By running optimization calculations using Finite Element Analysis (FEA), globally optimal design proposals can be obtained from a wide design space. Because the magnetic flux that passes through the rotor and stator facing each other is a 3D magnetic circuit, the analysis model must be modeled as 3D geometry. Analyzing 3D geometry requires long calculation times. However, by using surrogate models, the amount of calculation time needed for optimization calculations can be reduced.
In this example, the dimensions of an axial gap motor are optimized by using surrogate models, then the Pareto curves and the effect of reduction in calculation times when using surrogate models are checked.
The design variables for the geometry dimensions are the frame width, magnet inner diameter, magnet outer diameter, and the flatness ratio.
The definition of the flatness ratio is height a/outer diameter b. The volume of the cylinder is assumed to be constant, and the height a and outer diameter b are uniquely determined by specifying the flatness ratio.
Using Surrogate Models for Optimization Calculations
In optimization calculations using surrogate models, the calculation of particular generations is sped up by replacing surrogate models with machine learning models.
The training data is added to surrogate models after each FEA generation.
Effect of Reduction in Calculation Time When Using Surrogate Models
The Pareto curves both with and without using a surrogate model are shown in Fig. 3, and the calculation times are shown in Fig. 4.
In this example, the optimization using a surrogate model calculates three patterns of FEA intervals: every two generations, every four generations, and every ten generations.
Fig. 3 shows that the Pareto curves of the FEA intervals for every two and four generations are equivalent to those obtained without using a surrogate model.
Fig. 4 shows that calculation times are reduced to 1/3 when the FEA intervals are for every four generations.
The Pareto curve obtained for the FEA intervals at every four generations is shown in Fig. 5, and the design proposals on the Pareto curve are shown in Fig. 6.
It can be seen that the greater the torque, the smaller the flatness ratio and the flatter the axial gap motor geometry. This is because of the wider surface area of the gap where the torque generates. Conversely, the flatter the axial gap motor geometry, the smaller the cross section where the coils are wound, increasing the electrical resistivity. Copper loss increases, which results in an increase in total loss.