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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 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.

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.

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.

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 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.

The purpose of this paper is to compare different reduced-order models for models of control of induction brazing process. In the presented application, the problem is to reconstruct temperature at the points of interests (hot spots) from information measured at accessible places.

The paper describes the process of induction brazing. It presents the full field model and evaluates the possibilities for obtaining reduced models for temperature estimation. The primary attention is paid to the model based on proper orthogonal decomposition (POD).

The paper shows that for the given application, it is possible to find low-order estimator. In the examined linear case, the best estimator was created using POD reduced model together with the linear Kalman filter.

The authors are aware of two main limitations of the presented study: material properties are considered linear, which is not a completely realistic assumption. However, if strong coupling and nonlinear material parameters are considered, the model becomes unsolvable. The process and measurement uncertainties are not considered.

The paper deals with POD of multi-physics 3 D application of induction brazing. The paper compares 11 different methods for temperature estimator design.

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority.

Adaptive hp‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular.

Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory.

The paper describes results obtained from an original and innovative implementation of the adaptive hp‐FEM.