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This paper aims to use a scaling approach to scale the solutions of a beforehand-simulated finite element (FE) solution of an induction machine (IM). The scaling procedure is coupled to an analytic three-node-lumped parameter thermal network (LPTN) model enabling the possibility to adjust the machine losses in the simulation to the actual calculated temperature.

The proposed scaling procedure of IMs allows the possibility to scale the solutions, particularly the losses, of a beforehand-performed FE simulation owing to temperature changes and therefore enables the possibility of a very general multiphysics approach by coupling the FE simulation results of the IM to a thermal model in a very fast and efficient way. The thermal capacities and resistances of the three-node thermal network model are parameterized by analytical formulations and an optimization procedure. For the parameterization of the model, temperature measurements of the IM operated in the 30-min short-time mode are used.

This approach allows an efficient calculation of the machine temperature under consideration of temperature-dependent losses. Using the proposed scaling procedure, the time to simulate the thermal behavior of an IM in a continuous operation mode is less than 5 s. The scaling procedure of IMs enables a rapid calculation of the thermal behavior using FE simulation data.

The approach uses a scaling procedure for the FE solutions of IMs, which results in the possibility to weakly couple a finite element method model and a LPTN model in a very efficient way.

This paper aims to describe a CAD tool of permanent magnet electric machines. The software tool is operational from the first design phases and allows to study coupled phenomena.

The described design methodology is based on the association of analytical and numerical approaches. A coupled electromagnetic‐thermal model is used for the analytical study. The numerical one uses the finite element method.

The sequential implementation of the two approaches highlights their complementarities and improves the time consuming and the reliability of the design process. The thermal coupling allows to anticipate the overheating of the machine and to take it into account in the design process.

The simplifying assumptions made in the analytical model degrade the accuracy of temperature calculation.

This is a useful tool for electric machines manufacturer planning to obtain a fast and reliable solution in response to datasheet specifications.

This paper describes a multidisciplinary design methodology which is performed by coupling methods and software tools at the aim to take advantage of each one.

The purpose of this paper is to present a low evaluation budget optimization strategy for expensive simulation models, such as 3D finite element models.

A 3D finite element electromagnetic model and a thermal model are developed and coupled in order to simulate the linear induction motor (LIM) to be conceived. Using the 3D finite element coupling model as a simulation model, a multi‐objective optimization with a progressive improvement of a surrogate model is proposed. The proposed surrogate model is progressively improved using an infill set selection strategy which is well‐suited for the parallel evaluation of the 3D finite element coupling model on an eight‐core machine, with a maximum of four models running in parallel.

The proposed strategy allows for a significant gain of optimization time. The 3D Pareto front composed of the finite element model evaluation results is obtained, which provides the designer with a set of optimal trade‐off solutions for him/her to make the final decision for the engineering design.

An infill set selection strategy is proposed, which allows the parallel evaluation of the finite element model, and at the same time guides the progressive construction of an improved surrogate model during the multi‐objective optimization run. The paper may stand as a good reference for researchers/engineering designers who have to deal with optimal design problems implying costly simulation models.

This work aims to study a new design of linear permanent magnet transverse flux induction heating devices of nonmagnetic parallelepipedic workpiece. In these topologies, the permanent magnet inductor produces a static magnetic field, and the workpiece to be heated is subjected to a linear movement. To study the magnetothermal process, a new analytical coupling method between the magnetic and thermal phenomena is developed. This analytical model described in this study takes into account the variation of the physical properties of the heated workpiece. The analytical results are compared with good agreement to those issued from finite elements simulations, as well as those issued from measurements on an actual prototype.

The research methodology is based on analytical development of coupled problem, including the electromagnetic and thermal boundary problems. A strongly coupled magneto-thermal analytical model is developed; the time dependent magnetic problem is first solved by using the separation of variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained, thanks to strong involvement of this magnetic model in a new analytical thermal model based on a synergy of separation of variables method and Green’s function transient regime analysis method.

The results show that an efficient transient magneto-thermal analytical model was developed allowing fast analysis of permanent magnet induction heater for deep heating of parallelepipedic workpieces. Developed model allows also fast and precise simulations of nonlinear and transient magneto-thermal phenomena for different types of permanent magnet induction heating devices.

The developed magneto-thermal analytical model can be used for fast designing of permanent magnet linear induction heating devices for moving parallelepipedic nonmagnetic workpiece.

A new analytical coupled model, including the electromagnetic and transient thermal boundary problem with additional algebraic equations and taking into account the nonlinearity, has been developed. The developed model accuracy was validated with a permanent magnet linear induction heating device. Developed coupled analytical model allows fast analysis and designing of such permanent magnet linear induction heating devices.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

The aim of this paper is to simulate, test and evaluate an induction heating process considering the converter's performance.

In case of continuous induction hardening processes, the load changes abruptly during the transition to Curie temperature, becoming significant considering the converter's behavior. In this paper, an induction heating system is simulated combining the numerical analysis of the electromagnetic‐thermal and electrical problem, focusing mainly on the converter's performance. The simulations are realized by using commercial FEM software and the voltage and the frequency are manually varied according to the converter's control. The system has also been implemented in an experimental setup and the results obtained have been compared with the simulations.

The importance of considering the converter's dynamics was observed during the simulations. The simulation results showed a correspondence with the experimental results, validating the simulation procedure and demonstrating that the converter's behavior has to be considered.

A power converter for a real industrial induction heating process where there is a sudden change in the load parameters is simulated and experimentally tested. The importance of considering the variation of frequency and voltage during the simulation of induction heating systems is demonstrated. Some considerations for induction heating modeling regarding converter's performance are given and the importance of converter's dynamics is introduced. In addition, a simple and flexible method of simulating the converter operation with commercial software is presented.

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.

Induction machines for traction applications are operated at working points of high ferromagnetic saturation. Depending on the working point, a broad spectrum of harmonic frequencies appears in the magnetic flux density of induction machines. Detailed loss analysis therefore requires local and temporal highly resolved nonlinear field computation. This loss analysis can be performed in the post processing of nonlinear transient finite element simulations of the magnetic circuit. However, it takes a large number of transient simulation time steps to build up the rotor flux of the machine.

In this paper, hybrid simulation approaches that couple static FEA, transient FEA and analytic formulations to significantly decrease the number of simulation time steps to calculate the magnetic field in steady state are discussed, analyzed and compared.

The proposed hybrid simulation approaches drastically decrease the simulation time by shortening the transient build-up of the rotor flux. Depending on the maximum error of the rotor flux linkage amplitude compared to the steady state value, a reduction of simulation time steps in the range of 55.5 to 98 per cent is found.

The presented hybrid simulation approaches allow efficient performing of the transient FE magnetic field simulations of induction machines operated as traction drives.

This paper aims to introduce and illustrate a computational technique capable of determining the geometry and complex permittivity of a supplementary dielectric insert making distributions of microwave-induced dissipated power within the processed material as uniform as possible.

The proposed technique is based on a 3D electromagnetic model of the cavity containing both the processed material and the insert. Optimization problem is formulated for design variables (geometrical and material parameters of the insert) identified from computational tests and an objective function (the relative standard deviation [RSD]) introduced as a metric of the field uniformity. Numerical inversion is performed with the method of sequential quadratic programming.

Functionality of the procedure is illustrated by synthesis of a dielectric insert in an applicator for microwave fixation. Optimization is completed for four design variables (two geometrical parameters, dielectric constant and the loss factor of the insert) with 1,000 points in the database. The best three optimal solutions provide RSD approximately 20 per cent, whereas for the patterns corresponding to all 1,000 non-optimized (randomly chosen) sets of design variables this metric is in the interval from 27 to 136 per cent with the average of 78 per cent.

As microwave thermal processing is intrinsically inhomogeneous and the heating time is not a part of the underlying model, the procedure is able to lead only to a certain degree of closeness to uniformity and is intended for applications with high heating rates. The initial phase of computational identification of design variables and their bounds is therefore very important and may pre-condition the “quality” of the optimal solution. The technique may work more efficiently in combination with advanced optimization techniques dealing with “smart” (rather than random) generation of the data; for the use with more general microwave heating processes characterized by lower heating rates, the technique has to use the metric of non-uniformity involving temperature and heating time.

While the procedure can be used for computer-aided design (CAD) of microwave applicators, a related practical limitation may emerge from the fact that the material with particular complex permittivity (determined in the course of optimization) may not exist. In such cases, the procedure can be rerun for the constant values of material parameters of the available medium mostly close to the optimal ones to tune geometrical parameters of the insert. Special manufacturing techniques capable of producing a material with required complex permittivity also may be a practical option here.

Non-uniformity of microwave heating remains a key challenge in the design of many practical applicators. This paper suggests a concept of a practical CAD and outlines corresponding computational procedure that could be used for designing a range of applied systems with high heating rates.

This study aims to investigate the feasibility of saturated AC heating of magnetic metals. In AC heating of magnetic steel below the Curie temperature, because of the high magnetic permeability, the penetration depth is in the order of 1-6 mm at 50 Hz. Surface heating is then obtained, in practice, if large slabs are processed. The necessity to provide the required surface-to-core temperature uniformity (about 25°C) at the end of the heating process, avoiding excessive thermal stresses which can lead to cracks, thus implies a long heating time.

The penetration depth can be increased if the material is brought to saturation by applying an external DC magnetic field, and a faster in-depth heating can be obtained. The DC saturating field can be produced with no losses over large volumes by means of superconducting (SC) coils.

The feasibility of in-depth induction heating of a 200 × 1,000 × 5,000 mm magnetic steel slab with an applied 2 T DC saturating field is numerically investigated. The results show that the use of a DC saturating field leads to shorter processes which fulfil the heating objectives.

A DC saturating field cannot be produced by means of copper coils because of the large amount of material and the unaffordable power required. However, this field can effectively be produced by means of SC magnets based on state-of-the-art materials.

Superconductivity may be the enabling technology for fast and efficient induction heating of magnetic steel slabs if the increase in productivity can balance the additional costs due to the SC magnet.