Material Tradeoff of Rotor Architecture for Lightweight Low-Loss Cost-Effective Sustainable Electric Drivetrains

Abstract

The art of the successful design of high-speed electrical machines comes with many challenges in the mass, size, reliability, and energy efficiency. Material engineering of electrical machines has been identified as a key solution for higher power dense electric drivetrains. One of the main challenges at high speed is the eddy-current losses in the active electromagnetic parts, especially magnetic materials and permanent magnets (PMs). This study is devoted to the selection of PM rotor materials using multidisciplinary design optimization for a high-speed electric drivetrain. Beside AC loss minimization, more disciplines are considered, such as the minimization of weight, and cost. Different laminations are investigated with different magnetic properties as well as cost. Additionally, different PMs are optimized considering low-cost ferrite and high-coercivity permanent magnets (HCPMs). Moreover, the optimal materials are identified which have the best balance between loss, weight, cost, ripples. Finally, different rotor designs are prototyped, assembled, and tested using the same stator configuration. Also, the best rotor design is selected, and the electromagnetic performance is measured and compared with conventional designs. The optimal design results in 8% extra torque with at least 20% weight reduction.

1. Introduction

Nowadays, the engineering of a high-performing electrical machine requires many considerations during the early-stage design process, such as limitations in design, environmental conditions, international standards, customer’s needs, and manufacturability. At the end, a successful design should have an optimal balance between the performance and the cost of manufacturing. The materials used in an electrical machine impose limitations in design such as saturation in laminations, current density in conductors, and temperature of the insulation. Therefore, special attention is given to the selection of materials with the necessary properties during the design process of the machine.

The importance of material selection in the design of electrical machines cannot be overstated, as it significantly impacts their performance, efficiency, and cost-effectiveness [1]. Furthermore, the choice of materials plays a pivotal role in addressing contemporary challenges such as environmental sustainability and energy efficiency. In recent years, research efforts have focused on exploring innovative materials and their applications in electric drivetrains. These materials encompass a wide range of components, from static elements like housings and bearings to active electromagnetic components like laminations, conductors, and permanent magnets. The optimization of these materials is integral to achieving the desired balance between machine performance and manufacturing costs [2,3,4,5].

Sustainability and environmental concerns surrounding FeSi laminations in electrical machines are of growing importance [6]. These concerns span various stages of the laminations’ life cycle, from raw material extraction to disposal. The production of electrical steel involves resource-intensive processes, including iron ore extraction and silicon alloy processing, contributing to energy consumption, water use, and greenhouse gas emissions. Additionally, waste generation and improper disposal of byproducts pose environmental challenges. Transporting laminations over long distances further adds to their carbon footprint. To address these concerns, various strategies are being employed. Life cycle assessments help identify areas for improvement, while recycling efforts promote a circular economy approach. Researchers are exploring alternative materials that offer similar magnetic properties with reduced environmental impact. Energy efficiency, a primary purpose of FeSi laminations, aligns with sustainability goals by reducing energy consumption in electrical machines. Manufacturers are adopting green practices, such as renewable energy use and waste reduction, while regulatory compliance ensures adherence to environmental standards. Additionally, raising consumer and industry awareness regarding sustainable choices is essential. In summary, mitigating the environmental impact of FeSi laminations involves improving production processes, recycling, and adopting sustainable practices throughout the supply chain and product life cycle. This holistic approach aims to minimize the environmental footprint of electrical machines, contributing to a more eco-friendly and sustainable energy infrastructure. With this being said, material engineering of lamination materials can help in the downsizing of the electrical machine as well as improving its energy consumption [7].

Numerous studies in the literature have addressed the crucial aspect of material selection for electric machines [8]. In [9], the role of advanced materials is discussed for unconventional applications. Advanced magnetic and conducting materials, advanced PMs, and advanced insulation systems have been compared. In [10], different windings materials are introduced including additively manufactured coils. Also, a comparison between 3D printed windings and magnetic materials has been reported in [11,12]. In [13], the thermal and electromagnetic impacts of using different steel laminations on machine performance have been studied. Furthermore, in [14], the impact of manufacturing post processes (cutting and stacking) is investigated on the magnetic laminations. The fundamental calculations for the choice of material in the design of PMs are first introduced in [15]. Additionally, in [16], a shape optimization method is introduced for PMs to improve the gap flux density. To the best of the author’s knowledge, there is no study that considered the material tradeoff between all active magnetic components of the rotor.

This paper introduces the material tradeoff of magnetic materials in the electrical machine. First, the rotor architecture is investigated using different barrier shapes. Then, an advanced parametric model is created for multidisciplinary optimization targeting the minimization of AC loss, weight, cost, and torque ripples. Targeting a 300 kW electric drivetrain, the optimal dimensions as well as lamination and PM materials are selected. Additionally, different rotor designs are prototyped and tested. Finally, the electromagnetic performance of the optimal design is measured and compared with conventional designs.

2. Rotor Barrier Shape Profiling

A three-phase 300 kW PM-assisted synchronous reluctance machine (SynRM) is selected as the reference model of this study. The machine configuration and finite element modeling of the full design are shown in Figure 1. A 48-slot stator is used with a parallel-sided slot shape in order to suit a hairpin winding configuration. The reference rotor resign has eight poles with a double-V (dV) magnet shape.

The focus on SynRM and rotor design in this study stems from several key motivations and considerations:

• Industry Relevance: SynRM technology has gained significant traction in recent years, particularly in industrial and automotive applications, due to its potential for high efficiency, reduced energy consumption, and sustainability. The drive towards more energy-efficient and environmentally friendly solutions intensifies, leading to a growing interest in optimizing SynRMs for various applications. This study aligns with this industry trend by addressing critical aspects of SynRM design.
• Challenges in Rotor Design: The rotor is a pivotal component of electric motors, significantly influencing their performance, efficiency, and cost-effectiveness. The rotor’s design intricacies, including material selection, dimensions, and barrier angles for q-magnets, present complex optimization challenges. By focusing on rotor design, this study aims to provide insights into how these design parameters impact motor performance and how they can be optimized for superior results.
• Multidisciplinary Approach: A multidisciplinary design optimization (MDO) approach is adopted to address the complexities of rotor design. This approach enables the simultaneous consideration of multiple objectives, including minimizing losses, weight, cost, and torque ripples. By concentrating on SynRM rotor design, this study showcases the applicability and effectiveness of MDO in the context of electric machine design, which has broader implications for the field.
• Material Tradeoff Analysis: This study delves into the material tradeoffs within the rotor, considering various active electromagnetic components, such as laminations, conductors, and permanent magnets. This comprehensive analysis fills a gap in the literature, as prior studies have often focused on individual rotor components in isolation. The approach allows for a more holistic perspective on material selection.

Five additional rotor designs are investigated for the same stator geometries. The average area of permanent magnets (PMs) per pole remains unchanged across all six designs. The original design features a dV shape without any empty spaces in the back iron, as shown in Figure 2a. These empty spaces could be utilized to reduce the weight of the rotor. However, implementing this approach poses a significant risk of iron saturation and demagnetization of the PMs. In the second design (in Figure 2b), a single-V (sV) shape is used, and an air space is incorporated in the back iron. In the third design, illustrated in Figure 2c, a modified dV (mdV) shape is utilized by incorporating a deeper PM barrier and removing additional back iron. In the fourth design, presented in Figure 2d, a double-U (dU) shape is employed, with the PMs integrated along the direct axis (d-axis). In the fifth design, showcased in Figure 2e, a delta (DL) shape is utilized, incorporating the PMs along both the d-axis and q-axis. Finally, in Figure 2f, a hybrid design referred to as UV shape is employed, combining elements of both U-shape and V-shape designs. In this design, the PMs exist along both the d-axis and q-axis arranged in a delta shape.

The finite element simulations of the six rotor designs are compared under the same materials and operating conditions as shown in Figure 3. The simulation results are summarized in

Table 1. Comparison between different rotor shapes using FEA.

Rotor Design		Av Torque	Torque Ripples	PM Demag.	Rotor Losses	B_Max	% Saturation Area *
1	dV (Ref)	725 N.m	4.6%	0.1%	1.00 p.u.	2.31 T	38%
2	sV	723 N.m	2.9%	1.8%	1.09 p.u.	2.73 T	56%
3	mdV	733 N.m	7.2%	3.3%	1.02 p.u.	2.46 T	53%
4	dU	730 N.m	5.3%	6.2%	1.10 p.u.	2.80 T	67%
5	DL	741 N.m	2.1%	5.4%	0.98 p.u.	2.25 T	32%
6	UV	759 N.m	3.8%	0.2%	0.95 p.u.	2.22 T	21%

* Area of saturation = Area of Iron with B ≥ 1.8 T/Total area of the rotor iron.

. As can be seen, in the first design, there is a great unbalance in the flux density distribution of the rotor iron. Also, despite having the lowest PM demagnetization risk, the reference design is not the optimal choice for higher average torque. The second design (sV) has nearly the same average torque with relatively lower torque ripples. However, the PM losses increase significantly by 9%, and the maximum flux density is much higher than the reference case. In the third design (mdV), there is a slight improvement in the average torque. Yet, there is a large increase in the torque ripples compared to the reference design. In the fourth design (dU), the rotor yoke iron is much lower than the reference case. Also, the average torque is nearly the same value. Yet, the PM losses and demagnetization are the highest among all designs. In the fifth design (DL), the average torque increased considerably by 2.2% with lower torque ripples. However, the demagnetization risk is still higher than the reference case. Finally, in the sixth design (UV), the average toque improved remarkably by 4.4% and PM losses are decreased by 5% with nearly the same demagnetization and ripple levels. Furthermore, the saturated area is the lowest despite having air spaces in the rotor. That is why this shape is selected for further investigation and optimization.

3. Benchmarked Electrical Machine

3.1. Baseline PM-Assisted SynRM

The main dimensions including the stator, rotor, and PMs are highlighted in Figure 4. The specifications of the optimization parameters are listed in

Table 2. Variables of the multi-objective optimization.

Input Parameters of the Full Machine
Parameter	Symbol	Range	Parameter	Symbol	Range
Stator Outer Diameter	$D_{so}$	250 mm (fixed)	d-Barrier width	$w_{BD}$	$\mathrm{fun}. (D_{ro}$)
Rotor Outer Diameter	$D_{ro}$	$KSR\ast D_{so}$	q-Barrier width	$w_{BQ}$	$\mathrm{fun}. (D_{ro},w_{BD}$)
Machine Stack Length	$L_s$	$KAR\ast D_{so}$	d-Magnet width	$w_{MD}$	$K_{MD}\ast w_{BD}$
Aspect Ratio = ${\mathit{L}}_{\mathit{s}}/{\mathit{D}}_{\mathit{s}\mathit{o}}$	$KAR$	0.6:1	q-Magnet width	$w_{MQ}$	$K_{MQ}\ast w_{BQ}$
Split Ratio = ${\mathit{D}}_{\mathit{r}\mathit{o}}/{\mathit{D}}_{\mathit{s}\mathit{o}}$	$KSR$	0.7:0.8	d-Magnet ratio = $w_{MD}/w_{BD}$	$K_{MD}$	0.3:1
Airgap Length	Gap	0.85 mm (fixed)	q-Magnet ratio = $w_{MQ}/w_{BQ}$	$K_{MQ}$	0.05:0.95
Yoke Height	$H_y$	$\mathrm{fun}. (D_{so},KSR$)	Barrier angle	${\theta }_{BQ}$	5°:20°
Slot Height	$H_s$	$\mathrm{fun}. (D_{so},H_y$)	Lamination Materials	LAMMAT	1–12 (discrete)
Slot Width	$w_s$	$\mathrm{fun}. (KSR,H_y$)	Magnet Materials	MAGMAT	1–13 (discrete)

. The stator outer diameter ($D_{so}$) is maintained at a fixed value of 250 mm. All the other geometries are defined as variables. Among those variables, two main ratios have higher contributions to the machine size, which are aspect ratio ($KAR$) and the split ratio ($KSR$) [17]. $KAR$ is the ratio between the machine stack length ($L_s$) and the stator outer diameter ($D_{so}$). Since the stator outer diameter is fixed, this ratio is mainly dependent on the stack length. $KSR$ is the ratio between the rotor outer diameter ($D_{ro}$) and the stator outer diameter ($D_{so}$). This ratio depends mainly on the rotor outer diameter. For the magnets, two main ratios define the magnet sizes, which are $K_{MD}$ and $K_{MQ}$.

3.2. Full Design Optimization

The optimization flowchart for the complete machine is shown in Figure 5. The main target is to identify the optimal dimensions of the baseline machine. First, a fully parametrized model is created using a finite element software. The input variable ranges for the stator, rotor, and PMs are defined, including dimensions and materials. In the optimization process, the dimensions and materials of the PMs are determined simultaneously. Then, the main objective and constraints are specified. There are four objectives of the simulations, which are minimizing of losses, weight, torque ripples, and cost. The losses are calculated for all the active parts, including winding losses, PM losses, and iron losses. The weight is calculated for the overall machine based on the material mass density and volume. The cost includes the material cost and the processing cost such as cutting, stacking, assembly, etc.

Four constraints are selected to identify passed and failed samples. The first and the second criteria are that the machine rating at base speed and top speed must be equal or higher that the target value of 300 kW.

The third constraint is regarding the temperature limits, which are selected based on the electrical insulation of the windings and the PM maximum working temperature. Regular neodymium magnets can operate efficiently up to 80 °C but above this level, they will experience irrecoverable losses in performance and start to lose their magnetic output [18]. Eventually, structural changes occur to the magnet material and the magnetic properties are permanently lost. For high-temperature applications, samarium cobalt and high-temperature neodymium magnets should be considered. For instance, grades like UH rating have a maximum working temperature of 180 °C [19]. The maximum operating temperature for each grade is listed in

Table 3. Maximum working temperature of permanent magnets.

Max. Working Temperature for Each PM Grade
N50/N52	60 °C	SH	150 °C
STANDARD	80 °C	UH	180 °C
M	100 °C	EH	200 °C
H	120 °C	AH	230 °C

.

The fourth constraint is to have zero reverse field demagnetization in the PMs. This type of demagnetization can occur when an external magnetic field is reversely applied. As a result, the working point is pushed below the knee point of the magnet BH curve. At this situation, the PMs start to lose some of the original remanence ($B_r$). Among different PM materials, the rare earth PM has the lowest chances of demagnetization due to its very high intrinsic coercive force ($H_c$).

In parallel with the objective function calculations, we evaluate whether the machine ratings at base speed and top speed meet the target value of 300 kW. This is essential as it ensures that the machine’s power output aligns with the intended application requirements. The final step in our optimization workflow involves the selection of the optimal design from the pool of generated candidates. This step is strategically placed at the end of the workflow for several reasons:

• Comprehensive Evaluation: By waiting until the end of the optimization process to select the optimal design, we ensure that all generated design candidates have undergone a thorough evaluation against the defined objectives and constraints. This allows us to make an informed decision based on a comprehensive assessment of each candidate’s performance.
• Tradeoff Analysis: Selecting the optimal design at this stage allows us to perform a detailed tradeoff analysis. We can consider how each design candidate balances the competing objectives of minimizing losses, weight, torque ripples, and cost. This analysis ensures that the chosen design aligns with the overall goals of the project while considering potential tradeoffs between different criteria.
• Practicality and Feasibility: It is essential to evaluate the practicality and feasibility of the optimal design in real-world applications. At this stage, we can assess factors such as manufacturability, maintenance requirements, and compatibility with existing systems. This evaluation ensures that the selected design is not only theoretically optimal but also viable for implementation.
• Consideration of External Factors: The selection of the optimal design allows us to take into account external factors that may influence the decision, such as market conditions, regulatory requirements, and customer preferences. This consideration ensures that the chosen design aligns with broader contextual factors that may impact its success.
• Resources and Documentation: Once the optimal design is selected, we can dedicate the necessary resources to thoroughly document and report on the chosen configuration. This documentation should include detailed specifications, performance characteristics, and any relevant design considerations. This step is essential for communicating the results of the optimization process effectively.

In summary, the workflow is structured to progress from foundational model creation to variable definition, followed by the establishment of objectives and constraints. Subsequently, objective and constraint calculations, machine rating evaluations, and temperature and demagnetization considerations are addressed in a logical sequence. This systematic approach ensures that the optimization process is both guided and well-informed at each stage, ultimately leading to the identification of optimal machine designs. Eventually, incorporating the selection of the optimal design into our optimization workflow emphasizes the importance of making a well-informed and contextually aware decision at the conclusion of the optimization process. It ensures that the chosen design not only meets technical criteria but also aligns with practical considerations and external factors.

The number of samples was generated through a systematic exploration of the design space, guided by the defined input parameters, objectives, and constraints. Further, the optimization algorithm included initial boundaries and an early stopping criterion to manage the computational resources effectively. If an optimal design was reached before the pre-defined maximum number of samples, the algorithm would terminate early, enhancing the efficiency of the optimization process. Due to the high number of input and output variables and well-constrained optimization problem, 7000 samples are solved using transient electromagnetic and thermal FE simulation. The multidisciplinary design optimization (MDO) is started on a high-speed workstation using an evolutionary algorithm [20]. With the high-performing processor (6248R) and the high-capacity RAM memory (192 GB), the workstation can solve different designs simultaneously on 30 parallel workers. Each set of parallel designs can be solved in about 40 min. That means 1000 solutions per day can be generated using one workstation. Among the 7000 samples, nearly 70% of them passed the criteria. Over 90% of the failed samples did not fulfill the rating requirements at top speed. Also, over 50% of the failed samples have a non-zero demagnetization value in the PMs. Finally, given equally weighted objectives, the rank of each passed sample is calculated as follows.

$$Ran{k}_i=\frac{1}{4} \left(\frac{Los{s}_{min}}{Los{s}_i}+\frac{Weigh{t}_{min}}{Weigh{t}_i}+\frac{Cos{t}_{min}}{Cos{t}_i}+\frac{Rippl{e}_{min}}{Rippl{e}_i}\right)$$

(1)

where

• Rank_i: This represents the calculated rank for the i-th design candidate, indicating how well it performs compared to others in the optimization process.
• Loss_min: This term represents the minimum loss among all design candidates, serving as a reference point for assessing the relative loss of the i-th candidate.
• Loss_i: Refers to the loss associated with the i-th design candidate.
• Weight_min: This term represents the minimum weight among all design candidates.
• Weight_i: Denotes the weight of the i-th design candidate.
• Cost_min: This term signifies the minimum cost among all design candidates.
• Cost_i: Represents the cost associated with the i-th design candidate.
• Ripple_min: This term signifies the minimum ripple among all design candidates, offering a benchmark for evaluating the relative ripple of the i-th candidate.
• Ripple_i: Denotes the ripple associated with the i-th design candidate.

Equation (1) essentially normalizes the loss, weight, cost, and ripple of each design candidate with respect to the best-performing candidate in each category. The reciprocal of these normalized values is then summed to determine the rank, where a lower rank indicates a more favorable design. This ranking methodology allows us to identify designs that strike a balance between the considered objectives while considering equal weights for each metric.

The outcomes of the successful design candidates, coupled with their respective rankings, are presented in Figure 6. It is evident that the results exhibit notable variations in terms of losses, weight, and cost, largely influenced by the chosen dimensions and material selections. Among these candidates, the “best-in-class” (BIC) designs emerge as those characterized by superior attributes, boasting low losses, reduced weight, minimal cost, and negligible ripples. The selection of the top-ranked design is showcased in Figure 7. Furthermore, our investigation extends to the examination of torque ripples in relation to different barrier angles of the q-magnets, as illustrated in Figure 8. This analysis underscores the significance of barrier angle selection in achieving optimal performance. The optimal design, characterized by a small barrier angle (below 10°), demonstrates a remarkable achievement: average ripples below 4%. Conversely, less favorable designs are identified when employing high barrier angles (above 20°). Interestingly, despite not achieving the absolute minimum in losses, cost, weight, or ripples individually, the optimal design stands out for its exceptional balance across all four objectives. This balance is a testament to its prowess in simultaneously minimizing losses, weight, cost, and ripples. It exemplifies a holistic approach to design optimization, where the synergistic interaction of these objectives results in an overall superior design. In summary, our study showcases how intricate tradeoffs between various design aspects, such as dimensions, materials, and barrier angles, can yield optimal designs that strike an exceptional balance among multiple competing objectives, ultimately leading to high-performance electric drivetrains.

The scatter of the PM width ratio in the d-axis versus the q-axis is shown in Figure 9 for all designs and materials. As noticed, $K_{MD}$ has much wider tolerance compared to $K_{MQ}$. In the d-direction, the magnet width ratio can have any value between 0.3 and 1. However, in the q-axis, the magnet width ratio is limited between 0.55 and 0.85. The optimal design has a $K_{MD}$ of 0.61 and a $K_{MQ}$ of 0.66. Furthermore, the machine overall size can be evaluated by plotting the scatter of aspect ratio and split ratio for the feasible samples as shown in Figure 10. As noticed, the highly ranked designs have KAR between 0.65 and 0.8, and KSR between 0.7 and 0.8. For the optimal design, these ratios are 0.726 and 0.753, respectively. This equals to an optimal axial length ($L$) of 181.5 mm and an optimal rotor outer diameter ($D_{ro}$) of 188.25 mm.

3.3. Material Tradeoff

This section explains in detail the materials used in the full design optimization (Section 3.2). A matrix of different materials for laminations and PMs is used for the MDO. The investigated materials are listed in

Table 4. Investigated materials of the laminations and PMs.

Index	Lamination Material (LAMMAT)	PM Material (MAGMAT)	Index	Lamination Material (LAMMAT)	PM Material (MAGMAT)
1	NO20	G38UH	8	B27AV1400	G54UH
2	NO27	G40UH	9	B35A250	N38UH
3	NO30	G42UH	10	HIPERM_49	N40UH
4	M235_35A	G45UH	11	HYPOCORE_25	N42UH
5	M250_35A	G48UH	12	20JNEH	N45UH
6	M270_35A	G50UH	13	VACOFLUX	MAGFINE_S5P12ME
7	M300_35A	G52UH	14	-	TDK_FB

along with their index. In the lamination materials (LAMMAT), the materials vary in thickness and specific core losses. Also, the cost is different form one grade to another and from one supplier to another. Figure 11 shows the BH curve for the different LAMMAT, and the corresponding magnetic induction at high saturation levels of 50 kA/m are compared in Figure 12. Among the selected laminations, LAM13 (VACOFLUX) has the best BH magnetization curve. However, it has the highest price. Yet, using this 17% cobalt–iron alloy VACOFLUX is considerably cheaper than machines’ designs based on 49% cobalt–iron. A comparison between the prices can be found in [21]. In the second place, LAM11 (HYPOCORE25) has high induction, high permeability, and low core loss. However, the price is relatively high compared to most materials [22]. On the other hand, LAM12 (20JNEH) has a very comparable performance to LAM11 alongside with a remarkably lower price compared to the other materials [23]. LAM10 (HIPERM-49) is a high permeability nickel–iron alloy that possesses a flux density of 1.6 T at high saturation levels near 50 kA/m [24]. The main disadvantage of this material is the low-saturation magnetic flux density, which leads to increased size and mass.

The specific core losses for all lamination materials are compared at 50 Hz in Figure 13. As can be seen, LAM11 (HYPOCORE25) has the lowest core losses at high magnetization levels. LAM12 (20JNEH1200) comes in second place with remarkably low core losses compared to other materials with nearly the same magnetization characteristics.

For the PM materials (MAGMAT), the investigated materials are also listed in Table 4. The corresponding magnetic remanence and coercivity are also compared in Figure 14. The G-class magnets (MAG1–MAG8) are sintered neodymium–iron–boron magnets which are also referred to as NdFeB magnets. These PM alloys offer a combination of high magnetic output at moderate cost [25]. It is worth mentioning that using grain boundary diffusion (GBD), new grades of PMs can be produced with the same induction (Br) alongside with a higher coercivity (resistance to demagnetization). Also, using GBD, higher grades of high-coercivity permanent magnets (HCPMs) can be produced that were previously impossible by any other method such as G54UH (MAG8) [26,27,28]. The N-class (MAG9–MAG12) are also NdFeB magnets of the traditional method without GBD. As such, their costs are relatively lower [29]. A ferrite magnet like TDK_FB (MAG14) has the lowest prices due to the easier manufacturability using a wet molding process [30]. Yet, it has the worst of the magnetic properties, such as a residual magnetic flux density (Br) of 0.45 T, and a significantly low coercive force of 350 kA/m.

The material tradeoff analysis is started using the objective and constraints in Figure 5. Aiming at higher rank solutions, 182 unique designs are selected from the total number of evaluations using the different combination of materials aforementioned in Table 4. Among the investigated combinations, 82 designs have fulfilled the criteria. Thus, 100 design failed to achieve the constraints of the ratings, temperature limits, and demagnetization. The torque speed characteristics for both passed and failed samples are shown in Figure 15. Also, the corresponding power speed profiles are compared in Figure 16. As can be seen in some failed samples, certain material combinations can achieve the target torque and power requirements. However, the other criteria (thermal or demagnetization) are not fulfilled. Figure 17 shows lamination materials versus magnet materials indicating top ranked cases. Between the top 10 samples, 10 different MAGMAT can be used. However, only two LAMMAT are among them. Obviously, LAM12 has the best rank for nine different magnet materials. In the second place, LAM11 is a good alternative which is compatible with the highest number of magnets. It is also clear that certain materials have completely failed to fulfill the criterial, such as LAM(8, 10), MAG(1, 13, 14). It is also important to note that some LAMMAT have very limited options in the PMs. By way of example, LAM1 is only feasible with MAG(6,7,8). These powerful magnets have one thing in common, which is the highest coercivity compared to the other magnets. Similarly, some MAGMAT have very limited options in the laminations. For instance, MAG9 can only achieve the power requirements if it is used only with LAM11, which has the lowest losses. Another example is MAG2, which is only feasible with LAM(11,12).

To identify the best-in-class (BIC) materials, the lamination materials are ordered based on their top rank as shown in Figure 18a. Similarly, the BIC PMs are ordered in Figure 18b. It is clear that LAM12 has the highest rank due to its low losses combined with the low cost compared to the other materials. Also, MAG10 comes in first place due to the good balance between remanence, coercivity, loss, and cost. The torque speed characteristics of the top ten combinations are shown in Figure 19. All samples have equal or higher torque than the target value at both base speed and top speed. Yet, the higher torque does not necessarily mean higher rank, because there are other objectives to meet beside power requirements. Finally, the geometrical and electromagnetic specifications of the optimal design are listed in

Table 5. Geometrical and electromagnetic parameters of the optimal design.

Parameter	Value	Parameter	Value
Number of slots	48	Motor Power	307.4 kW
Stator outer diameter	250 mm	Base Speed	3850 RPM
Stack length	181.5 mm	Top Speed	13,000 RPM
Rotor outer diameter	188.25 mm	Torque @ Base Speed	737.6 N.m
Airgap length	0.85 mm	Torque @ Top Speed	225.8 N.m
Slot width (${\mathit{w}}_{\mathit{s}}$)	6.42 mm	Rated MMF per slot	5547 AT
Yoke height (${\mathit{H}}_{\mathit{y}}$)	16.1 mm	Number of armature phases	3
Q-magnet width ( ${\mathit{w}}_{\mathit{M}\mathit{Q}}$)	27.6 mm	Number of roto poles	8
Q-magnet height ( ${\mathit{H}}_{\mathit{M}\mathit{Q}}$)	5.98 mm	Number of Turns per Slot	8
D-magnet width ( ${\mathit{w}}_{\mathit{M}\mathit{D}}$)	14.9 mm	Lamination material	20JNEH1200
D-magnet height ( ${\mathit{H}}_{\mathit{M}\mathit{D}}$)	8 mm	PM material	N40UH

.

After the materials are selected for laminations and PMs, the last step is to select the winding material based on the optimal slot design and the ampere-turns requirements.

4. Prototyping and Measurement Results

Using the optimal dimensions and materials, a PM-assisted SynRM is prototyped using one stator configuration and six different rotor designs. The reference design (dV) is shown in Figure 20a along with a 48-slot stator core. A test platform is used to measure the performance of the motor in different conditions as shown in Figure 20b. A drive unit is used to supply the motor with three-phase currents with variable frequency levels to control the speed. The torque and power are measured using the data acquisition of the DSP MicroLabBox. The corresponding schematic diagram is shown in Figure 20c.

The machine assembly is shown in Figure 21. A distributed winding configuration is employed in the stator using hairpin windings. Each rotor is divided into six parts. One half of these parts is mechanically shifted by a swing angle of 5° to reduce the torque ripples.

Apart from the reference design, five additional rotor designs are prototyped as shown in Figure 22, which are sV, mdV, dU, DL, and UV, respectively. A comparison between the different rotor design is listed in

Table 6. Comparison between rotors with different barrier shapes.

	Rotor Weight	Power Losses @ Base Speed	Peak Torque	Torque Density * N.m /kg
dV (Ref)	29.61 kg	9.52 kW	716 N.m	24.2
sV	27.14 kg (−8.3%)	10.37 kW (+9%)	714 N.m (−0.3%)	26.3 (8.6%)
mdV	27.58 kg (−6.8%)	9.71 kW (+2%)	724 N.m (+1.1%)	26.3 (8.6%)
dU	26.22 kg (−11.4%)	10.48 kW (+10%)	721 N.m (+0.7%)	27.5 (13.6%)
DL	25.97 kg (−12.3%)	9.32 kW (−2%)	733 N.m (+2.4%)	28.2 (16.5%)
UV	26.36 kg (−11.0%)	9.04 kW (−5%)	748 N.m (+4.5%)	28.4 (17.4%)

* Peak Torque/Rotor weight.

. As can be seen, the UV shape has the highest peak torque. It also combines between highest power density and lowest power losses. Therefore, the UV design is identified as the optimal design. The machine power and torque for the optimal design are shown in Figure 23. As can be seen, the required torque at base and top speeds is reported. It is also clear that the machine can deliver far higher output power above the base speed compared to the target rated value.

In the second place, the DL shape also has lower power losses compared to the reference design. It also has the lowest rotor weight. In the dU and sV rotor shapes, the rotor weight is reduced significantly. However, the power losses increased by about 10% compared to the reference design. In the mdV rotor shape, the torque density is improved by over 8% and the rotor weight is reduced by at least 6%. Yet, power losses are slightly higher.

To sum up, one of the primary contributions of this paper is the application of a multidisciplinary design optimization approach to the material selection and design of the rotor in high-speed electric drivetrains. By simultaneously considering objectives related to losses, weight, cost, and torque ripples, our MDO methodology enables the identification of designs that strike an optimal balance among these competing factors. This holistic approach results in improved electric drivetrain performance and cost-effectiveness. On the counterpart, the multidisciplinary design optimization process involves a substantial computational effort due to the high number of input and output variables. This complexity may require significant computational resources, limiting its immediate applicability in resource-constrained environments.

5. Conclusions

This paper presented the prototyping and measurement results of a Permanent Magnet (PM)-assisted Synchronous Reluctance Motor (SynRM) with a focus on optimizing rotor design. A material tradeoff is introduced using multidisciplinary optimization (MDO) of the rotor structure. Aiming at high performance and cost-effectiveness, a SynRM electric drivetrain is optimized using different lamination, and PM materials. The rotor sizes are optimized using multiple lamination grades with different magnetic properties as well as costs. To avoid irreversible, unrecoverable demagnetization, different PMs are evaluated starting from low-cost ferrite to high-coercivity PMs. Through a comprehensive experimental investigation, the performances of six different rotor designs are evaluated with different barrier shapes, including the reference design, dV, and five alternative designs: sV, mdV, dU, DL, and UV. The results clearly demonstrate that the UV rotor design stands out as the optimal choice, offering the highest peak torque and an impressive combination of superior power density and minimal power losses. Compared to the reference case, the UV shape offers an additional 4.5% peak torque, 5% lower losses, and 11% lower rotor weight. This finding highlights the potential for significant performance improvements in PM-assisted SynRM technology. In summary, this study has provided valuable insights into the design and performance of PM-assisted SynRM technology, demonstrating the significant impact of rotor design choices on motor performance. The identification of the optimal rotor design opens up exciting possibilities for enhancing motor efficiency and torque output in various industrial applications. Future research may explore further refinements and applications of this innovative motor technology.