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Much of the early work on the design of electrical machinery was based on the use of the two-dimensional approximation and conformal mapping, with particular reference to the Schwarz-Christoffel transformation. The attainment of closed form solution is, however, limited to the simplest geometries.
Most of the recent work is based on purely numerical solutions obtained with the help of computer programs appropriate to two and three dimensional geometries.
The desire to establish general guiding principles for the design as an alternative to studying particular configurations, as well as extension of the method to include iron-saturation effects, prompted the adoption of a hybrid method.
This consists of a combination of the Schwarz-Christoffel transformation with numerical integration. It offers the possibility of becoming a useful tool for studying the most complex geometries, as well as arbitrary excitations.
Recently, this technique was applied to the evaluation of the flux distribution of a synchronously operating linear motor of the homopolar inductor type. Ignoring saturation of the poles, the distribution of the magnetic flux density in the gap was obtained as a function of geometrical parameters.
In order to operate the homopolar inductor machine efficiently one would like to drive it hard into saturation. Faced with a difficult choice about geometry and magnetic stresses, the designer needs a simple but accurate tool for determining the saturated reluctances.
To account for saturation of the poles, the magnetic flux in the air gap region resulting from the combined field and armature excitations (unsaturated) is subdivided into tubes of equal flux. The computer calculates the coordinates of these flux lines along the iron surface of the pole.
The poles will be saturated therefore neither conformal mapping nor any other linear technique will give an exact solution. However, an approximate graphical solution based on the method of curyilinear squares seems to be adequate. The corresponding MMF drops in each tube of flux is evaluated with the help of the iron magnetization curves.
The deviation in magnetostatic potential caused by these drops is then treated as an additional excitation, applied to the pole structure, and handled like the armature reaction. The process can be iterated, although such accuracy does not seem warranted.
The main advantage of using super position in an essentially nonlinear problem is that the designer can separate out and evaluate quantitatively each of the contributory factors and modify the design accordingly.
In conjunction with results obtained in, it will be shown that in order to optimize a new design a computer program can be constructed that requires less than 10 minutes in the IBM 360/65 computer.