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

Authors: Gao Zhenjun; Hu Chaoqun; Hong Feng; Liu Jianrui; Su Huashan
Journal: Mathematical Problems in Engineering
 (2019)

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## 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 magnetr= 80 mm, thickness of permanent magnett
m = 8 mm, axial lengthL
b = 144 mm, and thickness of yoke iront
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.


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## Body

## 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 magnetr, axial length of magnetic rotorL
b, air gapt
g, magnet thicknesst
m, and yoke iron thicknesst
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.r: Internal radius of the magnet (mm)
t
i: Yoke iron thickness (mm)
L
b: Axial length of magnetic rotor (mm)
T
m
a
x: Maximum magnetostatic torque (N·m)
t
g: Air gap (mm)
P
w: Eddy current loss (W)
t
m: Magnet thickness (mm)
V: Volume of permanent magnet (mm3)
m: Number of magnetic poles
R
i: Range
K
i: The sum of the corresponding test results when the horizontal sign on any column is i
k
i: The arithmetic mean of the test results when the factors in any column are taken at level i.


### 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 Figures1, 2, 3, 4, 5, 6, and 7.Figure 1
Influence of internal radius r of internal magnet on magnetic performance.
(a)
Effect of internal radiusr of the magnet on torque
(b)
Effect of internal radiusr of the magnet on eddy current lossFigure 2
Influence of magnet thicknesst
m on magnetic properties.
(a)
effect of magnet thicknesst
m on magnetic torque
(b)
effect of magnet thicknesst
m on eddy current lossFigure 3
Influence of air gap widtht
g on magnetic properties.
(a)
Influence of air gap widtht
g on magnetic torque
(b)
Influence of air gap widtht
g on eddy current lossFigure 4
Influence of axial lengthL
b on magnetic properties.
(a)
Influence of axial lengthL
b on magnetic torque
(b)
Influence of axial lengthL
b on eddy current lossFigure 5
Influence of isolation sleeve thicknesst on magnetic performance.
(a)
Effect of spacer sleeve thicknesst on magnetic torque
(b)
Effect of spacer sleeve thicknesston eddy current lossFigure 6
Effect of yoke iron thicknesst
i on magnetic properties.
(a)
Effect of yoke iron thicknesst
i on magnetic torque
(b)
Effect of yoke iron thicknesst
i on eddy current lossFigure 7
Effect of the number of magnetic poles m 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 lossAs can be seen from Figure1, the greater the internal radiusr of the magnet is, the greater the magnetic torque and eddy current loss will be. The main reason is that the greater the internal radiusr 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 t
m is, the greater the magnetic torque and eddy current loss will be. As the thickness of the magnet t
m 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.


## 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 magnetr, axial length of magnetic rotorL
b, air gapt
g, magnet thicknesst
m, and yoke iron thicknesst
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.r: Internal radius of the magnet (mm)
t
i: Yoke iron thickness (mm)
L
b: Axial length of magnetic rotor (mm)
T
m
a
x: Maximum magnetostatic torque (N·m)
t
g: Air gap (mm)
P
w: Eddy current loss (W)
t
m: Magnet thickness (mm)
V: Volume of permanent magnet (mm3)
m: Number of magnetic poles
R
i: Range
K
i: The sum of the corresponding test results when the horizontal sign on any column is i
k
i: The arithmetic mean of the test results when the factors in any column are taken at level i.


## 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 Figures1, 2, 3, 4, 5, 6, and 7.Figure 1
Influence of internal radius r of internal magnet on magnetic performance.
(a)
Effect of internal radiusr of the magnet on torque
(b)
Effect of internal radiusr of the magnet on eddy current lossFigure 2
Influence of magnet thicknesst
m on magnetic properties.
(a)
effect of magnet thicknesst
m on magnetic torque
(b)
effect of magnet thicknesst
m on eddy current lossFigure 3
Influence of air gap widtht
g on magnetic properties.
(a)
Influence of air gap widtht
g on magnetic torque
(b)
Influence of air gap widtht
g on eddy current lossFigure 4
Influence of axial lengthL
b on magnetic properties.
(a)
Influence of axial lengthL
b on magnetic torque
(b)
Influence of axial lengthL
b on eddy current lossFigure 5
Influence of isolation sleeve thicknesst on magnetic performance.
(a)
Effect of spacer sleeve thicknesst on magnetic torque
(b)
Effect of spacer sleeve thicknesston eddy current lossFigure 6
Effect of yoke iron thicknesst
i on magnetic properties.
(a)
Effect of yoke iron thicknesst
i on magnetic torque
(b)
Effect of yoke iron thicknesst
i on eddy current lossFigure 7
Effect of the number of magnetic poles m 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 lossAs can be seen from Figure1, the greater the internal radiusr of the magnet is, the greater the magnetic torque and eddy current loss will be. The main reason is that the greater the internal radiusr 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 t
m is, the greater the magnetic torque and eddy current loss will be. As the thickness of the magnet t
m 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 (T
m
a
x), magnetic eddy current loss (P
w), 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 onT
m
a
x of magnetic torque and P
w of eddy current loss are magnetic seriesm, air gap widtht
g, magnet thicknesst
m, internal magnet radiusr, permanent magnet axial lengthL
b, yoke iron thicknesst
i, and isolation sleeve thicknesst. According to the formula for calculating the volume of permanent magnet in magnetic coupling, the geometric parameters that have a great influence on the volumev of permanent magnet are internal magnet radiusr, magnet thicknesst
m, air gap widtht
g, and permanent magnet axial lengthL
b. To sum up, the main geometrical factors affecting the orthogonal test indexes are magnetic seriesm, air gap widtht
g, magnet thicknesst
m, internal magnet radiusr, axial lengthL
b of permanent magnet, yoke iron thicknesst
i, and isolation sleeve thicknesst. 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 polesm 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 thicknesst, and the eddy current loss increases with the increase of the isolation sleeve thicknesst at any time. On the premise of satisfying the design requirements of magnetic drive coupling, the smaller the isolation sleeve thicknesst, the better. According to the calculation, when the thickness of spacer sleevetis the minimum, 1.2 mm, it meets the design requirements. Therefore, the thickness of spacer sleevet in this paper is determined to be 1.2 mm. The magnetic torque and eddy current loss decrease with the increase of air gap widtht
g, so in the actual design process, the smaller the air gap widtht
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 widtht
g is 6 mm, it meets the design requirements of machining and assembly, so the air gap widtht
g in this paper is determined to be 6 mm. After the specific values of magnetic seriesm, air gap widtht
g, and isolation sleeve thicknesst are known, the magnet thicknesst
m, inner magnet radiusr, permanent magnet axial lengthL
b, and yoke iron thicknesst
i 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 Table1 is arranged.Table 1
Factor level table.
Level
A
B
C
D
r(mm)
t
m(mm)
L
b(mm)
t
i(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
T
m
a
x
P
w
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 (T
m
a
x), eddy current loss (P
w), and permanent magnet volume (V) can be obtained based on the finite element calculation results, where K
i represents the sum of the corresponding test results when the horizontal number on any column isi; k
i is the arithmetic mean of the test results when the above factors in any column are taken as leveli; andR
i is the range, which is the difference between the maximum and minimum arithmetic mean of the test results when leveli 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 torqueT
m
a
x are shown in Table 3. Table 3 shows that the range order of the four factors ist
m
>r>L
b
>t
i. It can be obtained that the thickness of permanent magnett
m has the greatest influence on the maximum magnetostatic torque T
m
a
x, followed by the radiusr, axial lengthL
b and yoke thicknesst
i. The relationship between the maximum magnetostatic torque T
m
a
x and each test factor is shown in Figure 10. Figure 10 shows that the maximum magnetostatic torque T
m
a
x increases with the increase of the radiusr, the maximum magnetostatic torque T
m
a
x increases with the increase of the thickness of permanent magnet tm, the maximum magnetostatic torque T
m
a
x increases with the increase of the axial lengthL
b, and the maximum magnetostatic torque T
m
a
x increases with the increase of the thickness of yoke iront
i. When yoke iron thickness exceeds 10 mm, the growth rate of maximum magnetostatic torque T
m
a
x 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 torqueT
m
a
x.
Variable
r (mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
11
1235
1339
1186
1182
K
12
1166
1187
1176
1179
K
13
1128
1003
1167
1168
k
11
411.66
446.33
395.33
394
k
12
388.66
395.66
392.00
393
k
13
376
334.33
389.00
389.33
R
1
35.66
112
6.33
4.66Figure 10
Relation diagram of maximum magnetostatic torqueT
m
a
x and each test factor.The results of range analysis of eddy current lossP
w are shown in Table 4. As can be seen from Table 4, the range order of the four factors ist
m
>r>L
b
>t
i. It can be concluded that the permanent magnet thicknesst
m has the largest influence on the P
w of eddy current loss, followed by the internal radiusr of the internal magnet, the axial lengthL
b, and the yoke iron thicknesst
i. The relationship between the eddy current loss P
w and the experimental factors is shown in Figure 11. The figure shows that P
w of eddy current loss increases with the increase of the internal radiusr. With the increase of the permanent magnet thickness tm, the eddy current loss P
w increases. With the increase of axial lengthL
b, the eddy current loss P
w increases, and with the increase of yoke thickness, the eddy current loss P
w 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 lossP
w.
Variable
r (mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
21
5871
6435
5678
5672
K
22
5579
5638
5634
5634
K
23
5405
4782
5543
5549
k
21
1957
2145
1892.66
1890.66
k
22
1859.66
1879.33
1878.00
1878.00
k
23
1801.66
1594.00
1847.667
1849.66
R
2
155.33
551.00
45.00
41.00Figure 11
Relation diagram of eddy current lossP
w with each test factor.The range analysis results of the volumeV of permanent magnets are shown in Table 5. As can be seen from Table 5, the range order of the four factors ist
m
>L
b
>r>t
i (wheret
i does not affect the change of permanent magnet volumeV), and the thickness of the permanent magnett
m has the greatest influence on the eddy current loss P
w, followed by the axial lengthL
b and the radiusr of the internal magnet. The relationship between the volumeV of permanent magnet and each test factor is shown in Figure 12. The figure shows that with the increase ofr, the volumeV of permanent magnet increases. With the increase of the permanent magnet thicknesst
m, the permanent magnet volumeV increases. With the increase of axial lengthL
b, the volumeV of permanent magnet increases.Table 5
Range analysis of permanent magnet volumeV.
Variable
r(mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
31
4271600
4752100
4351900
4195400
K
32
4158200
4176400
4182700
4164500
K
33
4112900
3614200
4008100
4182800
k
31
1423867
1584033
1450633
1398467
k
32
1386067
1392133
1394233
1388167
k
33
1370967
1204733
1336033
1394267
R
3
52900
379300
114600
10300Figure 12
Relation diagram of the volumeV 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 meank
i 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 k
i 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 k
i 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
T
m
a
x
P
w
V
Magnet inner radiusr
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Permanent magnet thicknesst
m
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Axial lengthL
b
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Axial lengtht
i
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
33
> k
32
Optimal parameter scheme
r
1
t
m1
L
b1
t
i1
r
3
t
m3
L
b3
t
i3
r
3
t
m3
L
b3
t
i2In theory, the maximum magnetostatic torque of all geometric parameter schemes in Table2 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 magnetr: For the maximum magnetostatic torque, it is better to taker
1 as the factor. For eddy current loss and permanent magnet volume, this factor is best taken asr
3. As can be seen from Table 2, when the factor is taken asr
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 isr
3, the value ofr
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 isr
3.(2) Permanent magnet thicknesst
m: For the maximum magnetostatic torque, it is better to taket
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 ast
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 ast
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 ift
m value ist
m1. Therefore, in order to prevent the occurrence of the above phenomenon,t
m value of permanent magnet thickness is determined to bet
m2.(3) The axial lengthL
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 lengthL
b on maximum magnetostatic torque and eddy current loss is relatively small, so the axial lengthL
b is determined to beL
b3.(4) The thickness of the yoke iront
i: For the maximum magnetostatic torque, it is better to taket
i1 for this factor; for eddy current loss and permanent magnet volume, it is better to taket
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 thicknesst
i ist
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 radiusr= 80 mm, permanent magnet thicknesst
m = 8 mm, axial lengthL
b = 144 mm, and yoke iron thicknesst
i = 10 mm. After finite element calculation, the magnetic properties of the optimal scheme are as follows: T
m
a
x = 368 N·m, P
w = 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 Figure9. 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.


## 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 (T
m
a
x), magnetic eddy current loss (P
w), 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 onT
m
a
x of magnetic torque and P
w of eddy current loss are magnetic seriesm, air gap widtht
g, magnet thicknesst
m, internal magnet radiusr, permanent magnet axial lengthL
b, yoke iron thicknesst
i, and isolation sleeve thicknesst. According to the formula for calculating the volume of permanent magnet in magnetic coupling, the geometric parameters that have a great influence on the volumev of permanent magnet are internal magnet radiusr, magnet thicknesst
m, air gap widtht
g, and permanent magnet axial lengthL
b. To sum up, the main geometrical factors affecting the orthogonal test indexes are magnetic seriesm, air gap widtht
g, magnet thicknesst
m, internal magnet radiusr, axial lengthL
b of permanent magnet, yoke iron thicknesst
i, and isolation sleeve thicknesst. 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 polesm 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 thicknesst, and the eddy current loss increases with the increase of the isolation sleeve thicknesst at any time. On the premise of satisfying the design requirements of magnetic drive coupling, the smaller the isolation sleeve thicknesst, the better. According to the calculation, when the thickness of spacer sleevetis the minimum, 1.2 mm, it meets the design requirements. Therefore, the thickness of spacer sleevet in this paper is determined to be 1.2 mm. The magnetic torque and eddy current loss decrease with the increase of air gap widtht
g, so in the actual design process, the smaller the air gap widtht
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 widtht
g is 6 mm, it meets the design requirements of machining and assembly, so the air gap widtht
g in this paper is determined to be 6 mm. After the specific values of magnetic seriesm, air gap widtht
g, and isolation sleeve thicknesst are known, the magnet thicknesst
m, inner magnet radiusr, permanent magnet axial lengthL
b, and yoke iron thicknesst
i 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 Table1 is arranged.Table 1
Factor level table.
Level
A
B
C
D
r(mm)
t
m(mm)
L
b(mm)
t
i(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
T
m
a
x
P
w
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 (T
m
a
x), eddy current loss (P
w), and permanent magnet volume (V) can be obtained based on the finite element calculation results, where K
i represents the sum of the corresponding test results when the horizontal number on any column isi; k
i is the arithmetic mean of the test results when the above factors in any column are taken as leveli; andR
i is the range, which is the difference between the maximum and minimum arithmetic mean of the test results when leveli 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 torqueT
m
a
x are shown in Table 3. Table 3 shows that the range order of the four factors ist
m
>r>L
b
>t
i. It can be obtained that the thickness of permanent magnett
m has the greatest influence on the maximum magnetostatic torque T
m
a
x, followed by the radiusr, axial lengthL
b and yoke thicknesst
i. The relationship between the maximum magnetostatic torque T
m
a
x and each test factor is shown in Figure 10. Figure 10 shows that the maximum magnetostatic torque T
m
a
x increases with the increase of the radiusr, the maximum magnetostatic torque T
m
a
x increases with the increase of the thickness of permanent magnet tm, the maximum magnetostatic torque T
m
a
x increases with the increase of the axial lengthL
b, and the maximum magnetostatic torque T
m
a
x increases with the increase of the thickness of yoke iront
i. When yoke iron thickness exceeds 10 mm, the growth rate of maximum magnetostatic torque T
m
a
x 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 torqueT
m
a
x.
Variable
r (mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
11
1235
1339
1186
1182
K
12
1166
1187
1176
1179
K
13
1128
1003
1167
1168
k
11
411.66
446.33
395.33
394
k
12
388.66
395.66
392.00
393
k
13
376
334.33
389.00
389.33
R
1
35.66
112
6.33
4.66Figure 10
Relation diagram of maximum magnetostatic torqueT
m
a
x and each test factor.The results of range analysis of eddy current lossP
w are shown in Table 4. As can be seen from Table 4, the range order of the four factors ist
m
>r>L
b
>t
i. It can be concluded that the permanent magnet thicknesst
m has the largest influence on the P
w of eddy current loss, followed by the internal radiusr of the internal magnet, the axial lengthL
b, and the yoke iron thicknesst
i. The relationship between the eddy current loss P
w and the experimental factors is shown in Figure 11. The figure shows that P
w of eddy current loss increases with the increase of the internal radiusr. With the increase of the permanent magnet thickness tm, the eddy current loss P
w increases. With the increase of axial lengthL
b, the eddy current loss P
w increases, and with the increase of yoke thickness, the eddy current loss P
w 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 lossP
w.
Variable
r (mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
21
5871
6435
5678
5672
K
22
5579
5638
5634
5634
K
23
5405
4782
5543
5549
k
21
1957
2145
1892.66
1890.66
k
22
1859.66
1879.33
1878.00
1878.00
k
23
1801.66
1594.00
1847.667
1849.66
R
2
155.33
551.00
45.00
41.00Figure 11
Relation diagram of eddy current lossP
w with each test factor.The range analysis results of the volumeV of permanent magnets are shown in Table 5. As can be seen from Table 5, the range order of the four factors ist
m
>L
b
>r>t
i (wheret
i does not affect the change of permanent magnet volumeV), and the thickness of the permanent magnett
m has the greatest influence on the eddy current loss P
w, followed by the axial lengthL
b and the radiusr of the internal magnet. The relationship between the volumeV of permanent magnet and each test factor is shown in Figure 12. The figure shows that with the increase ofr, the volumeV of permanent magnet increases. With the increase of the permanent magnet thicknesst
m, the permanent magnet volumeV increases. With the increase of axial lengthL
b, the volumeV of permanent magnet increases.Table 5
Range analysis of permanent magnet volumeV.
Variable
r(mm)
t
m (mm)
L
b (mm)
t
i (mm)
K
31
4271600
4752100
4351900
4195400
K
32
4158200
4176400
4182700
4164500
K
33
4112900
3614200
4008100
4182800
k
31
1423867
1584033
1450633
1398467
k
32
1386067
1392133
1394233
1388167
k
33
1370967
1204733
1336033
1394267
R
3
52900
379300
114600
10300Figure 12
Relation diagram of the volumeV 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 meank
i 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 k
i 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 k
i 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
T
m
a
x
P
w
V
Magnet inner radiusr
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Permanent magnet thicknesst
m
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Axial lengthL
b
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
32
> k
33
Axial lengtht
i
k
11
> k
12
> k
13
k
21
> k
22
> k
23
k
31
> k
33
> k
32
Optimal parameter scheme
r
1
t
m1
L
b1
t
i1
r
3
t
m3
L
b3
t
i3
r
3
t
m3
L
b3
t
i2In theory, the maximum magnetostatic torque of all geometric parameter schemes in Table2 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 magnetr: For the maximum magnetostatic torque, it is better to taker
1 as the factor. For eddy current loss and permanent magnet volume, this factor is best taken asr
3. As can be seen from Table 2, when the factor is taken asr
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 isr
3, the value ofr
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 isr
3.(2) Permanent magnet thicknesst
m: For the maximum magnetostatic torque, it is better to taket
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 ast
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 ast
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 ift
m value ist
m1. Therefore, in order to prevent the occurrence of the above phenomenon,t
m value of permanent magnet thickness is determined to bet
m2.(3) The axial lengthL
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 lengthL
b on maximum magnetostatic torque and eddy current loss is relatively small, so the axial lengthL
b is determined to beL
b3.(4) The thickness of the yoke iront
i: For the maximum magnetostatic torque, it is better to taket
i1 for this factor; for eddy current loss and permanent magnet volume, it is better to taket
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 thicknesst
i ist
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 radiusr= 80 mm, permanent magnet thicknesst
m = 8 mm, axial lengthL
b = 144 mm, and yoke iron thicknesst
i = 10 mm. After finite element calculation, the magnetic properties of the optimal scheme are as follows: T
m
a
x = 368 N·m, P
w = 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 Figure9. 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 Table7. 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)
351Figure 15
Manual horizontal torsion tester.As can be seen from Table7, 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 Figure16, 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 Table8. 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


## 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 Table7. 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)
351Figure 15
Manual horizontal torsion tester.As can be seen from Table7, 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 Figure16, 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 Table8. 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 torqueT
m
a
x show that the range sequence of the four factors ist
m
>r>L
b
>t
i, the range analysis results of P
w of eddy current loss show that the range order of the four factors ist
m
>r>L
b
>t
i, and the range analysis results of the volumeV of permanent magnet show that the range sequence ist
m
>L
b
>r>t
i. The thickness of permanent magnett
m has the greatest effect on T
m
a
x, P
w, andV.(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 magnetr= 80 mm, thickness of permanent magnett
m = 8 mm, axial lengthL
b = 144 mm, and thickness of yoke iront
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.



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*Source: 4243020-2019-06-02.xml*