### Overview

Anisotropic plastic magnets with good magnetic properties need magnetic field orientation. For this reason, a magnetic circuit is created to generate the magnetic flux necessary for magnetic field orientation in the product cavity in the mold used.

Design requirements for the magnetic circuit are that the magnetic flux generated in the cavity has the magnitude necessary and sufficient for the magnetic field orientation, that flux parallel to the analysis target main axis be produced, and that the magnetic circuit be formed as small as possible.

In the case of simple magnetic circuits, these requirements can be met by hand calculation, but FEA is effective for obtaining a generated spatial magnetic flux density distribution, angles, etc. in detail in the cavity. In addition, since trial and error cannot be avoided in an optimum design that minimizes geometry size while satisfying the above requirements, and time is consumed, automation of analysis combined with optimization tools is widely used.

In this example, a use case is presented in which a magnetic circuit of a product-forming mold, in a magnetic field aligned with the mold’s main axis, is optimized, with the mold’s dimensions used as design variables.

### Optimization Conditions

The design variables are: a, the radius of the magnets; b, the width of the nonmagnetic material; and c, the width of the yoke. The objective function is set so that the diameter (a+b+c) of the entire magnetic circuit can be minimized.

The constraint condition specifies the angle between the magnetic flux density B generated in the cavity and the Y-axis direction, and the threshold for the magnitude of B.

Two constraint conditions are set where the angle is not more than 5 deg and B is not less than 0.3 T.

### Optimization Results

Fig. 2 and Fig.3 shows the The response graphs for the results after optimization. Show graphs plotting degy_theta and Bmin, respectively, vs. the radius of the magnetic circuit under the constraints. The yellow plot is at the optimum value. The optimum value is the minimum value of the radius of the magnetic circuit under the constraints. The optimum value plot shown in Fig. 2 and in Fig. 3 are for the same case.

Fig. 4 shows the results magnetic flux density contour plots and flux lines obtained with the initial geometry and with the optimum geometry. The initial values of the variables a, b, c and the values obtained after optimization. It can be seen that in the region of the cavity surrounded by the red rectangle, for the initial geometry some of the flux enters at an angle, however, for the optimized geometry obtained the flux has parallel flux lines and is nearly uniform.