A. Razek

Finite element analysis in electromagnetic systems-accounting for electric circuits

Two approaches for the numerical simulation of electromagnetic systems, accounting for electric circuit equations, are presented. First, the indirect coupled model, which permits the simulation of synchronous machines fed by controlled inverters with moderate calculation time is considered. Second, a direct coupled model where the magnetic and electric circuit equations (2-D or 3-D) are solved simultaneously is developed. This approach takes more calculation time but gives more precision. Applications concerning several electromagnetic systems are treated, and numerical results are compared with experimental ones to verify the validity of the models. >

A model for coupled magnetic-electric circuits in electric machines with skewed slots

A model permitting the simulation of skewed-slot saturated machines associated with nonlinear external circuits is proposed. To take the slot effects into account, the magnetic circuit is modeled through the combined two-dimensional calculations along the machine axis. In this simulation the electric circuit equation is directly coupled with the magnetic one. The solution of the resulting nonlinear time-dependent equation is obtained using step-by-step numerical integration and the Newton-Raphson iterative procedure. The model is used for the simulation of a 4.6-N-m permanent-magnet synchronous machine in various modes of operation. >

Local force computation in deformable bodies using edge elements

A local force calculation method based on the virtual work principle and the use of the edge element is presented. In the edge elements, the magnetic coenergy or magnetic energy is expressed by the circulation of magnetic field along edges or by the magnetic flux density across facets according to the use of a magnetic formulation or an electric formulation. The magnetic force is obtained by the derivative of magnetic coenergy or energy with respect to configuration parameters while keeping the circulation of magnetic field or the magnetic flux constant. An eddy current problem is taken as a numerical example. The magnetic force is calculated by the present method and by the j*b method. Results are compared with analytical ones. It is shown that a better accuracy is obtained by the present method. >

Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells

We describe a novel and rigorous vector eigenfunction expansion of electric-type Greens dyadics for radially multi- layered uniaxial anisotropic media in terms of the modified spherical vector wave functions, which can take into account the effects of anisotropy ratio systematically. In each layer, the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary. Both the unbounded and scattering dyadic Greens functions (DGFs) for rotationally uniaxial anisotropic media are derived in spherical coordinates (r, thetas, phi). The coefficients of scattering DGFs, based on the coupling recursive algorithm satisfied by the coefficient matrix, are derived and expressed in a compact form. With these DGFs obtained, the electromagnetic fields in each layer are straightforward once the current source is known. A specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres, and some novel performance regarding anisotropy effects is revealed.

A non-linear coupled 3D model for magnetic field and electric circuit equations

The authors propose a 3-D numerical model in which the magnetic field and electric circuit equations in the absence of eddy currents are solved simultaneously. To consider the magnetic equations, use is made of a magnetic vector potential formulation with the gauge condition (A.w=0) which makes it possible to reduce the number of unknowns. To take into account the magnetic and electric nonlinearities, the Newton-Raphson algorithm has been used. Two applications have been considered: an iron core coil fed by sinusoidal voltage through a diode and a current transformer. For the latter example the results obtained from the simulation are compared with experimental ones. >

A new hybrid model using electric field formulation for 3-D eddy current problems

A hybrid finite-element-boundary integral method using an electric variational formulation (3-D code Trifou-e) is presented. Whitneys edge elements are used in conducting regions and the boundary element technique is used for exterior regions. The electric field is taken as the state variable for both of the regions, whether modeled by the finite-element or boundary-integral techniques, so that the problem of multiply connected regions can be treated in a convenient way. >

A generalized finite element model of magnetostriction phenomena

We present a generalized finite element model of magnetostriction phenomena where the direct and inverse effects are taken into account. The variational formulation in terms of magnetic vector potential and displacement is used to solve this coupled problem. Different computing steps in 3D and 2D cases are reported.

Torque ripple minimization in permanent magnet synchronous servodrive

In this paper the electromagnetic torque developed in permanent magnet synchronous motors is analyzed. Two strategies are discussed for torque ripple minimization. The first is based on numerical predetermination of the current waveform which is imposed by the control in machine phases to obtain a constant torque. The second is a torque regulation based on its on-line instantaneous estimation. To optimize the current waveform and minimize copper losses, two methods for current modulus minimization are compared. One is relative to the optimal current which leads to a perfect constant instantaneous torque with minimum instantaneous current modulus, and the second concerns only the mean current modulus. Relation between current components and torque reference can be expressed by functions after normalization. These functions optimizing the mean torque are easy to implement and can be used for torque ripple minimization.

Calculation of mechanical deformation of magnetic materials in electromagnetic devices

A coupled model is developed to calculate mechanical deformation of magnetic materials in a magnetic field. The two equations governing magnetic and mechanical phenomena are solved simultaneously using the finite element method. The magnetic force distribution is calculated through a local application of the virtual work principle. The saturation of the material is considered. The nonlinear coupled system is solved by the Newton-Raphson method and the whole matrix is symmetrized. An example is given showing the effectiveness of the model. >

Calculation of eddy currents with edge elements on non-matching grids in moving structures

In this paper we present a nonconforming nonoverlapping domain decomposition method to approximate the eddy current problem, formulated in terms of the electric field variable, in nonstationary structures. This approximation, that allows for nonmatching grids at the sliding interface, is based on the mortar element method combined with edge elements in space and finite differences in time. Numerical results illustrate how the method works and the influence of the free part movement on the electric field distribution.