[JAC267] IPM Motor Topology Optimization Using the Density Method

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Motor design requirements are becoming more sophisticated. While satisfying the torque ripple rate and back electromotive voltage, line voltage limits, magnet demagnetization resistance, the stress on cores, and displacement constraints due to centrifugal force, it is required that torque is maximized at both low and high speeds.
Optimization that uses FEA is effective in satisfying these strict requirements. Design proposals can be obtained with a high degree of freedom because topology optimization in particular can perform searches that are not dependent on initial shapes.
Magnetic field and structural coupled analysis is run in this example. While accounting for rotor core strength, topology optimization that uses the density method is used to perform searches for a rotor shape that maximizes average torque.

Optimization Conditions

Fig. 1 shows the design region, Table 1 shows the evaluation item and objective functions.
The red frame shown in Fig. 1 is the design region. Topology accounts for the symmetry per each 1/2 pole while accounting for the rotor strength.

Fig. 1. Design Region
Table 1. Evaluation Items and Objective Functions

Optimization Results

The graph for the average torque-torque ripple rate for all cases when both accounting for and not accounting for rotor strength is shown in Fig. 2, and the optimum case average torque and torque ripple rate are shown in Table 2.
Average torque increases when rotor strength is not accounted for.
The results showing the optimum case material density distribution contours and magnetic flux lines when both accounting for and not accounting for rotor strength are shown in Fig. 3.
Flux barriers are generated in either circumstance to suppress the magnetic flux that short-circuits in the rotor, which results in larger average torque. When accounting for rotor strength, however, the formation of a bridge makes it easier for the magnetic flux to short-circuit. It is therefore thought that average torque is larger when not accounting for rotor strength.
The results showing R direction displacement contours for the optimum case when both accounting for and not accounting for rotor strength are shown in Fig. 4.
Not accounting for rotor strength means that the bridge is not generated, and there exists the structural issue of the increasingly large rotor displacement. Accounting for rotor strength means that the bridge is generated, and the displacement is suppressed.
From this we understand that optimization accounting for rotor strength can be useful.

Fig. 2. Average Torque-Torque Ripple Rate for All Cases
Table 2. Optimization Case Average Torque and Torque Ripple Rate
Fig. 3. Optimization Case Material Density Distribution Contours and Flux Lines
Fig. 4. Optimization Case R Direction Displacement Contours

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