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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 purpose of this paper is to present the calibration of a laser welding model suitable for solving problems with input data that are either unknown or known only approximately.

The calibration starts from the measured temperature profile of the weld, and the aim is to get a similar profile by the solution of the model. The corresponding procedure is based on replacing the material characteristics that are known only approximately by polynomial or rational functions whose coefficients are determined using a suitable optimization process. The algorithm is supplemented with a simplified model of the keyhole shape.

The big advantage of the proposed approach is the velocity of solution of the problem and low consumption of the sources (hardware and software). In comparison with solving the full model of laser welding, the methodology provides results of a still acceptable accuracy by several orders faster. On the other hand, the results also depend on the strategy of selecting the points at which the temperature is verified and on “manual” setting of the deformation parameters.

Application of the methodology is conditioned by several experiments with the used material (without experiment it is impossible to carry out the calibration and set the shape of the keyhole), while the full model allows it. On the other hand, the full model is not able to predict the errors in the case when some input data is unknown or known only approximately and the results have to be also confirmed experimentally.

The presented methodology may be used for determining unknown material characteristics and faster modelling of laser welding.

This paper proposes a novel methodology for evaluation of quality of laser welds in cases of unknown or partially unknown material parameters and substantial acceleration (by 2-3 orders) of the numerical solution of the model of laser welding.

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.