Electromagnetic Characterization of Silicon–Iron Additively Manufactured Cores for Electric Machines

Abstract

This paper deals with the electromagnetic characterization of a laminated toroidal ferromagnetic core made through additive manufacturing, specifically using the laser powder bed fusion process. The continuing demand for increasingly efficient, lightweight, and higher performance electric machines is creating huge challenges in the design and realization of new electric motor solutions. The constant improvements in additive manufacturing technologies have prompted researchers to investigate the possibility of adopting these production techniques for the manufacture of high-value electric motors. For these reasons, this paper investigates the ferromagnetic characteristics of an additively manufactured core made with FeSi6.5 powder. The BH curve and the specific iron losses of the processed material have been measured so that they can be compared with a commercial lamination, and have the possibility of carrying out more precise finite element simulations.

1. Introduction

In recent years, the demand for even more high-performance components is increasing day by day for many reasons. For example, climate change [1,2] and zero-emission aims [3,4,5] are stimulating several industrial sectors to move toward the electrification and energy efficiency of their products. To achieve this goal, innovative solutions are being experimented on, including additive manufacturing (AM) [6,7,8,9,10,11,12,13,14,15], also called 3D printing. This new manufacturing method allows high-value components to be produced with a wider degree of freedom in the design process. A vast variety of complex geometric shapes can be made, as long as the practical limits of the AM machine are not exceeded [16,17]. Moreover, it is possible to achieve significant volume production of components through AM. This is further supported by the fact that some aerospace companies have already declared the integration of AM into their production processes [18,19].

Because of its promising characteristics, AM has attracted attention from the perspective of electric machine manufacturing. However, unlike traditional manufacturing methods, the AM process has not reached an advanced stage for electric machines. In any case, with continued advances in the field of AM, it is poised to emerge as an alternative for the production of electric machines. This is due to the flexibility of the design possibilities offered by AM, which allows the integration of structural and thermal management components with active parts, making it the optimal solution for various applications.

From a design and manufacturing perspective, any electrical machine can be divided into several subcomponents, such as the ferromagnetic core, coils/winds, permanent magnets, thermal management components, and the mechanical apparatus.

The windings, consisting of coils, insulating material, and supports, are critical to generate the magnetic field inside the electrical machine. From the perspective of electrical machine design and construction, it is essential to minimize the power losses of this component to improve the efficiency of the electrical machine and avoid overheating problems. Therefore, low electrical resistivity should be pursued. However, in modern machine applications requiring high-speed and high-frequency operation, problems arise due to the predominance of losses associated with skin and proximity effects, which complicate the design of the winding assembly. Traditional design and manufacturing techniques often struggle to maintain a balance between these crucial factors. The adoption of AM for the production of new types of windings has been studied, demonstrating how windings can be made to meet multiple requirements, from improving the resistivity of materials to reducing high-frequency losses and finally to thermal dissipation [20,21,22].

Machines that emphasize efficiency, compactness and high torque-to-weight ratio use permanent magnets. Consequently, the manufacturing process and the resulting PM properties are of fundamental importance in these applications. Also in this area, AM has been considered and used for the production of magnets. Several production processes have been studied and have provided promising results for the production of high-performance magnets [23,24,25,26].

Mechanical and structural components are also being considered for production using additive manufacturing (AM) techniques, giving designers and electrical machine manufacturers the opportunity to reconsider the design of these components. The wide range of material options and design freedom make it easier to reduce the size and weight of structural parts through the use of different lattice structures. In addition, AM allows the integration of various features that conventional manufacturing techniques cannot achieve. This results in the creation of more compact, high power density, low inertia electrical machines without compromising reliability. Different example of these applications, as for example heat exchangers and various potential options for structural topologies, have been presented in [27,28].

The core of an electrical machine is a high-permeability magnetic structure used to confine and direct the magnetic field. When thinking about its design and construction, several magnetic properties must be considered, including magnetic saturation, permeability, hysteresis losses, and eddy current losses. The possibility of realizing complex magnetic geometries by using AM techniques would allow new motor structures to be designed and investigated with the aim of improving their performance. However, it is necessary that the printed core presents good magnetic properties, comparable to those of a commercial lamination. The electromagnetic characteristics of the material obtained by using AM processes are fundamental, so several specific specimens were fabricated and tested in the literature to measure the magnetic properties of the printed material and to verify their relation to the process parameters used to produce them (e.g., power and speed of the laser, hatch distance, and layer thickness) and the composition of the powder. The most widely used geometric shape in the literature for this purpose is a solid toroid. Different powder compositions have been studied: pure iron [29], FeSi3.7 [30], Fe91Si9 [31], FeSi4 [32], FeSi6.7 [33], and FeSi2.9 [34]. Instead of producing a solid toroid, a laminated toroidal sample has been chosen in this work to fine-tune the AM process for laminated structures, and to characterize the magnetic behavior and measure the iron losses. In current manufacturing processes for metal sheets, a high silicon content can lead to several production and technical problems, prompting manufacturers to use compositions that do not exceed 4% of silicon. Some of the problems associated with high silicon content include the following [35,36,37,38]:

• Fragility of Material: Increased silicon content can make ferromagnetic sheets more brittle. This can lead to difficulties when processing and handling the sheets.
• High Production Costs: The introduction of high silicon content can result in higher production costs due to the need for more sophisticated machinery and processes to ensure the desired quality of the material.
• Weldability Issues: High silicon content can affect the weldability of sheets. Welding of materials with high silicon content may require additional attention and special techniques to avoid the formation of defects in welded joints.

All these problems can be overcome in AM processes by fine-tuning the printing parameters to produce ready-to-use components that require limited post-processing. This study is a first investigation needed to enable the development of new electrical machines, as for example the synchronous reluctance motor presented in [39,40,41]. The knowledge of the BH curve of the printed material and its losses will allow more accurate simulations to be performed, while the optimization of the AM process parameters will permit laminated magnetic cores able to satisfy the various technical requirements demanded by the motor to be realized.

The paper is divided into four main sections. The first one provides a detailed explanation of how the toroid was manufactured, including information about the materials used, the production process, and features. The goal is to provide the reader with a clear understanding of the toroid’s manufacturing process and the specific factors which can influence its properties and performance.

The second section includes information about the toroid’s magnetic properties and its behavior under different conditions. In particular, the BH curve of the AM material and its power losses are presented in detail.

The third section focus on a specific application of the AM toroid presented in the paper. It describes how the characterization of the magnetic properties of the AM material are used within the design and analysis of electric machines. Moreover, some experimental measurements on an actual AM synchronous reluctance rotor are shown.

Finally, the last section summarizes the key findings and implications of the research.

2. Description of the Manufacturing Process

The AM process used in this work is laser powder bed fusion (L-PBF) [42,43,44]. This process consists in melting selectively the powder with a layer-by-layer approach, so as to obtain an object with complex geometry that would be difficult to produce with traditional manufacturing processes. The L-PBF process can be split into three main parts:

1.

The realization of a CAD model of the specimen to be produced;

2.

The manufacturing process itself;

3.

The post-process operations to finalize the sample.

The L-PBF manufacturing process consists in spreading consecutive thin layers of powder with a coater over the build platform and melting the powder with a laser following the CAD model. The powder tank is raised by one layer thickness while the build platform is lowered by the same amount at each iteration. The process is repeated until the component is finished. Figure 1 shows the L-PBF machine (i.e., SISMA MySint100 [45]) used during the fabrication of the specimen.

In this work a commercial silicon/iron powder (supplier: Höganäs [46]) was used to realize all the samples. The silicon percentage was equal to 6.5% (FeSi6.5) to exploit the advantages that high-silicon powders provide. The addition of silicon to iron allows the electrical resistivity of the alloy to be increased, reducing losses due to hysteresis and eddy currents when the material is subjected to varying magnetic fields [47,48,49,50]. On the other hand, the presence of silicon affects the ferromagnetic properties of the alloy. Therefore, a compromise percentage of silicon was chosen to achieve good magnetic properties and low ferromagnetic losses.

Powder characterization was carried out using X-ray computed tomography (Nikon Metrology MCT225 [51]). This technology enables three-dimensional analysis, characterizing the size and shape of particles. The powders were placed in a cylindrical container with a diameter of 5 mm to obtain high-resolution scans and facilitate the analysis of a large number of particles. The obtained results are reported in

Table 1. Powder particle morphology.

Min. dimension $\left[\mathrm{\mu }\mathrm{m}\right]$	Max. dimension $\left[\mathrm{\mu }\mathrm{m}\right]$	Avg. dimension $\left[\mathrm{\mu }\mathrm{m}\right]$
3.72	59.3	27.7
D10 $\left[\mathrm{\mu }\mathrm{m}\right]$	D50 $\left[\mathrm{\mu }\mathrm{m}\right]$	D90 $\left[\mathrm{\mu }\mathrm{m}\right]$
18.7	27.2	37.5

.

Before fabricating the laminated toroid, the L-PBF process parameters were optimized by producing dedicated specimens (maximum thickness equal to 1 mm) using different combinations of parameters, with the aim of reducing the presence of defects (porosity and cracks) and avoiding classic problems associated with this type of technology, such as keyhole [52,53,54,55] or lack of fusion [56,57,58,59], for better quality and magnetic performance of the final components. In particular, laser power, laser speed, and hatch distance were varied to obtain different energy densities from 58 to 159 J/mm³. The best parameter setup was identified based on the achieved relative density, which is typically reduced in L-PBF parts by the intrinsic presence of internal closed pores. For this reason the printing process was mainly optimized to minimize the presence of hollow spaces inside the material but also considering all the other problems listed so far.

The specimens density was measured using the Archimedes method [60]. This technique consists in weighing the sample in air and in a fluid, and applying the following formula:

$$\rho ={\displaystyle \frac{m_a}{m_a-m_{fl}}}{\rho }_{fl}$$

(1)

where ${\rho }_{fl}$ is the density of the fluid, $m_a$ is the mass of the sample in air (equal to $1.5968$ $\mathrm{g}$), and $m_{fl}$ is the mass of the sample in the fluid (equal to $1.3812$ $\mathrm{g}$). The fluid used in this case was pure water $\left({\rho }_{fl}=1 \mathrm{g}/\mathrm{c}{\mathrm{m}}^3\right)$. The density of the AM material was $7.4038$ $\mathrm{g}$/$\mathrm{c}$${\mathrm{m}}^3$. The porosity, $\varphi$, of the specimens was calculated considering the reference density of a standard FeSi6.5 alloy equal to $7.48$ $\mathrm{g}$/$\mathrm{c}$${\mathrm{m}}^3$ and it was equal to 1.02%.

The final optimized parameters, corresponding to the lowest achieved porosity content (i.e., 0.91%) were laser powder 125 $\mathrm{W}$, speed 750 $\mathrm{m}$$\mathrm{m}$/$\mathrm{s}$, hatch distance $0.08$ $\mathrm{m}$$\mathrm{m}$, and layer thickness $0.02$ $\mathrm{m}$$\mathrm{m}$. Based on the density achieved using the optimized process parameters, the ferromagnetic mass of the toroidal sample was estimated to be equal to 46 $\mathrm{g}$.

3. Characterization of the Toroid

The BH curve of the magnetic material is a key aspect to obtain motors with high performance. The knowledge of this property allows both new magnetic materials to be compared with the existing ones and more accurate finite element analyses to be performed. For this reason, a laminated toroidal specimen, shown in Figure 2, was realized by L-PBF using the optimized process parameters to characterize the magnetic behavior of the additively manufactured material. The windings are distributed regularly all around the circumference, as show in Figure 2b, in order to produce a more uniform magnetic field distribution and improving the mutual coupling between the coils. The sample consists of 10 equally spaced concentric ferromagnetic paths with a total area equal to 50 mm² and a mean magnetic path of $124.1$ $\mathrm{m}$$\mathrm{m}$. In the hollow spaces, resin was inserted after the L-PBF process to hold the printed material together. Figure 3 shows a cross-section of the specimen with its main dimensions.

For the measurement of the electromagnetic characteristics, a state-of-the-art procedure, i.e., Ref. [61], has been adopted. The circuit used for the measurements is reported in Figure 4. A controlled AC source is utilized to vary the frequency and the maximum current during the measurements. The other quantities of interest are achieved by post-elaboration.

3.1. BH Curve

The BH curve of the toroidal specimen can be obtained elaborating the signals of current and voltage probes of Figure 4. As an example, Figure 5 shows the waveforms for a supply frequency of 50 $\mathrm{Hz}$. The resulting BH loops are reported in Figure 6 where different current levels are considered as well. From each BH loop, the peak value of the magnetic field and the associated flux density can be extracted so as to create the BH curve of the printed material. Figure 7 shows the effects of process parameters on the magnetic properties of the printed material. All the BH curves are computed considering the same sample geometry and powder composition but using different parameters during the manufacturing process. It can be noticed that the printing parameters strongly affect the magnetic properties of the material. This is due to the different microstructures created within the printed material, so they need to be chosen carefully. In Figure 8, the measured BH characteristic is compared with that of a commercial lamination with a silicon content of 3% and a thickness equal to 0.5 mm [62]. Moreover, the characteristics of the printed material presented in [34] are also included in the comparison. The powders considered in this work (FeSi6.5) and in [34] (FeSi2.9) are different, as well as the process parameters, so different material performances are expected. Therefore, the found discrepancy is reasonable. It can be noted that the proposed FeSi6.5 specimen exhibits a slightly worse performance behavior compare to the FeSi2.9 specimen in the first part of the BH curve but shows higher values of flux density when the material starts to saturate, even for relatively low magnetic fields (around 3–4 $\mathrm{k}$$\mathrm{A}$/$\mathrm{m}$). The proposed FeSi6.5 sample has a BH characteristic very similar to the reference lamination, especially for high magnetic fields.

3.2. Power Losses

Power losses are measured using the wattmeter shown in Figure 4. This quantity is strictly connected to the specimen dimension so the specific iron losses $p_{ir}$ will be considered hereafter. The iron losses are affected by the flux density intensity at which the ferromagnetic material works and by the operating frequency. To have a comprehensive idea of the iron losses, several experimental tests have been carried out varying the frequency of the power supply and the current amplitude. Figure 9 shows the experimental results obtained. The specific power losses can be analytically computed as a function of the flux density B and the supply frequency f using the following equation based on the Steinmetz formula:

$$p_{ir}\left(B,f\right)={\left(\frac{B}{B^{\ast }}\right)}^2\left(\frac{f}{f^{\ast }}\right)\left[p_{ist}+p_{ec}\left(\frac{f}{f^{\ast }}\right)\right]$$

(2)

where $p_{ist}$ and $p_{ec}$ represent the hysteresis and eddy currents specific losses, while $B^{\ast }$ and $f^{\ast }$ are assumed equal to 1 $\mathrm{T}$ and 50 $\mathrm{Hz}$, respectively, as for the usual ferromagnetic data sheet. Fitting the measured losses with Equation (2) allows the following values to be computed for $p_{ist}$ and $p_{ec}$; this permits the losses to be expressed with good accuracy in the considered current-frequency range.

$$p_{ir}\left(B,f\right)=B^2\left(\frac{f}{50}\right)\left[2.392+0.208\left(\frac{f}{50}\right)\right]$$

(3)

Figure 9 shows the specific iron losses computed with Equation (3) (solid line) as a function of the flux density for the different frequencies considered during the measurements. Figure 10 shows the BH loops for different frequencies of the power supply. The area inside the BH loop grows with the increase in the frequency as expected, since it is proportional to the total iron losses.

4. Application Example: Synchronous Reluctance Motor Magnetic Characteristic

As an application example, the magnetic characteristics of a synchronous reluctance motor with additively manufactured rotor are presented in this section. A preliminary design and analysis of the considered machine has been carried out in [39]. Using the experimental measurements obtained in the previous sections, it is possible to perform accurate finite element simulations [63] of the magnetic characteristics of the motor which are a key aspect to calculate the motor performance, since the torque of the electric machine can be computed as $3/2p\left({\Lambda }_d{I}_q-{\Lambda }_q{I}_d\right)$ where p is the number of pole pairs, ${\Lambda }_d$ is the direct flux linkage, and ${\Lambda }_q$ is the quadrature flux linkage while $I_d$ and $I_q$ are the feed currents of the two axes. Figure 11 shows a cross-section of the lamination. The stator is formed by reference lamination (see also the characteristic of Figure 8) while for the rotor the BH curve measured on the sample of Figure 2 has been adopted. The flux linkages can be calculated by integrating the vector magnetic potential over the stator slots. For a generic $j\mathrm{th}$ phase ($j=a,b,c$) the formula is as follows:

$${\Lambda }_j=\sum _{i=1}^{Q_{sim}}{\displaystyle \frac{Q_s}{Q_{sim}}}{\displaystyle \frac{n_c{k}_j\left(i\right)}{n_{pp}{S}_{slot}}}{\int }_{S_{slot}}{A}_{z}d{S}_{slot}$$

(4)

where $A_z$ is the vector magnetic potential, $k_j\left(i\right)$ is a coefficient which represents the filling of the $i\mathrm{th}$ slot by the conductors of the $j\mathrm{th}$ phase, $Q_{sim}$ is the number of simulated slots, $S_{slot}$ is the cross-area section of the slot, $n_c$ is the number of conductors in the slot, and $n_{pp}$ the number of the winding parallel paths. Once the flux linkages ${\Lambda }_a$, ${\Lambda }_b$, and ${\Lambda }_c$ are obtained, the flux linkages ${\Lambda }_d$ and ${\Lambda }_q$ can be computed using the Clarke–Park transformation (5) and (6) where ${\vartheta }_m$ is the rotor mechanical position.

$${\Lambda }_d={\displaystyle \frac{2}{3}}\left[{\Lambda }_{a}cos\left({\vartheta }_m\right)+{\Lambda }_{b}cos\left({\vartheta }_m-\frac{2}{3}\pi \right)+{\Lambda }_{c}cos\left({\vartheta }_m+\frac{2}{3}\pi \right)\right]$$

(5)

$${\Lambda }_q=-{\displaystyle \frac{2}{3}}\left[{\Lambda }_{a}sin\left({\vartheta }_m\right)+{\Lambda }_{b}sin\left({\vartheta }_m-\frac{2}{3}\pi \right)+{\Lambda }_{c}sin\left({\vartheta }_m+\frac{2}{3}\pi \right)\right]$$

(6)

Figure 11b shows an example of the flux lines when only the $d$-axis of the motor is excited. Figure 12a shows the rotor obtained from the printing process described in the previous sections, while Figure 12b,c show the test bench, the measurement system, and the assembled motor ready to be tested. The prototype is rotated at a constant speed and supplied with different current values. By means of voltage probes, the phase voltages are measured from which, knowing the rotational speed of the motor, the flux linkages are calculated. Figure 13 shows the simulated and measured flux linkage of the motor. It is worth noticing the good agreement between the simulations and measurements thanks to the accurate characterization of the printed material adopted in the rotor.

5. Conclusions

This paper provides a detailed description of the manufacturing process and the magnetic characterization of a toroid realized by additive manufacturing. In particular the BH curve and power losses have been analyzed for different operating frequencies. It is highlighted that the printing process strongly influences the core properties but, thanks to a proper design, magnetic characteristics similar to laminations can be achieved. The realized prototype, in fact, shows a good BH curve and power losses, comparable with those of commercial laminations. The developed magnetic analysis is mandatory for further research in the electric machine field in order to perform accurate simulations which involve electric machines with AM cores. As a real electric motor design example, an AM synchronous reluctance motor is considered. The flux-linkage simulation results have been compared with experimental measurements carried out on a motor prototype.