The paper will present two general methods for the deduction of global information from the final result of the finite element computation of an electromagnetic device. The first one, called the local jacobian derivative, may be used for evaluation of the derivative of any integral quantity versus the parameter of motion of a rigid body. Typically, this method when applied to electromagnetic systems, can be used for the computation of magnetic force or torque by virtual-work principle. Compared with the popular Maxwell's tensor method, this procedure is easier to implement in a finite element package especially for 3D problems. The second method which is based on a stationary property of the field solution, allows the evaluation of a second order derivative of any integral quantity. For instance, computation of the stiffness of a magnetic system (derivative of a force or a torque) may be achieved as the second order derivative of the magnetic energy. It may be pointed out that this method requires the field computation once for a linear problem as well as for a non-linear one.

A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness

A numerical approach is described that overcomes the deficiencies of other methods through the use of a two-dimensional, nonlinear, time-stepping finite-element method for excitation from a constant voltage source. Comparison of stator current for no-load and load conditions shows good agreement with test values on a large induction motor. It is shown that the method can provide a great deal of information on flux distribution and harmonic rotor bar currents. >

Induction motor analysis by time-stepping techniques

The different ways of considering the movement in field equations are first presented. Then the proposed methods and the accuracy of the obtained results are illustrated by simulation examples.

The movement in field modeling

Different methods are presented for the calculation of torque as a function of rotation angle in an electrical machine. These methods are integrated in a calculation code by using the finite element method. The movement is taken into account by means of the moving band technique, involving quadrilateral finite elements in the airgap. The torque is calculated during the displacement of the moving part by using the following methods: Maxwell stress tensor, coenergy derivation, Coulomb's virtual work, A. Arkkio's method (1988), and the magnetizing current method. The results obtained by the different methods are compared with experimental data and make it possible to obtain practical information concerning the advantages and limitations of each method. >

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Finite element torque calculation in electrical machines while considering the movement

In the design of electric machine working under unbalanced conditions or supplied by non sinusoidal current, a detailed knowledge of the magnetic field distribution is required to predict the machine performance. Under such conditions this field distribution must be calculated using a dynamic model for the machine air-gap: A particular element constituted by the uniform part of the air-gap (u.p.a.g.) allows such a dynamic model in the present paper. An analytical solution of the Laplace equation in the air-gap is done. The field distribution in a saturated machine can be obtained within this air-gap model, combined with the classical finite element solution. The results of field calculation obtained using such a method are more precise than those calculated when modelling the air-gap with classical elements. Examples are given in the paper, showing this fact for both the cases of static and dynamic calculations.

Conception of an air-gap element for the dynamic analysis of the electromagnetic field in electric machines

In many engineering applications the calculation of forces and torques is subject of great importance [7] , [8]. A method for the calculation of the electromagnetic torque in electric machines is proposed in the paper. This method is based on an analytical field calculation in the air-gap combined with finite element field calculations in the saturated rotor and stator iron. The results of field calculation obtained using such a method are more precise than those calculated by the classical finite element method; thus the accuracy of the calculated torque will be better. An application for the case of synchronous machine is given at the end of the paper.

A. Abdel-Razek

Papers

Conception of an air-gap element for the dynamic analysis of the electromagnetic field in electric machines

The calculation of electromagnetic torque in saturated electric machines within combined numerical and analytical solutions of the field equations