Correction: Selema, A. Material Tradeoff of Rotor Architecture for Lightweight Low-Loss Cost-Effective Sustainable Electric Drivetrains. Sustainability 2023, 15, 14413

The author would like to make the following corrections to the published paper [1]. In the original publication, Figures 7–14, 18, and Table 4 were reproduced without appropriate copyright permission. As these figures and table do not affect, the scientific information presented in the paper in any way, it has been deleted from the corrected manuscript. In addition, text related to the copyrighted content was removed in Sections 3.2 and 3.3, as well as the belonging references [20–30].

In the original publication, the figure labels were not accurate in Figure 2 and Figure 3 as The corrected Figure 2 and Figure 3 appear below with updated labels.

There was also a mistake in

Table 1. Comparison between different rotor shapes using FEA.

Version	Design	Av Torque	Torque Ripples	PM Demag.	Rotor Losses	BMax	%Saturation Area *
Ver1 (Ref)	dV	725 N.m	4.6%	0.1%	1.00 p.u.	2.31 T	38%
Ver2	sV	723 N.m	2.9%	1.8%	1.09 p.u.	2.73 T	56%
Ver3	mdV	733 N.m	7.2%	3.3%	1.02 p.u.	2.46 T	53%
Ver4	dU	730 N.m	5.3%	6.2%	1.10 p.u.	2.80 T	67%
Ver5	DL	741 N.m	2.1%	5.4%	0.98 p.u.	2.25 T	32%
Ver6	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 published. The figure labels were not accurate. The corrected Table 1 appears below.

To clearly indicate the investigated machine parts, the author wishes to rephrase Section 3.1. Material Tradeoff, delete the citation of original reference [17] and correct an error in Table 2, as follows:

3.1. 

Material Tradeoff

Synchronous Reluctance Machines (SynRMs) are gaining prominence in various industrial applications due to their energy efficiency and robust performance characteristics. The choice of materials for the rotor construction is a critical factor that directly influences the machine’s efficiency and cost. This article explores the material tradeoff and selection criteria for SynRM rotors, particularly focusing on the comparison between Synchronous Reluctance Machine Rotors and Permanent Magnet Rotors. The study aims to provide insights into the design and optimization of SynRMs for enhanced performance and sustainability.

Synchronous Reluctance Machines have emerged as a promising alternative to traditional induction and permanent magnet synchronous machines due to their simplified construction, reduced cost, and improved efficiency. The rotor design of SynRMs plays a pivotal role in determining their operational characteristics. This article delves into the tradeoffs and selection criteria of materials for SynRM rotors, with a particular emphasis on choosing between Synchronous Reluctance Machine Rotors and Permanent Magnet Rotors.

SynRM rotors are typically constructed using laminated steel cores. The choice of rotor material primarily depends on factors such as magnetic flux density, electrical resistivity, and mechanical strength. Low-carbon steel laminations are commonly used due to their favorable magnetic properties and cost-effectiveness. However, the tradeoff lies in the need for increased rotor dimensions to achieve the desired magnetic performance, potentially leading to higher losses and manufacturing costs.

Permanent magnet (PM) rotors are characterized by high magnetic flux density, resulting in superior performance and efficiency compared to SynRM rotors. Neodymium iron boron (NdFeB) magnets are the preferred choice for PM rotors due to their outstanding magnetic properties. However, the tradeoff here is that these rare-earth magnets are costly, subject to supply chain uncertainties, and pose environmental concerns. Additionally, the disposal of rare-earth magnets can be challenging.

The choice between SynRM and PM rotors depends on the specific performance requirements of the application. For applications demanding high efficiency and power density, PM rotors are preferred. SynRM rotors may be suitable for applications prioritizing cost-effectiveness over maximum performance.

SynRM rotors are generally more cost-effective in terms of material and manufacturing costs. If cost is a primary concern, SynRM rotors may be the preferred choice.

PM rotors, particularly those utilizing rare-earth magnets, raise environmental concerns due to resource scarcity and extraction-related environmental issues. SynRM rotors, with their simpler materials and reduced reliance on rare earths, may be considered a more sustainable option. For applications with strict size and weight constraints, PM rotors’ high magnetic flux density allows for compact designs. SynRM rotors may require larger dimensions to achieve comparable performance.

The choice between SynRM Rotors and PM Rotors involves a careful evaluation of performance requirements, cost considerations, sustainability, and size constraints. Each rotor type has its own set of advantages and tradeoffs, making it crucial for designers and engineers to make informed decisions based on the specific needs of their applications. As technology evolves and environmental concerns become more prominent, the selection of rotor materials for SynRMs will continue to be a dynamic and evolving field of study.

In Table 2, some symbols were not similar to the ones in the literature. The corrected Table 2 appears below.

Table 2. Variables of the multi-objective optimization.

Input Parameters Of the Full Machine
Parameter	Symbol	Range	Parameter	Symbol	Range
Stator outer diameter	$D_{so}$	fixed	d-Barrier width	$w_{BD}$	$\mathrm{fun}. (D_{ro}$)
Rotor outer diameter	$D_{ro}$	$SR\ast D_{so}$	q-Barrier width	$w_{BQ}$	$\mathrm{fun}. (D_{ro},w_{BD}$)
Machine stack length	$L_s$	$AR\ast D_{so}$	d-Magnet width	$w_{MD}$	$K_{MD}\ast w_{BD}$
Aspect Ratio	$AR$	$L_s/D_{so}$	q-Magnet width	$w_{MQ}$	$K_{MQ}\ast w_{BQ}$
Split Ratio	$SR$	$D_{ro}/D_{so}$	d-Magnet ratio	$M_D$	$w_{MD}/w_{BD}$
Airgap length	Gap	fixed	q-Magnet ratio	$M_Q$	$w_{MQ}/w_{BQ}$
Yoke height	$H_y$	$\mathrm{fun}. (D_{so},SR$)	Barrier angle	${\theta }_{BQ}$	Indicated in F4
Slot height	$H_s$	$\mathrm{fun}. (D_{so},H_y$)	Lamination Materials	LM	1–12 (discrete)
Slot width	$w_s$	$\mathrm{fun}. (SR,H_y$)	Magnet Materials	MM	1–13 (discrete)

Table 2. Variables of the multi-objective optimization.

Input Parameters Of the Full Machine
Parameter	Symbol	Range	Parameter	Symbol	Range
Stator outer diameter	$D_{so}$	fixed	d-Barrier width	$w_{BD}$	$\mathrm{fun}. (D_{ro}$)
Rotor outer diameter	$D_{ro}$	$SR\ast D_{so}$	q-Barrier width	$w_{BQ}$	$\mathrm{fun}. (D_{ro},w_{BD}$)
Machine stack length	$L_s$	$AR\ast D_{so}$	d-Magnet width	$w_{MD}$	$K_{MD}\ast w_{BD}$
Aspect Ratio	$AR$	$L_s/D_{so}$	q-Magnet width	$w_{MQ}$	$K_{MQ}\ast w_{BQ}$
Split Ratio	$SR$	$D_{ro}/D_{so}$	d-Magnet ratio	$M_D$	$w_{MD}/w_{BD}$
Airgap length	Gap	fixed	q-Magnet ratio	$M_Q$	$w_{MQ}/w_{BQ}$
Yoke height	$H_y$	$\mathrm{fun}. (D_{so},SR$)	Barrier angle	${\theta }_{BQ}$	Indicated in F4
Slot height	$H_s$	$\mathrm{fun}. (D_{so},H_y$)	Lamination Materials	LM	1–12 (discrete)
Slot width	$w_s$	$\mathrm{fun}. (SR,H_y$)	Magnet Materials	MM	1–13 (discrete)

To clearly indicate the material in a standard formate, the author wishes to add a new Table 3 in Section 3.2. Replacing the original version with:

Table 3. Investigated materials of the laminations and PMs.

Index	Lamination Material (LM)	PM Material (MM)	Index	Lamination Material (LM)	PM Material (MM)
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
7	M300_35A	G52UH	14	-	TDK_FB

Table 3. Investigated materials of the laminations and PMs.

Index	Lamination Material (LM)	PM Material (MM)	Index	Lamination Material (LM)	PM Material (MM)
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
7	M300_35A	G52UH	14	-	TDK_FB

There was a mistake in Table 5 and Table 6 as published. The captions were not correct and a colored version was used to highlight the simulated and measured results. The corrected Table 5 and Table 6 appear below.

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

Parameter	Value	Parameter	Value
Number of slots	48	Motor Power	307.4 kW
Stack length	181.5 mm	Base Speed	3850 RPM
Rotor outer diameter	188.25 mm	Torque @ Base Speed	737.6 N.m
Airgap length	0.8 mm	Torque @ Top Speed	225.8 N.m
Slot width (ws)	6.42 mm	Rated MMF per slot	5547 AT
Yoke height (Hy)	16.1 mm	Number of armature phases	3
q-magnet width (wMQ)	27.6 mm	Number of rotor poles	8
q-magnet height (HMQ)	5.98 mm	Number of Turns per Slot	8
d-magnet width (wMD)	14.9 mm	Lamination material	20JNEH1200
d-magnet height (HMD)	8 mm	PM material	N40UH

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

Parameter	Value	Parameter	Value
Number of slots	48	Motor Power	307.4 kW
Stack length	181.5 mm	Base Speed	3850 RPM
Rotor outer diameter	188.25 mm	Torque @ Base Speed	737.6 N.m
Airgap length	0.8 mm	Torque @ Top Speed	225.8 N.m
Slot width (ws)	6.42 mm	Rated MMF per slot	5547 AT
Yoke height (Hy)	16.1 mm	Number of armature phases	3
q-magnet width (wMQ)	27.6 mm	Number of rotor poles	8
q-magnet height (HMQ)	5.98 mm	Number of Turns per Slot	8
d-magnet width (wMD)	14.9 mm	Lamination material	20JNEH1200
d-magnet height (HMD)	8 mm	PM material	N40UH

Table 6. Comparison between rotors with different barrier shapes.

Version	Rotor Weight		Power Losses @ Base Speed		Peak Torque		Torque Density (*) N.m/kg
Ver1 (Ref)	29.61 kg		9.52 kW		716 N.m		24.2
Ver2	27.14 kg (−8.3%)		10.37 kW (+9%)		714 N.m (−0.3%)		26.3 (8.6%)
Ver3	27.58 kg (−6.8%)		9.71 kW (+2%)		724 N.m (+1.1%)		26.3 (8.6%)
Ver4	26.22 kg (−11.4%)		10.48 kW (+10%)		721 N.m (+0.7%)		27.5 (13.6%)
Ver5	25.97 kg (−12.3%)		9.32 kW (−2%)		733 N.m (+2.4%)		28.2 (16.5%)
Ver6	26.36 kg (−11.0%)		9.04 kW (−5%)		748 N.m (+4.5%)		28.4 (17.4%)
* Peak Torque/Rotor weight
Measured		Extrapolation based on measurements		FE Simulation		Calculated based on (*)

Table 6. Comparison between rotors with different barrier shapes.

Version	Rotor Weight		Power Losses @ Base Speed		Peak Torque		Torque Density (*) N.m/kg
Ver1 (Ref)	29.61 kg		9.52 kW		716 N.m		24.2
Ver2	27.14 kg (−8.3%)		10.37 kW (+9%)		714 N.m (−0.3%)		26.3 (8.6%)
Ver3	27.58 kg (−6.8%)		9.71 kW (+2%)		724 N.m (+1.1%)		26.3 (8.6%)
Ver4	26.22 kg (−11.4%)		10.48 kW (+10%)		721 N.m (+0.7%)		27.5 (13.6%)
Ver5	25.97 kg (−12.3%)		9.32 kW (−2%)		733 N.m (+2.4%)		28.2 (16.5%)
Ver6	26.36 kg (−11.0%)		9.04 kW (−5%)		748 N.m (+4.5%)		28.4 (17.4%)
* Peak Torque/Rotor weight
Measured		Extrapolation based on measurements		FE Simulation		Calculated based on (*)

The author would like to replace references 11 and 12 with the following:

[11] Selema, A.; Ibrahim, M.N.; Sergeant, P. Mitigation of High-Frequency Eddy Current Losses in Hairpin Winding Machines. Machines 2022, 10, 328, doi:10.3390/machines10050328.

[12] Selema, A.; Gulec, M.; Ibrahim, M.N.; Sprangers, R.; Sergeant, P. Selection of Magnet Wire Topologies With Reduced AC Losses for the Windings of Electric Drivetrains. IEEE Access 2022, 10, 121531–121546, doi:10.1109/ACCESS.2022.3222773.

With this correction, the order of some figures, tables, and references has been adjusted accordingly. The author states that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.