David Pánek

Numerical solution of coupled problems using code Agros2D

New code Agros2D for 2D numerical solution of coupled problems is presented. This code is based on the fully adaptive higher-order finite element method and works with library Hermes2D containing the most advanced numerical algorithms for the numerical processing of systems of second-order partial differential equations. It is characterized by several quite unique features such as work with hanging nodes of any level, multimesh technology (every physical field can be calculated on a different mesh generally varying in time) and a possibility of combining triangular, quadrilateral and curved elements. The power of the code is illustrated by three typical coupled problems.

Combined heat treatment of metal materials

Purpose – 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. Design/methodology/approach – 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. Findings – 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 g...

Accurate Control of Position by Induction Heating-Produced Thermoelasticity

An alternative possibility of highly accurate control of position is suggested, realized by a simple device with a cylindrical dilatation element that works on the principle of thermoelasticity produced by induction heating. The paper describes the device, presents its complete mathematical model in common with the methodology of its numerical solution, and also the algorithm of the control process. The theoretical analysis is illustrated by a typical example, whose results are discussed.

Numerical modeling of hybrid laser welding taking into account phase change of material

Purpose 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. Design/methodology/approach 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. Findings 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). Research limitations/implications 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. Practical implications 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. Originality/value 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.

Digitally Controllable Current Amplifier and Current Conveyors in Practical Application of Controllable Frequency Filter

Abstract This paper presents the simulations results in comparison with the measured results of the practical realization of the multifunctional second order frequency filter with a Digitally Adjustable Current Amplifier (DACA) and two Dual-Output Controllable Current Conveyors (CCCII +/−). This filter is designed for use in current mode. The filter was designed of the single input multiple outputs (SIMO) type, therefore it has only one input and three outputs with individual filtering functions. DACA element used in a newly proposed circuit is present in form of an integrated chip and the current conveyors are implemented using the Universal Current Conveyor (UCC) chip with designation UCC-N1B. Proposed frequency filter enables independent control of the pole frequency using parameters of two current conveyors and also independent control of the quality factor by change of a current gain of DACA.

Model of laser heating with induction pre- and post-heating and its experimental verification

Mathematical model of laser heating with induction pre- and/or post-heating is presented and solved. The purpose of this combined way of heat treatment is to reduce residual mechanical stresses in the surface layers of the processed material produced by high temperature gradients at the spots heated by the laser beam. The 3D model takes into account all important nonlinearities including the temperature dependencies of physical parameters of involved materials (such as the magnetic permeability, electric or thermal conductivity, specific heat capacity etc.). Its numerical solution is carried out by the finite element method. The methodology is illustrated with a practical example whose selected results are verified by measurements.

Novel algorithm for modeling combined laser and induction welding respecting keyhole effect

Numerical model of combined laser and induction welding is presented and solved. From the physical viewpoint, the process represents a coupled problem of nonlinear and nonstationary interaction of the magnetic and temperature fields respecting the phase change and evaporation of heated molten metal (keyhole effect). A specific algorithm was developed for manipulation with the space and time variation of interface between solid and molten metal. Selected results are compared with the realized experiment.

Modeling of selected 3D electroheat coupled problems with time-varying geometries

Novel approach to modeling of 3D coupled electroheat problems with time-varying geometries is presented. Instead of time-expensive remeshing of the whole system in every time step it is used the initial mesh that takes into account the expected geometric changes. In the course of computations, its relevant elements are able to adaptively change their shapes and material parameters. The methodology is illustrated with an example of combined cladding.

Optimization of inductor for pre- and post-heating metal parts during their edge laser welding

The shape of an inductor for pre-heating and/or post-heating metal parts is optimized with the aim to reach the prescribed pattern of temperature along the place to be consequently welded by laser beam. The task represents a nonlinear inverse multi-parametric problem that is solved for a given range of field current frequencies. While the direct part of the problem is solved by a fully adaptive higher-order finite element method using own code, the inverse part is solved by selected genetic algorithms. Tested is also the influence of frequency of the field current. The methodology is illustrated with a typical example.

Optimized control of field current in thermoelastic actuator for accurate setting of position

A novel device for control of position working with accuracies on the order of 10^-^5-10^-^3m is proposed. The device has no movable parts. It works with an inductively heated metal cylindrical element of appropriate dimensions, whose longitudinal dilatation of thermoelastic origin is controlled by the harmonic field current in the inductor. The principal aim of the paper is to find such a time evolution of the field current that allows reaching the required dilatation in the shortest time possible.