*4.1. Description of the Multiphysics Problem*

Boundary conditions and design parameters of the IM are defined on the basis of a reference geometry, whose cross sectional area is shown in Figure 4a. This is a four-pole IM with a rated power of 41.5 kW. An unchorded three-phase copper winding is inserted into the stator, which is connected in delta. The rotor of the machine is a squirrel cage rotor with bars and rings made of a die-cast aluminum with an electrical conductivity of 28 · 106 S/m. The stator and rotor laminations are made of electrical steel sheets of type M400-50A, the designation of which is given by DIN EN 10027-1. The main rated and geometrical parameters are summarized in Table 1. The geometry of the reference machine was designed electromagnetically in an experience-based, iterative process. By solving the problem using the presented optimization environment, a machine geometry with identical boundary conditions and design parameters is to be realized starting from the roughly designed IM in an automated process. The geometry properties and operating behavior of the resulting optimized machine should be similar to those of the reference machine. The cross sectional area of the roughly designed machine is shown in Figure 4b.

To evaluate the machine behavior, two differently weighted decision parameters *p*j,indiv are introduced, which are used to determine the fitness value of a geometry relative to the reference machine according to (23).

The first decision parameter is the average losses over a given driving cycle. For this purpose, the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) class 3 driving cycle is considered, which is a part of the Worldwide Harmonized Light Vehicles Test Procedure (WLTP). Based on this driving cycle, the associated speed and torque combinations of the WLTC 3 can be derived for an example small car defined by the vehicle parameters from Table 2 using the vehicle model according to [38]. To ensure that the driving cycle is fully represented by the reference machine, the resulting speeds and torques are additionally scaled by the factor 0.7. This is due to the fact that the vehicle data of the reference machine are not known. However, this has no influence on the methodical optimization of the machine. Using these speed and torque combinations, the average losses over the driving cycle can be determined via the operating map of the machine.

The second decision parameter is the installation space of the machine. The installation space is not only used as a decision parameter but is further restricted by boundary conditions. The installation space is weighted by a factor of three less than the losses over the driving cycle.

The reference machine is also be used to define the other design-relevant parameters of the multiphysics problem, on the basis of which the rough design of the IM is carried out.

**Figure 4.** Representation of the cross sectional area of the reference (**a**), roughly designed (**b**) and optimized machine (**c**).


**Table 1.** Rated and geometrical parameters of the reference machine.

**Table 2.** Parameters of the example vehicle.

