*2.5. Challenges*

Iron loss characteristics of printed FeSi is still a major concern. At DC or quasi-static excitation, additive manufactured iron-silicon has been shown to achieve hysteresis loss comparable to iron-silicon laminations [43]. The intrinsic coercivity of SLM-processed and BJP-processed FeSi is nearly 4 times lower than SMCs. At low excitation frequency of 50 Hz, the total iron loss density of additively manufactured iron-silicon is between 2 and 6W/kg at 1 T. This puts printed iron-silicon in line with SMCs in terms of total iron loss, and a bit higher in comparison to iron-silicon lamination steels. These iron loss values at low frequency range, however, are promising providing that this is still at an early stage of applying AM for soft magnetic materials. As the excitation frequency increases, however, the total iron loss of 3D printed iron-silicon increases exponentially [43]. The resistivity and eddy current loss of 3D printed iron-silicon must be reduced. In [47], a rotor core of a switched reluctance machine is printed and compared directly with a laminated rotor core, Figure 5. Experimental results show that at base speed, 3D printed machine is about 20% lower in efficiency in comparison to the benchmark laminated machine, Figure 5b. Higher operating speed leads to even higher eddy current loss and higher reduction in efficiency. Eddy current loss remains a concern with 3D printed iron core, especially when the core is printed as bulk.

(**a**) Laminated rotor and 3D printed rotor of a switched reluctance machine.

**Figure 5.** Illustration of eddy current loss impacts on efficiency of 3D printed electrical machine. Figures are adapted from [47].

> Some strategies have been suggested for improving eddy current loss within printed ferromagnetic materials. These strategies take advantage of unique capabilities of additive manufacturing. In [45,48], AM is proposed to fabricate iron-silicon cores with complex cross-section geometries. Figure 6 shows an example of an iron-silicon rod made of multiple parallel thin plates of 400 μm thickness, where struts are added to connect the plates together. This complex cross-section geometry disrupts the paths of the eddy current, which leads to the reduction of eddy current loss when compared to the solid iron-silicon rod. Printed iron-silicon with Hilbert cross-section geometry can also result in a lower eddy current loss. Another example of complex cross-section geometries is shown in [45], where the layering technique using different materials is used to 3D print iron alloy. Here, layers of iron and iron-aluminum alloy are stacked back to back in an alternative fashion, as shown in Figure 7. Due to the differences in the resistivity between the iron alloy and the iron-aluminum alloy, the eddy current is restricted in each layer, which leads to a lower eddy current loss and total iron loss. At the excitation frequency of 100 Hz, the measured eddy current loss shows a reduction of 15 times compared to the bulk printed iron alloy. Tuning layering materials and thickness can help with further reduction in eddy

current loss, which is significant for when applying such materials for high-speed electrical machine applications.

**Figure 6.** Examples of geometry structure in additive manufactured iron-silicon that can help with reducing eddy current loss. Printed iron-silicon with parallel plates or Hilbert cross-section can have a significant reduction in eddy current loss. Illustration adapted from [48].

**Figure 7.** Optical microscopy cross-section image of printed soft magnetic sample. Here iron layer and iron-aluminum alloy layer are stacked back to back [45]. This printing strategy is implemented to reduce eddy current loss.

There are still many challenges in fabricating high performance ferromagnetic materials for electric motors and generators. The electromagnetic and mechanical properties of 3D printed materials, although advancing rapidly, still need to match or exceed the current properties of many existing commercial equivalents. Judging at the performance development of SMCs a couple of decades ago [19], and the current performance of SMCs today [49], it is encouraging knowing that the performance of additively manufactured ferromagnetic materials will continue to improve. Material characterization is thus important, especially in the development of the correlation between the 3D printing parameters, the microstructure, the crystallographic texture, and the desired properties of printed ferromagnetic parts. Other efforts in optimization of the starting powder/filament, recovery of unused material, and improvement in printing bed size, and build rate can contribute to cost reduction of the printed parts [50], furthering the application of AM beyond just prototyping. Another concern typically seen in additively manufactured parts is the surface roughness, which can potentially lead to the 3D printed iron cores with rough surface. A poor contact between the stator core and the housing of the electrical machine can change

the contact thermal resistance between the core and the housing, which in turns can lead to negative impacts in the heat transfer between them [51].

### **3. Additive Manufacturing of Permanent Magnets**

There are three main requirements for permanent magnets used in electrical machines:


Regarding the magnetic properties, the important characteristics include remnant flux density, *Br*, intrinsic coercive force, *Hci*, and the maximum energy product (*BH*)*max*. Permanent magnets typically seen in electrical machines are NdFeB, AlNiCo, SmCo, and ferrite magnets. For NdFeB-based magnets, rare earth element such as Dy is used to help enhancing the intrinsic coercive force of the magnets [52], especially at temperature of 180 ◦C and higher [53,54]. This is beneficial to permanent magne<sup>t</sup> machines operated in high temperature settings as magne<sup>t</sup> flux remnant flux density is less susceptible to thermal degradation. However, the use of critical rare earth elements such as Dy and Nd can increase the cost of NdFeB-based magnets, and constrain the supply. By reducing the use of rare earth elements, it is possible to lower the magne<sup>t</sup> cost and diversify the magne<sup>t</sup> supply [54].

The production process of sintered permanent magnets includes crushing molten or strip cast alloys into fine powder, and aligning the powder particles under strong external magnetic field. The aligned powder particles are then compacted via cold isostatic pressing or other pressing techniques. The green part is then sintered, heat-treated, and machined to desired geometries. For bonded magnets, magnetic alloy powders are mixed with polymers and then formed to desired shapes by compression or injection molding. Additive manufacturing can potentially allow both sustainability and cost reduction in manufacturing magnets as well as increasing the magne<sup>t</sup> supply chain by reducing mechanical steps, and allowing for complex geometries without use of molds. At this current stage, the magnetic properties of 3D printed NdFeB bonded magnets are highly comparable to those found in commercial bonded NdFeB magnets [55]. These commercial bonded magnets are typically manufactured with injection molded (IM) method. The magnetic properties of printed magnets, however, are dependent on the printing technology, the density of the printed parts, and the chemical composition of the filament or powder mixture used in 3D printing.

### *3.1. Status on Additively Manufactured NdFeB Magnets*

Powder bed fusion, binder jetting, and material extrusion methods are three main technologies that have been investigated at fabricating NdFeB magnets. Big Area Additive Manufacturing (BAAM) is a special technology within the category of material extrusion, developed at Cincinnati Inc. together with ORNL's Manufacturing Demonstration Facility, has also been used to fabricate NdFeB magnets [56]. One major advantage of BAAM is that it is capable of printing large scale parts of volume up to 26 cubic meters [57].

The powder bed technology with SLM shows promise in printing magnets at above 90% density [58]. In this laser-based AM process, the laser can introduce significant cracks and residual stresses in the printed magnets which may negatively impact the magnetic and mechanical properties of the magnets. Thus, optimization of the laser parameters, such as proper selection on the scan speed and laser power, can lead to optimal performance of magnetic properties of printed magnets. Additionally, optimization of the laser scanning pattern can also help with the practical distribution of heat within the printed magnet, which can help improve its overall the performance. Here, the reported magnetic polarization of the laser-based printed magne<sup>t</sup> is around 0.55 T. Other performance characteristics of the printed magnet, however, are not included.

The material extrusion and binder jetting technologies, which do not use laser as an energy source, are widely investigated for printing NdFeB magnets. Magnetic properties of NdFeB produced via BJP have similar properties compared to NdFeB fabricated via fused deposition modeling (FDM), a technology within material extrusion, as shown in [59]. They share similar performance in density, remnant flux density, and intrinsic coercivity [60]. Magnets fabricated via BJP have a density value around 3.5 g/cm3, which is approximately above 40% of the NdFeB theoretical density. One of the current challenges in fabricating magnets via BJP is to increase the volume content of NdFeB powder in the printed parts, which can help improving the magne<sup>t</sup> density and the remnant flux density. Infiltration of NdCuCo and PrCuCo alloys toward as-built BJP magnets can help improve density and mechanical integrity of the magnets and the intrinsic coercive force, as shown in [61]. However, there is a slight tradeoff of remnant flux density with the inclusion of these additives.

NdFeB magnets fabricated via BAAM, however, outperform magnets prepared with the other printing technologies [62]. Density of BAAM magnets is approximately 20% higher in comparison with BJP magnets, while remnant flux density and the maximum energy product are 20% and 40% better, respectively. The magnetic properties of BAAM magnets can further be improved with a higher volume percentage of the magne<sup>t</sup> powder used in the printing mixture [63]. A direct comparison with commercial injection molded NdFeB magnets in [56] shows competitive performance of BAAM magnets, in terms of intrinsic coercive force, remnant flux density, and magne<sup>t</sup> energy product. Thermal performance of BAAM magnets also shows similar behavior when compared to injection molded magnets, as shown in Figure 8. Here, degradation of performance of BAAM magne<sup>t</sup> as a function of temperature shows similar negative trend as ambient temperature increases. A brief comparison of the current status of magnetic properties for different additive manufacturing technologies as well as injection molded magnets is shown in Table 2.

(**a**) Remnant flux density as function of ambient temperature

(**b**) Intrinsic coercive force as function of ambient temperature

**Figure 8.** A comparison on thermal degradation of performance between commercial injection molded magne<sup>t</sup> and BAAM fabricated magnet. Figures are plotted using data in [56].



### *3.2. Status on Other Additively Manufactured Magnets*

Research on additively manufactured SmCo magnets is still at the early stage, so far focusing on printing magnets made of recycled magne<sup>t</sup> powder. The authors in [64] shows the process on producing magne<sup>t</sup> filament, made of recycled SmCo magne<sup>t</sup> powder and polylactic acid (PLA) plastic, for 3D printing bonded magnet. The produced magne<sup>t</sup> filament, however, has low remanent flux density, below 0.1 T. This is due to the low volume percentage loading of the magne<sup>t</sup> powder (less than 20%), in the production of the magne<sup>t</sup> filament. Increasing the loading of the magne<sup>t</sup> powder can potentially lead to magne<sup>t</sup> filament with higher remnant flux density and maximum energy product.

On the other hand, investigation on additively manufactured AlNiCo magnets shows promising results toward application in electrical machines. The 3D printed AlNiCo magnets, via LENS technology, can achieve maximum energy product (*BH*)*max* with values between 48% and 66.7% in comparison to commercial sintered or cast AlNiCo magnets [65]. Regarding the intrinsic coercive force of printed AlNiCo magnets, it is equivalent to commercial AlNiCo magnets, varying between 140 kA/m to 160 kA/m. The remanent flux density, *Br*, of printed AlNiCo magnets varies between 0.75 T and 0.92 T, which is approximately 10 to 15% lower than typically values found in commercial AlNiCo. These early findings show the competitiveness of 3D printing as an alternative AlNiCo permanent magne<sup>t</sup> manufacturing process. Here, optimization of the printing process, as well as further exploration in material composition can potentially produce additively manufactured AlNiCo with magnetic properties exceeding commercial equivalents. One of the key advantages of AlNiCo magnets is that the (*BH*)*max* value of AlNiCo can stay relatively constant at temperatures up to 300 ◦C. Thus, the ability to have an alternative supply chain of AlNiCo magnets is beneficial to electrical machine applications where high operating temperature is a concern.

### **4. Topology Optimization for Magnetic Structures**

The shaping of the magnetic structures for electrical machines can be generally categorized into two groups: (1) conventional shaping and optimization techniques, and (2) topology optimization. For the conventional shaping techniques, mathematical models and sensitivity analysis are typically used on a pre-selected machine geometry template [66,67]. The computational and analytical efforts are often intensive to improve the accuracy of the calculation of the airgap flux density, torque components, and the magnetic flux density distribution [68]. Conventional optimization, which is typically based on evolutionary multi-objective optimization algorithms, further refines the shape of the magnetic structures to improve the machine performance. As a result, the derivation of uniquely shaped magnetic structures for electrical machines can be slow.

Emerging from structural optimization, TO is increasingly applied in magnetic devices [69], and subsequently in design of electrical machines, especially at the component level such as magnetic cores [70] and permanent magnets [71]. In contrast to conventional optimization, TO can generate an initial geometry template from scratch with less analytical modeling [72]. In general, TO investigates optimal distribution of single or multiple materials within a defined design space [73]. Compared to conventional optimization shaping techniques, it offers additional flexibility in optimizing the geometry of the magnetic components for attaining the desired performance. Thus, TO can yield unique shapes that are generally not realizable with conventional optimization approach.

### *4.1. Topology Optimization Shaping Techniques*

In seeking unique and optimal geometry either made of single or multiple materials, TO can employ approaches such as the on/off method and the density-based method. For the on/off method, the design space is typically divided into cells or put into a grid-like structure. Each cell is then represented by a variable, such as normalized density *ρ<sup>n</sup>*, which can be assigned a value of zero or one, as illustrated in Figure 9a. Zero and one indicate the absence and presence of material, respectively. The pattern of the material distribution can

be determined via selection of objective functions and use of evolutionary multi-objective or gradient-based algorithm. Thus, in a finalized topology optimized design via on/off method, it typically has an unconventional geometry.

**Figure 9.** Illustrations of two topology optimization methods for magnetic cores. Here, *ρn* is the normalized density variable under optimization.

An on/off TO is modified to optimally distribute the soft magnetic material for a rotor core of an interior permanent magne<sup>t</sup> machine and then to smooth the shape of the design is presented as shown in Figure 10. Here, the TO algorithm in [8] first uses a genetic-based method to find an optimal solution in the global search space. The solution is then smoothed out via the use of a gradient-based method in the local search space. The illustration of the modified algorithm is shown in Figure 11.

**Figure 10.** Example of a rotor core of a permanent magne<sup>t</sup> machine achieved via on/off TO algorithm. The TO design is smoothed out. Figure is adapted from [8].

The on/off TO method can also be applied to find the optimal distribution of multiple materials such as iron, copper, and permanent magnet. In [74], a multi-material on/off TO algorithm is used to maximize the force acted on the plunger of a permanent magne<sup>t</sup> linear actuator. The TO optimal design achieves a unique structure compared to the original design and an additional increase of 40% in average force, as shown in Figure 12.

**Figure 11.** Example of an on/off TO algorithm where a genetic-based algorithm is combined with a gradient-based algorithm. The shape achieved with this algorithm is smoother. Figure is adapted from [8].

**Figure 12.** Illustration on the result of the on/off TO algorithm for multiple materials on a permanent magne<sup>t</sup> linear actuator. Figure is adapted from [74].

As the on/off method assigns the optimizing density variable to be binary, the densitybased method assigns the density variable *ρn* a continuous value between zero and one, as illustrated in Figure 9b. A version of the density-based method is applied on a rotor core of a permanent magne<sup>t</sup> synchronous machine in [9]. Here, the exclusive magnetic-based topology optimization works toward maximizing the average torque while constraining the torque ripple and cogging, and finally leads to the unique design of the rotor core as shown in Figure 13. The white areas in the rotor core represent the permanent magnet, while the dark red areas and the dark blue areas represent iron and air, respectively. In between them are regions with intermediate density values, which are represented with different shades of colors.

Magnetic-based topology optimization may result in unique designs that achieve desired electromagnetic performance. These unique designs also present challenges that must be considered. Exclusively using magnetic-based TO algorithm results in designs that are only optimized for electromagnetic performance. Since mechanical stress of the structure is not included as an objective, the mechanical integrity of the magnetic-based TO design may become a concern. A magnetic-based TO design with a unique distribution of air pockets is shown in Figure 14. Here the TO algorithm, however, does not include mechanical stress analysis in the iron regions adjacent to the air pockets. This can lead to durability performance of the design under real operating condition where the adjacent iron regions can be subjected to stress values between 240 MPa to above 450 MPa [75]. Coupled structural and electromagnetic analysis can provide tradeoff solutions to address this concern. In [76], the density-based method is applied on rotors of wound field synchronous machines. The optimized rotors are achieved via the integration of both magnetic and structural topology optimization analysis.

**Figure 13.** Illustration of density-based topology optimization for the rotor core of an interior permanent magne<sup>t</sup> synchronous machine, adapted from [9].

**Figure 14.** Example of magnetic-based topology optimization for the rotor core of an interior permanent magne<sup>t</sup> synchronous machine, adapted from [77]. Iron regions adjacent to air pockets and magnets can be subjected to high mechanical stress.

### *4.2. A Design Tool for Additive Manufacturing*

As TO is increasingly adopted in developing unique geometries for electrical machines, manufacturability of the unique magnetic core designs is equally important. Design complexities may increase manufacturing cost for electrical steel laminations. Additionally, manufacturing methods including subtractive techniques can compromise the magnetic properties of punched laminations [17], leading to magnetic cores with inferior magnetic performance compared the mother coil. Thus, topology optimized designs in Figure 10 and Figure 14 may not be able to achieve the desired magnetic performance. Powder metallurgy can potentially be used as an alternative approach to fabricate such complex designs, as shown in Figure 15. However, the added cost of molding and tooling may become a concern.

**Figure 15.** An example on topology optimization of a rotor core for a switched reluctance motor [78].

In application where non-homogeneous magnetic core is desired as in [79,80], powder metallurgy manufacturing approach is not a viable solution for production as it may reach the limits in fabricating such composite, non-homogenous structures. Similarly, designs of magnetic cores for electrical machines generated with the TO density-based method as in [9,76], may request material whose properties may not correspond to an available material [81]. Additive manufacturing can potentially overcome difficulties typically observed in conventional manufacturing methods, and in some cases is the only viable manufacturing solution [82].

Recent advancements in AM as well as the proliferation of its application in fabricating magnetic components for electrical machine have revitalized TO as an advanced design tool. The synergy between TO and AM can potentially lead to the development of magnetic components, whose properties and geometries are complex. Investigations in integration of TO toward AM in producing magnetic components for electrical machines have shown very promising results. In [10], a topology optimized design of a rotor core of a surface mount permanent magne<sup>t</sup> machine is additively manufactured via the SLM process, as shown in Figure 16. Here, the TO algorithm combines both the electromagnetic and structural optimization stages to achieve a rotor core geometry with 50% reduction in weight, at a tradeoff of less than 2% in average torque, while achieving maximum von Mises stress in the optimized rotor core well within the yield strength of the material. The result of this work highlights the exploitation of multi-physics TO as an advanced design tool for AM in developing new, unconventional electrical machines.

**Figure 16.** Optimized rotor core via coupled magnetic-structural TO. The design is then additively manufactured via SLM. Figure is modified from [10].

The integration of TO into AM is also seen in fabricating permanent magne<sup>t</sup> with unique shapes and structures. In [71], TO is implemented to generate the design of a permanent magne<sup>t</sup> such that it can provide magnetic flux density waveform close to the predefined external field. The design is then additively manufactured via the FDM process from a magnetic compound of NdFeB powder, ferrites, and polymers, Figure 17. In [11], permanent magne<sup>t</sup> made of multiple magne<sup>t</sup> grades is proposed for a surface mounted

machine to reduce manufacturing cost without penalizing machine performance. The multi-grade magne<sup>t</sup> is optimized, and investigated via finite element analysis. Although TO is not implemented, the analysis suggests the combined use of TO and AM technologies in potentially producing lower cost magnets.

**Figure 17.** Topology optimized magnet. The design is then additively manufactured via fused deposition modeling. Figure is modified from [71].

### **5. Discussion**

The implementation of AM technologies for magnetic components in electrical machines is still in its early stages. Common research themes for application of AM technologies for electrical machines focus either on understanding and improving the performance of individual components, or leveraging the freedom in design, an inherent characteristic of AM. An understanding of the characteristics of additively manufactured parts can help further the adoption of AM for electrical machines, as well as its integration with topology optimization as an enabling design tool.

#### *5.1. Impacts of Defects Due to AM Process*

Presently, there is opportunity to develop full density printed magnetic materials for electrical machines. Porosity can be observed in microstructural analysis of printed ironsilicon and printed magnets, as shown in Figure 18. Porosity, cracks, and residual stresses in the printing process typically hinder both the magnetic and mechanical properties in 3D printed parts. These defects reduce relative permeability, magnetic saturation, iron loss performance in printed soft magnetic materials, and decrease the remanent flux density and maximum energy product in printed permanent magnets. Printed iron cores and permanent magnets, if used in the rotor of electrical machines, can be susceptible to stress at high operating speed [83]. This can potentially lead to mechanical integrity issues for electrical machines. Enhancements of these magnetic and mechanical properties, however, are possible via the use of non-thermal method such as material infiltration or post-processing thermal methods [3,61].

**Figure 18.** Images of additively manufactured NdFeB bonded magnets and iron-silicon. Here, black features indicated by the arrows in the images represent pores. (**a**) Cross-section of bonded NdFeB magnets fabricated with material extrusion [59]; (**b**) Optical micrograph of selective laser melted iron-silicon [84].

### *5.2. Multi-Material AM for Electrical Machines*

At the current stage, the majority of AM technologies are employed for single components, using a single material for printing. The printed components are then assembled together with conventionally manufactured components to form the electrical machines [85,86]. Challenges in printing multiple materials are due to the dissimilarities in characteristics of the materials. Successful application of multi-material AM can open up opportunities for printing a complete electrical machine in a single step. Early exploration of multi-material AM for electrical machines show encouraging results, focuses on printing iron alloys, conductors, and insulation at the same time Figure 19. This proof of concept demonstrates the potential to reduce the production and assembly effort for electrical machines. The build time for the single material rotor core in Figure 16 is about 48 hours. Further research and development, however, is necessary for improving the printing process toward mass production [50].

**Figure 19.** Examples of printing multiple key materials for electrical machines: iron core, conductors, and ceramic insulation [87].

### *5.3. Integration with Topology Optimization*

As AM becomes a realization manufacturing method for topology optimization, there are still challenges remaining with combining these two enabling technologies. Since AM is a layer-based manufacturing technique, printed parts can suffer a degree of anisotropy. Electromagnetic properties can be slightly different in the build direction compared to the other directions. The formulation of the topology optimization algorithm has to account for the anisotropy effect when applying on a 3D optimization problem. Another concern associated with TO is the computation efforts. Optimization of just the permanent magne<sup>t</sup> rotor core in [88], via genetic algorithm, can take up to hundreds of generations to result in the Pareto front. Thus, significant computation effort would be required for of a multiobjective, multi-physics TO of multiple materials. The addition of complexities from the TO design can potentially prolong the printing time of the prototype.

## **6. Summary**

This paper presents the current research and trends on applications of additive manufacturing, topology optimization, and their integration toward magnetic components in electrical machines. As an enabling technology, additive manufacturing provides topology optimization a method to fabricate unique 3D geometries that are challenged to be manufactured via conventional methods. Successful combinations of additive manufacturing and topology optimization on fabricating both the iron core and permanent magne<sup>t</sup> with desired performance show a grea<sup>t</sup> potential as a design tool for electrical machine

designers. Capability of using multiple materials within additive manufacturing is another advantage that electrical machine designers can further exploit during the early machine design process. Recent results also show that additive manufacturing technologies have grea<sup>t</sup> potential as an alternative approach for realizing magnetic components for electrical machines. With the advancement in printing technology and the understanding between printing process and the magnetic properties of printed parts, there have been success toward printing of magnetic components. For soft magnetic materials, the current performance of the 3D printed parts is getting close to the parts manufactured using conventional methods. As for permanent magnets, performance of additively manufactured bonded NdFeB magnets is similar to the value seen in commercial counterparts. Additionally, results on printing magnets with good thermal performance as well as using producing magne<sup>t</sup> filament from recycled materials are encouraging. This provides the possibility to drive down the future cost of manufacturing high performance permanent magnets for electrical machine applications.

**Author Contributions:** Literature review, analysis, data collection, and the writing, T.P.; review and editing, P.K.; supervision, writing, and editing, S.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Department of Navy, Office of Naval Research for sponsoring the project, under ONR Award Number N00014-18-1-2514.

**Institutional Review Board Statement:** Not applicable

**Informed Consent Statement:** Not applicable

**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
