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The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

Magnetic hysteresis holds significant technical and physical importance in the design of electromagnetic components. Despite extensive research in this area, modeling magnetic hysteresis remains a challenging task that is yet to be fully resolved. The purpose of this paper is to study vector hysteresis play models for anisotropic ferromagnetic materials in a physical, thermodynamical approach.

In this work, hysteresis play models are implemented to interpret magnetic properties, drawing upon classical rate-independent plasticity principles derived from continuum mechanics theory. By conducting qualitative and quantitative verification and validation, various aspects of ferromagnetic vector hysteresis were thoroughly examined. By directly incorporating the hysteresis play models into the primal formulations using fixed point method, the proposed model is validated with measurements in a finite element (FE) environments.

The proposed vector hysteresis play model is verified with fundamental properties of hysteresis effects. Numerical analysis is performed in an FE environment. Measured data from a rotational single sheet tester (RSST) are validated to the simulated results.

The results of this work demonstrates that the essential properties of the hysteresis effects by electrical steel sheets can be represented by the proposed vector hysteresis play models. By incorporation of hysteresis play models into the weak formulations of the magnetostatic problem in the h-based magnetic scalar potential form, magnetic properties of electrical steel sheets can be locally analyzed and represented.

This paper aims to present an interactive design and simulation tool for permanent magnet synchronous machines based on the finite-element-method. The tool is intended for education and research on electrical machines.

A coupling between the software MATLAB and finite element method magnetics is used. Several functionalities are included as modular scripts and represented in the form of a graphical user interface. Included are fully parametrized motor models, automatic winding generations and the evaluation of torque waveforms, core losses and speed-torque-diagrams. A survey was conducted to determine how the motivation of students concerning the covered topics is influenced by using the tool.

Due to its simplicity and the intuitive visualization of the results, the tool provides direct access to the topic of electrical machines without having to deal with separate scripts. The modular structure of the software allows simple extensions with new functions. Because students can directly contribute to the tool with their own work, their motivation for using and extending it increases.

The presented tool offers more functionalities compared to similar free software packages, e.g. the calculation of core losses and speed-torque diagrams. Also, it is designed in such a way that it can be easily understood and extended by students.

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.