Optimization of Disk Magnetic Coupler Based on Orthogonal Test and Multiobjective Genetic Algorithm

Gong, Jianlong; Jiang, Meixia

doi:https://doi.org/10.1155/2023/7767662

Mathematical Problems in Engineering

On this page

Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest Authors’ Contributions Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 7767662 | https://doi.org/10.1155/2023/7767662

Optimization of Disk Magnetic Coupler Based on Orthogonal Test and Multiobjective Genetic Algorithm

Jianlong Gong¹and Meixia Jiang²

Academic Editor: Xiaodong Sun

Received02 Jan 2023

Revised03 Feb 2023

Accepted09 Feb 2023

Published08 Apr 2023

Abstract

In order to solve the optimization problem of the disk magnetic coupler, the two optimization schemes, the orthogonal test and multiobjective genetic algorithm, were used to optimize the disk magnetic coupler to maximize the magnetic torque while reducing the eddy current loss, and then the correctness of the optimization results was verified by electromagnetic simulation experiments. The eddy current loss and magnetic torque of the optimized disk magnetic coupler were normalized by using the comprehensive evaluation function. After orthogonal test and multiobjective genetic algorithm optimization, the comprehensive evaluation value of the disk magnetic coupler increased by 2.43 times and 3.30 times, respectively, and the optimization effect of multiobjective genetic algorithm is more significant. The relative errors between theoretical and simulated values of the maximum magnetic torque and eddy current loss by multiobjective genetic algorithm are 2.22%–4.72% and 1.13%–6.41%, respectively, suggesting that the optimization method is feasible. The research results show that the multiobjective genetic algorithm optimization can significantly improve the performance of magnetic disk coupler, which can provide theoretical and technical basis for the design of disk magnetic coupler.

1. Introduction

The permanent magnet coupler is a noncontact transmission device. Compared with the traditional contact transmission device, the permanent magnet coupler has some advantages such as low mechanical vibrations, less wear, energy saving, environmental protection, natural protection against overloads, and permits misalignment [1–3]. The permanent magnet coupler transmits torque by the magnetic coupling force, which without rigid contact and mechanical connection, effectively improves the reliability and service life of the machinery. It is widely used in industrial applications that require sealed isolation between the drive side and the load side through the isolation wall of air, vacuum, fluid, or other media, such as the mining and metallurgical industry, chemical industry, oil and gas industry, nuclear power, and military manufacturing field [4]. Moreover, it was also used in magnetic drive pumps and magnetic mixers for seal-less applications, such as pharmaceutical and food industries [5].

Due to the good characteristics and many applications of permanent magnet couplers, more and more scholars have carried out theoretical research on them, making the permanent magnet couplers have breakthroughs in efficiency and manufacturing [6]. Ose-Zala et al. [7] and Aman et al. [8] studied the influence of geometric parameter design on the performance of the magnetic coupler. Zhenjun et al. [9] proposed the single-factor test of the magnet drive coupling based on the finite element method to study the influence of single-factor change on the magnetic performance, and then optimized the design of the magnet drive coupling by the orthogonal test. Wang et al. [10] proposed the hybrid magnetic coupler and optimized its structural parameters by an improved response surface. These studies mainly considered the influence of structural parameters of the magnetic coupler on its single performance, but did not consider the optimization of its multiperformance. However, in practical engineering applications, engineering design generally involves multiparameter optimization, which is called multiobjective parameter optimization [11–14]. Multiobjective optimization technique can be used to solve problems with multiple objective functions. Using these optimization methods, several optimization objectives can be achieved simultaneously. Therefore, it is of great significance to study the multiobjective optimization design of permanent magnet coupler and find out the optimal structural parameters. The traditional multiobjective optimization method uses linear weighted sum method to transform multiobjective function into single objective function, but this method requires multiple operations to obtain a large number of compromised solutions, namely, Pareto optimal solution. To solve this problem, multiobjective evolutionary algorithms such as genetic algorithm, particle swarm optimization algorithm, and differential evolution were introduced, which can optimize multiple conflicting objective functions at the same time. The result obtained is not a specific solution, but a series of Pareto frontiers [15, 16]. Shi et al. [17] adopted the optimization method composed of response surface model and multiobjective optimization algorithm. Sun et al. [18, 19] proposed the multiobjective optimization based on sequential subspace optimization-based NSGA III. Song and Cui [20] pointed out that evolutionary algorithms provide strong automatic search capability in the optimization design of many engineering applications. Among them, genetic algorithm is the most popular and has good adaptive heuristic search. Tarvirdilu Asl et al. [21] used the genetic algorithm to optimize the structural parameters of the permanent magnet eddy current coupler, but only the influence of structural parameters on output magnetic torque was considered, and it did not optimize other performances. Compared with the above optimization methods, this article optimized the performance of the disk magnetic coupler in the form of multiobjective parameter optimization, comprehensively applied the range analysis method, nondominated sorting genetic algorithm (NSGA-II), and k-means clustering to obtain the optimal structural parameter combination of the disk magnetic coupler, and used the comprehensive evaluation function to evaluate and compare the optimization results, which has certain novelty.

In this article, taking the disk magnetic coupler in magnetic drive blender as the research object, the two optimization schemes the orthogonal test and multiobjective genetic algorithm were used to optimize the disk magnetic coupler to maximize the magnetic torque while reducing the eddy current loss. The optimization variables are the radial width of the disk magnet in the inner rotor (₁), the radial width of the disk magnet in the outer rotor (₂), and the air gap spacing (), respectively, and the objective functions are the maximum magnetic torque (T_max) and eddy current loss (P), respectively. Orthogonal experiment was designed and numerical simulation was carried out by ANSYS MAXWELL software. Then, the range analysis method, nondominated sorting genetic algorithm (NSGA-II), and K-means clustering analysis were comprehensively applied to obtain the optimal structural parameter combination of the disk magnetic coupler, which provided a certain reference for the optimization of the maximum magnetic torque and eddy current loss of the disk magnetic coupler.

2. Disk Magnetic Coupler Model

2.1. Disk Magnetic Coupler Structure Model

Taking the disk magnetic coupler in magnetic drive blender as the research object, the structural parameters of the magnetic disk coupler were optimized to improve the performance of the disk magnetic coupler. The local section structure of the disk magnetic coupler in the magnetic drive blender is shown in Figure 1, which is mainly composed of a driving outer rotor, driven inner rotor, input shaft, output shaft, air gap, bearing, sealing device, isolation hood, and load blade. The disk magnetic coupler is composed of the inner and outer magnetic rotors separated by a certain distance of air gap, as shown in Figure 2. The inner rotor and the outer rotor are noncontact and have a certain distance. The permanent magnets are evenly embedded in the circumferential direction of the inner rotor and the outer rotor, respectively. The permanent magnets on the inner rotor and the outer rotor are magnetized radially, and the magnetic poles of N and S are interlaced adjacent to each other. Starting from the magnetic N-pole, the magnetic flux traverses the air gap between the inner and outer rotors radially, then traverses the conductor axially, and then returns radially to the adjacent S-pole through the air gap between the inner and outer rotors to form a closed circuit. The outer rotor is directly connected with the input shaft. When the servo motor drives the input shaft to rotate, the permanent magnets in the circumferential direction of the inner rotor and the outer rotor participate in the meshing work, and a continuously rotating drive magnetic torque will be generated within the distance that the interactive magnetic force can affect to drive the inner rotor and load blade.

(a)

(b)

2.2. Disk Magnetic Coupler Finite Element Model

In order to reduce the calculation of the finite element model, the disk magnetic coupler model is simplified. After removing subtle features and unimportant components, the simplified model comprises an inner rotor, outer rotor, spacer disk, permanent magnet, air gap, and air domain. The finite element model of the disk magnetic coupler is established by ANSYS Maxwell software. The following assumptions are made in the finite element simulation [22]:(1)The influence of temperature on material properties is ignored(2)When the air gap is tiny, the magnetic flux leakage of the permanent magnets is ignored(3)The magnetic field of the permanent magnet is evenly distributed in the air gap(4)The permeability and conductivity of the conductor rotor are constant(5)The elastic deformation of the permanent magnet is ignored

The main structural parameters of the disk magnetic coupler are as follows: r₁ is the inner radius of the permanent magnet on the inner rotor, r₂ is the outer radius of the permanent magnet on the inner rotor, R₁ is the inner radius of the permanent magnet on the outer rotor, R₂ is the outer radius of the permanent magnet on the outer rotor, W₁ is the radial width of the permanent magnet on the outer rotor, W₂ is the radial width of the permanent magnet on the inner rotor, t_im is the axial thickness of the permanent magnet on the inner rotor, t_om is the axial thickness of the permanent magnet on the outer rotor, α₀ is the angle of the permanent magnet on the outer rotor, α₁ is the air gap angle between the permanent magnets on the outer rotor, β₀ is the angle of the permanent magnet on the inner rotor, β₁ is the air gap angle between the permanent magnets on the inner rotor, and is the average thickness of the air gap between the inner rotor and the outer rotor. According to the above parameters, the finite element model of the disk magnet coupler is shown in Figure 3. The permanent magnet material is Nd-Fe-B, which needs to be set separately. The coercive force of the permanent magnet is −880000 A/m. The remanence of the permanent magnet is 1.18 T. The relative angular velocity of the inner and outer rotors is 1500 rad/s.

2.3. Mesh Generation and Independence Verification

The hexahedral meshing of the disk magnetic coupler was carried out by ANSYS Maxwell software. Different objects should adopt different mesh precision. The mesh size of inner rotor and outer rotor needs to be smaller, and the mesh size of solution domain and rotation domain can be relatively larger. In order to reduce the amount of calculation and ensure the accuracy of the numerical calculation results, the mesh independence analysis was carried out [23].

When the grid size of the solution domain and the rotation domain is set as 2 mm, six groups of meshes with different sizes were selected for the grid independence test of the inner rotor and outer rotor, which was 0.85 mm, 0.70 mm, 0.55 mm, 0.40 mm, 0.25 mm, and 0.05 mm, respectively, as shown in Table 1. The maximum magnetic torque (T_max) and eddy current loss (P) were evaluation indicators. Figure 4 shows the variation of the maximum magnetic torque and eddy current loss with reducing element size, and for the first three groups of grids, the result changes obviously, but for the last four groups of grids, the result changes are relatively little. When the total number of grids exceeds 52120, the maximum magnetic torque and eddy current loss deviation were merely 0.38%–0.73% and 0.42%–0.73%, respectively. Therefore, in order to ensure the accuracy of the calculation results and save the calculation time, 52120 was selected as the grid number for the numerical simulation of the disk magnetic coupler. The disk magnetic coupler grid model was shown in Figure 5.

3. Optimal Design of Disk Magnetic Coupler

3.1. Single-Factor Test Analysis

Taking the structural parameters of the disk magnetic coupler in magnetic drive blender as an example, the single factor test of the disk magnetic coupler was carried out to study the influence law of single factor change on the performance of the disk magnetic coupler. The disk magnetic coupler was numerically analyzed by finite element method, and the magnetic torque and eddy current loss were calculated by the ANSYS Maxwell software. The results of single-factor test were shown in Figures 6–10.

Figures 6 and 7 show that with the increase of the radial width of the permanent magnet in the inner rotor (W₁) and the radial width of the permanent magnet in the outer rotor (W₂), the greater the force arm of the magnetic force of the magnetic rotor, the greater the maximum magnetic torque and eddy current loss. Figure 8 shows that with the increase of the air gap spacing (), the magnetic flux density of the air gap between the magnetic rotors decreases, which leads to the decrease of the maximum magnetic torque and eddy current loss. Figures 9 and 10 show that the maximum magnetic torque and eddy current loss of the axial thickness of the permanent magnet on the inner rotor (t_im) and the axial thickness of the permanent magnet on the outer rotor (t_om) increase with the increase of thickness in a certain range. Beyond a certain range, the axial thickness of the permanent magnet on the inner rotor (t_im) and the axial thickness of the permanent magnet on the outer rotor (t_om) have little effect on the eddy current loss.

3.2. Optimization Variables and Objective Functions

In this article, based on the single factor test analysis, the radial width of the permanent magnet in the inner rotor (₁), the radial width of the permanent magnet in the outer rotor (₂), and the air gap spacing () were taken as the optimization variables. Then, the variables, i.e., ₁, ₂, and were changed in the range of 5–15 mm, 5–15 mm, and 3–7 mm, respectively, to obtain the optimum structure parameters. The maximum magnetic torque and eddy current loss are two important indexes to evaluate the performance of the disk magnetic coupler, so the maximum magnetic torque (T_max) and eddy current loss (P) are taken as objective functions.

The maximum magnetic torque is defined as follows [24]:where B_r, , S_m, and R are the remanence of disk magnetic coupler, the magnetic field strength of the disk magnetic coupler, the total area of interaction between inner and outer permanent magnetic poles, and average radius of action of inner and outer permanent magnets, respectively.

The magnetic field strength of the disk magnetic coupler is defined as follows [24]:where H_i and H₀ are the magnetic field intensity generated by the inner magnetic rotor and the outer magnetic rotor, respectively. L_s1 is the inner arc length of the inner permanent magnet, L_s2 is the outer arc length of the inner permanent magnet, L_s3 is the inner arc length of the outer permanent magnet, L_s4 is the outer arc length of the outer permanent magnet, and L_b is the axial length of the permanent magnet.

The eddy current loss is defined as follows [25]:where V is the permanent magnet volume of the inner rotor and outer rotor, γ is electrical conductivity, and is the eddy current density of the permanent magnet.

3.3. Comprehensive Evaluation Function

The two objective functions have different influence on the performance of the disk magnetic coupler. In order to evaluate the performance of the optimized disk magnetic coupler, the comprehensive evaluation function was proposed. All the objective functions were normalized by using the comprehensive evaluation function. The comprehensive evaluation function (η) was defined as follows [26]:where the maximum magnetic torque evaluation accounts for 60% in the comprehensive rate, the eddy current loss evaluation accounts for 40% in the comprehensive rate, T_MIN and T_MAX are the minimum and maximum values of maximum the magnetic torque, respectively, P_MIN and P_MAX are the minimum and maximum values of the eddy current loss, respectively, and T_max and P are the experimental values of the maximum magnetic torque and eddy current loss, respectively. The greater the comprehensive function evaluation value, the better the performance of disc magnetic coupler.

4. Optimization of Disk Magnetic Coupler Based on Orthogonal Test

4.1. Determinations of Orthogonal Test Factors and Levels

The orthogonal test is an experimental design method that uses orthogonal tables to arrange experiments and perform multifactor and multilevel data analysis [27]. In this article, the purpose of the orthogonal test is to investigate the influence of geometric parameters of the disk magnetic coupler on maximum magnetic torque and eddy current loss. Three factors have been studied, and each factor has three levels, as shown in Table 2. The three factors are the radial width of the permanent magnet in the inner rotor (₁), the radial width of the permanent magnet in the outer rotor (₂), and the air gap spacing (), respectively. The factors of ₁, ₂, and are denoted by codes A, B, and C, respectively. The values of each factor were set within a specific range of the structural parameter value on the disk magnetic coupler.

4.2. Orthogonal Test Design and Results

The L9 (3³) orthogonal test schemes were adopted to obtain the nine orthogonal test schemes, and the finite element simulation was carried out for each structural parameter scheme, as shown in Table 3.

4.3. Analysis of Orthogonal Test Results

According to the finite element calculation results, the range analysis of the comprehensive evaluation results is carried out, so as to determine the primary and secondary order of the influence of the level change of each factor on the comprehensive evaluation results and the best combination scheme. represents the sum of the corresponding comprehensive evaluation value when the horizontal number of the factor is i, represents the arithmetic mean value of the corresponding comprehensive evaluation value when the horizontal number of the factor is i. R is the difference between the maximum arithmetic mean and the minimum arithmetic mean of the comprehensive evaluation value of each factor. The larger the value of R, the greater the influence of this factor on the comprehensive evaluation value will be, and vice versa. The range analysis results of the comprehensive evaluation value are shown in Table 4. Table 4 shows that the range order of the three factors is . It shows that the air gap spacing () has the greatest influence on the comprehensive evaluation value, followed by the radial width of the permanent magnet in the outer rotor (₂) and the radial width of the permanent magnet in the inner rotor (₁). The relationship between comprehensive evaluation value and each factor is shown in Figure 11. Figure 11 shows that the comprehensive evaluation value increases first and then decreases with the increase of the radial width of the permanent magnet in the inner rotor (₁), the comprehensive evaluation value increases with the increases of the radial width of the permanent magnet in the outer rotor (₂), and the comprehensive evaluation value decreases first and then increases with the increase of the air gap spacing (). It shows that the optimal combination scheme by orthogonal test is . Hence, the structure parameters of the optimal scheme of the disk magnetic coupler by orthogonal test are as follows: = 10 mm, = 15 mm, and = 3 mm.

5. Optimization of Disk Magnetic Coupler Based on Genetic Algorithm

5.1. Model Formation

The response surface approximation was performed to obtain the fitting polynomial function between the objective functions and the design variables [27]. The response surface approximation model is a second-order model, which has an intercept term, a linear term, a square term, and a quadratic interaction term [27, 28]:where x_j is the design variable, i.e., ₁, ₂, and ; N is the number of the design variables, i.e., N = 3; and is the number of undetermined coefficient, and its value can be obtained by equation (6).

According to the orthogonal test schemes and test results in Table 3, the approximate fitting of maximum magnetic torque and eddy current loss was obtained by response surface approximation as follows:where x₁, x₂, and x₃ are the variables ₁, ₂, and , respectively. The corresponding undetermined coefficients, which are a_j and b_j are shown in Table 5.

The root mean square error, the sum of squared errors, and multivariate statistical coefficients were used to estimate the effectiveness of the fitting equation of the maximum magnetic torque and eddy current loss, which is defined as follows [27]:where Y is the experiment value, y is the predicted value, and n is the number of samples. The performance evaluation indexes of the fitting equations about maximum magnetic torque and eddy current loss are shown in Table 6. The root mean square error (RMSE) and the sum of squared error (SSE) of maximum magnetic torque and eddy current loss are both very close to 0, and the multivariate statistical coefficients (R²) of maximum magnetic torque and eddy current loss is very close to 1. It shows the fitting equations of the maximum magnetic torque and eddy current loss have high precision and can meet the accuracy requirements of engineering applications.

5.2. Multiobjective Genetic Algorithm Optimization

The nondominated sorting genetic algorithm II (NSGA-II) is one of the most popular multiobjective genetic algorithms [29]. When there are more objectives and variables, NSGA II is an effective multiobjective optimization method [30]. It has some advantages such as fast operation speed, good convergence of solution set, and can reduces the complexity of the noninferior sorting genetic algorithm. Therefore, NSGA-II with multiobjective function optimization is adopted to optimize the structural parameters of the disk magnetic coupler, and obtain optimal parameter combination of the disk magnetic coupler. The maximum magnetic torque and the minimum eddy current loss are the objective functions for this optimization process, which can be described as follows:

The main parameters of the NSGA-II algorithm include a population size of 100 individuals, the crossover probability is 0.85, and the mutation probability is 0.2. After iterative calculation, the Pareto optimization solution set of maximum magnetic torque and eddy current loss is obtained by the NSGA-II algorithm, as shown in Figure 12. The experiment results show that under the same maximum magnetic torque, the value on the Pareto optimal solution set can obtain the optimal eddy current loss; under the same eddy current loss, the value on the Pareto optimal solution set can obtain the optimal maximum magnetic torque.

5.3. The K-Means Clustering Analysis

In the multiobjective optimization design of the disk magnetic coupler, the Pareto optimal solution is not unique, but multiple solutions form Parteo optimal solution set [27]. The Pareto solution set of the objective functions is clustered by K-means clustering algorithm to find a group of the representative solution set in the Pareto solution set, as shown in Figure 13. The variable parameters of the five clustering points in the Pareto optimization solution and the comparison between the theoretical values and the simulated values are shown in Table 7. Table 7 shows that the relative errors between theoretical values and simulated values of magnetic torque range from 2.22%–4.72%, and the relative errors between theoretical values and simulated values of eddy current loss range from 1.13%–6.41%. The results show that the theoretical values are in good agreement with the simulation values.

5.4. Analysis of Multiobjective Genetic Algorithm Optimization Results

Figure 12 shows scatter plots of Pareto optimal solutions for maximum magnetic torque and eddy current loss, representing the Pareto front. The two ends of the Pareto front represent the maximum value of the maximum magnetic torque and the minimum value of the eddy current loss, respectively. The greater the maximum magnetic torque, the greater the eddy current loss, and vice versa. The five representative solutions were obtained by K-means clustering algorithm, which were A, B, C, D, and E, respectively. The Pareto optimal solution was divided into six regions by five representative solutions, which were region1, region2, region3, region4, region5, and region6, respectively, as shown in Figure 13. The maximum magnetic torque and the eddy current loss are small in region 1. The maximum magnetic torque and eddy current losses are large in region 6. Table 7 shows that the maximum magnetic torque at E is 5.33 times that at A, and the eddy current loss at E is 1.82 times that at A. It shows that the improvement of one objective always comes at the expense of the other. Hence, the designer can select the appropriate solution in the Pareto solution set according to the actual needs to obtain the best parameter combination.

6. Results and Discussion

The original and optimized maximum magnetic torque output values are shown in Figure 14. Figure 14 shows that the maximum magnetic torque of the disc magnetic coupler was improved by orthogonal test and multiobjective genetic algorithm optimization, and the optimization effect was more obvious by multiobjective genetic algorithm. The nephogram of the eddy current loss for them is shown in Figures 15(a)–15(g). Figure 15 shows that the eddy current loss of the disc magnetic coupler was reduced by orthogonal test and multiobjective genetic algorithm optimization. The comprehensive evaluation results of original and optimized disk magnet coupler are shown in Table 8. Table 8 shows that the comprehensive evaluation value increased by 2.43 times, 1.40 times, 1.69 times, 2.20 times, 2.55 times, and 3.30 times for the optimized disk magnetic coupler by orthogonal test and multiobjective genetic algorithm, respectively, and the most obvious improvement is the case E optimized by multiobjective genetic algorithm, which was increased by 3.30 times.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

7. Conclusion

The magnetic torque and eddy current loss are important indexes to evaluate the performance of disk magnetic coupler and these performances of the disk magnetic coupler are improved by the two optimization schemes the orthogonal test and multiobjective genetic algorithm, respectively. The structural parameters optimal combination of the disk magnetic coupler obtained by orthogonal test were A2 = 10 mm, B3 = 15 mm, and C1 = 3 mm, respectively, and the comprehensive evaluation value increased by 2.43 times. The multiobjective genetic algorithm and K-means clustering algorithm were used to optimize its structural parameters to obtain the five representative solutions (case A to case E), the structural parameters optimal combination of the disk magnetic coupler obtained were A2 = 14.58 mm, B3 = 14.33 mm, and C1 = 3.03 mm, respectively, and the comprehensive evaluation value was increased by 3.30 times. The relative errors between theoretical and simulated values of the maximum magnetic torque and eddy current loss by multiobjective genetic algorithm are 2.22%–4.72% and 1.13%–6.41%, respectively, suggesting that the optimization method is feasible. The results show that these properties of the disk magnetic coupler are improved by orthogonal test and multiobjective genetic algorithm optimization, and the optimization effect is more significant after multiobjective genetic algorithm than orthogonal test.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

J. G. designed this project and wrote the initial draft of the manuscript. M. J. carried out some of the experiments and data analysis. All authors have read and agreed to the published version of the manuscript.

Acknowledgments

This research was funded by Guangdong Provincial College Youth Innovation Talent Project (2019GKQNCX038), Scientific Research Project of Guangdong Communication Polytechnic (GDCP-ZX-2021-001-N1), Guangdong Provincial College Youth Innovation Talent Project (2020KQNCX199), and University Scientific Research Project of Guangzhou Education Bureau (202032765).

References

O. de la Barriere, S. Hlioui, H. Ben Ahmed et al., “3-D formal resolution of Maxwell equations for the computation of the no-load flux in an axial flux permanent-magnet synchronous machine,” IEEE Transactions on Magnetics, vol. 48, no. 1, pp. 128–136, 2012.
View at: Publisher Site | Google Scholar
Y. Li, H. Lin, H. Yang, S. Fang, and H. Wang, “Analytical analysis of a novel flux adjustable permanent magnet eddy-current coupling with a movable stator ring,” IEEE Transactions on Magnetics, vol. 54, no. 3, pp. 1–4, 2018.
View at: Publisher Site | Google Scholar
B. Kou, Y. Jin, H. Zhang, L. Zhang, and H. Zhang, “Modeling and analysis of force characteristics for hybrid excitation linear eddy current brake,” IEEE Transactions on Magnetics, vol. 50, no. 11, pp. 1–5, 2014.
View at: Publisher Site | Google Scholar
W. H. Li, D. Z. Wang, Q. Z. Gao, D. S. Kong, and S. H. Wang, “Modeling and performance analysis of an axial-radial combined permanent magnet eddy current coupler,” IEEE Transactions on Magnetics, vol. 51, pp. 1–5, 2020.
View at: Google Scholar
L. Belguerras, S. Mezani, and T. Lubin, “Analytical modeling of an axial field magnetic coupler with cylindrical magnets,” IEEE Transactions on Magnetics, vol. 57, no. 2, pp. 1–5, 2021.
View at: Publisher Site | Google Scholar
P. Y. Pan, D. Z. Wang, and B. W. Niu, “Design optimization of APMEC using chaos multi-objective particle swarm optimization algorithm,” Energy Reports, vol. 7, pp. 531–537, 2021.
View at: Publisher Site | Google Scholar
B.1 Ose-Zala, O. Onzevs, and V. Pugachov, “Formula synthesis of maximal mechanical torque on volume for cylindrical magnetic coupler,” Electrical, Control and Communication Engineering, vol. 3, no. 1, pp. 37–43, 2013.
View at: Publisher Site | Google Scholar
J. L. B. Aman, J. J. Abbott, and S. Roundy, “Optimal parametric design of radial magnetic torque couplers via dimensional analysis,” IEEE Transactions on Magnetics, vol. 58, no. 6, pp. 1–8, 2022.
View at: Publisher Site | Google Scholar
G. Zhenjun, H. Chaoqun, H. Feng, L. Jianrui, and S. Huashan, “A study on the influencing factors and optimization design of combined push-pull magnetic drive coupling,” Mathematical Problems in Engineering, vol. 2019, Article ID 4243020, 14 pages, 2019.
View at: Publisher Site | Google Scholar
S. Wang, K. Hu, and D. Y. Li, “Optimal design method for the structural parameters of hybrid magnetic coupler,” Journal of Mechanical Science and Technology, vol. 33, no. 1, pp. 173–182, 2019.
View at: Publisher Site | Google Scholar
J. Wang, Yl Zhai, P. Y. Yao, and M. Y. Ma, “Structural optimization of microchannels based on multi-objective genetic algorithm,” Journal of Chemical Engineering of Chinese Universities, vol. 34, no. 4, pp. 1034–1043, 2020.
View at: Google Scholar
L. Luo, W. Du, S. T. Wang, L. Wang, B. Sunden, and X. Zhang, “Multi-objective optimization of a solar receiver considering both the dimple/protrusion depth and delta-winglet vortex generators,” Energy, vol. 137, pp. 1–19, 2017.
View at: Publisher Site | Google Scholar
K. R. Ram, S. P. Lal, and M. R. Ahmed, “Design and optimization of airfoils and a 20 kW wind turbine using multi-objective genetic algorithm and HARP_Opt code,” Renewable Energy, vol. 144, pp. 56–67, 2019.
View at: Publisher Site | Google Scholar
D. Paul, S. Saha, and J. Mathew, “Fusion of evolvable genome structure and multi-objective optimization for subspace clustering,” Pattern Recognition, vol. 95, pp. 58–71, 2019.
View at: Publisher Site | Google Scholar
W. X. Zhao, T. Yao, L. Xu, X. Chen, and X. Song, “Multi-objective optimization design of a modular linear permanent-magnet vernier machine by combined approximation models and differential evolution,” IEEE Transactions on Industrial Electronics, vol. 68, no. 6, pp. 4634–4645, 2021.
View at: Publisher Site | Google Scholar
P. Yao, Y. Zhai, Z. Li, X. Shen, and H. Wang, “Thermal performance analysis of multi-objective optimized microchannels with triangular cavity and rib based on field synergy principle,” Case Studies in Thermal Engineering, vol. 25, Article ID 100963, 2021.
View at: Publisher Site | Google Scholar
Z. Shi, X. Sun, G. Lei, X. Tian, Y. Guo, and J. Zhu, “Multiobjective optimization of a five-phase bearingless permanent magnet motor considering winding area,” IEEE, vol. 27, no. 5, pp. 2657–2666, 2022.
View at: Publisher Site | Google Scholar
X. Sun, B. Wan, G. Lei, X. Tian, Y. Guo, and J. Zhu, “Multiobjective and multiphysics design optimization of a switched reluctance motor for electric vehicle applications,” IEEE Transactions on Energy Conversion, vol. 36, no. 4, pp. 3294–3304, 2021.
View at: Publisher Site | Google Scholar
X. Sun, N. Xu, and M. Yao, “Sequential subspace optimization design of a dual three-phase permanent magnet synchronous hub motor based on NSGA III,” IEEE Transactions on Transportation Electrification, vol. 9, no. 1, pp. 622–630, 2022.
View at: Publisher Site | Google Scholar
R. Song and M. Cui, “Single- and multi-objective optimization of a plate-fin heat exchanger with offset strip fins adopting the genetic algorithm,” Applied Thermal Engineering, vol. 159, Article ID 113881, 2019.
View at: Publisher Site | Google Scholar
R. Tarvirdilu Asl, H. M. Yüksel, O. Keysan, and O. Keysan, “Multi-objective design optimization of a permanent magnet axial flux eddy current brake,” Turkish Journal of Electrical Engineering and Computer Sciences, vol. 27, pp. 998–1011, 2019.
View at: Publisher Site | Google Scholar
W. H. Li, D. Wang, Q. Gao, D. Kong, and S. Wang, “Modeling and performance analysis of an axial-radial combined permanent magnet eddy current coupler,” IEEE Access, vol. 8, pp. 78367–78377, 2020.
View at: Publisher Site | Google Scholar
F. Zhao, F. Y. Kong, Y. S. Zhou, B. Xia, and Y. X. Bai, “Optimization design of the impeller based on orthogonal test in an ultra-low specific speed magnetic drive pump,” Energies, vol. 12, no. 24, p. 4767, 2019.
View at: Publisher Site | Google Scholar
J. P. Li, Research and analysis on transmission efficiency of magnetic drive pump, Master’s Dissertation Jiangsu University, Zhenjiang, China, 2010.
L. X. Yu, D. Z. Wang, S. Li, and D. Zheng, “Loss calculation and analysis of efficient permanent magnet coupler,” Journal of Northeastern University, vol. 38, pp. 1524–1529, 2017.
View at: Publisher Site | Google Scholar
Z. Dong, Q. Boyi, L. Pengfei, and A. Zhoujian, “Comprehensive evaluation and optimization of rural space heating modes in cold areas based on PMV-PPD,” Energy and Buildings, vol. 246, Article ID 111120, 2021.
View at: Publisher Site | Google Scholar
M. X. Jiang and Z. L. Pan, “Optimization of open micro-channel heat sink with pin fins by multi-objective genetic algorithm,” Thermal Science, vol. 26, no. 4 Part B, pp. 3653–3665, 2022.
View at: Publisher Site | Google Scholar
X. J. Shi, S. Li, Y. D. Wei, and J. M. Gao, “Multi-objective optimization on the geometrical parameters of a nanofluid-cooled rectangular micro-channel heat sink,” Journal of Xi'an Jiaotong University, vol. 52, pp. 56–61, 2018.
View at: Google Scholar
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.
View at: Publisher Site | Google Scholar
M. Yue, T. W. Ching, W. N. Fu, and S. Niu, “Multi-objective optimization of a direct-drive dual-structure permanent magnet machine,” IEEE Transactions on Magnetics, vol. 55, pp. 1–4, 2019.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2023 Jianlong Gong and Meixia Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies