Analysis and Design Optimization of Axial–Radial Flux Hybrid Excitation Permanent Magnet Eddy Current Coupling

This paper proposes an axial–radial flux hybrid excitation permanent magnet eddy current coupling (HE-PMEC), where the ferrite magnet is employed for producing the radial flux and the DC excitation current is adopted for producing the axial flux. Moreover, a shielding layer is developed to regulate the radial magnetic field. Its magnetic field distribution, electromagnetic performance, and temperature distribution are calculated based on the 3D finite element method (FEM). By adjusting the applied DC excitation current density and the insertion depth of the shielding layer, the variable current starting process, the variable current braking process, and the speed regulation characteristic of the proposed HE-PMEC are obtained. It can be seen that the starting process, braking process, and speed regulation ability of the HE-PMEC have been enhanced greatly. Furthermore, the copper ring shape of the HE-PMEC is optimized by using the proposed improved multilevel optimization method. It can be seen that the performance of the HE-PMEC can be improved by using the new optimized copper ring shape. Lastly, compared with the conventional PMECs, the proposed HE-PMEC has shown its superior electromagnetic performance.


Introduction
Traditional gears or couplings require a mechanical connection to transfer torque, however, when the shaft is overloaded, it faces the risk of being broken, which puts the safety of the equipment at risk.Permanent magnet coupling (PMC) makes it possible to transfer the torque in a noncontact way.Moreover, when the torque is exceeded, the loading equipment can be protected by the magnetic slip [1,2].The absence of mechanical wear is another benefit of PMC.The vibration that is felt on the shaft will be amplified step by step due to the mechanical connection.While in the PMC, the amplification of shaft vibration can be avoided through the non-contact connection.Therefore, the service life of the coupling can be prolonged.
Permanent magnet eddy current coupling (PMEC) is one of the PMCs that possesses all of the benefits of PMC.It consists of a primary rotating disc with a permanent magnet (PM) and a load rotating disc with a copper ring.When the primary rotating disc is propelled by a prime mover, a rotating magnetic field will be resulted from the PM and pass through the copper ring.Therefore, the corresponding eddy current will be produced in the load rotating disc, allowing for the production of the so-called armature magnetic field.Therefore, the electromagnetic torque can be generated via the interaction between the copper ring eddy currentinduced magnetic field of the armature and the PM magnetic field.The copper ring and PM design determine the PMEC's performance [3][4][5].
The mechanism of a conventional disc type permanent magnet eddy current drive was first proposed by A. Wallace and C. Wohlgemuth in 1995, and thus the first PMEC has manufactured.A. Wallace also proposed the variable-speed disc type PMEC in 2001 [6,7].For the PMEC, two distinct structures were developed in the past decades, including the axial flux PMEC and the radial flux PMEC [8,9].The axial flux PMEC has capable of maximizing magnetic flux utilization and thus the high torque ability can be achieved.The magnetic flux can be regulated by inserting a shielding layer in radial flux PMEC, therefore the speed can be regulated more straightforwardly.For the conventional PMEC, the PM is mounted on the surface of the primary rotating disc.The PM will be subjected to centrifugal force, therefore the conventional PMEC cannot be employed for high speed drive application.By installing the PM in the rotating disc, the mechanical strength of the PMEC has been improved greatly, therefore it can be employed for high speed operation.[10].Meanwhile, for improving the performance of the PMEC, the PM designed with the Halbach array is proposed [11].
To obtain the electromagnetic performance of the PMEC, the analytical method was extensively investigated in the past.The 3D magnetic structure of the PMEC is simplified with the 2D magnetic circuit for the magnetic field calculation and performance prediction, and the combination of the analytical method and the finite element method (FEM) was proposed [12][13][14][15][16].The eddy current loss produced in the copper ring is the main heat source of PMEC, and obtaining the accurate eddy current loss is the basis for the temperature field calculation.For computing the eddy current loss accurately, combining a 3D analytic eddy current field calculation model with the 3D FEM is an effective way [17].The electric-magnetic-thermal coupling method was proposed for determining the stable long-term temperature of PMEC components precisely [18,19].
PMEC has been successfully employed in pumps, fans, conveyor belts and other motor drives in power generation, metallurgy, petrochemical, water treatment, and other industries.PMEC is mainly utilized in blower and water feeder drive systems where the speed must be variable.The manner in which a converter is used to manage the speed is heavily influenced by the surrounding environment.When driving a high-temperature or high-pressure corrosive load, converter maintenance is a challenging issue.Meanwhile, the switching loss and conduction loss of the converter reduce the energy conversion efficiency.Through experimental verification, compared with the converter, the adjustable speed PMEC has the advantages of low loss, highly reliable operation, and low vibration noise [20].However, the performance of PMECs in speed regulation has been given little attention in the past, as conventional PMECs have some structural disadvantages.By changing the coupling depth, the speed of the traditional axial flux PMEC can be regulated, whereas by varying the shielding layer insertion depth the speed of the radial flux PMEC can be controlled.Traditional PMEC is plagued by the following issues [21]: • Imprecise speed regulation • Lagging speed regulation • narrow speed regulation range • Large installation space • Low space utilization In this paper, an axial-radial flux hybrid excitation permanent magnet eddy current coupling (HE-PMEC) is proposed.Both the axial and radial air gap are employed for the energy conversion, therefore, the space utilization and the performance of the proposed HE-PMEC can be enlarged when compared with the PMEC.The axial magnetic field is produced by a DC excitation current, whereas the radial magnetic field is produced by a ferrite magnet.Consequently, compared with the PMEC which is only excited by the PM, the proposed HE-PMEC can achieve superior starting and braking performance, as well as a greater capacity for speed regulation.
The structure of this paper is as follows: Sect. 2 explains HE-PMEC's construction and parameters.Section 3 examines the magnetic field distribution, presents the variable current starting and braking curves and speed regulation performance, and validates the temperature stability of HE-PMEC.Section 4 examines the effect of the axial pole number and radial pole number on the maximum load torque, and a new improved multilevel optimization technique is proposed to optimize the copper ring shape.In Sect.5, the main performance of the proposed HE-PMEC is compared with PMECs of different structures: single radial flux (SRE), single axial flux (SAE), dual radial flux (DRE), dual axial flux (DAE), axial-radial NdFeB permanent magnet flux (ARNE), and axial-radial ferrite flux (ARFE), and HE-PMEC.The final section is the conclusion.

Structure of HE-PMEC
The structure of the HE-PMEC can be seen in Fig. 1, and it consists of two primary electromagnetic parts: the first is the primary rotating disc, which is connected with the prime mover, and both the PM and the shielding layer are located on the primary rotating disc; the second is the load rotating disc, which is connected with the load, and it is the location of the copper ring and the side wall.
The detail of the primary rotating disc and the load rotating disc are shown in Fig. 2. Figure 2(a) shows the primary rotating disc.The ferrite magnet is employed to produce the PM magnetic field in the radial air gap.Specifically, the ferrite magnets are magnetized along the radial direction and the magnetization direction of the adjacent PMs is opposite.Meanwhile, the DC winding is taken to produce the axial air gap magnetic field.Therefore, both the axial air gap and radial air gap can be employed for the electromagnetic energy conversion and both the PM and DC excitation current can be adopted for producing the magnetic field.Figure 2(b) shows the load rotating disc, which includes the radial copper ring and axial copper ring which mounted on the inner surface of the load rotating disc.
The stainless steel shielding layer can be inserted and removed between the copper ring and the PMs, which can play the role of insulating the copper ring from the magnetic field generated by the ferrite magnet.There is no eddy current resulted in the shielding layer since it rotates at the same speed as the primary rotating disc, without relative displacement.
Table 1 tabulates the main parameters of HE-PMEC.The HE-PMEC proposed in this paper is applied to the blower load, for which a rated torque of around 20 Nm is required.Considering the safety of operation, the maximum torque is set at 30 Nm. Within the mechanical strength of the coupling shaft, it is possible to arbitrarily determine the rotational speed of the prime mover.In this article, 1500 rpm is used.3 Performance Analysis of HE-PME

Magnetic Field Analysis
For the magnetic field analysis and performance calculation, the JMAG transient electromagnetic field analysis module based on the 3D FEM is used.Figure 3 illustrates the noload magnetic flux density distribution (no relative rotation between the primary rotating disc and the load rotating disc).
As shown, the maximum magnetic flux density in the radial copper ring is around 0.27 T, while the maximum magnetic flux density in the axial copper ring is approximately 0.43 T.
Figure 4 shows the distribution of magnetic flux density on each component of HE-PMEC under the rated load condition ( the loading speed is 1451 rpm, and the load is dragged for 30 Nm).The maximum magnetic flux density in the radial copper ring is around 0.34 T, while the maximum magnetic flux density in the axial copper ring is approximately 0.32 T.
Under the rated load state, the magnetic flux density on the radial copper ring and the axial copper ring is comparable, as indicated.Under load operation, the magnetic density of the axial copper ring decreases compared with that under the no-load operation, while the magnetic density of the radial copper ring increases.The eddy current in the radial copper ring strengthens the magnetic field, whereas the eddy current in the axial copper ring weakens the magnetic field.
Figure 5 illustrates the magnetic flux density distribution in the axial and radial air gaps under rated load and no load.Figure 5(a) and (b) depict the radial air gap magnetic density distribution before and after load operation.As shown, the eddy current distributed on the radial copper ring enhances the air gap magnetic field.Figure 5(c) and (d) depict the magnetic density distribution in the axial air gap before and after load operation, respectively.It can be seen that the eddy current resulted in the axial copper ring reduces the axial air gap magnetic field.

Starting Process Analysis
The starting torque can be regulated flexibly during the starting process in the HE-PMEC.The relationship between starting torque and speed is determined by,  where, J is the mechanical moment of inertia, ω L is the mechanical angle velocity of the load shaft, θ L is the mechanical angle of the load shaft, T e is the electromagnetic torque provided by the load rotating disc, T L is the load torque, D is the torque damping coefficient, K is the torsional elastic torque coefficient.
If the damping torque and torsional elastic torque are ignored, the above equation can be simplified as, According to the operating characteristics of PMEC, Eq. ( 2) can be written as, where, GD 2 is the moment of inertia, n is the rotational speed of the load rotating disc, and T start is the starting torque of HE-PMEC.
According to Eq. ( 3), the starting process is determined by the starting torque, and the higher the starting torque, the faster the speed of the load shaft rises.The relationship between the starting torque and the force on the shaft is determined by, where a n is the acceleration of the load shaft.
As shown, as the starting torque increases, the force on the shaft increases as well.However, the force on the shaft may be caused to exceed the mechanical limit if the acceleration process is too fast.The maximum starting torque(MST) is related to the diameter of the shaft and the material, in this paper, we use a 24 mm diameter No.45 steel shaft, so MST is set to 191Nm.
Figure 6 illustrates the torque of the HE-PMEC at various load shaft speeds and DC winding current densities.To provide a speedy and gentle starting process, the shielding layer is not put between the PM and copper ring.As demonstrated, during the starting procedure, torque increases before decreasing.MST is approximately 97.3 Nm when the DC excitation current is around 8 A/mm 2 .Increasing the DC excitation current density enhances the starting torque.As load speed increases, the torque steadily declines until it reaches the rated value of 30 Nm at 1435 rpm.
During the starting process (speed increasing from 0 to rated), the torque increases first and then decreases.The blue curve shown in Fig. 6 is the starting curve with a DC excitation current density of 8 A/mm 2 .The red curve shows the torque versus the speed when the speed varied from 0 to 700 rpm and the DC excitation current density equals 20 A/mm 2 , and the torque when the speed increases from 700 to 1200 rpm and the DC excitation current density falls progressively.As illustrated in Fig. 6, when the speed increases from 1200 to 1348 rpm, the DC excitation current density should be increased gradually to maintain a starting torque of 182 Nm.Maintaining a DC excitation (4) current density of 20 A/mm 2 until boosting speed to rated.Finally maintain 8 A/mm 2 rated operating current.By adjusting the DC excitation current, the average torque and MST of the HE-PMEC can be increased to 179 Nm and 182 Nm, respectively, which are significantly greater than keeping a constant current of 8 A/mm 2 .Consequently, by using the variable current starting (VC starting) method, the HE-PMEC is with superior starting performance compared to other PMECs.The red curve is the VC starting curve.

Speed Regulation Process
The speed can be regulated by changing the insertion depth of the shielding layer or the DC excitation current.Figure 7 illustrates the effect of shielding layer insertion depth and DC excitation current on speed regulation.Considering that the load torque of HE-PMEC is fixed constantly.When the shielding layer is completely absent and the maximum DC excitation current density is 20 A/mm 2 , the maximum load speed can reach 1451 rpm.The rotational speed will decrease as the DC excitation current decreases or the insertion depth of the shielding layer increases.
Under the rated DC excitation current density (8 A/mm 2 ), the load shaft speed without the shielding layer inserted between the radial PM and the copper rings is approximately 1435 rpm.When the shielding layer is fully placed in between the radial PM and the copper ring, the load shaft speed can be decreased to 1267 rpm, with a speed regulation range of around 168 rpm.When the DC excitation current density is 0 A/mm 2 , the lowest possible speed is 1082 rpm, and the speed regulation range is around 308 rpm.
If the shielding layer's insertion depth remains unchanged, the speed can be controlled by adjusting the DC excitation current.Specifically, the load shaft speed decreases as the DC excitation current diminishes.Meanwhile, the speed regulation range expands as the insertion depth of the shielding layer grows.By adjusting the DC excitation current and the insertion depth of the shielding layer, the adjustable speed range and the speed regulation range of the HE-PMEC are 1082 rpm to 1451 rpm and 369 rpm respectively.
Figure 8 illustrates the variation of speed regulation range from the rated load torque of 30 Nm to the load torque of 5 Nm.As illustrated, as the load torque reduces, the maximum speed increases, however, the minimum speed also increases, and then the speed regulation range steadily decreases.

Braking Process
Braking is another key function of the HE-PMEC.When the prime mover's rotor shaft is fixed, the braking torque can be produced to progressively halt the load rotor shaft.The relationship between braking torque and speed during the braking process can be expressed by, where, T stop is the braking torque of HE-PMEC.The relationship between the rising speed of braking torque and the decline of speed can be expressed by, As starting torque, an increase in braking torque also leads to an increase in force on the rotating shaft.The maximum braking torque (MBT) is set to the same value as the MST to protect safe operation.The DC excitation current density must be regulated to provide a rapid and smooth braking action.
Figure 9 shows the braking curve of the HE-PMEC when the insertion depth of the shielding layer is 0 mm.As shown, the greater the DC excitation current, the greater the braking torque can be produced.The blue curve shown in Fig. 9 (5) GD 2 375

Temperature Field Analysis
The torque provided by HE-PMEC is the result of the interaction between the magnetic field produced by the PM and DC excitation current and the magnetic field produced by the eddy currents on the copper rings.The resulting eddy currents are the primary heat sources, and the resulting significant temperature rise poses a very high demagnetization risk for the PM; hence, thermal analysis is crucial for the design and study of HE-PMEC.The computed core loss and eddy current loss serve as the basis for the thermal field analysis, and Fig. 10 illustrates the coupling flowchart.2. As illustrated, the temperature of the axial copper ring is 55.5 ℃, the temperature of the radial copper ring is 56.4 ℃, the highest temperature of the axial flux core is 153.7 ℃, and the temperature of radial flux PM is 86.7 ℃.As the Curie temperature of the ferrite magnet is about 300 ℃, and its performance will be decreased greatly when its working temperature is over 100 ℃, the ferrite magnet worked in the proposed HE-PMEC can work safely.

Structural Design Optimization
The axial pole number (APN) and radial pole number (RPN) are critical for determining the main performance of HE-PMEC. Figure 12 illustrates the maximum load torque and PM temperature of the HE-PMEC with different APN while RPN equals 12.As shown, when RPN equals 12, the maximum load torque increases as the APN increases.However, when APN equals 14, the maximum load torque improves slightly compared to when APN equals 12, however the PM temperature increases significantly.In particular, the PM temperature of HE-PMEC with a 12/14 structure is 19.1% higher than that of HE-PMEC with a 12/12 structure, while the maximum load torque is 3.06% greater.Consequently, HE-PMEC with a 12/12 structure is determined for the study in this paper.

Optimization of HE-PMEC
The magnetic field distribution generated by the eddy current is determined by the magnetic flux density distributed on the copper ring.Therefore, it is vital to optimize the copper ring's shape in order to improve the torque performance of HE-PMEC.The magnetic flux density pattern of HE-PMEC without the shielding layer is shown in Fig. 13.Since the increase in temperature will decrease the performance of the HE-PMEC, the optimization focuses on achieving a balance between the resulting eddy current and heat dissipation.
As shown in Fig. 13, the magnetic flux density spread on the copper rings generates an eddy current that is circularly distributed between two adjacent poles.This phenomenon is referred to as an eddy current ring.In this paper, the shape of the eddy current ring is optimized.
The parameters for determining the copper ring forms of HE-PMEC are illustrated in Fig. 14.The air ring is designed near the center of the copper ring, where the magnetic flux density and eddy current are both extremely low, and the copper ring's shape is determined by its position and the corresponding eight parameters as depicted in Fig. 14.The design range of these parameters is shown in Table 3.  Copper consumption and temperature rise on PMs are chosen as optimization objectives, and DC current density, load speed, and maximum load torque as the constraints.Initially, the copper rings of the HE-PMEC do not have grooves.The optimization model is shown as follows, where, W cu and W cu0 are copper consumption and initial copper consumption respectively, T PM and T PM0 are PM temperature rise and initial PM temperature rise respectively, J c is the DC excitation current density, Speed load is the load speed, and T max is the maximum load torque.
Using intelligent optimization algorithms (such as a multi-objective genetic algorithm) for the design optimization of the above model directly is very difficult, due to there are 8 parameters need to be optimized.In order to reduce the optimization time, the multilevel optimization approach is employed.In this research, a new technique is proposed to further enhance the optimization result and efficiency of the multi-level optimization strategy.The flowchart of the enhanced new optimization technique is depicted in Fig. 15.
Step 1 Generate an experiment matrix with 8 parameters based on the Hyperlatin Cube method, and construct the surrogate model based on the obtained training set from the 3D FEM calculation results, then calculate the sensitivity of   Step 2 Divide the high-dimensional optimization problem with 8 parameters into three low-dimensional optimization problems with less than 3 parameters through sensitivity analysis.
Step 3 Optimize each low-dimensional optimization problem sequentially based on the multi-objective genetic algorithm, and the parameters with high sensitivity are optimized first.
Step 4 After optimizing all the parameters, the sensitivity of parameters are recalculated, and Step 2 and 3 will be done again.
Step 5 Repeat the optimization process until the target error of the two optimization cycles is within 1%.
Due to the recalculation of the parameter sensitivity, the second round of optimization has a more reasonable ranking and faster convergence can be achieved compared with the traditional multilevel optimization.
Table 4 illustrates the design parameters for the various low-dimensional optimization processes.It can be seen that several design parameters are re-ranked, during the second round of optimization, while L 1 and L 4 continue to be the two parameters with the highest sensitivity.Table 5 tabulates the parameter values before and after each level's optimization.
Figure 16 illustrates the structure and the magnetic density distribution of the two copper rings of the optimized HE-PMEC.As illustrated, the magnetic flux density distribution of the optimized HE-PMEC is more concentrated.Table 6 shows the copper consumption, maximum load torque, maximum temperature of axial and radial copper rings, permanent magnet temperature, and speed regulation range of HE-PMEC before and after optimization.After optimization, the maximum temperature of the copper ring and PM decreases significantly.In the meantime, copper consumption falls from 4.81 kg to 4.33 kg.However, both the maximum load torque and the speed regulation range are slightly reduced.Figure 18 shows the starting and braking curves comparison between these PMECs and HE-PMEC.
As shown, SRE and DRE have the lowest starting torque and braking torque, whereas DAE and SAE have greater starting torque and braking torque, respectively.Due to the high remanence of NdFeB, ARNE is able to  The speed regulation range of these PMECs is depicted in Fig. 19.As shown, the greatest speed regulation range for HE-PMEC occurs when the DC excitation current density is less than 20 A/mm 2 .As the insertion depth of the shielding layer can be adjusted flexibly, PMECs with radial flux structure can have excellent speed regulation performance and a broad speed regulation range.For the PMECs with axial flux structure, adjusting the air gap distance between the primary rotating disc and the load rotating disc may regulate the speed of the load shaft.However, the speed regulation range is narrow.The speed regulation range of DRE is greater than that of SRE, however, the speed regulation range of DAE and SAE are comparable.ARFE's speed regulation range is significantly greater than ARNE's.From the viewpoint of speed regulation, NdFeB is also inappropriate for the PMEC poles.
As shown, among these PMECs.ARNE has the maximum speed, and the lowest speed that can be adjusted is greater than the maximum speed of all other PMECs.HM-PMEC has the largest speed regulation range.The maximum speed that can be adjusted by HE-PMEC is only second to ARNE, and the minimum speed that can be adjusted is the smallest of all PMECs.

Conclusion
A HE-PMEC is proposed and analyzed in this paper.The ferrite magnet is adopted for producing the radial magnetic field and the DC excitation current is employed for producing the axial magnetic field.Moreover, the shielding layer is developed for adjusting the radial magnetic field.As the axial magnetic field is produced by the DC excitation current, therefore the starting and braking performance, and the speed regulation range of the HE-PMEC can be controlled flexibly.By comparing the calculated no load and rated load magnetic flux density in the axial and radial air gap, it can be seen that the axial air gap flux density will be reduced while the radial air gap flux density will be enhanced when the HE-PMEC is under loading.Moreover, the axial and radial air gap flux density are comparable when the HE-PMEC is under rated loading state.Through the temperature field analysis, it can be seen that the temperature rise is within the allowable range and has large design redundancy.For the design optimization, an improved multilevel design optimization is proposed, it can be seen that the heat dissipation can be increased and the temperature rise can be reduced by deleting some copper in the copper ring.Compared with other PMECs, HE-PMEC shows better starting and braking performance and more wide speed regulation range, as both the radial PM magnetic field and the axial magnetic field can be regulated.

Fig. 2 a
Fig. 1 Structure of HE-PMEC of the radial permanent magnet 335 mm The circumferential angle of radial PM 20 deg Number of axial flux core sections 12 -The sectional area of the axial flux coil 370 mm The outer diameter of the axial flux core 300 mm The inner diameter of the axial flux core 236 mm

Fig. 3
Fig. 3 No load flux density distribution a on the axial flux structure and b on the radial flux structure

Fig. 4
Fig. 4 Rated load flux density distribution a on the axial flux structure and b on the radial flux structure

Fig. 5 aFig. 6
Fig. 5 a No load radial air gap flux density distribution, b rated load radial air gap flux density distribution, c no load axial air gap flux density distribution, and d rated load radial air gap flux density distribution.

Fig. 7
Fig. 7 Speed regulation curve of HE-PMEC Fig. 8 Speed regulation range under different load torque

Figure 11 Fig. 9 Fig. 11 a
Figure 11 illustrates the temperature of each component of HE-PMEC during stable long-term operation (temperature rise of no more than 1 ℃ per hour).The temperature of

Fig. 12 a
Fig. 12 a Maximum load torque versus the APN b Temperature of permanent magnet versus the APN

Fig. 13 Fig. 14
Fig. 13 Magnetic flux density on the radial and axial copper ring

Fig. 15
Fig. 15 Flowchart of multi-level sequential optimization strategy

Fig. 16
Fig. 16 Optimized magnetic density distribution of copper ring

Fig. 17 Fig. 18 a
Fig. 17 PMEC with different structures a SRE b SAE c DRE d DAE e ARNE fARFE

Table 1
Main Parameters of HE-PMEC

Table 3
Parameters of HE-PMEC

Table 4
Parameters for different

Table 5
Value