## 3 Numerical Modeling and Novel Technologies and Materials
### 3D Printed Electrical Machines  
One of the interesting research fields of electrical machines, where optimization plays a big role, is Additive Manufacturing (AM), also known as 3D printing (Figure 10). AM refers to a manufacturing process where a three-dimensional (3D) object is built in layers by depositing a material. This process allows making complex parts that would be difficult or even impossible to make with conventional manufacturing methods. Due to its advantages, AM technology is gaining more and more popularity in various applications. AM refers to a wide range of techniques as there are different methods to produce the 3D component. For example, the American Society for Testing and Standards (ASTM) has defined seven types of AM based on the manufacturing process [238]:  
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* vat photopolymerization;
* material jetting;
* binder jetting;
* material extrusion;
* powder bed fusion;
* sheet lamination;  
Figure 9: Complex framework of electrical drive system-level design optimization. direct energy deposition. From the electrical machine design point of view, AM offers several advantages. 3D printing offers the ability to produce complex three-dimensional shapes that can be used in every component of an electrical machine, as illustrated in Figure 10. It is possible to produce the frames of the machine using plastic or metal printers, which can result in lower weight or in better cooling capability. It is possible to design and manufacture a three-dimensional magnetic core for the stator and/or rotor, resulting in better usage of magnetic material or increasing the power density of the machine (Figure 11). It is possible to print electrically conductive materials, and this allows producing the windings of the machine. Through this, it is possible to increase the winding filling factor, increase the cooling capability, or reduce the end winding effect. It is also possible to produce special heat exchangers for the machine. Furthermore, it is possible to print out a full working electrical machine, resulting in rapid prototyping. This all sounds very good, but there is still much research work needed before all these advantages can be implemented in electrical machines. The AM research community is ever-growing, developing new printing technologies and improving the existing ones to resolve its main drawbacks [239]: relatively slow manufacturing speed, internal defects from layer-by-layer fabrication, limited multi-material capabilities, and the necessary post-production of printed parts. From the material point of view, there is much work going on in the field of 3D printed materials. With magnetic materials, the main aim of most research work is to achieve material characteristics equal to or better than conventional materials [240; 241; 242; 243]. From the magnetic point of view, there are two main things that need to be focused on: the material hysteresis loop and material conductivity, resulting in eddy current losses. One of the biggest challenges in using these materials in electrical machines is how to reduce the eddy current losses. One way to reduce these losses may be to groove the surfaces in which the eddy currents are formed, but this can greatly affect the average torque [244; 245]. Another option could be to choose materials that have ferromagnetic properties, but lower conductivity. From the modeling point of view, the non-homogeneity of the printed materials and the unknown properties create new challenges for the designers [246]. However, there are new obstacles: 3D printed parts can suffer from internal defects; post-processing is often required; and key properties are often unknown about the materials from which it is printed. In addition, these materials often show anisotropy, both mechanically and electromagnetically. Therefore, if we want the resulting machine to be resistant to these phenomena, it is necessary to use robust optimization tools.