Mathematical Problems in Engineering
Volume 2019 (2019), Article ID 4243020, 14 pages
https://doi.org/10.1155/2019/4243020

Research Article

A Study on the Influencing Factors and Optimization Design of Combined Push-Pull Magnetic Drive Coupling

Gao Zhenjun,1,2,3 Hu Chaoqun,¹ Hong Feng,¹ Liu Jianrui,⁴ and Su Huashan¹

¹Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, China Three Gorges University, Yichang 443002, China
²Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, China
³Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, China
⁴Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Hu Chaoqun; 1353341292@qq.com and Su Huashan; 187351314@qq.com

Received 16 January 2019; Accepted 6 May 2019; Published 2 June 2019

Academic Editor: Giorgio Besagni

Copyright © 2019 Gao Zhenjun et al. 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.

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 push-pull 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 tm = 8 mm, axial length Lb = 144 mm, and thickness of yoke iron ti = 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 high-speed 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 self-excited 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 high-speed 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 rotor-bearing 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 rotor-bearing 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 Single-Factor 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 Lb, air gap tg, magnet thickness tm, and yoke iron thickness ti 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 (mm³) : 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. Single-Factor Test Analysis

Taking the geometric parameters of the designed magnetic drive coupling as an example, the single-factor 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 thin-walled 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 k-ε model, RNG k-ε model, Standard k-ω model, and SST k-ω 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 single-factor 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 single-factor 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

Figure 1: Influence of internal radius r of internal magnet on magnetic performance.

(a) effect of magnet thickness tm on magnetic torque

(b) effect of magnet thickness tm on eddy current loss

Figure 2: Influence of magnet thickness tm on magnetic properties.

(a) Influence of air gap width tg on magnetic torque

(b) Influence of air gap width tg on eddy current loss

Figure 3: Influence of air gap width tg on magnetic properties.

(a) Influence of axial length Lb on magnetic torque

(b) Influence of axial length Lb on eddy current loss

Figure 4: Influence of axial length Lb on magnetic properties.

(a) Effect of spacer sleeve thickness t on magnetic torque

(b) Effect of spacer sleeve thickness t on eddy current loss

Figure 5: Influence of isolation sleeve thickness t on magnetic performance.

(a) Effect of yoke iron thickness ti on magnetic torque

(b) Effect of yoke iron thickness ti on eddy current loss

Figure 6: Effect of yoke iron thickness ti on magnetic properties.

(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

Figure 7: Effect of the number of magnetic poles m on magnetic properties.

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 two-dimensional 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.

Figure 8: Orthogonal optimization program.

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 multi-index 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 single-factor 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 tg, magnet thickness tm, internal magnet radius r, permanent magnet axial length Lb, yoke iron thickness ti, 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 tm, air gap width tg, and permanent magnet axial length Lb. To sum up, the main geometrical factors affecting the orthogonal test indexes are magnetic series m, air gap width tg, magnet thickness tm, internal magnet radius r, axial length Lb of permanent magnet, yoke iron thickness ti, and isolation sleeve thickness t. According to the single-factor 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 tg, so in the actual design process, the smaller the air gap width tg, 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 tg is 6 mm, it meets the design requirements of machining and assembly, so the air gap width tg in this paper is determined to be 6 mm. After the specific values of magnetic series m, air gap width tg, and isolation sleeve thickness t are known, the magnet thickness tm, inner magnet radius r, permanent magnet axial length Lb, and yoke iron thickness ti are finally selected as the experimental factors for this orthogonal optimization.

Figure 9: The distribution of magnetic inductance line in the optimal geometric scheme.

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 single-factor 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.

Table 1: Factor level table.

Level
A
B
C
D

r (mm)
tm(mm)
Lb(mm)
ti(mm)

1
83
9
156
14

2
81
8
150
10

3
80
7
144
6

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. Sm₂Co₁₇ 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.

Table 2: Orthogonal test scheme and test results.

Test serial number
A
B
C
D

Pw
V

(N·m)
(W)
(mm³)

1
83
9
156
14
471
2267
1676100

2
83
8
150
10
416
1974
1417500

3
83
7
144
6
348
1630
1178000

4
81
9
150
6
440
2114
1577700

5
81
8
144
14
391
1859
1331800

6
81
7
156
10
335
1606
1248700

7
80
9
144
10
428
2054
1498300

8
80
8
156
6
379
1805
1427100

9
80
7
150
14
320
1546
1187500

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 Ri 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 tm>r>Lb>ti. It can be obtained that the thickness of permanent magnet tm has the greatest influence on the maximum magnetostatic torque , followed by the radius r, axial length Lb and yoke thickness ti. 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 Lb, and the maximum magnetostatic torque increases with the increase of the thickness of yoke iron ti. 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 single-factor test results.

Table 3: Range analysis of maximum magnetostatic torque .

Variable
(mm)
(mm)
(mm)
(mm)

K₁₁
1235
1339
1186
1182

K₁₂
1166
1187
1176
1179

K₁₃
1128
1003
1167
1168

k₁₁
411.66
446.33
395.33
394

k₁₂
388.66
395.66
392.00
393

k₁₃
376
334.33
389.00
389.33

R₁
35.66
112
6.33
4.66

Figure 10: Relation diagram of maximum magnetostatic torque and each test factor.

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 tm>r>Lb>ti. It can be concluded that the permanent magnet thickness tm has the largest influence on the of eddy current loss, followed by the internal radius r of the internal magnet, the axial length Lb, and the yoke iron thickness ti. 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 Lb, 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 single-factor test results.

Table 4: Range analysis of magnetic eddy current loss Pw.

Variable
(mm)
tm (mm)
Lb (mm)
ti (mm)

K₂₁
5871
6435
5678
5672

K₂₂
5579
5638
5634
5634

K₂₃
5405
4782
5543
5549

k₂₁
1957
2145
1892.66
1890.66

k₂₂
1859.66
1879.33
1878.00
1878.00

k₂₃
1801.66
1594.00
1847.667
1849.66

R₂
155.33
551.00
45.00
41.00

Figure 11: Relation diagram of eddy current loss with each test factor.

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 tm>Lb>r>ti (where ti does not affect the change of permanent magnet volume V), and the thickness of the permanent magnet tm has the greatest influence on the eddy current loss , followed by the axial length Lb 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 tm, the permanent magnet volume V increases. With the increase of axial length Lb, the volume V of permanent magnet increases.

Table 5: Range analysis of permanent magnet volume V.

Variable
r (mm)
tm (mm)
Lb (mm)
ti (mm)

K₃₁
4271600
4752100
4351900
4195400

K₃₂
4158200
4176400
4182700
4164500

K₃₃
4112900
3614200
4008100
4182800

k₃₁
1423867
1584033
1450633
1398467

k₃₂
1386067
1392133
1394233
1388167

k₃₃
1370967
1204733
1336033
1394267

R₃
52900
379300
114600
10300

Figure 12: Relation diagram of the volume V of permanent magnet with each test factor.

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.

Table 6: Combination of optimal geometric parameter schemes for single index study.

Test factors
Maximum magnetostatic torque
Eddy current loss
Volume of permanent magnet

Pw
V

Magnet inner radius r
k₁₁> k₁₂> k₁₃
k₂₁> k₂₂> k₂₃
k₃₁> k₃₂> k₃₃

Permanent magnet thickness tm
k₁₁> k₁₂> k₁₃
k₂₁> k₂₂> k₂₃
k₃₁> k₃₂> k₃₃

Axial length Lb
k₁₁> k₁₂> k₁₃
k₂₁> k₂₂> k₂₃
k₃₁> k₃₂> k₃₃

Axial length ti
k₁₁> k₁₂> k₁₃
k₂₁> k₂₂> k₂₃
k₃₁> k₃₃> k₃₂

Optimal parameter scheme
r₁tm1Lb1ti1
r₃tm3Lb3ti3
r₃tm3Lb3ti2

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 r₁ as the factor. For eddy current loss and permanent magnet volume, this factor is best taken as r₃. As can be seen from Table 2, when the factor is taken as r₁, 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 r₃, the value of r₃ 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 r₃.

(2) Permanent magnet thickness tm: For the maximum magnetostatic torque, it is better to take tm1 as the factor. For eddy current loss and permanent magnet volume, tm3 is the best choice for this factor. As can be seen from Table 2, when this factor is taken as tm1, 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 tm2, 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 tm value is tm1. Therefore, in order to prevent the occurrence of the above phenomenon, tm value of permanent magnet thickness is determined to be tm2.

(3) The axial length Lb: For the maximum magnetostatic torque, Lb1 is the best choice for this factor. For eddy current loss and permanent magnet volume, Lb3 is the best choice for this factor. According to the range diagram and relation diagram, the effect of axial length Lb on maximum magnetostatic torque and eddy current loss is relatively small, so the axial length Lb is determined to be Lb3.

(4) The thickness of the yoke iron ti: For the maximum magnetostatic torque, it is better to take ti1 for this factor; for eddy current loss and permanent magnet volume, it is better to take ti3 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 ti is ti1.

According to the above analysis, the optimal scheme is determined as follows: r₃tm2Lb3ti2. 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 tm = 8 mm, axial length Lb = 144 mm, and yoke iron thickness ti = 10 mm. After finite element calculation, the magnetic properties of the optimal scheme are as follows: = 368 N·m, = 1763 W, V = 1317400 mm³. 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 mm³.

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.

Figure 13: The distribution of magnetic induction intensity in the optimal geometric scheme.

Figure 14: The distribution of magnetic eddy current vector in the optimal geometric scheme.

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.

Table 7: Test results of static performance of magnetic drive coupling.

serial number
Test project
Test data

Magnetic dip (°C)
0
1
2
3
4
5
6
7
8

1
Magnetic torque (N·m)
0
63
126
186
237
281
324
332
351

2
0
69
136
197
244
293
317
355
351

3
0
69
132
189
251
289
321
339
350

statistics
Maximum magnetostatic torque (N·m)
351

Figure 15: Manual horizontal torsion tester.

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.

Figure 16: Test bench schematic diagram of dynamic characteristics of magnetic drive coupling.

Figure 17: Testing bench for dynamic magnetic performance.

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.

Table 8: Test results of dynamic performance of magnetic drive coupling.

Test method
Serial number
Input
Output
Loss (W)
Efficiency (%)
Loss statistics (W)
Efficiency statistics (%)

Torque
Power
Torque
Power

(N·m)
(W)
(N·m)
(W)

Non-isolation sleeve
1
210.13
31894
204.26
31138
756
97.62
776
97.55

2
208.67
31885
204.37
31079
806
97.47

3
212.62
31861
204.21
31093
768
97.58

Isolation sleeve
1
225.28
34041
204.28
31081
2960
91.30
2949
91.33

2
223.91
34046
204.33
31105
2941
91.36

3
223.17
34027
204.54
31080
2947
91.33

5. Conclusions

(1) Based on the finite element method, the single-factor test of magnetic drive coupling was carried out to study the effect of single-factor 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 tm>r>Lb>ti, the range analysis results of of eddy current loss show that the range order of the four factors is tm>r>Lb>ti, and the range analysis results of the volume V of permanent magnet show that the range sequence is tm>Lb>r>ti. The thickness of permanent magnet tm 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 tm = 8 mm, axial length Lb = 144 mm, and thickness of yoke iron ti = 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 (szjj2017-098); the university basic research projects of Yi Chang (A17-302-a09); the Opening Foundation of Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance (2017KJX13); talent-specific projects of Three Gorges University (2016KJX03); and the Opening Foundation of Farmland Irrigation Research Institute, CAAS/Key Laboratory of Water-Saving Agriculture of Henan Province (FIRI2017-21-01).

References

K. Shoda, S. Matsumoto, T. Furukawa, Y. Tozaki, A. Umeda, and S. Takahashi, “Study on nonliner numerical simulation of vibration of power transmission gear system: 2nd report, nonliner dynamic characteristics of stiffness and damping of gear coupling,” Transactions of the Japan Society of Mechanical Engineers Part C, vol. 71, no. 704, pp. 1153–1160, 2005.

H. Chang, W. Li, W. Shi, and J. Liu, “Effect of blade profile with different thickness distribution on the pressure characteristics of novel self-priming pump,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 11, 2018.

H. Chang, W. Shi, W. Li, and J. Liu, “Energy loss analysis of novel self-priming pump based on the entropy production theory,” Journal of Thermal Science, vol. 28, no. 2, pp. 306–318, 2019.

J. Ynagyi, “Torsional vibration of shafts connected by gear joints: 1st report, analysis of steady-state response,” Proceedings of the Japan Society of Mechanical Engineering: Part C, vol. 51, no. 4, pp. 773–780, 1985.

M. Calistrat, “Friction between high speed gear coupling teeth,” Journal of Mechanical Design, vol. 103, no. 1, pp. 54–60, 1981.

Z Guang, L. Zhansheng, and Y. Jianwei, “Gear coupling misalignment meshing force model and its influence on dynamic characteristics of the rotary subsystem,” Journal of Harbin Engineering University, vol. 30, no. 1, pp. 33–39, 2009.

G. Zhao, J.-N. Guo, X.-F. Wang, and Z.-S. Liu, “Dynamics of rotor-gear coupling-bearing system with misalignment,” Journal of Dalian University of Technology, vol. 51, no. 3, pp. 338–345, 2011.

Z. Guang, L. Zhansheng, and Y. Jianwei, “Dynamic characteristics of rotor-misaligned spline coupling system,” Vibration and Impact, vol. 28, no. 3, pp. 78–82, 2009.

A. Kahraman, “A spline joint formulation for drive train torsional dynamic models,” Journal of Sound and Vibration, vol. 241, no. 2, pp. 328–336, 2001.

I. Chalghoum, S. Elaoud, H. Kanfoudi, and M. Akrout, “The effects of the rotor-stator interaction on unsteady pressure pulsation and radial force in a centrifugal pump,” Journal of Hydrodynamics, vol. 30, no. 4, pp. 672–681, 2018.

Y. Tang, M. Xiao, and L. Tang, “Piecewise least squares polynomial curve fitting algorithm for tested pump performance data,” Journal of Drainage and Irrigation Machinery Engineering, vol. 35, no. 9, pp. 744–748, 2017.

D. Han, F. Yu, and S. Zhang, “Numerical simulation of unsteady three-dimensional flow in turbine mode of a pump-turbine,” Journal of Drainage and Irrigation Machinery Engin, vol. 35, no. 4, pp. 325–332, 2017.

Q. Li, M. Liu, J. Zhang, and Q. Liu, “Flow characteristic of guide vane region in turbine braking operation of pump-turbine,” Journal of Drainage and Irrigation Machinery Engin, vol. 35, no. 6, pp. 495–501, 2017.

F. Zhang, J. Zhang, X. Zhang, and S. Yuan, “Internal flow characteristic analysis on outlet conduit based on whole flow field,” Journal of Drainage and Irrigation Machinery Engin, vol. 36, no. 12, pp. 1246–1251, 2018.

L. Qi-Fei, L. Chao et al., “Cavitation characteristics research of pump turbine under partial load condition,” Journal of Drainage and Irrigation Machinery Engin, vol. 35, no. 8, p. 680, 2017.

B. Thamsen, R. Mevert, M. Lommel et al., “A two-stage rotary blood pump design with potentially lower blood trauma: a computational study,” The International Journal of Artificial Organs, vol. 2016, no. 0, 2016.

Y. Zhong, L. Yi, and X. Chuang, “Calculation method and simulation study of permanent magnet rotor of traveling wave magnetic field driven blood pump,” Journal of Huazhong University of Science and Technology (Natural Science Edition), vol. 2013, no. 9, Article ID 871516, 20 pages, 2013.

T.-Y. Li, L. Ye, F.-W. Hong, D.-C. Liu, H.-M. Fan, and Z.-M. Liu, “The simulation of multiphase flow field in implantable blood pump and analysis of hemolytic capability,” Journal of Hydrodynamics, vol. 25, no. 4, pp. 606–615, 2013.

Z. Guowei, Y. Zizhao, Z. Guozhong, and W. Yuanxun, “Calculation of magnetic torque of magnetic coupling by finite element method,” Water Pump Technology, vol. 04, pp. 24–26, 2005.

Z. Kezhong, Magnetic Drive Technology and Equipment, Chemical industry press, Beijing , China, 2003.

H. Zhu, G. Bo, Y. Zhou, R. Zhang, and J. Cheng, “Pump selection and performance prediction for the technical innovation of an axial-flow pump station,” Mathematical Problems in Engineering, vol. 2018, Article ID 6543109, 9 pages, 2018.

T. Linwei, Design and Research of DLC Vertical Multistage Magnetic Pump, Jiangsu University, 2014.

K. Fanyu, W. Zhiqiang, Z. Hongli, and G. Cuilan, “Magnetic field analysis and performance calculation of magnetic pump magnetic coupling,” Magnetic Materials and Devices, vol. 03, pp. 24–27+31, 2009.

K. Fanyu, F. Zizheng, B. Yuxing, and H. Dan, “3d simulation and analysis of magnetic pump coupling,” Mechanical Design and Manufacturing, vol. 10, pp. 36–39, 2014.

W. Yong, Research on Magnetic Mechanical Analysis and Design Method Combining Field Path and considering Coupling, Hefei University of technology, 2006.

Z. Qun, Study on Energy Consumption of Magnetic Pump and Simulation Calculation of mAgnetic Eddy Field, Jiangsu University, 2006.

W. Juan, L. Xianfei, Z. Zhibao, and J. Shengfa, “Analysis of new high temperature resistant magnetic coupling based on ANSYS,” Mechanical Design and Manufacture, vol. 09, pp. 90–92, 2009.

A. Lucius and G. Brenner, “Numerical simulation and evaluation of velocity fluctuations during rotating stall of a centrifugal pump,” Journal of Fluids Engineering, vol. 133, no. 8, pp. 81–102, 2011.

Y. Danqing, L. Jianping, H. Youquan et al., “Halbach type magnetic coupling transmission torque characteristics analysis,” Magnetic materials and devices, vol. 2011, no. 2, pp. 36–40, 2011.

O. Pacot, C. Kato, Y. Guo, Y. Yamade, and F. Avellan, “Large eddy simulation of the rotating stall in a pump-turbine operated in pumping mode at a part-load condition,” Journal of Fluids Engineering, vol. 138, no. 11, p. 11110, 2016.

S. Kim, K.-Y. Lee, J.-H. Kim, and Y.-S. Choi, “A numerical study on the improvement of suction performance and hydraulic efficiency for a mixed-flow pump impeller,” Mathematical Problems in Engineering, vol. 2014, Article ID 269483, 17 pages, 2014.

Y. Wang, P. Liu, and H. Ding, “Optimal design of radial magnetic couplings with internal and external shaft,” Optical Precision Engineering, vol. 16, no. 11, pp. 2244–2251, 2008.

C. Yan, J. Yu, J. Xu et al., “On the achievements and prospects for the methods of computational fluid dynamics,” Advances in Mechanics, vol. 41, no. 5, pp. 562–589, 2011.

S. Derakhshan and N. Kasaeian, “Optimization, numerical, and experimental study of a propeller pump as turbine,” Journal of Energy Resource Technology-Transactions of the ASME, vol. 136, no. 1, 2014.

L. Tan, S. Cao, Y. Wang, and B. Zhu, “Direct and inverse iterative design method for centrifugal pump impellers,” in Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 226, no. 6, pp. 764–775, 2012.

J. González and C. Santolaria, “Unsteady flow structure and global variables in a centrifugal pump,” Journal of Fluids Engineering, vol. 128, no. 5, pp. 937–946, 2006.

T. Lei, C. Shuliang, and G. Shaobo, “Hydraulic design and pre-whirl regulation law of inlet guide vane for centrifugal pump,” Science China Technological Sciences, vol. 53, no. 8, pp. 2142–2151, 2010.

G. Pavesi, G. Cavazzini, and G. Ardizzon, “Time-frequency characterization of the unsteady phenomena in a centrifugal pump,” International Journal of Heat and Fluid Flow, vol. 29, no. 5, pp. 1527–1540, 2008.

W. Dexi and Z. Shiwei, “Characteristic analysis of coaxial magnetic coupling,” Journal of Liaoyang petrochemical college, vol. 2000, no. 01, pp. 42–45, 2000.

Y. Zhiyi and Z. Han, “Calculation and characteristic analysis of axial force and transmission torque of axial magnetic coupling,” Magnetic Materials and Devices, vol. 32, no. 6, pp. 22–26, 2001.

L. Jianrui, “Chemical pump magnetic coupling transmission design,” The International Journal of Fluid Machinery and Systems, vol. 2001, no. 12, pp. 36-37, 2001.

H. Lu and C. J. Rutland, “Structural subgrid-scale modeling for large-eddy simulation: a review,” Acta Mechanica Sinica, vol. 32, no. 4, pp. 567–578, 2016.

W. Yuliang and Chunyi, “Magnetic circuit structure and characteristics of permanent magnet coupling,” Magnetic Materials and Devices, vol. 2005, no. 04, 11 pages, 2005.

P.-J. Zhou, F.-J. Wang, Z.-J. Yang, and J.-G. Mou, “Investigation of rotating stall for a centrifugal pump impeller using various SGS models,” Journal of Hydrodynamics, vol. 29, no. 2, pp. 235–242, 2017.