Magnetic Field Simulation and Torque-Speed Performance of a Single-Phase Squirrel-Cage Induction Motor: An FEM and Experimental Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study presents a detailed investigation of the torque-speed characteristics of a  single-phase squirrel-cage induction motor.The reviewer thinks that the innovation of the paper is insufficient. This is more of a simulation experiment report than a research paper. Suggest authors to make some improvements in the following areas:
1.What are the innovations of this paper as perceived by the authors?
2.In the abstract, the authors mention "simulation using MATLAB and Simulink." Since Simulink is a part of MATLAB, is this phrasing appropriate? Additionally, in the term "single-phase squirrel-cage induc-tion motor," why is a hyphen used in "induc-tion"? Furthermore, why is "The Magnetic Finite Element Method" abbreviated as FEMM instead of the standard FEM?
3.The authors need to supplement the explanations of each component and section in the equivalent circuit of Figure 1, specifying their physical meanings and roles in the model.
4.Please check Equation (7) to confirm whether the denominator should be 2e. Additionally, verify if the numerator in Equation (16) is correct. The formulas in the paper lack annotations for critical parameters ( p，Nsl，a，qwd...), severely impairing readability for readers."
5.The resolution of Figures 2 and 3 is too low, resulting in blurred images. Figure 4 requires labeling of all components with their names.
6.Given the experimental setup illustrated in Figure 4, why did the authors choose to perform simulations instead of direct performance testing? Wouldn’t experimental testing under these conditions hold greater practical significance?
7.Is the publication year of Reference 8 and Reference 14 incorrect? The year in the DOI clearly conflicts with the text, and the authors need to conduct further verification.

Author Response

1.What are the innovations of this paper as perceived by the authors?

The main innovations can be summarized as follows: Integrated approach: classical parameter estimation (including Suhr’s) and simulation in Simulink and finite element analysis in FEMM. Although these methods are well-known, their combined and comparative of torque-speed across multiple supply voltages is novel, rarely addressed in similar studies. Test bench: A complete test module was designed and implemented to emulate mechanical loads, allowing real-time acquisition not only of static parameters but of dynamic performance curves, which are often missing in similar works. SPSCIMs: Most available literature focuses on three-phase induction machines.

It was added in conclusions of this paper as a paragraph as; “A key innovation of this work lies in the integrated and comparative approach, combining classical estimation methods, FEM simulations, and dynamic MATLAB modeling to evaluate the torque-speed behavior of the SPSCIM under multiple voltage levels. A perspective rarely addressed in previous literature together, particularly for single-phase machines. Furthermore, most previous studies focus on three-phase induction motors, while this paper highlights the importance and characterization of single-phase motors, specifically SPSCIMs, as an extended basis for future work in the optimization of their design and control”.

 

2.In the abstract, the authors mention "simulation using MATLAB and Simulink." Since Simulink is a part of MATLAB, is this phrasing appropriate? Additionally, in the term "single-phase squirrel-cage induc-tion motor," why is a hyphen used in "induc-tion"? Furthermore, why is "The Magnetic Finite Element Method" abbreviated as FEMM instead of the standard FEM?

We will use the phrasing “MATLAB®/Simulink®” to clearly reflect that both environments were utilized: MATLAB code for processing and plotting data, and Simulink® specifically for the simulation of the motor model. On the hyphenation in “induc-tion”: This was an unintentional typographical error. On the last term, we clarify that FEMM refers to the specific software tool Finite Element Method Magnetics. We agree that the distinction from the general “FEM” (Finite Element Method) should be clarified. The correction was as follow;

“...using a finite element analysis approach via the FEMM (Finite Element Method Magnetics) software).

3.The authors need to supplement the explanations of each component and section in the equivalent circuit of Figure 1, specifying their physical meanings and roles in the model.

To address this point, we have expanded the explanation of each component in the equivalent circuit of Figure 1 as follow before the figure;

“…protection ODF, and an operating temperature of 40°C. In the equivalent circuit of Fig \ref{fig1}, $R_1$ and $X_1$ represent the stator resistance and leakage reactance, while $R_2$ and $X_2$ are the rotor resistance and leakage reactance referred to the stator side. The magnetizing branch, formed by $R_c$ and $X_m$, models the core losses and the magnetizing current. The term $R_2/s$ accounts for the slip-dependent rotor power conversion. This standard single-cage model captures the essential steady-state behavior of the motor. This nameplate information”

4.Please check Equation (7) to confirm whether the denominator should be 2e. Additionally, verify if the numerator in Equation (16) is correct. The formulas in the paper lack annotations for critical parameters ( p，Nsl，a，qwd...), severely impairing readability for readers."

The equation (7) was corrected to include the factor 1/2, which is standard in the calculation of magnetic energy stored in a volume. The equation (16) accurately reflects the calculating the reactance from the measured reactive power and the square of the no-load current, it was added into the paragraph.

“…or $X_{Q}$ and $X_{0}$ the no-load test is required with power measurements in the auxiliary and main windings, respectively, as detailed in the work [13]. To determine $X_{Q}$, the reactive power measured is given by the equation \eqref{eq16}, in fuction of the no load current $I_NL$ as follows;”

The annotations for critical parameters were included contextually within the corresponding paragraphs of Section 2. It was made a modification to include poles as “p”, as follow;

“…onally, certain constructive data about the total winding named $q_{T}$, can be obtained, such as its distribution around the number of slots $N_{sl}$ of the stator for 2 poles $p$:”

5.The resolution of Figures 2 and 3 is too low, resulting in blurred images. Figure 4 requires labeling of all components with their names.

The resolution of Figures 2 and 3 has been significantly improved to ensure clear visibility of all dimensions and elements shown in the diagrams. In figure 4, simple and clear labels have been added to identify the main components. We appreciate the reviewer’s suggestion.

6.Given the experimental setup illustrated in Figure 4, why did the authors choose to perform simulations instead of direct performance testing? Wouldn’t experimental testing under these conditions hold greater practical significance?

The decision to rely primarily on simulations was motivated by several factors signalized in the introduction. The main objective of this paper, and its innovative contribution, lies in the comprehensive contrast of multiple evaluation criteria for the SPSCIM under different voltage levels. Unlike previous works that typically address these analyses separately and mainly focus on three-phase motors, this study integrates four complementary approaches: simulations in MATLAB/Simulink, finite element analysis using FEMM, parameter estimation via the classical and Suhr methods, and experimental validation. This combined methodology provides a more complete understanding of the single-phase motor's behavior and performance, offering a novel perspective not commonly found in the existing literature. We recognize the importance of experimental testing and intend to include these results in a future extension of this work.

7.Is the publication year of Reference 8 and Reference 14 incorrect? The year in the DOI clearly conflicts with the text, and the authors need to conduct further verification.

We have verified the publication years of References 8 and 14. Although the DOI metadata indicates an earlier online publication date, we confirm that the correct year to cite is the one corresponding to the official journal issue in which the articles appeared.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The work is interesting but has several shortcomings.

1. The purpose of the work and its contents should be presented at the end of the introduction.
2. The paper includes a photo of the nameplate of the motor under study, which even when enlarged is not readable.
3. The substitute diagram of the motor ( Fig.1) refers to two equal windings . but the SPSCIM winding is divided into two different parts: 2/3 and 1/3 (lines 150-152)
4. The work is inconsistent. Fig. 2 gives drawings of slots with detailed dimensions (without specifying the unit of measurement), but the mechanical parameters (dimensions, masses) of the stator and rotor are not included in the work.
5. Fig. 3 incomprehensible caption.
6. line 158 : What is “ Industrial design constant”, how is its value determined?
7. error in formula (14).
8. line (215) how the reactive power measured, by what definition?
9. figure 6. it is not marked where the working winding and where the auxiliary winding.
10. the title of Table 5 is vague. What type of load is meant and in what units is it measured
11. mistake in the acronym - line 338.
12. :The authors refer to the use of Simulink, but no Simulink schematic is included in the paper.

Author Response

The work is interesting but has several shortcomings.

1. The purpose of the work and its contents should be presented at the end of the introduction.

According to this suggestion, it was added ad the end of the introduction as follow,

“….Despite the preference for single-phase induction motors in industrial and domestic applications, the optimization and behaviour of these motors has been less extensively researched. The focus of this work is to integrate different methodologies related to parameter estimation and the evaluation of the characteristic performance curve of the Single-Phase Squirrel Cage Induction Motor (SPSCIM), highlighting its potential for future research in design optimization and control.”

2. The paper includes a photo of the nameplate of the motor under study, which even when enlarged is not readable.

The figure was updated to reduce resolution loss, making the nameplate clearer. Additionally, the motor’s key specifications were included directly in the surrounding text to ensure that the information is accessible even if the image is not perfectly legible."

3. The substitute diagram of the motor ( Fig.1) refers to two equal windings . but the SPSCIM winding is divided into two different parts: 2/3 and 1/3 (lines 150-152)

The equivalent circuit diagram shown in Fig. 1 is a simplified representation used for general analysis and comparison purposes. The text paragraph clarifies that in the specific case of the SPSCIM under study, the winding distribution corresponds to 2/3 for the main winding and 1/3 for the auxiliary winding. This distinction is considered in the subsequent calculations and modeling." It was added before figure 1 as follow,

“…model shown in Fig.\ref{fig1} enabled, through calculations and simulations, the description of the classical and Suhr methods for determining the motor parameters in the characteristics and real distribution of the windings. These methods are based on direct current (DC) tests, the locked-rotor test, and the open-circuit test.”

4. The work is inconsistent. Fig. 2 gives drawings of slots with detailed dimensions (without specifying the unit of measurement), but the mechanical parameters (dimensions, masses) of the stator and rotor are not included in the work.

Thank you for the observation. Figure 2 has been updated to a higher resolution, and a note has been added to indicate that all dimensions are in millimeters. While the mechanical dimensions and material characteristics of the stator and rotor were not included initially, they are now clarified and incorporated in the finite element analysis section, where the materials and structural assumptions are described in detail.

5. 3 incomprehensible caption.

Figure 3 has been replaced with a higher-resolution version to improve clarity, and the caption has been revised to ensure it clearly describes the content of the image.

6. line 158 : What is “ Industrial design constant”, how is its value determined?

The term "industrial design constant" (C) refers to an empirical coefficient commonly used in preliminary design equations for estimating the number of turns in induction motor windings. Its value accounts for standard industrial practices, including insulation type, manufacturing tolerances, and expected performance margins. In this study, a value of C = 133 was selected, which is typical for 60 Hz industrial motor design and is often used. As these expressions were included to offer a practical context rather than to drive the core experimental validation of the work, a deeper analytical exploration of the constant was not considered necessary for the scope of this study. It was extended in the explication as;

“… coil, equation \eqref{eq5} was used, which is a function of the slot length $L_{sl}$, the slot diameter $D_{sl}$, a current density factor $K_{d}$, the magnetic flux density $B$ and an industrial design constant $C$. A value of $133$ was considered for this study for a $60 Hz$ frequency of the grid, following standard practice for industrial machines operating”.

7. error in formula (14).

This expression was modified in accordance with standard machine modeling practices as follow, X_m = \frac{|E_f|}{\sqrt{I_{NL}^2 - \left(\frac{|E_f|}{R_m}\right)^2}}. The previous error involving an unjustified factor of 2 has been eliminated.

8. line (215) how the reactive power measured, by what definition?

A clarification has been added to the text to specify that the reactive power Q in Equation \eqref{eq16} is obtained from the measurement of apparent and active power in the auxiliary winding during the no-load test, using the classical definition. It was added as;

“…To determine $X_{Q}$, the reactive power is also measured in the auxiliary winding during the no-load testis given by the equation \eqref{eq16}, in fuction of the no load current $I_{NL}$ as follows;”

9. figure 6. it is not marked where the working winding and where the auxiliary winding.

We appreciate the reviewer’s observation regarding Figure 6. To address this, we clarified the roles of Figures 5 and 6. Specifically, Figure 5 was included to visualize the distribution of the windings, the mesh convergence, and the node formation in the FEMM simulation.

It also provides context for the main and auxiliary windings, which were previously described: the main winding uses 18 AWG wire with 32 turns per slot, while the starting (auxiliary) winding uses 21 AWG wire with 100 turns per slot.

Meanwhile, Figure 6 focuses solely on the magnetic flux distribution and the concentration related to pole formation. This distinction has been clarified in the figure captions and accompanying text.

 

 

10. the title of Table 5 is vague. What type of load is meant and in what units is it measured

Thanks for the observations. We modified the caption as;

\caption{Load Current and Motor Speed Measurements at $39 V$, $65 V$, $80 V$, and $120 V$ Supply Voltages.\label{tab5}}

11. mistake in the acronym - line 338.

The mistake was revolved in the acronym “parame-terization” in the conclusions section.

12. The authors refer to the use of Simulink, but no Simulink schematic is included in the paper.

"We chose not to include the Simulink schematic diagrams to save space, as the connections and experiments are well-known. However, we did include the simulation results, which were compared against the parameters obtained from the experimental tests on the SPSCIM.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper looks at how a single-phase squirrel-cage induction motor (SPSCIM) works by combining experimental tests with simulations using the finite element method (FEM). The authors use both the classical method and the Suhr method, along with FEM modeling, to study the motor’s torque-speed performance. The approach is solid, and the paper includes useful comparisons. However, there are several parts that need to be improved before the paper can be ready for publication.

Suggestions:
1.    The abstract gives a good overview of the work, but it’s a bit too detailed in describing the methods. It might help to simplify that part and focus more on the main results and what’s new in this study. Also, would it be possible to include some numerical results (like percentage errors) to clearly show how well your model performed?
2.    The introduction covers many studies, which is great, but it feels a little unfocused at times. Some references are listed without clearly connecting them to your own work. You might consider shortening a few sections and making the link to your research question more direct. Also, could you please clarify what makes this work different or new compared to similar studies, like [13] and [16]?
3.    (Lines 111–219): This section is quite detailed and informative. However, some of the equations (especially Eqs. 1–7) could be clearer if you briefly explained the meaning and units of the variables. A simple table listing what each symbol means and the units would be very helpful for readers.
4.    Could you please add more detail about the FEMM simulation setup? For example, what boundary conditions did you use? Was a mesh refinement or convergence test done to ensure the accuracy of the results?
5.    There is a noticeable difference (about 20%) in the rotor resistance (R2) value between FEMM simulation and experimental results. Do you think this could be caused by assumptions about material properties or simplifications in the motor geometry? It would be helpful to hear your thoughts on this.
6.    Figure 7 shows useful results, but it could be improved by making the legend and axis labels easier to read. Adding units to the axes would also make the graph clearer.
7.    Throughout the text and especially in tables, please make sure there’s a space between numbers and units (for example, write “230 V” instead of “230V”). This helps keep the formatting in line with standard scientific writing.
8.    The paper includes useful references, but many of them are a bit old. To improve the background and show that the authors are up to date with the latest research, I recommend adding some newer studies from the last 2–3 years, especially on FEM simulations, modern ways to estimate motor parameters, or new methods for analyzing single-phase induction motors.
9.    I suggest doing a careful grammar and spell-check. There are a few small errors and typos that, once corrected, will really help improve the overall readability and professional appearance of the paper.

Comments on the Quality of English Language

The English in the paper is mostly understandable, but there are some grammar mistakes, spelling errors, and formatting issues. I recommend careful proofreading to improve clarity and make the paper easier to read.

Author Response

1.    The abstract gives a good overview of the work, but it’s a bit too detailed in describing the methods. It might help to simplify that part and focus more on the main results and what’s new in this study. Also, would it be possible to include some numerical results (like percentage errors) to clearly show how well your model performed?

The corrections were considered in the abstract as follow;

“…the results revealed strong agreement between the FEM simulations, Surh method, and experimental data, demonstrating the reliability and accuracy of the combined simulation and analytical methods for modeling the motor's performance. The estimations using classical and Suhr methods, Simulink simulations, and FEMM yielded low error percentages, mostly below 2\%. However, in the FEMM simulation, rotor resistance showed a higher error of around 20\% due to unavailable data on the exact number of windings turns, a modifiable parameter that can be corrected through further adjustments in the simulation”

2.    The introduction covers many studies, which is great, but it feels a little unfocused at times. Some references are listed without clearly connecting them to your own work. You might consider shortening a few sections and making the link to your research question more direct. Also, could you please clarify what makes this work different or new compared to similar studies, like [13] and [16]?

The main innovations that make a huge difference with other works as [13] and [16] can be summarized as follows: Integrated approach: classical parameter estimation (including Suhr’s) and simulation in Simulink and finite element analysis in FEMM. Although these methods are well-known, their combined and comparative of torque-speed across multiple supply voltages is novel, rarely addressed in similar studies. Test bench: A complete test module was designed and implemented to emulate mechanical loads, allowing real-time acquisition not only of static parameters but of dynamic performance curves, which are often missing in similar works. SPSCIMs: Most available literature focuses on three-phase induction machines. It was included in comparison with other reviewer suggestions in the conclusions as follows,

“…A key innovation of this work lies in the integrated and comparative approach, combining classical estimation methods, FEM simulations, and dynamic MATLAB modeling to evaluate the torque-speed behavior of the SPSCIM under multiple voltage levels. A perspective rarely addressed in previous literature together, particularly for single-phase machines. Fur-thermore, most previous studies focus on three-phase induction motors, while this paper highlights the importance and characterization of single-phase motors, specifically SPSCIMs, as an extended basis for future work in the optimization of their design and control”.

3.    (Lines 111–219): This section is quite detailed and informative. However, some of the equations (especially Eqs. 1–7) could be clearer if you briefly explained the meaning and units of the variables. A simple table listing what each symbol means and the units would be very helpful for readers.

Some of the equations are used for specific parameter calculations and, although not all are deeply analyzed in detail, they are included due to their relevance in the context of the methodology. To maintain clarity and avoid excessive detail, their use is referenced within the explanatory paragraphs. However, based on reviewer feedback, a few key variables have been further clarified, and a table has been added to define the main symbols and units used in Equations (1) to (7), enhancing the readability of the section. For example;

“…onally, certain constructive data about the total winding named $q_{T}$, can be obtained, such as its distribution around the number of slots $N_{sl}$ of the stator for 2 poles $p$:”

“…protection ODF, and an operating temperature of 40°C. In the equivalent circuit of Fig \ref{fig1}, $R_1$ and $X_1$ represent the stator resistance and leakage reactance, while $R_2$ and $X_2$ are the rotor resistance and leakage reactance referred to the stator side. The magnetizing branch, formed by $R_c$ and $X_m$, models the core losses and the magnetizing current. The term $R_2/s$ accounts…”

“…or $X_{Q}$ and $X_{0}$ the no-load test is required with power measurements in the auxiliary and main windings, respectively, as detailed in the work [13]. To determine $X_{Q}$, the reactive power measured is given by the equation \eqref{eq16}, in fuction of the no load current $I_NL$ as follows;”

4.    Could you please add more detail about the FEMM simulation setup? For example, what boundary conditions did you use? Was a mesh refinement or convergence test done to ensure the accuracy of the results?

 

 

Those corrections were made in section 4.1 as follows, “\subsection{Parameter Extraction Using the Finite Element Method.}

After evaluating the various mathematical equations and expressions, a simulation was conducted using the FEMM software and physical parameters. The material properties were defined as follows: the stator core was modeled using “Gray Iron, As Cast” to represent the magnetic steel with its associated saturation curve, the shaft was modeled using “304 Stainless Steel,” the rotor consisted of “Aluminum 1100” bars, and the windings were specified as $18$ AWG copper wire with $32$ turns per slot for the main winding, and $21$ AWG copper wire with $100$ turns per slot for the starting winding of the single-phase squirrel-cage induction motor (SPSCIM) and air gaps were modeled using FEMM’s predefined air material. These definitions ensured a realistic magnetic response aligned with the motor’s physical construction, as illustrated in Fig. \ref{fig5}.”

5.    There is a noticeable difference (about 20%) in the rotor resistance (R2) value between FEMM simulation and experimental results. Do you think this could be caused by assumptions about material properties or simplifications in the motor geometry? It would be helpful to hear your thoughts on this.

This point has been addressed in the abstract according to the first observation, where it was indicated that most calculated errors remained below 2%, except for the rotor resistance (R₂) estimated via FEMM, which showed a discrepancy of around 20%. This difference is primarily attributed to the approximated number of turns used in the simulation, based on typical manufacturer data. The actual number of turns would require disassembling the motor. Additionally, it was clarified in the discussion of Table 3 as,

“…..in Table \ref{tab3} that for the stator resistance R1 there is a difference between the calculations and simulations of 0.41\% and 1.87\%, respectively. For the rotor resistance R2 a 2.18\% and 20\% error is observed, and a difference of 0.66\% and 11.9\% for both reactances X1 and X2 remembering that they are identical for stator and rotor in this SPSCIM. Finally, in the magnetization circuit, we see a discrepancy in the magnetizing resistance Rm of 6.5\% and 16\% with the simulations, and for the magnetizing reactance Xm 1.15\% and 1.47\%, respectively. The discrepancies, mainly in obtaining the results for the rotor resistance and series reactances, vary according to the physical characteristics of the SPSCIM, material and more affected by the number of turns into the windings, which could be adjusted with a more precise number, but it requires an intrusive action not addressed in this work.”

6.    Figure 7 shows useful results, but it could be improved by making the legend and axis labels easier to read. Adding units to the axes would also make the graph clearer.

Thank you for the suggestion. The image has been adjusted to improve the clarity of the axes and labels, making them easier to read. Additionally, units have been added to the axes to enhance the graph's clarity.

7.    Throughout the text and especially in tables, please make sure there’s a space between numbers and units (for example, write “230 V” instead of “230V”). This helps keep the formatting in line with standard scientific writing.

Thank you for your comment. A revision was made throughout the entire document to ensure consistent formatting, including proper spacing between numbers and units, in line with standard scientific writing.

8.    The paper includes useful references, but many of them are a bit old. To improve the background and show that the authors are up to date with the latest research, I recommend adding some newer studies from the last 2–3 years, especially on FEM simulations, modern ways to estimate motor parameters, or new methods for analyzing single-phase induction motors.

An extensive review of recent works was conducted, and while it is true that more recent studies exist on FEM simulations and the use of FEMM software, not many are directly related to the specific topic of SPSCIM motors. Therefore, we opted for the most relevant and suitable references for our case study. Additionally, one of the innovations of this work is to include a variety of methods and analyses focused on the SPSCIM.

9.    I suggest doing careful grammar and spell-check. There are a few small errors and typos that, once corrected, will really help improve the overall readability and professional appearance of the paper.

Thank you for your suggestion. A thorough grammar and spell-check has been conducted in the revised version to improve the overall readability and professional presentation of the manuscript.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The paper presents a comprehensive study combining FEM simulations, MATLAB/Simulink modeling, 
and experimental validation for a single-phase squirrel-cage induction motor (SPSCIM).

1-The primary contribution of the paper is not clearly 
defined. We recommend clarifying this aspect to better highlight the originality and significance of your work.

2- Clearly state the research gap or specific problem this paper addresses. 

3- The introduction could be streamlined to avoid overwhelming the reader with 
too many references. Focus on the most relevant studies and highlight their limitations.

4-Provide more justification for the choice of the Suhr method over other parameter estimation 
techniques. How does it compare in terms of accuracy or computational efficiency?

5-Include a flowchart or schematic summarizing the overall methodology to improve readability.

6-Add a brief discussion on the calibration or accuracy of the measurement devices (PZEM meters, Hall effect sensor). 
How were potential errors minimized?

7-Include photos or diagrams of the test station to complement Figure 4 and enhance clarity.

8- Discuss the practical implications of the observed discrepancies (20% error in rotor resistance). 
Are these errors acceptable for real-world applications?

9- Provide more context for the choice of 1.15 as the compensation factor in Equation (8). Is this value standard, or was it derived experimentally?

10 -  Suggest future work, such as extending the analysis to other motor types or incorporating real-time parameter estimation techniques.

Author Response

1-The primary contribution of the paper is not clearly defined. We recommend clarifying this aspect to better highlightthe originality and significance of your work.

The main innovations can be summarized as follows: Integrated approach: classical parameter estimation (including Suhr’s) and simulation in Simulink and finite element analysis in FEMM. Although these methods are well-known, their combined and comparative of torque-speed across multiple supply voltages is novel, rarely addressed in similar studies. Test bench: A complete test module was designed and implemented to emulate mechanical loads, allowing real-time acquisition not only of static parameters but of dynamic performance curves, which are often missing in similar works. SPSCIMs: Most available literature focuses on three-phase induction machines.

According to a similar suggestion from other revision, It was added in the abstract of this paper as a paragraph as;

“…the results revealed strong agreement between the FEM simulations, Surh method, and experimental data, demonstrating the reliability and accuracy of the combined simulation and analytical methods for modeling the motor's performance. The estimations using classical and Suhr methods, Simulink simulations, and FEMM yielded low error percentages, mostly below 2\%. However, in the FEMM simulation, rotor resistance showed a higher error of around 20\% due to unavailable data on the exact number of windings turns, a modifiable parameter that can be corrected through further adjustments in the simulation”

2- Clearly state the research gap or specific problem this paperaddresses.

The specific research gap addressed in this paper is the lack of integrated studies focused on Single-Phase Split Capacitor Induction Motors (SPSCIMs), particularly combining classical and Suhr parameter estimation methods, MATLAB/Simulink simulations, FEM analysis, and experimental validation. While these approaches are commonly applied to three-phase motors, they are rarely explored in a unified framework for single-phase machines, especially across multiple voltage levels with simulations and comparatives together in the same case of study. This work aims to fill that gap and provide a structured base for future design and control optimization of SPSCIMs, as can be specified in the modification made in the abstract and particularly extended in the conclusions.

According to a similar suggestion from other revision, It was added in conclusions of this paper as a paragraph as; “A key innovation of this work lies in the integrated and comparative approach, combining classical estimation methods, FEM simulations, and dynamic MATLAB modeling to evaluate the torque-speed behavior of the SPSCIM under multiple voltage levels. A perspective rarely addressed in previous literature together, particularly for single-phase machines. Furthermore, most previous studies focus on three-phase induction motors, while this paper highlights the importance and characterization of single-phase motors, specifically SPSCIMs, as an extended basis for future work in the optimization of their design and control”.

3- The introduction could be streamlined to avoid overwhelming the reader with too many references. Focus on the most relevant studies and highlight their limitations.

While we agree that a concise introduction improves readability, the decision to extend this section was intentional. Given the limited availability of recent references specifically focused on SPSCIMs, we chose to include a broader context to highlight that, although there are similar works addressing individual methods, very few integrate classical estimation, simulation, and FEM analysis specifically for these motors. This contextualization helps to justify the novelty and scope of our approach. In was also mentioned in the modification of the abstract. I hope this will be enough to clarify the suggestion.

4-Provide more justification for the choice of the Suhr method over other parameter estimation techniques. How does it compare in terms of accuracy or computational efficiency?

The Suhr method, as referenced in [13] between others, was selected because it yields reliable and positive results in the parameter estimation of the motor using the same measurement setup as the classical method. Its main difference lies in the calculation of reactance, specifically addressed in equations 15 and 16. This approach was well-suited to the experimental module developed and implemented in Section 3, allowing for consistent data acquisition and comparative analysis without requiring additional testing setups.

5-Include a flowchart or schematic summarizing the overallmethodology to improve readability.

The Suhr method, as referenced in [13], was selected because it yields positive results in the parameter estimation using the same measurement setup as the classical method. Its main difference lies in the calculation of reactance (equations 15 and 16). This approach was well-suited to the experimental module developed and implemented in Section 3. It was added details for this suggestion as;

“….From equation \eqref{eq15}, we can deduce that $X_{1}$ can be determined from the locked-rotor test of the classical method, and for $X_{Q}$ and $X_{0}$ the no-load test is required with power measurements in the auxiliary and main windings, respectively, as detailed in the work [13], this characteristic makes the Suhr method suitable to the test station capacities. To determine $X_{Q}$, the reactive power ….”

6-Add a brief discussion on the calibration or accuracy of the measurement devices (PZEM meters, Hall effect sensor). How were potential errors minimized?

Measuring devices used as PZEM modules and the Hall effect current sensors, were employed as provided by the manufacturer, without additional calibration. The accuracy and error margins indicated in the manufacturer datasheets were taken as reference, and these were considered acceptable for the scope of the experimental validation. Calibration could improve accuracy, but the objective was to develop and evaluate a practical and reproducible test setup using commercially available tools.

7-Include photos or diagrams of the test station to complement Figure 4 and enhance clarity.

In figure 4, simple and clear labels have been added to identify the main components and improved their quality. We appreciate the reviewer’s suggestion. According to the same suggestion as other revisors, the resolution of Figures 2 and 3 has been also significantly improved.

8- Discuss the practical implications of the observed discrepancies (20% error in rotor resistance). Are these errors acceptable for real-world applications?

This point has been addressed in the abstract according to the first observation, where it was indicated that most calculated errors remained below 2%, except for the rotor resistance (R₂) estimated via FEMM, which showed a discrepancy of around 20%. This difference is primarily attributed to the approximated number of turns used in the simulation, based on typical manufacturer data. The actual number of turns would require disassembling the motor, it was proved but not considered in the work to emphasize the discrepancy. Additionally, it was clarified in the discussion of Table 3 as,

“…..in Table \ref{tab3} that for the stator resistance R1 there is a difference between the calculations and simulations of 0.41\% and 1.87\%, respectively. For the rotor resistance R2 a 2.18\% and 20\% error is observed, and a difference of 0.66\% and 11.9\% for both reactances X1 and X2 remembering that they are identical for stator and rotor in this SPSCIM. Finally, in the magnetization circuit, we see a discrepancy in the magnetizing resistance Rm of 6.5\% and 16\% with the simulations, and for the magnetizing reactance Xm 1.15\% and 1.47\%, respectively. The discrepancies, mainly in obtaining the results for the rotor resistance and series reactances, vary according to the physical characteristics of the SPSCIM, material and more affected by the number of turns into the windings, which could be adjusted with a more precise number, but it requires an intrusive action not addressed in this work.”

9- Provide more context for the choice of 1.15 as the compensation factor in Equation (8). Is this value standard, or was it derived experimentally?

The compensation factor of 1.15 used in Equation (8) is widely referenced in standard motor testing procedures to overcome the skin effect, but it is a standard empirical value commonly adopted in the literature for DC resistance tests in induction motors. It accounts for the skin effect and temperature influence during AC operation.

10 - Suggest future work, such as extending the analysis to other motor types or incorporating real-time parameter estimation techniques.

It was added at the end part of the conclusions as;

“….while this paper highlights the importance and characterization of single-phase motors, specifically SPSCIMs, as an extended basis for future work in the optimization of their design and control”.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I think the paper is acceptable.

Reviewer 4 Report

Comments and Suggestions for Authors

Accept in present form