Design and Multi-Objective Optimization of a Composite Cage Rotor Bearingless Induction Motor
Round 1
Reviewer 1 Report
In this work, the authors have designed a composite cage rotor bearingless induction motor. Its overall structure is designed, and the mathematical model of suspension force and torque are developed. At the end, the authors used RSM, and NSGA II to optimize three objectives: starting torque, suspension force, suspension force pulsation. The work is good and acceptable for the journal. The following are some of the comments:
* The abstract needs the discussion of results in quantitative format.
* There are many bulk references like [1-2], which should be avoided.
* In the Introduction, the literature review was not logically organized, and all literature cited seem separate descriptions without connections. The readers can't know what the state-of-art methodologies or gaps the current study plans to resolve or fill, are and how significant or what contribution the current study is. The novelty of this paper is not clear. The difference between the present work and previous works should be highlighted. Research gaps and objectives of the proposed work should be justified.
* The suspension force model requires relative references.
* Equation 23, please clearly identify the design variables.
* Figure 11, why the authors have called it *improved* NSGA II?
* The original reference of the developers of NSGA II is missing in section 3.1.
* The authors have not provided the details like population size, iterations, etc. which are specific tuning parameters of NSGA II.
* Please give the generic format of the data which is modeled through RSM in equation 25.
* Figure 20, the Pareto front should be improved because it is not suitable to contain so many different colors of the non dominating optimal points.
* The authors have done a good job through experimental verification.
Author Response
*1. The abstract needs the discussion of results in quantitative format.
Response: Thanks for your helpful comments. The authors revise the abstract in the manuscript. And add the results in quantitative format. The revised content is as follows, and the revised part is also marked in yellow in the revised manuscript.
Finally, the results of the experimental setup prove that the starting torque increases by 6.98%, the suspension force increases by 5.45%, and the the suspension force pulsation decreases by 18.54%. The effectiveness of the proposed motor and the correctness of the multi-objective optimization strategy are verified.
*2. There are many bulk references like [1-2], which should be avoided.
Response: Thanks for your helpful comments. According to the comments given by the reviewer, the authors have deleted bulk references.The revised part is marked in yellow in the revised manuscript.
*3. In the Introduction, the literature review was not logically organized, and all literature cited seem separate descriptions without connections. The readers can't know what the state-of-art methodologies or gaps the current study plans to resolve or fill, are and how significant or what contribution the current study is. The novelty of this paper is not clear. The difference between the present work and previous works should be highlighted. Research gaps and objectives of the proposed work should be justified.
Response: Thanks for your helpful comments. The author has rewritten the introduction and revised it according to the comments. The specific revisions are as follows, and at the same time, the revisions are marked in yellow in the revised manuscript.
Based on the structural design of CCR-BIM, the structural parameters need to be optimized to obtain the optimal performance of the motor.
The intelligent algorithm combining the response surface model (RSM) with the particle swarm optimization algorithm, genetic algorithm, NSGA-II and other algorithms has been applied in the multi-objective optimization of various motors, and the performance of the optimized motor had been significantly improved [8,9,10,11]. NSGAII has the advantages of simple operation, good convergence speed, and good robustness, and the NSGAII also has a small amount of calculation, which is very suitable for these optimization parameters and objectives. However, although the crossover and mutation operations of NSGA-II can increase the diversity of the population, the algorithm has a high probability of falling into the local optimum. Therefore, a variable neighborhood search (VNS) algorithm is introduced in the NSGA-II algorithm. Therefore, an improved NSGA-II algorithm is designed to optimize the structural parameters of the motor.
*4. The suspension force model requires relative references.
Response: Thanks for your helpful comments. The reference [15] for the suspension force model was added. The revised content is as follows, and the revised part is also marked in yellow in the revised manuscript.
15.Lu C, Yang Z, Sun X, et al. A decoupling control of composite cage rotor bearingless induction motor based on SA‐PSO support vector machine inverse. International Transactions on Electrical Energy Systems 2021, 31(8), e12988.doi: 10.1002/2050-7038.12988.
*5. Equation 23, please clearly identify the design variables.
Response: Thanks for your helpful comments. Design variables are revised, and the revisions are marked in yellow in the revised manuscript.
where yT, yF and yFpul are respectively the objective function values of the starting torque, the suspension force and the suspension force pulsation. Because the NSGA-II algorithm can only find the minimum value, the starting torque and average suspension force are preceded by a minus sign respectively in front of Tst and Favg. ycsf is the slot space factor. slot space factor refers to the proportion of the space occupied by the windings after it is placed in the slot. If the slot space factor is too high, slot insulation may be damaged, so the slot space factor is limited to 0.62. The suspension performance is an important index to measure CCR-BIM. To ensure the stability of suspension, the suspension force pulsation cannot be too large, so yFpul cannot exceed 0.95.
*6. Figure 11, why the authors have called it *improved* NSGA II?
Response: Thanks for your helpful comments. On the basis of NSGA-II algorithm, a variable neighborhood search (VNS) algorithm is introduced in the NSGA-II algorithm. The improved NSGA-II can prevent falling into local optimum. Figure 19 has been revised to better illustrate this problem, as shown in the figure 19. The revised part is also marked in yellow in the revised manuscript.
*7. The original reference of the developers of NSGA II is missing in section 3.
Response: Thanks for your helpful comments. The original reference is added, and the revised part is also marked in yellow in the revised manuscript.
22.Nguyen H L, Duy L T. Using the Box–Behnken Response Surface Method to Study Parametric Influence to Improve the Efficiency of Helical Gears. Machines 2021, 9(11), 264. doi: 10.3390/machines9110264.
*8. The authors have not provided the details like population size, iterations, etc. which are specific tuning parameters of NSGA II.
Response: Thanks for your helpful comments. The revised content is as follows, and the revised part is also marked in yellow in the revised manuscript.
The initial population samples are set to 400, and the number of iterations is set to 300.
*9. Please give the generic format of the data which is modeled through RSM in equation 25.
Response: Thanks for your helpful comments. The generic format of the data which is modeled through RSM has been added and highlighted in yellow. As follows:
Tst=18.30-0.64*Hsl+0.46*Rw1-0.60*Sw2+2.03*L+0.77*Hsl*Rw1-3.58*Hsl*Sw2+0.46*Hsl*L-2.26*Rw1*Sw2+1.06*Rw1*L -0.19*Sw2*L -2.66*Hsl^2+1.19*Rw1^2-2.88*Sw2^2-0.29*L^2.
Favg=36.60-1.38*Hsl-0.62*Rw1-0.41*Sw2-3.39*L-0.62*Hsl*Rw1+5.98*Hsl*Sw2-1.10*Hsl*L+2.60*Rw1*Sw2-1.99*Rw1*L+0.096*Sw2*L+3.89*Hsl^2-2.01*Rw1^2+4.80*Sw2^2+0.70* L ^2.
Fpul=0.63+0.028*Hsl+0.016*Rw1+0.017*Sw2+0.060*L-9.616E-004*Hsl*Rw1-0.020*Hsl* Sw2+0.043*Hsl*L-1.433E-003*Rw1*Sw2+0.037*Rw1*L+4.827E-003*Sw2*L-0.038*Hsl^2+0.031* Rw1^2-0.045*Sw2^2+0.017*L^2.
*10. Figure 20, the Pareto front should be improved because it is not suitable to contain so many different colors of the non dominating optimal points.
Response: Thanks for your helpful comments. Figure 20 is improved. As shown in the figure 20.
*11. The authors have done a good job through experimental verification.
Response: Thank you for your admire.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The article discusses the optimization of a bearingless induction motor (BIM) with a two-cage rotor to increase the starting torque. Target performances such as starting torque, average rotor holding force and rotor holding force pulsations are optimized using the response surface model and the genetic method. During optimization, the parameters of the rotor and stator slots varied. The Pareto front of the optimal solution was constructed. As a result of optimization, the target performances of BIM were significantly improved. The strength of the study is a comprehensive experimental verification. The experiment shows a significantly higher stability of the BIM rotor for the proposed motor design. The article may be of interest to researchers in the field of designing electrical machines. However, some points need to be explained:
1. What are the rated efficiency, power, and RPM of the considered motor configurations? Compare the efficiency of the BIM designs shown in Table 3.
2. Please add in section 4 the wiring diagram for connecting the BIM stator to the mains.
3. Explain notation I2 and Dmax from table 3 when using them for the first time.
Author Response
*1.What are the rated efficiency, power, and RPM of the considered motor configurations? Compare the efficiency of the BIM designs shown in Table 1.
Response: Thanks for your helpful comments. the rated efficiency, power, and RPM of the considered motor are 0.82,1.8kW and 3000r/min respectively, the efficiency of the motor is added in Table 1.
*2.Please add in section 4 the wiring diagram for connecting the BIM stator to the mains.
Response: Thanks for your helpful comments. wiring diagram for connecting the BIM stator to the mains is added, and Figure 21(b) has been revised.
*3. Explain notation I2 and Dmax from table 3 when using them for the first time.
Response: Thanks for the positive suggestion which is greatly important for improving the quality of the manuscript. The explainations of I2 and Dmax have been added. The revised content is as follows, and the revised part is also marked in yellow in the revised manuscript.
I1 represents torque winding current, I2 represents suspension winding current. The suspension force winding current I2 of the optimal CCR-BIM is 0.43A, the suspension force winding current I2 of the initial CCR-BIM is 0.46A, and the suspension force winding current of the BIM is 0.5A.
The maximum fluctuation amplitude is marked as Dmax, which is the result of the interaction between the x-axis radial displacement and the y-axis radial displacement.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Thank you authors for the revised manuscript. The work is acceptable. Overall, the work is an excellent research contribution containing a concise mixture of theoratical research and experimentation.
