An Accelerated Newton-Raphson Technique for Finite Element Analysis of Magnetic Fields in Electrical Machines

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Abstract
An accelerated (modified) Newton-Raphson technique is presented. The new method reduces the computational (CPU) time required to carry out a finite element magnetic field analysis in saturated electrical machines by up to about 60% of typical CPU times required by present state of the art methods. In order to illustrate practical use of the method, the technique is applied to the problem of field determination in a 6-pole, 18 slot, samarium cobalt permanent magnet brushless dc motor system rated at 120 Volt, 15 hp (11.2 KW). The investigated cases include overloads of more than 4 times the rated armature current, thus insuring a substantial degree of magnetic saturation throughout the flux paths in the stator (armature) teeth and yoke. Numerical results of the field solution and armature winding inductances obtained using this method are compared with those obtained using the standard state of the art Newton-Raphson method. It is found that practically no numerical errors are introduced as a result of use of this accelerated Newton-Raphson process. Meanwhile, substantial savings can be made in the computation cost incurred for such analysis, particularly in computer-aided design situations in which large numbers of field solution cases are often required.

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