OPTIMIZATION OF A MAGNETIC SEPARATOR AIR-GAP

The paper describes a method of optimization of a magnetic separator air-gap which serves to separate magnetic particles from volatile power plant dust. The method consists in seeking the air-gap dimensions, assuming that the shape of poles is known on the basis of magnetic force field analysis, or in seeking the shape of poles for the assumed force field distribution. In the second case the problem is reduced to solving a certain inverse boundary problem of the Dirichlet type.


i. INTRODUCTION
In recent years there has been an increasing interest in the separation of magnetic particles from volatile power plants 1 dust. Authors of a previous paper have described a certain laboratory model of magnetic separator and preparatory results of tests. Performances of such a type of separator proved to be so good that an industrial model has been built and has been installed in the power station "Rybnik" Further investigation into new applications of this type of separator has been carried out in a separation chamber. In another paper a method of force field analysis in the separator airgap has been suggested. Forces were determined on the basis of the magnetic field distribution, which was computed by solving a Laplace equation with Dirichlet boundary conditions by the integral equation method. This method has been found very efficient and the results obtained are correct, which 98 K. ADAMIAK was confirmed by an experimental investigation The magnetic forces in the air-gap, calculated numerically and measured with the help of a specially designed sensor, differ from one another at most by a few per cent. This paper is a continuation of the above-mentioned papers. Its purpose is to formulate a method of optimization of the separator air-gap an element which has an essential influence on the separation process.

OPTIMUM PITCH OF POLES SHAPED LINEARLY
The distribution of mmgnetic forces in the air-gap is a very important factor which exerts influence on the separator's performance. The volume density of these forces depends on where H is the magnetic field.
Thus, in order to determine a force field, we should at first determine a magnetic field. In the paper a simpli- It was assumed that the poles are made from an ideal ferromagnetic with permeability B. Thanks to it, at each point ol the pole surface, the scalar magnetic potential T has an identical value. This problem was reduced to solving a Laplace equation with Dirichlet boundary conditions. Next, using a single-layer potential, a Fredholm integral equation of the first kind was obtained. After its solution, it is very easy to determine all the quantities characterising the magnetic field at an arbitrary point in space.
The result of optimization executed in this way is rather unexpected, because tan opt=fl(b/a) is a linear function to a very high accuracy (Fig. 4). But the minimum value of b is, however, frequently delimited by the separator's capacity. Thus, assuming b to be fixed, a may then be optimized.
The plots E=f(8) for different parameters b/a are drawn up in Fig. 5. For high b/a, the curve =f(8) monotonically decreases. For small b/a there exist a local minimum and maximum on the curve. However, the value of e always increases when b/a increases. Comparing E for 8opt the optimum angle in the sense of the previous section it becomes also evident that E attains maximum values for high b/a (Fig. 6). Thus, if it is possible, one should tend to design air-gaps with small a or large b.

OPTIMIZATION OF THE POLE SHAPE
The results presented so far refer to an air-gap with poles shaped linearly. Optimization of that system consists in a choice of the parameters a/b and 8. However, another treatment is also possible. Namely, assumption of the force field distribution and seeking the pole shape.
After applying the integral equation method to the model of the air-gap described in paper 3, we obtain the following Dust containing magnetic particles is transferred through the separation chamber in a rather compact shape. Magnetic particles, pushing through nonmagnetic ones to the conveyor belt, must conquer considerable resistance of friction. Therefore, it is very important that, at points lying far away from the conveyor belt, these forces have to be high.  The results obtained fulfil the requirement with fairly high accuracy (Fig. 8). Improvement in force field homogeneity, in comparison with a force field of the poles shaped linearly, is observed not only on the symmetry plane but in the whole airgap too. (Fig. 9).
Similarly, computation of the pole shape has been performed assuming that fo(X) is a linearly-increasing function fo(X) m+nx The results, i/e/ the shape of the pole surface and the force density distribution in the air-gap symmetry plane, are shown in Fig. i0.

CONCLUSIONS
A method of optimization of the separator air-gap has been suggested in this paper. It consists in optimizing the airgap dimensions (assuming the pole shape to be known) or in determining the optimum pole geometry. Assumption of the magnetic force distribution has been the criterion for optimization. Integral equations in the calculations are easily reducible to algebraic equations which significantly save on computational time.