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The purpose of this paper is to find the method for determining the displacement of the active element in a giant magnetostrictive transducer.

The giant magnetostrictive transducer with the active element made of Terfenol-D has been considered. A structure with an axisymmetrical transducer has been proposed. In the proposed model the coupling of magnetic and mechanical field has been taken into account. Maxwell’s equations for electromagnetics and Navier’s equations for mechanical systems are formulated in weak form and coupled using a nonlinear magneto-mechanical constitutive law for Terfenol-D. In order to obtain the distribution of the magnetic and mechanical fields the finite element method was used. The elaborated nonlinear magnetostrictive model has been implemented by using a finite element weak formulation with COMSOL Multiphysics.

The elaborated model for the giant magnetostrictive transducer allows to take into account the magneto-mechanical coupling as well as the material’s nonlinearity. The calculation results of the strain distributions caused by magnetostrictive forces have been presented. The output displacement of a transducer vs supply current for different compressive preload stresses has been calculated and measured. The simulation and measurements results are in close agreement.

Taking advantage of the geometrical structure of the prototype of the giant magnetostrictive transducer the computations are performed in an axial-symmetric domain with cylindrical coordinates (r, z, ϑ). The axisymmetric formulation describes the giant magnetostrictive transducers (GMT) without significant loss of accuracy. This approach leads to smaller numerical models and reduced computational time.

The elaborated magneto-mechanical model can be used to the design and optimize the structure of GMT.

The paper offers the magneto-mechanical model of the giant magnetostrictive transducer. The elaborated model can predict behavior of the magnetostrictive materials it can be used as a tool for the design process of the giant magnetostrictive transducer.

The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.

The proposed algorithms are related to the analysis of electrical machines using the methods of equivalent magnetic networks. The presented permeance and reluctance networks are formulated using FE methods. Attention is paid to the algorithms of electromagnetic torque calculation for 3D models. The virtual work principle is applied. The principle is adapted to the discrete network models. The network representations of Maxwell's stress formula are given.

The proposed method of electromagnetic torque calculation can be successfully applied in the 3D calculations of rotating electrical machines. It can be used for scalar and vector potential formulations. The obtained results and their comparison with the measurements show that the method is sufficiently accurate.

The presented formulas of electromagnetic torque calculation are universal and can be successfully applied in the FE analysis of electrical machines using nodal and edge elements.

The equivalent fixed grid and moving grid models for the finite element (FE) analysis of an induction machine are presented. The discussed transformation is the FE representation of the classical commutator transformation. The obtained fixed grid model takes into account the higher space harmonics of the flux density wave and can be used in the FE analysis of the machines with solid rotor, drug‐cap rotor, and squirrel cage winding. The models have been applied in the calculations of TEAM Workshop problem No. 30. The test problem has been solved analytically. The FE results and analytical results are very close.

This paper demonstrates how the 3D edge element method can be applied to the analysis of permanent magnet motors. The edge element method using the vector magnetic potential has been used. Special attention has been paid to the analysis of systems with inhomogeneously magnetized permanent magnets. The magnets are not skewed and are mounted on a cylindrical laminated rotor. Calculations have been performed for different magnet widths and different distribution of the magnetization vector. Brushless motors with radially and inhomogeneously magnetized magnets have been compared.

The paper presents a method for the 3D edge element analysis of saturation effects in the classical rotating electrical machines of cylindrical structure. The edge element (EE) method using vector magnetic potential has been applied. Special attention is paid to the saturation effects in permanent magnet motors. In order to solve the non‐linear EE equations the authors propose to apply the modified Newton algorithm with block relaxation solver and Cholesky decomposition procedure for block matrices. The convergence of the algorithm is analysed. The influence of core non‐linearity on the values of electromagnetic torque and armature inductances is considered. The results for 3D and 2D models are compared.