Research Article  Open Access
Gao Zhenjun, Hu Chaoqun, Hong Feng, Liu Jianrui, Su Huashan, "A Study on the Influencing Factors and Optimization Design of Combined PushPull Magnetic Drive Coupling", Mathematical Problems in Engineering, vol. 2019, Article ID 4243020, 14 pages, 2019. https://doi.org/10.1155/2019/4243020
A Study on the Influencing Factors and Optimization Design of Combined PushPull Magnetic Drive Coupling
Abstract
In order to study the effect of geometrical parameters of magnetic drive coupling on magnetic torque and magnetic eddy current loss, based on the basic theory of electromagnetic field, the influence factors of magnetic performance of combined pushpull magnetic drive coupling are analyzed and optimized by means of finite element numerical calculation and orthogonal experiment. The optimal geometrical parameter scheme of magnetic drive coupling was obtained, and the magnetic performance of the optimal geometrical parameter model was studied experimentally. The geometrical parameters of the optimal scheme of magnetic drive coupling are internal radius of magnet r = 80 mm, thickness of permanent magnet t_{m} = 8 mm, axial length L_{b} = 144 mm, and thickness of yoke iron t_{i} = 10 mm. The research shows that the optimization design method proposed in this paper is reliable in the design of magnetic drive coupling and can provide some theoretical reference for the design of magnetic drive coupling and the optimization of magnetic torque and magnetic eddy current loss.
1. Introduction
The key technical indicators of magnetic drive coupling include magnetic torque and magnetic eddy current loss, the former determines whether the magnetic drive coupling meets the working requirements, and the latter directly affects the working efficiency of magnetic drive coupling and magnetic drive centrifugal pump. In the design process, not only the magnetic torque index of the magnetic drive coupling should meet the design requirements, but it should also ensure that the magnetic eddy current loss of the magnetic drive coupling is minimum, and the volume of the magnetic drive coupling should be taken into account. At present, the design method of magnetic drive coupling in industrial production is mainly based on empirical formula. Because the calculation accuracy of empirical formula in dealing with different design requirements of magnetic drive coupling becomes insufficient, it is necessary to optimize and modify the designed magnetic drive coupling.
Shoda [1] analyzed the nonlinear characteristics of the gear coupling through the method of gear tooth contact analysis and experimental verification and found that the load and misalignment would lead to the change of the contact area of the gear coupling and thus generate the nonlinear damping and stiffness. Hao Chang [2, 3], Yang yi [4], Calistrat [5] studied the misalignment and highspeed transmission characteristics of the gear coupling and showed that the sliding friction and additional bending moment between the tooth surfaces were the main causes of selfexcited vibration and wear of the equipment shaft system due to the misalignment between the internal and external gears of the gear coupling. In the case of highspeed rotation, the vibration and wear caused by it are more serious, which is one of the main reasons for the instability of shaft system. Guang. Z [6–8] established the model of misaligned meshing force of the gear coupling, established the rotorbearing dynamic model of the gear coupling with the finite element method, and analyzed the influence of the misalignment of the gear coupling on the dynamic characteristics of the rotorbearing system through numerical methods and experimental tests. Kahraman [9] established piecewise linear dynamics model of involute spline coupling with side gap and pitch error, but did not solve the model or analyze the dynamic characteristics.
According to the analysis of [10–18], the finite element method has advantages in calculation accuracy and reliability compared with other methods. Considering the design requirements and the feasibility of the calculation process, the design variables are a series of discrete variable values. It is necessary to carry out a large number of comparative analyses of design schemes to obtain the optimal combination of design parameters.
In order to reduce the time of calculation and analysis, this paper adopts the method of combining orthogonal experiment with finite element calculation to study the influence of geometric parameters of magnetic drive coupling on magnetic torque and eddy current loss, so as to provide some reference for the optimization of magnetic torque and eddy current loss of magnetic drive coupling.
2. Analysis of SingleFactor Change Based on Finite Element Calculation
2.1. Finite Element Numerical Method
In this paper, the magnetic drive coupling designed by empirical formula is taken as the initial model. The magnetic drive coupling models are directly generated in ANSYS software. The finite element calculation process of the magnetic performance of the magnetic drive coupling is as follows [19–21]:
(1) ANSYS software was used to analyze the magnetic field. The mathematical model is established by taking internal radius of the magnet r, axial length of magnetic rotor L_{b}, air gap t_{g}, magnet thickness t_{m}, and yoke iron thickness t_{i} as parameters.
(2) Four kinds of materials, namely, spacer sleeve, air gap, inner and outer yoke iron, and inner and outer permanent magnet were defined, respectively. Relative permeability and resistivity of spacer sleeve were defined. Air and yoke iron define relative permeability.
(3) The defined material, the selected unit, and its coordinate system were allocated to each region of the model, and the unit of velocity is rad/s (Hz).
(4) The smart mesh divider of ANSYS was used to divide the mesh, the smart size was used to control the mesh size, and the mesh in the isolation sleeve and air gap was partially encrypted.
(5) The boundary conditions of the model were set to parallel boundary conditions, and all its entities were selected for static solution.
(6) After the solution is completed, the results are checked after the magnetic field processing. The postprocessing module of ANSYS electromagnetic field simulation can provide a lot of magnetic field data, such as node magnetic line distribution, node magnetic induction density, and node magnetic field intensity. : Internal radius of the magnet (mm) : Yoke iron thickness (mm) : Axial length of magnetic rotor (mm) : Maximum magnetostatic torque (N·m) : Air gap (mm) : Eddy current loss (W) : Magnet thickness (mm) : Volume of permanent magnet (mm^{3}) : Number of magnetic poles : Range : The sum of the corresponding test results when the horizontal sign on any column is : The arithmetic mean of the test results when the factors in any column are taken at level .
2.2. SingleFactor Test Analysis
Taking the geometric parameters of the designed magnetic drive coupling as an example, the singlefactor experimental study of the magnetic drive coupling was carried out based on the finite element calculation method with reference to the previous solution methods [22–31] and calculation experience. These regions of magnetic drive pump were meshed by ICEM software with hexagonal structured and tetrahedral unstructured grids. The boundary layer grid was encrypted; that is, local mesh encryption was used for the regions with larger flow change and thinwalled structure to improve grid quality when the tetrahedral unstructured grids were adopted. In addition, the mesh size of interface between hexagonal structured and tetrahedral unstructured grids should not differ too much, and the total grid number of magnetic drive coupling was 5618310 with the grid independence check. The internal flow of magnetic drive coupling is a kind of complex turbulent flow, so the appropriate turbulence model should be selected for numerical calculation, and the common turbulence models in CFD software mainly include Standard kε model, RNG kε model, Standard kω model, and SST kω model. The four kinds of turbulence models were adopted for the calculation of interflow in magnetic drive coupling.
This paper mainly studies the influence law of singlefactor change on magnetic performance and determines reasonable test factors and reasonable factor level for the next orthogonal test analysis. In this paper, finite element numerical analysis of magnetic drive coupling is carried out, and Torqc2d command in ANSYS postprocessing is used to calculate the magnetic torque on the outer circle of the internal magnetic rotor and the eddy current loss power in the isolation sleeve. In the calculation results, the units of torque and power, N·m and W, can be multiplied by the axial calculation length to obtain the magnetic torque of the entire internal magnetic rotor and the magnetic eddy loss in the isolation sleeve. The results of singlefactor test are shown in Figures 1, 2, 3, 4, 5, 6, and 7.
(a) Effect of internal radius r of the magnet on torque
(b) Effect of internal radius r of the magnet on eddy current loss
(a) effect of magnet thickness tm on magnetic torque
(b) effect of magnet thickness tm on eddy current loss
(a) Influence of air gap width tg on magnetic torque
(b) Influence of air gap width tg on eddy current loss
(a) Influence of axial length Lb on magnetic torque
(b) Influence of axial length Lb on eddy current loss
(a) Effect of spacer sleeve thickness t on magnetic torque
(b) Effect of spacer sleeve thickness t on eddy current loss
(a) Effect of yoke iron thickness ti on magnetic torque
(b) Effect of yoke iron thickness ti on eddy current loss
(a) Effect of the number of magnetic poles m on magnetic torque
(b) Effect of the number of magnetic poles m on eddy current loss
As can be seen from Figure 1, the greater the internal radius r of the magnet is, the greater the magnetic torque and eddy current loss will be. The main reason is that the greater the internal radius r is, the greater the force arm of the magnetic force will be, and the greater the magnetic torque and eddy current loss will be. It can also be seen from Figure 2 that the greater the thickness of the magnet is, the greater the magnetic torque and eddy current loss will be. As the thickness of the magnet increases, the air gap flux density increases, leading to an increase in the magnetic torque and eddy current loss. It can be seen from Figure 3 that the larger the air gap width is, the smaller the magnetic torque and eddy current loss will be. As the air gap width increases, the flux density of the air gap decreases, leading to a decrease in the magnetic torque and eddy current loss. It can be seen from Figure 4 that the greater the axial length is, the greater the magnetic torque and eddy current loss will be. Because the effective length and area of magnetic force increase with the increase of axial length, the magnetic torque and eddy current loss increase. It can be seen from Figure 5 that with the increase of the thickness of the spacer sleeve, the eddy current loss increases and the magnetic torque hardly changes. As the thickness of the isolator increases, the eddy current generated by the alternating magnetic field sweeping through the isolator increases, and the loss of the eddy current increases. The material of the spacer sleeve is titanium alloy, and the permeability is close to 1. When the thickness of the spacer sleeve increases, there is almost no effect on the magnetic field line passing through the air gap, so the change of magnetic torque is small. Figure 6 shows that the magnetic torque and eddy current loss of yoke iron increase with the increase of thickness in a certain range. Beyond a certain range, yoke thickness has little effect on magnetic torque and eddy current loss. When the thickness of yoke iron is small, magnetic saturation occurs near the yoke iron, air gap flux density decreases, and magnetic performance decreases. When the thickness of yoke iron increases to a certain extent, the increase of yoke iron thickness has little effect on magnetic performance. However, the increase of yoke iron thickness will increase the inertia of the magnetic rotor, increase the starting torque, and reduce the utilization ratio of materials. As can be seen from Figure 7, the influence of the number of magnetic poles on the magnetic torque first increases and then decreases. Because the number of magnetic poles is too small for the storage of static magnetic energy, it will affect the magnetic transfer performance. If the number of magnetic poles is too large, the magnetic leakage will increase, which will also affect the magnetic transfer performance. The eddy current loss decreases with the increase of the series. As the number of magnetic poles increases, the number of magnetic leakage increases, leading to the decrease of eddy current loss. Therefore, the number of magnetic poles should be determined according to the actual situation in the design process.
3. Orthogonal Experimental Study on Magnetic Performance of Magnetic Drive Coupling
3.1. Introduction to Orthogonal Test
Orthogonal test [32–37] is a design method that uses orthogonal table to arrange tests and conduct multifactor and multilevel data analysis. The advantage of orthogonal experimental design method is that it can get the significant effect of factors on the objective function and its influence law through fewer times of experiments and can deduce the best test conditions. Therefore, based on the twodimensional finite element calculation of magnetic performance of magnetic drive coupling, orthogonal experimental optimization method is used to optimize the design of magnetic drive coupling in this paper. The process is shown in Figure 8.
The purpose of the orthogonal experiment is to explore the influence of geometric parameters of magnetic drive coupling on magnetic torque and eddy current loss and find the geometric parameters that meet the design requirements of magnetic torque, the minimum eddy current loss, and the minimum volume of permanent magnet of magnetic drive coupling.
3.2. Orthogonal Test Index
The maximum magnetostatic torque (), magnetic eddy current loss (), and permanent magnet volume (V) of the magnetic drive coupling are investigated. There are three indexes in this test, belonging to the multiindex orthogonal test. In order to find out the main factors and the optimization scheme, the comprehensive balance method was used for the intuitive analysis of the test results; that is, the independent intuitive analysis of each index was carried out first, and then the comprehensive comparative analysis of the analysis results of each index was carried out.
3.3. Orthogonal Test Factors
According to the theoretical calculation formula and the above singlefactor analysis results, the geometric parameters that have a great influence on of magnetic torque and of eddy current loss are magnetic series m, air gap width t_{g}, magnet thickness t_{m}, internal magnet radius r, permanent magnet axial length L_{b}, yoke iron thickness t_{i}, and isolation sleeve thickness t. According to the formula for calculating the volume of permanent magnet in magnetic coupling, the geometric parameters that have a great influence on the volume v of permanent magnet are internal magnet radius r, magnet thickness t_{m}, air gap width t_{g}, and permanent magnet axial length L_{b}. To sum up, the main geometrical factors affecting the orthogonal test indexes are magnetic series m, air gap width t_{g}, magnet thickness t_{m}, internal magnet radius r, axial length L_{b} of permanent magnet, yoke iron thickness t_{i}, and isolation sleeve thickness t. According to the singlefactor test above, the influence of the number of magnetic poles m on the magnetic torque and eddy current loss firstly increases and then decreases. The magnetic torque reaches the maximum value when the number of magnetic poles m is 22; the number of magnetic poles is shown in Figure 9. Therefore, the number of magnetic poles m in this paper is determined to be 22. The magnetic torque decreases with the increase of the isolation sleeve thickness t, and the eddy current loss increases with the increase of the isolation sleeve thickness t at any time. On the premise of satisfying the design requirements of magnetic drive coupling, the smaller the isolation sleeve thickness t, the better. According to the calculation, when the thickness of spacer sleeve t is the minimum, 1.2 mm, it meets the design requirements. Therefore, the thickness of spacer sleeve t in this paper is determined to be 1.2 mm. The magnetic torque and eddy current loss decrease with the increase of air gap width t_{g}, so in the actual design process, the smaller the air gap width t_{g}, the better after meeting the processing, assembly, and other design requirements of magnetic drive coupling. Through calculation and analysis, it is known that when the narrowest gap width t_{g} is 6 mm, it meets the design requirements of machining and assembly, so the air gap width t_{g} in this paper is determined to be 6 mm. After the specific values of magnetic series m, air gap width t_{g}, and isolation sleeve thickness t are known, the magnet thickness t_{m}, inner magnet radius r, permanent magnet axial length L_{b}, and yoke iron thickness t_{i} are finally selected as the experimental factors for this orthogonal optimization.
3.4. Level of Factors in Orthogonal Test
Based on the designed magnetic drive coupling model, three levels were selected for each test factor by referring to the above singlefactor test results. By referring to the orthonormal table and combining the allowable variation range of each variable value, the orthogonal table of 3 levels and 4 factors as shown in Table 1 is arranged.

3.5. Orthogonal Test Scheme and Results
Nine orthogonal test schemes were obtained according to the orthogonal test table, and the finite element calculation was carried out for each parameter scheme. Sm_{2}Co_{17} was used as permanent magnet material, TC4 as isolation sleeve material, and carbon steel as yoke iron material, which are the materials often used in manufacture. Their material properties were defined and invoked, respectively, and the finite element method was used for calculation. The orthogonal test scheme and finite element calculation results are shown in Table 2.

3.6. Analysis of Orthogonal Test Results
The range analysis results of maximum magnetostatic torque (), eddy current loss (), and permanent magnet volume (V) can be obtained based on the finite element calculation results, where represents the sum of the corresponding test results when the horizontal number on any column is i; is the arithmetic mean of the test results when the above factors in any column are taken as level i; and R_{i} is the range, which is the difference between the maximum and minimum arithmetic mean of the test results when level i is taken for each factor. Range indicates the influence of the level change of each factor on the test results. Generally speaking, the larger the value is, the greater the influence of this factor on the test results will be.
The range analysis results of the maximum magnetostatic torque are shown in Table 3. Table 3 shows that the range order of the four factors is t_{m}>r>L_{b}>t_{i}. It can be obtained that the thickness of permanent magnet t_{m} has the greatest influence on the maximum magnetostatic torque , followed by the radius r, axial length L_{b} and yoke thickness t_{i}. The relationship between the maximum magnetostatic torque and each test factor is shown in Figure 10. Figure 10 shows that the maximum magnetostatic torque increases with the increase of the radius r, the maximum magnetostatic torque increases with the increase of the thickness of permanent magnet tm, the maximum magnetostatic torque increases with the increase of the axial length L_{b}, and the maximum magnetostatic torque increases with the increase of the thickness of yoke iron t_{i}. When yoke iron thickness exceeds 10 mm, the growth rate of maximum magnetostatic torque decreases. By comparing Figure 1 to Figure 7, it can be seen that the calculation results of orthogonal test are consistent with the change trend of singlefactor test results.

The results of range analysis of eddy current loss are shown in Table 4. As can be seen from Table 4, the range order of the four factors is t_{m}>r>L_{b}>t_{i}. It can be concluded that the permanent magnet thickness t_{m} has the largest influence on the of eddy current loss, followed by the internal radius r of the internal magnet, the axial length L_{b}, and the yoke iron thickness t_{i}. The relationship between the eddy current loss and the experimental factors is shown in Figure 11. The figure shows that of eddy current loss increases with the increase of the internal radius r. With the increase of the permanent magnet thickness tm, the eddy current loss increases. With the increase of axial length L_{b}, the eddy current loss increases, and with the increase of yoke thickness, the eddy current loss loss decreases. By comparing Figure 1 to Figure 7, it can be seen that the calculation results of orthogonal test are consistent with the change trend of singlefactor test results.

The range analysis results of the volume V of permanent magnets are shown in Table 5. As can be seen from Table 5, the range order of the four factors is t_{m}>L_{b}>r>t_{i} (where t_{i} does not affect the change of permanent magnet volume V), and the thickness of the permanent magnet t_{m} has the greatest influence on the eddy current loss , followed by the axial length L_{b} and the radius r of the internal magnet. The relationship between the volume V of permanent magnet and each test factor is shown in Figure 12. The figure shows that with the increase of r, the volume V of permanent magnet increases. With the increase of the permanent magnet thickness t_{m}, the permanent magnet volume V increases. With the increase of axial length L_{b}, the volume V of permanent magnet increases.

3.7. Analysis of the Optimal Scheme
In order to meet the requirements of magnetic torque design, the optimization objective of magnetic drive coupling is to find the geometric parameter scheme with minimum eddy current loss and minimum permanent magnet volume of magnetic drive coupling, which belongs to the category of multiobjective optimization design. In this paper, the comprehensive balance method is adopted in the optimization process to find the optimal geometric parameter scheme; that is, the single index is analyzed first, the combination of the optimal geometric parameter scheme within a single index is studied, and then the comprehensive balance analysis is carried out on the basis of the single index study to find the geometric parameter scheme that meets the design requirements as far as possible. The optimal geometric parameters of a single index can be obtained by analyzing the order of the arithmetic mean of different experimental factors. When the maximum magnetostatic torque is analyzed as a single index, the bigger the maximum magnetostatic torque is, the better; the combination of larger Ki should be selected, on the premise that the eddy current loss and the volume of permanent magnet are the same or similar and meet the design requirements. When the eddy current loss is analyzed as a single index, under the premise of meeting the design requirements, the smaller the eddy current loss, the better. At the same time, smaller combination should be selected. When the permanent magnet volume is analyzed as a single indicator, the smaller the permanent magnet volume is, the better it will be. And the combination with smaller should be selected. The optimal geometric parameter scheme for a single indicator is shown in Table 6.

In theory, the maximum magnetostatic torque of all geometric parameter schemes in Table 2 can meet the design requirements, but in the design process, it can be seen from literature [38–44] that the numerical results of the maximum magnetostatic torque in finite element calculation are often higher than the actual values. In the design, if the calculation result of finite element was too approximate to the design value, the actual value of the maximum magnetostatic torque of the designed magnetic drive coupling would be smaller than the design value, which cannot meet the design requirements. Therefore, the interference in this aspect should be considered in the comprehensive evaluation, and the larger finite element calculation value should be selected. The comprehensive equilibrium analysis is carried out based on the calculation results in Table 6.
(1) Internal radius of the magnet r: For the maximum magnetostatic torque, it is better to take r_{1} as the factor. For eddy current loss and permanent magnet volume, this factor is best taken as r_{3}. As can be seen from Table 2, when the factor is taken as r_{1}, the magnetic torque value, magnetic eddy current loss, and the volume value of permanent magnet far exceed the design value, which is not in line with the design principles of high efficiency, energy saving, and material saving. When the factor is r_{3}, the value of r_{3} is the minimum, which conforms to the design principle of small friction loss of internal magnetic rotor, and the magnetic torque meets the design requirements, so the inner radius of the inner magnet is r_{3}.
(2) Permanent magnet thickness t_{m}: For the maximum magnetostatic torque, it is better to take t_{m1} as the factor. For eddy current loss and permanent magnet volume, t_{m3} is the best choice for this factor. As can be seen from Table 2, when this factor is taken as t_{m1}, the magnetic torque, eddy current loss, and the volume value of permanent magnet are much higher than the design value. When this factor is taken as t_{m2}, the magnetic torque meets the design requirements. According to the range diagram and relation diagram, tm has the largest influence on magnetic torque and eddy current loss. In addition, the value of numerical calculation is generally larger than the actual value, and the actual value of magnetic torque may not meet the design requirements if t_{m} value is t_{m1}. Therefore, in order to prevent the occurrence of the above phenomenon, t_{m} value of permanent magnet thickness is determined to be t_{m2}.
(3) The axial length L_{b}: For the maximum magnetostatic torque, L_{b1} is the best choice for this factor. For eddy current loss and permanent magnet volume, L_{b3} is the best choice for this factor. According to the range diagram and relation diagram, the effect of axial length L_{b} on maximum magnetostatic torque and eddy current loss is relatively small, so the axial length L_{b} is determined to be L_{b3}.
(4) The thickness of the yoke iron t_{i}: For the maximum magnetostatic torque, it is better to take t_{i1} for this factor; for eddy current loss and permanent magnet volume, it is better to take t_{i3} for this factor (yoke iron thickness does not affect permanent magnet volume). According to the design principle of yoke iron thickness, yoke iron thickness should be slightly larger than permanent magnet thickness. Referring to Table 2, range diagram, and relation diagram, it is determined that the value of yoke iron thickness t_{i} is t_{i1}.
According to the above analysis, the optimal scheme is determined as follows: r_{3}t_{m2}L_{b3}t_{i2}. That is to say, the geometric parameters of the optimal scheme of magnetic drive coupling are as follows: internal magnet radius r = 80 mm, permanent magnet thickness t_{m} = 8 mm, axial length L_{b} = 144 mm, and yoke iron thickness t_{i} = 10 mm. After finite element calculation, the magnetic properties of the optimal scheme are as follows: = 368 N·m, = 1763 W, V = 1317400 mm^{3}. Compared with the original geometric parameters, the maximum magnetostatic torque of the optimal scheme meets the design requirements. The internal radius of the internal magnet is reduced by 1 mm, the axial length is reduced by 6 mm, the friction loss of the internal magnetic rotor is smaller, the eddy current loss is reduced by 219 W, and the volume of the permanent magnet is reduced by 69927 mm^{3}.
The magnetic line distribution (maximum magnetic rotation angle) of the optimal geometric parameter scheme is shown in Figure 9. As can be seen from Figure 9, the 22 closed coils of magnetic induction line are periodically distributed along the circumference. The magnetic induction line in a single closed coil is evenly distributed with less magnetic leakage, and the magnetic saturation phenomenon does not appear in the distribution of magnetic induction line at the yoke iron. The distribution of magnetic induction intensity (maximum magnetic rotation angle) of the optimal geometric scheme is shown in Figure 13. As can be seen from Figure 13, the periodic distribution law of magnetic induction intensity is similar to the distribution law of magnetic induction line. The magnetic induction intensity at the junction of two adjacent magnetic blocks is larger than that in the surrounding area, which is prone to magnetic sharp angle effect. The vector distribution of eddy current loss (maximum magnetic rotation angle) for the optimal geometric scheme is shown in Figure 14. It can be seen from Figure 14 that the vector distribution of eddy current loss of the optimal geometric scheme presents a periodic sinusoidal distribution, whose period is the same as that of the number of magnetic poles and the magnetic induction intensity. From the comprehensive analysis of Figures 9, 13, and 14, it can be seen that the magnetic performance distribution of the optimal geometric parameter scheme is reasonable, and the distribution of the overall magnetic field is conducive to the transmission of torque.
4. Magnetic Performance Test
4.1. Testing of Maximum Magnetostatic Torque
The magnetic drive coupling designed above is entrusted to a pump enterprise for processing, the static and dynamic performance of the magnetic drive coupling are tested on the magnetic performance test bench of the enterprise, and the experimental process and data are shown in Table 7. The maximum magnetostatic torque test of the magnetic drive coupling was measured on the torsion test machine modified by the enterprise. The torsion test machine is shown in Figure 15, and the test results are shown in Table 7.

As can be seen from Table 7, the maximum static magnetic torque test value of magnetic drive coupling is 351 N·m, which meets the design requirements of magnetic drive coupling, indicating that the optimization design method proposed in this paper is reliable in the design of magnetic drive coupling. In addition, the calculation value of the empirical formula of the maximum magnetostatic torque of the magnetic drive coupling is 311 N·m, and the finite element numerical calculation value is 368 N m. The difference between the calculated value of the empirical formula and the test value is 11.4%, and the difference between the finite element numerical calculation value and the test value is 5.5%. The finite element calculation results are found to be approximate to the test results and their calculation accuracy is higher than the one obtained by the use of the empirical formula.
4.2. Testing of Eddy Current Losses
The principle of dynamic performance test bench for magnetic drive coupling is shown in Figure 16, and the dynamic performance test bench is shown in Figure 17. Firstly, the magnetic drive coupling is installed in the dynamic characteristic test bed, the test bed motor is started to drive the internal and external magnetic rotor to rotate synchronously, and the motor speed is adjusted by the frequency conversion controller. When the motor runs stably at the rated speed, the load is adjusted to the rated torque value of the pump shaft through the tension controller, and the torque power value of each torque speed sensor at this speed is recorded. When measuring the eddy current loss, it is necessary to compare the torque transfer situation in the two cases with or without the isolation sleeve. The difference between the two is the eddy current loss power in isolation sleeve. In order to reduce the test error, each group of data is measured three times to obtain the average value.
The test results of dynamic performance of magnetic drive coupling with and without isolation sleeve are shown in Table 8. It can be seen from Table 8 that the power loss is 776 W and efficiency is 97.55% without isolation sleeve, and the power loss with isolation sleeve is 2949 W. The calculation shows that the eddy current loss in the isolation sleeve of the magnetic drive coupling is 2173 W, the transmission efficiency of the magnetic drive coupling reaches 91.33%, and the magnetic transmission efficiency meets the design requirements. This also shows that the optimization design method of the magnetic drive coupling proposed is reliable in the design and calculation of the magnetic drive coupling.

5. Conclusions
(1) Based on the finite element method, the singlefactor test of magnetic drive coupling was carried out to study the effect of singlefactor change on magnetic performance. Torqc2d command in ANSYS postprocessing was used to calculate the magnetic torque on the outer circle of the internal magnetic rotor and the eddy current loss power in the isolation sleeve. The main influencing factors are determined to be the inner radius of internal magnet, the thickness of permanent magnet, the axial length, and the thickness of yoke iron.
(2) The design of the magnetic drive coupling is optimized by means of orthogonal test. At the same time, the influence of geometric parameters on magnetic performance of magnetic drive coupling is studied emphatically. The range analysis results of the maximum magnetostatic torque show that the range sequence of the four factors is t_{m}>r>L_{b}>t_{i}, the range analysis results of of eddy current loss show that the range order of the four factors is t_{m}>r>L_{b}>t_{i}, and the range analysis results of the volume V of permanent magnet show that the range sequence is t_{m}>L_{b}>r>t_{i}. The thickness of permanent magnet t_{m} has the greatest effect on , , and V.
(3) The magnetic performance distribution of the optimal geometric parameter scheme is studied. The maximum magnetostatic torque and magnetic eddy current loss of magnetic drive coupling are tested and studied with the static and dynamic test devices of magnetic drive coupling. The geometrical parameters of the optimal scheme of magnetic drive coupling are internal radius of magnet r = 80 mm, thickness of permanent magnet t_{m} = 8 mm, axial length L_{b} = 144 mm, and thickness of yoke iron t_{i} = 10 mm.
The results show that the maximum magnetostatic torque of magnetic drive coupling is 351 N·m, which has lower eddy current loss, higher magnetic transfer efficiency, and magnetic performance meeting the design requirements. The distribution of magnetic properties of the optimal geometrical parameter scheme is reasonable, and the distribution of the overall magnetic field is conducive to the transfer of torque.
Data Availability
The numerical 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.
Acknowledgments
This work was financially supported by the Science and Technology Research Project supported by Educational Commission of Hubei Province of China (Q20171204); the Opening Foundation of Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University (SLK2018B03); the Open Research Subject of Key Laboratory of Fluid and Power Machinery (Xihua University), Ministry of Education (szjj2017098); the university basic research projects of Yi Chang (A17302a09); the Opening Foundation of Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance (2017KJX13); talentspecific projects of Three Gorges University (2016KJX03); and the Opening Foundation of Farmland Irrigation Research Institute, CAAS/Key Laboratory of WaterSaving Agriculture of Henan Province (FIRI20172101).
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