrodifferential approach may be an advantage. The paper seeks to present the theoretical background of the method.

The mathematical model consists of a system of integrodifferential equations for current densities in electrically conductive domains.

The methodology is illustrated on an example. All computations are realized by a code developed and written by the authors.

The presented algorithm based on the integrodifferential approach makes it possible to solve problems that are only hardly solvable by classical differential methods.

High-voltage overhead lines produce low-frequency electromagnetic fields around them. These fields are easy to compute wherever the line route is straight, as opposed to places where its direction is changed. The purpose of this paper is to perform a numerical analysis of an electromagnetic field occurring along a high-voltage overhead line at the places of the changed direction and to compare the results with the exposure limits for low-frequency electromagnetic fields in order to assess their effects on living organisms.

The computation was conducted in the MATLAB SW by means of a combination of integral and differential methods in a three-dimensional (3D) arrangement, taking into account the location and shape of the tower. Special procedures within the MATLAB software had to be coded.

Within the research, the following electromagnetic field quantities were computed: the distribution of electric field strength, magnetic flux density, Poynting vector, electric potential and surface charge density. The results obtained indicate the influence of both the line route changing its direction and the deviation tower location on the electromagnetic field around the tower.

In order to shorten the computation time, it was necessary to achieve a minimum number of degrees of freedom by adjusting the real shape of both the cross-section of the deviation tower beam and the conductors. In some further research, attempts could be made to further optimize the results by using the real shapes of the cross-section of the deviation tower beam and the conductors. Furthermore, it could be beneficial to shorten the set distance between two adjacent nodes in order to obtain a finer mesh while still achieving an optimal ratio between the number of nodes and the computation time.

The Czech Regulation no. 1/2008 Coll., concerning protection of health against non-ionized radiation, stipulates 100 μT to be the maximum safe value of magnetic flux density in case of an uninterrupted exposure and frequency of 50 Hz. The investigated area did not exhibit values exceeding this limit. The same was true for the maximum permissible level of electric field strength being specified at 5,000 V/m.

Similar problems are often solved by means of FEM in 2D arrangements. However, when applying this method for conductors passing through a large 3D area, it is difficult to model an optimal 3D mesh within the conductors and the tower beams. This research shows that the application of integral methods reduces the complexity of the generated mesh. Unlike FEM, requiring the generation of a 3D mesh, the integral method only requires a surface mesh on the conductors and tower beams, thus significantly reducing the number of degrees of freedom. FEM only remains necessary for areas adjacent to the tower beams and conductors.

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.

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.