Topology Optimization: Example

Let's consider the conception of the rotor of a three-phase synchronous reluctance machine.

With the topology optimization tools available in Flux 2D, it is now possible to obtain a rotor design that satisfies a set of specifications using only a rough initial design. In this example, the initial shape is simply a hollow solid cylinder, as shown in Figure 1.

Figure 1. Topology optimization of the rotor of a three-phase synchronous reluctance motor (a) using a hollow solid cylindrical rotor as an initial design (b). The geometrical face subjected to optimization is shown in yellow.

The desired performance specifications need to be translated into a topology optimization problem that tries to maximize the torque of the machine, while satisfying certain constraints. These are summarized in Table 1 below:

Table 1. The design goal and the constraints for designing the rotor of a reluctance machine through topology optimization in Flux 2D.
Objective or Constraint	Response or Constraint type	Definition
Objective	Torque	Maximize
Constraint	Von Mises stress	Lower than 260 MPa (i.e., 80% of the yield stress value of the electric steel M330_35A used in the rotor)
Constraint	Volume	Lower than 80% of the initial design volume
Constraint	Symmetry	45 degrees symmetry (i.e., with respect to the red dotted line shown in Figure 1).

The topology optimization has been executed on the yellow face shown in Figure 1 using the LevelSet method. A Mechanical problem has also been added to the description in this case to further constrain the topology optimization procedure.

Figure 2a shows the final design obtained after convergence of the topology optimization procedure and compares it to the rotor geometry of a reference machine (Figure 2b). The resulting geometry is quite similar to the reference, showing that the topology optimization techniques may be used efficiently in the conception of rotating electrical machinery.

Figure 2. The material density function of the final design displayed in SimLab (a) compared to the rotor geometry of a reference reluctance machine (b).