## 2. Stator Parametric Model  
At the beginning of the development process, the designer has information about the stator core, but not about the rest of the components. Hence, for the structural analysis, only the stator core is modeled, leaving the housing and the rotor core aside. The stator is the main energy transfer path and has the most important influence on the NVH characteristics. The stator is excited by the electromagnetic field and transfers the energy to the exterior, causing airborne noise. Therefore, in order to characterise the transfer path, a three-dimensional model is created within Simcenter 3D. The 3D stator model is constructed based on the geometric dimensions and material specifications of the electrical motor under study. Afterwards, the stator model is parameterized with the same degrees-of-freedom (DOFs) as in the electromagnetic optimization process [6], a DOF consistency being needed for multi-physics optimization routine. Figure 2 shows the cross-section and the DOFs of the parameterized model, where TWS represents the tooth width, YT is the yoke thickness, SOAng stands for the tooth tip angle, TGD is the tooth tip height, SO represents the slot opening, R is the stator inner radius, and \(R_{a}\) stands for the stator outer radius.  
Figure 1. Multi-attribute machine learning model workflow.  
Figure 2. Stator cross-section parameterization where DOFs marked with black are kept fixed and the DOFs marked with red are varied to construct the machine learning model [15].  
The parameterised model allows the generation of a set of feasible designs by performing a design of experiments using specific sampling techniques. The most important design parameters, TWS, YT, SOAng, TGD, SO, are varied within imposed boundaries, while the stator length (\(L_{sik}\)) and the stator inner and outer radii are kept constant. Each parameter is individually varied within imposed limits and the design space is filled with the help of the Latin Hypercube Sampling Technique (LHS). The variation interval, with its lower (LB) and upper (UB) boundaries, of the considered DOFs is presented in Table 1.  
The variable DOFs are chosen based on their impact on the structural characteristics and electromagnetic performances of the machine. The yoke thickness is the main contributor to the stator vibration response due to its direct influence on the stator stiffness. By increasing the yoke thickness, the stiffness value enlarges, shifting the natural frequencies corresponding to each mode-shape to a higher value. In particular, mode 0 (breathing mode) is strongly influenced by the variation of this parameter. At the same time, the yoke thickness, together with the tooth width have a massive impact on the electromagnetic characteristics by influencing the saturation levels of the electrical machine. The tooth width can also influence the structural behavior of the motor by creating local tooth bending modes. On the other hand, the variation of tooth tip height, slot opening and tooth tip, influence especially the electromagnetic quantities. The electromagnetic flux density harmonics are affected by this variation and, indirectly the structural vibration characteristics, by influencing the source of vibrations for the electrical motor.