Systematic Optimization Study of Line-Start Synchronous Reluctance Motor Rotor for IE4 Efficiency

Abstract

With the strengthening of international motor efficiency regulations, the new line-start synchronous reluctance motor (LS-SynRM), which does not require magnets or control units, is being studied to improve the efficiency of motors in industrial applications. However, the LS-SynRM features a complex structure with numerous design parameters, requiring the consideration of various factors such as electromagnetic performance, mechanical strength, starting capability, and ease of manufacturing. Additionally, starting capability analysis consumes a large amount of transient calculation time. The prototype stage typically comes after all simulation resources have been exhausted. The aim of this paper is to optimize the LS-SynRM by splitting the starting analysis and steady-state analysis, using a metamodel-based optimization method to quickly identify rotors of varying complexity (magnetic barriers and ribs) that meet steady-state efficiency and mechanical strength requirements. Finally, the rotor slot structure for starting is optimized within the magnetic barrier space. This approach significantly reduces the total optimization time from several weeks to just a few days. The final model obtained through the design process is analyzed using finite element analysis (FEA), and the results indicate that the target performance is achieved. To verify the FEA results, the final model is manufactured, and experiments are conducted.

1. Introduction

As the electric motor industry continues to expand, its associated electricity consumption has risen accordingly. According to the International Energy Agency, electric motors are responsible for approximately 45% of global electricity usage, and this figure reaches up to 70% within industrial sectors [1]. Inefficient motor systems significantly contribute to environmental concerns, including elevated greenhouse gas emissions. Driven by the increasing demand for energy-efficient and high-performance motor technologies, the efficiency classification of industrial motors has emerged as a key benchmark for evaluating motor performance [2,3,4]. According to the standards set by the International Electrotechnical Commission (IEC), industrial motors are classified into energy efficiency classes IE1 to IE5; as global demands for energy efficiency continue to increase, the standards for motor efficiency classes are constantly being raised. It is expected that in the coming years, IE4 and IE5 motors will become the industry standard, especially in fields with stricter energy-saving and environmental protection requirements (Figure 1 shows each efficiency class’s requirements for different power levels). Therefore, improving motor efficiency has become a major focus of research. At the same time, traditional asynchronous motors (IMs) and synchronous permanent magnet motors (SPMs) are gradually being replaced by more efficient, cost-effective, and reliable motor alternatives [5,6,7]. Synchronous reluctance motors (SynRMs) feature special rotor designs and have garnered considerable attention in industrial applications, especially in scenarios where load variation is minimal, such as in water pumps, fans, and compressors [8,9]. Compared to SPMs, the most significant advantage of SynRMs is that they do not rely on rare earth permanent magnet materials. This not only avoids the price volatility and supply risks of rare earth materials but also reduces manufacturing costs. Furthermore, since SynRMs do not contain permanent magnets, they have a higher tolerance to temperature and are less likely to lose magnetic properties due to overheating, offering stronger adaptability [10,11,12]. These advantages make SynRM highly promising for a wide range of applications. Despite the excellent static performance and energy-saving characteristics of SynRMs, their dynamic performance and starting characteristics remain challenging areas of research. SynRMs often require external control devices to optimize their starting process due to large torque fluctuations at startup [13].

Control methods such as Direct Torque Control (DTC) and Model Predictive Control (MPC) have been applied to SynRMs, improving their dynamic performance and effectively controlling torque ripple. Although the LS-SynRM has a more complex structure, with flux barriers and rotor slots, resulting in greater magnetic leakage and typically lower efficiency and power factor compared to simpler SynRMs [15,16], it has gained significant attention as a research hotspot due to the increasing demand for low-cost direct-drive systems.

LS-SynRMs must not only ensure good starting characteristics but also operate smoothly under low-speed and load fluctuation conditions. In this context, low-speed operation typically refers to rotational speeds at or below approximately 1500 rpm, which corresponds to 6–8 pole configurations under 50~60 Hz grid conditions. Therefore, designing a simplified yet efficient LS-SynRM that performs reliably under such conditions has become a key focus in current research. In past studies, scholars have proposed various methods to optimize SynRMs, including improving rotor geometry [17,18], optimizing magnetic reluctance distribution [19,20], and enhancing the squirrel-cage (SC) rotor structure [21]. These studies have shown that, by appropriately designing the rotor structure and materials, motor performance in terms of steady-state torque density and starting performance can be significantly improved. Therefore, this paper also investigates the design optimization of the LS-SynRM and its starting characteristics. Particular emphasis is placed on analyzing the relationship between the squirrel-cage (SC) rotor structure and the starting performance. By leveraging these insights, the rotor geometry and the arrangement of SC conductors and magnetic flux barriers are optimized to enhance the motor’s performance.

A key originality of this work lies in the proposed decoupled optimization strategy that separately addresses steady-state and transient (startup) performance. Unlike conventional approaches that require sequential mechanical strength verification after electromagnetic optimization, this study integrates mechanical constraints directly into the steady-state optimization process via a unified metamodel. This fusion eliminates the need for iterative loops between efficiency and mechanical analyses, significantly reducing the overall computation time. The metamodel-based framework enables the rapid identification of optimal designs with minimal simulation cost. Experimental validation confirms that the optimized and fabricated prototype fulfills the IE4 efficiency requirements while ensuring robust mechanical performance and reliable starting capability.

2. Basic Induction Motors (NEMA Standard Rotor Slot Shape) and Starting Performance

In this study, an IE3-level 5.5 kW, 54-slot, 6-pole IM was used as the basic motor model for comparison. The basic performance characteristics of the IM are provided in

Table 1. Main parameters of 5.5 kW basic IM (IE3).

Item	Unit	Value	8/12 Stator, Slot of Stator
Size (Outer Diameter) Stator/Rotor	mm	220, 144
Stack Length	mm	170
Pole/Slot Number		6/54
Air Gap	mm	0.5
Rotor Conductor Number	-	42
Coil Size (Bare)	mm	0.85
No. of Turns, Strands	-	17, 6
Phase Resistance@20 degC	Ω	0.52
Fill Factor	%	43
Insulation Paper Thickness	mm	0.22

. The stator design of the newly proposed Ls-SynRM follows the same structure as that of the IM, enabling a direct comparison between the two motor types. The IM structure is classified as NEMA Class B, which is commonly used in applications with moderate load demands.

Table 2. The relationship between the structure of the basic induction motors (NEMA standard rotor slot shape) and performance.

	NEMA Class A	NEMA Class B	NEMA Class C	NEMA Class D
Shape
Full-load slip	Low 5%	5%	5%	5~13%
Starting current/ Locked rotor current	High > 650%	Normal ≈ 650%	Normal ≈ 650%	Normal ≈ 650%
Locked rotor torque	Normal 90~100%	Normal 80~100%	High > 150%	Very high > 200%
Breakdown torque	Normal > 200%	Normal ≈ 200%	Normal ≈ 200%	Normal > 200%
Shape description	The cross-section is large (low resistance) and not too deep (low reactance).	It is similar to design A, except the deeper bar results in a lower irush and slightly lower torques.	The high resistance of the upper cage delivers a high start torque.	The bar shape and materials (brass or a similar alloy) are used for a high resistance (high starting torque) and high slip.
Application	Machines, tools, fans	General industrial applications	Conveyors	Hoists

shows the advantages and disadvantages of the rotor slots of various IM rotors [22,23]. And Figure 2 shows the speed–torque characteristic curves for each shape and shape with barriers. Due to the addition of multilayer flux barriers and rotor slots in the rotor lamination, the starting process of the LS-SynRM is divided into two stages: the asynchronous run-up phase and the synchronization phase.

When starting from rest, the rotor slots provide an asynchronous run-up torque similar to that of the IMs. The torque on the rotor slots, T_C, can be expressed as Equation (1):

$$T_c=K_T{\Phi }_m{I}_2\cos {\phi }_2$$

(1)

where K_T is the torque constant, Φ_m is the mutual flux, and I₂ and cos φ₂ are the rotor equivalent current and power factor, respectively.

When analyzing the torque–speed (slip) characteristics of IMs across various NEMA classes, one important observation is the relevance of pull-in torque compared to starting torque and pull-out torque. Pull-in torque plays a critical role during the startup phase. It is essential not only to overcome the load but also to compensate for the uncertainties in the reluctance torque, especially for the LS-SynRM, where at synchronous speed this component is “buried” in the torque on the rotor slots. The saliency pull-up torque can be expressed as follows:

$$T_{sb}=-{\displaystyle \frac{m}{2}}{\displaystyle \frac{V^{2}p{R}_{ph}}{\omega }}{\displaystyle \frac{{(X_d-X_q)}^2}{{[R_{ph}^2+X_d{X}_q]}^2}}$$

(2)

where m and p are the respective numbers of phases and poles, ω is the synchronous angular velocity of the LS-SynRM, X_d and X_q are the respective armature reactions of the D- and Q-axis reactance, R_ph is the phase resistance, and V is rotor voltage (phasor magnitude). Since LS-SynRMs rely heavily on the interaction between the rotor and the stator magnetic fields, the reluctance torque introduces additional challenges that must be overcome during startup. As the speed approaches synchronous speed, the slip tends to zero, and the LS-SynRM enters the synchronization phase. The basic IE3 IM discussed and used in this paper is classified under the NEMA Class B, and the NEMA standard rotor slot shape and performance are shown in Table 2. As observed in NEMA Class B motors, while the starting torque is adequate for many applications, there is a notable drop in torque near synchronous speed, which can lead to synchronization failure or the loss of synchrony, especially under heavy-load or high-torque-demand conditions. This is particularly concerning in applications where the motor needs to maintain stability at or near synchronous speed. In this context, the full-load slip (FLS) should not be excessively high. High slip values can exacerbate the issue of torque drop near synchronous speed, reducing the motor’s ability to maintain synchrony and resulting in performance instability or failure to synchronize under certain conditions. Therefore, when selecting the rotor design, it is important to avoid structures similar to those of NEMA Class D as much as possible, and instead, choose NEMA Class A or B structures whenever possible.

At synchronous speed and under balanced conditions, the steady-state performance of the LS-SynRM can be expressed using the following equation, where δ is the load angle. At steady state, the torque is called the reluctance torque, while the currents in the rotor slots are zero:

$$T_R={\displaystyle \frac{mp}{\omega }}\left[{\displaystyle \frac{V^2}{2}}\left({\displaystyle \frac{1}{X_q}}-{\displaystyle \frac{1}{X_d}}\right)\sin 2\delta \right]$$

(3)

2.1. Analysis of Synchronization

During the asynchronous startup, the slip decreases and the voltage phasor V advances at synchronous speed, while the electromotive force phasor E lags at a lower speed. As the rotor slip passes through the poles of the stator ampere–conductor distribution, it passes through successive regions of positive and negative polarization, known as “synchronizing torque”, corresponding to Equation (3). The synchronizing torque has no average value. If the asynchronous torque is less than the synchronous torque, the rotor will begin to accelerate above synchronous speed. The torque on the rotor SC becomes negative, causing the rotor to decelerate back to synchronous speed. The synchronization process can be explained using the following Equations (4) and (5), where T_L is the load torque, T_a is the total average asynchronous torque, and S stands for slip. If the T_a during startup is less than the load torque, synchronization cannot be achieved.

$$T_a(s)=T_c(s)+T_{sb}(s)$$

(4)

$$T_R(s)+T_a(s)-T_L(s)=J{\displaystyle \frac{d\omega }{dt}}$$

(5)

2.2. Optimization Process of LS-SynRM

Figure 3 shows a schematic diagram of the magnetic barrier constructed on the basic IM model. As indicated by Equation (3), the motor performance at steady state is influenced by the inductance difference, which is crucial for maximizing torque. First, the arrangement of the rotor bars and magnetic barriers must ensure that the rotor bars do not block the segments, preventing segment saturation and reducing the inductance difference. Additionally, longer Q-axis rotor bars reduce the available space for the arrangement of magnetic barriers, leading to a decrease in inductance difference, which negatively impacts performance. Therefore, the length of the Q-axis rotor bars should be minimized. Additionally, the rotor slots in the same position as the barrier should avoid using the NEMA Class C structure. This is because, in the Class C structure, the connection between the inner and outer bars is very narrow, which can easily cause magnetic leakage.

Next, the optimized length must ensure efficient performance and smooth startup, preventing torque drop at synchronous speed. To address startup difficulties caused by short Q-axis rotor bars, the dimensions of the D-axis rotor bars must be increased. This ensures sufficient torque at low speeds for smooth startup and synchronization. Balancing the Q-axis rotor bar length and the D-axis rotor bar size improves both startup performance and overall motor stability.

Finally, the structural strength of the rotor must also be considered to ensure it can withstand mechanical stresses under high torque and load conditions. Optimizing the rotor’s strength is crucial to prevent structural failure and ensure long-term reliability. The final design optimization process includes a comprehensive evaluation of these parameters to create an optimized motor model that meets the IE4 efficiency standard. Figure 4 visually demonstrates and guides the process of design improvements.

3. Design Optimization of LS-SynRM

Motor design typically involves conflicting goals which result in a multi-objective optimization problem. For instance, objectives such as reducing size and weight to minimize costs often clash with the goal of improving efficiency. In this context, an IM is employed with a fixed rotor volume, as the stator remains common across different designs. Key design factors include the magnetic flux barrier parameters and the placement of the rotor squirrel cage on the 2D plane. Given the large number of interrelated parameters influencing the final outcome, manual design is usually impractical. To achieve better results, mathematical optimization techniques are now commonly used. These techniques can be categorized into gradient-based methods and stochastic (or metaheuristic) approaches. Gradient methods offer faster convergence but face challenges in finding the global optimum, as they require an initial feasible solution, which can be difficult to identify in complex designs [24]. On the other hand, stochastic methods are frequently applied in motor optimization, although they can take a long time to converge and there is no mathematical guarantee they will reach the global optimum. Many popular metaheuristic algorithms, such as Genetic Algorithms (GAs) [25], Differential Evolution (DE) [26], and Particle Swarm Optimization (PSO), are based on natural processes, but they can also be iterative or approximation-based [27,28]. From an engineering standpoint, both methods can produce satisfactory results. The design of LS-SynRMs is significantly affected by saturation effects in the rotor, making computationally intensive FEA essential. A typical optimization workflow integrates FEA tools, like Ansys Motor-CAD 2025 (AMC), with optimization algorithms that manage model creation and communication with FEA software, such as Ansys optislang 2025 (AOSL). In this setup, the user specifies all design constraints and parameters, including upper and lower bounds. The optimization algorithm then proposes a set of parameters that define an optimization candidate (a complete motor model). After performing the necessary computations, the FEA results are returned to the optimization algorithm for evaluation. Simultaneously, the computed FEA results are transformed into a “metamodel”, which can be viewed as a mathematical model that approximates the real model. It serves as a “cheaper substitute”, significantly reducing computational resource consumption in optimization, sensitivity analysis, or uncertainty quantification. The metamodel has the following characteristics:

• Automatic selection: It automatically chooses the best-fitting model type based on prediction quality. The algorithm used is called the Adaptive Metamodel of Optimal Prognosis (AMOP).
• Accuracy evaluation: It uses metrics like the Coefficient of Prognosis (CoP) to assess model reliability.
• Multi-objective support: It is capable of modeling multiple objectives simultaneously.
• Efficient computation: It reduces simulation time by replacing costly simulations with fast surrogate models.

Next, by utilizing the data from the metamodel, the optimization process continues iteratively. New sets of parameters are generated, and the design is refined through successive generations until the optimal motor model is achieved.

3.1. Steady-State Optimization Analysis

Considering the minimization of design parameter variables, reference [17] identifies the basic design parameters for a magnetic barrier with four layers. At the same time, the inner and outer widths of the magnetic barrier and the segment are consistent. The design parameters and objectives are listed in

Table 3. List of constant design parameters, optimization variables, inequality constraints, and poetization goals.

Item (Constant Parameter)	Unit	Symbol	Value
Stator/rotor/shaft diameter	mm	Dso/Dro/Dri	220/144/50
Stack length	mm	Lstk	170
No. of phase/paths/tuns/strands	-	Nph/ap/Nc/NS	3/1/17/6
No. of poles/slots/barrier layers	-	p/Ns/Nb	6/54/4
Air gap	mm	δ	0.5
Item (Optimization Variables)	Unit	Symbol	Value/Range
Width of barrier layer 1~4	mm	W1b/W2b/W3b/W4b	[2/4]
Width of segment layer 1~4	mm	W1s/W2s/W3s/W4s	[3/5.5]
Width of rib layer 1~4	mm	W1s/W2s/W3s/W4s	[0.5/0.8]
Item (Optimization Goals)	Unit	Symbol	Criterion
Stress safety factor at 2*baserpm	-	SF	Maximize/>1.5
Maximum torque	Nm	Tmax	Maximize
Efficiency	%	Eff	Maximize

. Based on previous sections, steady-state conditions and transient startup analysis needed to be analyzed separately, because adding transient startup analysis requires at least 10 to 20 electrical cycles to determine the steady-state conditions. Therefore, directly analyzing the motor parameters under steady-state conditions can save significant analysis time. AMC can quickly analyze the motor’s electromagnetic parameters under steady-state conditions. Meanwhile, mechanical strength was also considered. All models within the analyzed metamodel set included mechanical analysis results. The safety factor was determined using the following Equations (6) and (7):

$$k_{safe}={\displaystyle \frac{{\sigma }_{Yield}}{{\sigma }_E}}$$

(6)

$${\sigma }_E={\displaystyle \frac{\sqrt{\begin{array}{l}({\sigma }_x-{\sigma }_y{)}^2+({\sigma }_y-{\sigma }_z{)}^2+{({\sigma }_z-{\sigma }_x)}^2\\ +6({\sigma }_{xy}^2+{\sigma }_{yz}^2+{\sigma }_{zx}^2)\end{array}}}{\sqrt{2}}}$$

(7)

In these expressions, σ_Yield denotes the material’s yield strength, while σ_E represents the equivalent (von Mises) stress. The terms σ_x, σ_y, σ_z, σ_xy, σ_yz and σ_zx correspond to the normal and shear stress components in three dimensions. Equivalent stress is widely used in engineering design as it condenses a complex 3D stress state into a single scalar value, simplifying failure prediction. It is a key parameter in the von Mises failure criterion, commonly applied to estimate yielding in ductile materials. The initial model was optimized in AOSL. The initial sensitivity study for building the multi-objective optimization process (MOP) used NDsg = 500 models. After the calculations were completed, the design response results of the 500 models could be referenced. For example, Figure 5a shows a comparison of the efficiency MOP with two parameters, L1 and L2, which represent the segment thickness. It could be observed that the smaller the segment thickness, the higher the efficiency. Next, optimization was performed using the built-in evolutionary algorithm in AOSL.

The key point here is that, since the metamodel was a mathematical function rather than a computationally intensive FEA calculation, its evaluation was almost instantaneous. For multi-objective problems, the optimal designs can be interpreted using the Pareto front (Figure 5b shows the Pareto front optimal solution set). Finally, the optimal design analysis results were validated through FEA, and the analysis results along with cross-sectional results are shown in Figure 5c,d.

3.2. Startup Optimization Analysis

After maximizing the steady-state analysis results, the next step was to analyze the starting torque and synchronization balance characteristics. In order to increase the maximum torque and reduce the leakage inductance for synchronization, the rotor resistance can be adjusted to an appropriate value. Therefore, the optimal model design considered the starting torque and adopted design variables for rotor slot regions No. 1, 2, 3, 5, 6, and 7. It should be noted that the widths of rotor slots No. 1, 2, 3, 5, 6, and 7 were optimized through the decision of the first step of design optimization, and their widths were the same as the width of the flux barrier. As a result, the target design variables could be simplified to the lengths Y1 (four-layer barrier) for rotor slots No. 1 and 7, Y2 (three-layer barrier) for rotor slots No. 2 and 6, and Y3 (one-layer barrier) for rotor slots No. 3 and 5. In addition, the maximum limit values of the design variables were also determined by the first step of the optimization process. In Step II, the magnetic reluctance (aluminum material) in the rotor slots was the same as that of air. Therefore, changing the lengths of rotor slots No. 1, 2, 3, 5, 6, and 7 did not affect the excitation torque under steady-state conditions. The inner side bridge had to ensure that there was no structural damage to the rotor inner side barrier under high-pressure die-casting conditions, so the inner side bridge took the minimum value to reduce the leakage flux. If the model synchronized successfully, the rotor current would rapidly decrease to near zero, and the rotor copper loss could be neglected.

• Optimization Design Step II.
• Objective function: Maximize the torque (T_max)/check whether it is synchronized.
• Constraint: Maximum torque > 45.1 N·m.
• Design variables: 0 mm ≤ Y1 ≤ 18 mm, 0 mm ≤ Y2 ≤ 12 mm, 0 mm ≤ Y3 ≤ 6 mm.

Due to spatial constraints, the length of rotor slot No. 4 was set to be the same as that of rotor slots No. 3 and 5. However, analysis showed that synchronization could not be achieved when Y3 was less than 6 mm. Therefore, the length of Y3 was determined first, and then the parameter analysis of Y1 and Y2 was conducted to observe the changes in starting performance. Figure 6a shows these characteristics as functions of Y1 and Y2. Figure 7 shows the time-step FEA result for the region and selected points. If synchronization fails, the torque and speed pulsate. In order to ensure successful synchronization, Y1 and Y2 were selected as 18 mm and 12 mm, respectively. At the end of the design, all the rotor groove edges were rounded to increase the die-casting fill rate. The optimal model is shown in Figure 6b. The results of the optimal design are shown in

Table 4. FEA result of final LS-SynRM.

Pictutre	Item	Unit	Value
flux density distribution at 5.5 kW, 1200 rpm	Power at 1200 rpm	kW	5.5
	Line voltage	Vrms	380
	Efficiency	%	92.6
	Power factor		0.73
	Current	Arms	12.3
	Iron loss	W	96.1
	Copper loss	W	239.2
	Rotor copper loss	W	33.1
	Additional loss	W	68.0

.

4. Prototype Manufacturing and Experiments

To verify the FEA results, the final optimized design of the LS-SynRM was manufactured. Figure 8a shows the rotor core of the manufactured porotype LS-SynRM. Additionally, in the die-casting process, endplates were added to the upper and lower ends of the rotor core, as shown in Figure 8b, to prevent the cast aluminum from being injected into the rotor’s barriers and ensure it was only injected into the rotor slots. Finally, Figure 8c shows the completed aluminum-cast squirrel-cage rotor before the shaft was inserted. The height of the end-ring was the same as that of the basic IE3 IM model, and the width of the end-ring was the length of the longest rotor slot (which must cover all rotor slots).

To verify the FEM analysis results, an experiment was conducted. Figure 9 shows the experimental setup. Both the basic IM and the optimized LS-SynRM were tested under no-load and load conditions. According to IEC 60034-2-1 [29], various losses were separated, and motor efficiency was tested under different loads. The test and comparison results are shown in

Table 5. Comparison of FEA and experimental results (LS-SynRM and IM).

Item	Unit	Value
		LS-SynRM/FEM	IM/Test	LS-SynRM/Test
Power	kW	5.5@1200 rpm	5.5@1175 rpm	5.5@1200 rpm
Efficiency	%	92.6	90.7	92.2
Power factor		0.73	0.754	0.685
Current	Arms	12.3	12.28	13.16
Iron loss	W	96.1	106	103.6
Copper loss	W	239.2	249.5	268.2
Rotor copper loss	W	33.1 *	124.6	1.0
Additional loss	W	68	84.7	91.1

* Rotor copper loss of FEM analysis is due to eddy currents from high-order magnetic field disturbances.

and Figure 10. As shown in Table 5, discrepancies between the FEM analysis and experimental results exist in power factor, rotor copper loss, and additional losses. These differences arise from the assumptions in the simulation compared to the real-world conditions.

Power Factor:

The FEM assumed an ideal, harmonic-free power supply, leading to a higher simulated power factor compared to the measured value, which includes real-world harmonic distortions.

Rotor Copper Loss:

In the FEM analysis, small eddy currents due to high-order magnetic field variations caused minimal rotor copper loss. In the experiments, rotor copper loss was negligible due to the measured rotor speed being close to synchronous speed.

Additional Losses:

In the simulations, additional losses were estimated using mechanical loss models and empirical data that relate losses to input power percentages, whereas the experiments subtracted known losses from input–output power measurements, introducing minor discrepancies.

These differences highlight the need to account for modeling assumptions and experimental uncertainties in comparisons between FEM analysis and experimental results. Overall, the results indicate that the efficiency obtained from the FEA is similar to the experimental results and fully meets the IE4 efficiency class requirements.

5. Conclusions

In this paper, a systematic optimization strategy for the line-start synchronous reluctance motor (LS-SynRM) rotor was proposed to achieve IE4-level efficiency while ensuring robust mechanical strength and starting performance. The originality of this work lies in its decoupled yet unified approach: steady-state and transient (startup) performance are optimized separately, while mechanical stress constraints are simultaneously embedded in the steady-state optimization phase via a metamodel. This integration eliminates the need for iterative mechanical checks post-electromagnetic optimization, thereby significantly reducing design time. A detailed comparison of computational time for each analysis and the overall reduction achieved by the metamodel-based approach is provided in Appendix A.

This metamodel was trained using a limited number of high-fidelity FEM analysis results through the AMOP algorithm and demonstrated high accuracy, with prediction errors below 5% (COP > 95%). This enabled the efficient exploration of 6000 rotor design candidates in under 12 min.

The final optimized rotor structure was validated by both FEA and experimental prototyping. The measured results confirm that the proposed design meets IE4 efficiency standards and exhibits satisfactory starting characteristics. The close alignment between the experimental and simulated results (efficiency deviation < 1%) verifies the reliability of the proposed method.