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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 create mathematical models and control algorithms allowing the authors to study and form effective modes of operation of multi-inductor system of electrical heating of moving hollow cylindrical blanks.

The developed mathematical models were based on the finite-difference method, the control volume method and their combination. The reliability of the results obtained was verified by comparing the calculated results with the experimental ones. The temperature control system was synthesized using methods of the object management theory with distributed parameters.

A set of mathematical instruments has been created that allow modelling the operation modes of installation for induction heating of moving hollow cylindrical blanks. Recommendations were given on the formation of an automatic control system that provides heating of a moving hollow cylindrical billet to the required temperature with simultaneous equalization of temperature along the length of the billet in case of highly uneven initial temperature along the length of the billet.

Part of the paper will be used by the industrial plant for the purpose of heat treatment of iron alloys workpiece. Particularly, a control system will be basically formed based on the models.

The scientific novelty of the paper is to create control algorithms and mathematical models for the induction heating system of tubular workpieces allowing to explore interrelated electromagnetic and thermal processes taking into account nonlinearities and design features of the system, as well as to form effective modes of its operation based on transfer functions and methods of the object management theory with distributed parameters.

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.