414 Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424

Frontiers of Information Technology & Electronic Engineering www.jzus.zju.edu.cn; engineering.cae.cn; www.springerlink.com ISSN 2095-9184 (print); ISSN 2095-9230 (online) E-mail: [email protected]

Design of a PCB coreless axial flux permanent * based on a novel topology Halbach array

Xiao-yuan WANG, Xiang LI†‡, Chun-peng LI, Si-jia XU, Le-tao LING College of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China †E-mail: [email protected] Received June 2, 2017; Revision accepted Sept. 13, 2017; Crosschecked Mar. 14, 2019

Abstract: A novel topology Halbach permanent magnet array is proposed and applied to the design of a printed circuit board (PCB) axial flux permanent magnet (AFPM) motor. Compared with the traditional coreless AFPM motor, this novel topology for a Halbach permanent magnet array PCB stator AFPM motor has larger air-gap magnetic flux density and air-gap flux per pole. The magnetic flux leakage is effectively reduced, and the air-gap magnetic density is close to the sine wave. Results of the finite element analysis and prototype experiments verify the feasibility and effectiveness of the novel Halbach permanent magnet array PCB stator motor. A reference basis and practical value for the design of the PCB AFPM motor are provided.

Key words: Axial flux permanent magnet synchronous motor; Printed circuit board; Halbach permanent magnet array; Finite element method https://doi.org/10.1631/FITEE.1700345 CLC number: TM351

1 Introduction 2011); thus, the motor servo is good and conducive for batch production (Wu, 2012). However, flux in the An axial flux permanent magnet (AFPM) motor stator coils will be reduced because of the coreless is different from a radial flux permanent magnet stator structure (Zhu et al., 2013); thus, there are many motor because the air-gap flux is along the axial di- design requirements for the air-gap magnetic flux rection and the air gap is in-plane (Tang, 1997). Be- density, and the air-gap magnetic density is close to cause its axial dimension and the winding the sine wave. In contrast to the traditional AFPM inductance are small (Dutta and Rahman, 2008), motor, stator winding of the PCB stator is directly AFPM has received increased attention (Wang et al., printed on the PCB. In a certain area of PCB, the 2007). AFPM motor performs well as a servo motor numbers of turns of stator winding, line width, and and is widely used in electric vehicles (Kumar et al., line distance are different. To give the PCB a certain 2014), wind power (Neethu et al., 2010), aerospace, flow capacity, considering heat dissipation, the PCB and other fields (Fan and Wu, 2010). A printed circuit plate must have a certain thickness; thus, the air-gap board (PCB) stator coreless AFPM motor can greatly length is not too small. Considering the weight of the reduce the weight of the motor with no cogging motor, the cost, and axial length of the stator, the torque (Kumar et al., 2015) or stator iron loss, and can PCB motor should not be too thick. Optimizing the achieve an accurate position of the coil (Yu et al., distribution of poles on the rotor magnetic steel has

become a preferred method to improve the perfor- ‡ Corresponding author mance of a PCB stator motor (Cao et al., 2014). * Project supported by the National Natural Science Foundation of A Halbach permanent magnet array has been China (No. 51577125) ORCID: Xiang LI, http://orcid.org/0000-0002-3022-617x widely used in the design of permanent magnet mo- © Zhejiang University and Springer-Verlag GmbH Germany, part of tors (Galea et al., 2015), and some researchers have Springer Nature 2019 studied this array (Huang et al., 2017). Jiao et al. Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 415

(2017) studied the applicability of the Halbach array central fan shapes, and the main and auxiliary pole on the AFPM motor, the influence of the magnetiza- distributions of the magnet are reasonable. Assume tion angle of this array on air-gap flux density, and the that the amount of permanent magnetic materials does performance of the AFPM motor. A coreless AFPM not change. Thus, the performance of the coreless motor was designed using a Halbach permanent AFPM motor stator of a PCB is optimized. A model magnet array (Zheng et al., 2010). Two-dimensional with 3D electromagnetic field was established using a (2D) simulation results were compared with 3D ones. finite element method (FEM) method to simulate the The influences of 45°, 60°, and 90° Halbach perma- air-gap magnetic flux density and magnetic flux nent magnet arrays on the air-gap magnetic flux den- leakage of the PCB stator coreless AFPM motor. The sity and torque density were analyzed (Ubani et al., fundamental frequency and sinusoidal distortion rate 2016). However, simulation analysis instead of ex- of the air-gap magnetic flux density were analyzed perimental verification was performed. The magnetic and compared with the counterparts of the main vector potential of the Halbach permanent magnet magnetic and auxiliary magnetic poles with different array magnetic field was analyzed and applied to the shapes. A finite analysis simulation verified the ac- coreless permanent magnet synchronous , curacy of the experimental results. Thus, our method showing that the harmonic was significantly weak- can provide a reference basis and practical value for ened and that the amplitude of the back electromotive the design of a magnetic steel structure for PCB stator force (EMF) slightly decreased (Zhang et al., 2013). coreless AFPM motors. The fundamental maximum/minimum amplitude hybrid with a global optimization algorithm for mul- tiple objectives and the sine distortion rate were dis- 2 A PCB stator coreless AFPM motor and a cussed, and the magnetic pole angle and magnetizing novel Halbach array angle of the air-gap flux density waveform of the 2.1 A PCB stator AFPM motor structure fundamental amplitude and harmonic distortion were studied (Fan et al., 2009). In addition, some works In this study, the PCB stator coreless AFPM improved the performance of the AFPM using Hal- motor is a single-stator double-rotor structure (Fig. 1), bach arrays by changing the permanent magnet ma- and the PCB stator is in the middle of the bilateral terials; however, this method will lead to a cost in- magnetic steel. The structure can overcome single- crease of the motor (Luise et al., 2016). The effect of side tension, reduce magnetic leakage, and effectively the motor’s permanent magnet array on different increase the air-gap magnetic flux density. The rotor lengths of the air gap and the thickness of the per- is made of type 45H neodymium iron boron perma- manent magnet on the application of the Halbach nent magnet material. The PCB stator winding uses a were studied by changing only the Halbach perma- three-phase winding with eight layers, and each layer nent magnet array angle instead of the Halbach per- contains 12 coils. manent magnet array shape (Li et al., 2015). Studies 2.2 Structure of a novel Halbach permanent of the Halbach permanent magnet array used in the magnet array AFPM motor focus on the magnetization angle of the magnet steel, the thickness ratio of the magnetic steel, The Halbach permanent magnet array can in- and the back iron. The influence of the shape of the crease the air-gap flux density and ensure the sine array on the air-gap magnetic flux density and mag- waveform of the air-gap density. It can make up the netic flux leakage, especially from the inner and outer negative influence of the coreless structure on the diameters of the rotor, has received little attention. main magnetic circuit flux and effectively increase In this study, we propose a design of a PCB the torque density of the motor. A traditional disk stator coreless AFPM motor rotor structure. Using a motor rotor using a Halbach permanent magnet array novel topology for a Halbach permanent magnet array, is shown in Fig. 2. This design uses a novel Halbach where the pole diameter and outer diameter of the permanent magnet array, which changes the tradi- polar angle parameters are independent, the main and tional Halbach permanent magnet array optimization auxiliary poles are optimized with different method by adjusting the main pole in the inner and 416 Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 outer diameters and the auxiliary pole in terms of arc Table 1 Basic parameters and design requirements of the length, i.e., the angle from the main pole in the inner motor and outer diameters to the center line, for an effect on Parameter Value the novel Halbach array’s motor performance. Com- Rated power 200 W pared with the traditional Halbach array, the novel Permanent magnet material model 45 H Halbach array makes the distribution of the main Thickness of the permanent magnet 8 mm magnetic and auxiliary magnetic poles more reason- Thickness of theback iron 5 mm able on the magnetic steel. The novel Halbach array is Rotor outer diameter 90 mm used in the design of the PCB stator coreless AFPM Rotor inner diameter 52 mm motor, which effectively improves the sine waveform Air- gap length 5 mm of the air-gap flux density and the no-load back EMF Number of turns 8 of the motor. Number of slots 12 Number of pole pairs 8

5 1 Coil 2 Permanent Back iron magnet 4 6

8

3 7

Fig. 1 Schematic of the stator slot

1: stator; 2: permanent magnet; 3: back iron; 4: bearing; 5: supporting member; 6: shaft; 7: shell; 8: prime mover

PCB stator

Fig. 3 PCB stator AFPM motor model

1. The permanent magnet is uniformly magnet- ized, the surface is smooth, and the two permanent can be perfectly combined. 2. Permeabilities of the PCB stator coil and air are approximately equivalent; thus, the PCB stator coil is treated as air when the gap flux density is

calculated without load. Fig. 2 Traditional 90° Halbach permanent magnet array 3. The influence of the rise of temperature on the magnetism of the permanent magnet and performance of the motor is ignored. 3 Design and analysis of the scheme In the design of the PCB stator AFPM motor, the correct selection of rotor size influences the size and 3.1 Scheme design waveform of the air-gap magnetic flux, and the cost To analyze the air-gap flux density, the magnetic and weight of the motor primarily depend on the size flux leakage, and no-load back EMF of the PCB stator of the permanent magnet used by the rotor. Therefore, AFPM motor, a model of the PCB stator AFPM motor the size of the permanent magnet on the rotor disk is established. Parameters of the motor are shown in must be optimized to achieve a sinusoidal distribution Table 1. and a large amplitude air-gap flux density. This is The PCB stator AFPM motor model is shown in achieved by changing the polar angle of the main Fig. 3. Three assumptions are made about the model: magnetic and auxiliary magnetic poles from the inner Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 417 and outer diameters. To ensure that the air-gap flux permanent magnet along the circumferential x axis density is adequate, flux leakage is reduced as much and axial z axis of the motor are Bx and Bz, respec- as possible; thus, the air-gap magnetic density tively, expressed as waveform is close to a sine wave. Compared with other AFPM motors, the PCB 4 π π  = ++αα Bx sin (2 nn 1)  sin (2pp )  , (3) stator coreless AFPM motor has the following ad- (2n + 1)π 22   vantages because of its structure: 1. The stator disk adopting a PCB stator with the 4B 1 Bn= r sin (2+− 1)(1α ) , (4) coreless structure can eliminate cogging torque and z p µ0 (2n + 1)π 2 core loss, improve motor efficiency, and reduce the motor weight. where αp is the polar arc coefficient, and Br is the 2. The magnetic steel disk using the Halbach remanence magnetic flux density of the permanent permanent magnet array in an axial and tangential magnet. combination direction can eliminate the rotor back Using Maxwell’s equation, the air-gap flux den- iron, reduce the rotor weight, and increase the air-gap sity in the axial direction can be expressed as flux density.

3. By arranging the permanent magnetic mate- 2π+1 2πh rial’s size and location in a practical manner, the si- sinxz  cosh m  (2nx+ 1)π ττ   nusoidal distribution of air-gap flux density can be BB= exp , (,)xz r τ πh easily obtained, without increasing the quantity of cosh m d permanent magnetic material, weakening harmonics, τ or reducing torque ripple. (5)

3.2 Parameter analysis where τ is the polar distance, hm the thickness of the 3.2.1 Air-gap magnetic flux density analysis permanent magnet, and d the distance between the permanent magnets on both sides. The air-gap magnetic field of an axial flux motor is a 3D magnetic field, which is difficult to analyze. 3.2.2 Back EMF analysis of motor output Here, the magnetic circuit at the average radius is The PCB stator coil adopted in this study has a analyzed. concentric spiral winding. Because the PCB stator has Assuming that the magnetic material is evenly a coreless structure, the magnetic flux of each wind- magnetized, then we have ing turn is different; therefore, it is necessary to sep- arately analyze each coil.

B=µ0 ( MH + ), (1) For a single turn of the coil, the effective value of the back EMF is expressed as where B is the magnetic flux density, M the magnet- ization intensity, and H the magnetic field strength. Efqm= 4.44Φ , (6) The axial flux is equal to that of a 2D linear motor model. The x axis is along the radius, and the z where f is the frequency of an induced electromotive axis is along the motor axis. The magnetization in- force in a conductor. Φm is the fundamental magnetic tensity function of the Halbach permanent magnet flux per pole of the motor, expressed as array can be expressed as n = 11   ΦmBS max ∑ i , (7) Mab=,BH−+  BH −  (2) i=1 µµxx zz 00   where Bmax is the fundamental amplitude of the where a is the x-axis unit vector and b is the z-axis air-gap flux density, and Si is the effective area of the unit vector. The magnetic flux densities of the ith turn of the coil at the pole. 418 Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424

The entire PCB stator can be considered as a is much smaller than that of PCB winding (especially combination of several turns of concentric coils. at a low speed). Table 2 shows the comparison of the Therefore, the winding coefficient of each turn of the reactance and resistance of PCB winding at different coil can be separately solved and then superimposed. speeds. The effective value of the back EMF for the entire PCB stator is

E=4.44 fN∑ knΦm , (8)

where ∑k is the sum of the winding coefficients of all n turns of the coil, and N is the number of layers of the

PCB winding. Fig. 4 PCB stator winding shape

Table 2 Winding reactance and resistance at different

4 Analysis of finite element simulation speeds results Speed (r/min) X (Ω) R (Ω) X/R 200 0.072 1.521 0.047 4.1 Establishment of the motor solution model 300 0.107 1.521 0.070 and evaluation function 400 0.145 1.521 0.095

In this study, the air-gap flux density of the novel 500 0.174 1.521 0.114 600 0.209 1.521 0.137 Halbach array AFPM motor is simulated and ana- lyzed using the FEM. Because the air-gap flux density of the disc motor continuously changes along the The rotor model of the PCB stator motor is axial direction, the magnetic field of the motor is shown in Fig. 5. Parameters of the novel Halbach three-dimensional. Therefore, we use a 3D FEM to permanent magnet array magnet steel in the rotor are simulate and analyze the magnetic field of the motor. shown in Fig. 6. Since the motor has eight pole pairs The PCB stator has eight plates and 12 coils. To fa- (p=8), the motor is divided into 16 parts with 16 cilitate finite element simulation, each turn conductor central lines, and the angle of each pole of the rotor, in the model is close to itself. The shape of the stator i.e., the angle between two central lines, is 2θ=360°/p. winding of the PCB is between a trapezoid and a Each auxiliary magnetic pole is β1 and β2 in the center circle (Fig. 4). This novel type of winding with cir- of the outer diameter; that is to say, α1+β1=θ satisfies cular winding and ladder winding is advantageous, α2+β2=θ at the same time. In case β1 and β2 can be because the electromotive forces obtained with trap- changed by changing α1 and α2, the distribution of the ezoidal windings are very small and their terminals main magnetic and auxiliary magnetic poles in the are short. This novel type of winding can reduce the Halbach permanent magnet array on magnetic steel winding resistance in the load with a decrease in can be adjusted by changing α1 and α2. copper consumption, thus reducing the temperature. The winding can thus occur due to a large power density, so that the AFPM motor can improve the power density and thereby increase the torque. Armature reaction is an important process in the motor. However, for the PCB stator AFPM motor, the effects of armature reaction are very limited, because the PCB stator winding is without core structure and limited to the PCB plate process. Therefore, the winding turns are few, and the armature reaction is difficult to influence the magnetic field formed by the Fig. 5 Rotor model of the PCB stator motor (pole coeffi- rotor. Thus, the reactance produced by PCB winding cient of the motor is one) Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 419

and outside contours of the permanent magnet are at the same center. The number of pole pairs p in the motor designed in this study is eight. In the conventional axial mag- netic field coreless , the permanent magnet can be magnetized along only one direction, i.e., the axial direction. The rotor of the motor in this study is a 90° Halbach array, and the center angle of each rotor is θ=360°/(2p)=22.5°. Supposing that α1=α2=α and β1=β2=β, then α+β=22.5°. Fig. 6 Schematic of a novel Halbach permanent magnet A 3D electromagnetic field model is established array magnet steel L and l are the length of the arc of the outer and inner diam- by changing α, and the FEM is used to simulate the eters between two central lines of the magnet steel, respec- model. The relationship between the flux per pole and tively. R and r are the outer and inner diameters of the magnet the fundamental magnitude of axial flux density is steel, respectively. α1 and α2 are the angles between the inner shown in Table 3. magnetic pole and the outer diameter between the central line, respectively Table 3 Relationship between the flux per pole and fun- damental magnitude of axial flux density In the design of the AFPM motor, the air-gap Angle of the Fundamental wave flux density has a direct influence on the back EMF main mag- Air-gap flux per amplitude of axial and output torque of the motor; that is to say, the sine netic pole pole (×10−4 Wb) magnetic flux waveform of the air-gap flux density can reflect the (°) density (T) flux leakage of the motor. Therefore, an evaluation 7.25 1.34 0.868 function including the fundamental magnitude of the 9.25 1.38 0.920 air-gap magnetic flux density and amplitude of each 11.25 1.45 0.945 sub-harmonic is used as the main evaluation param- 13.25 1.41 0.931 eter to evaluate the feasibility of the novel Halbach 15.25 1.39 0.884 permanent magnet array magnet steel, expressed as Table 3 shows that when the air-gap flux per pole B increases, the fundamental magnitude of the air-gap F = z1 , (9) BBB222++ flux density at the mean radius of the PCB stator axial zzz357 flux machine increases as well. Therefore, in the following analysis, the fundamental amplitude and where Bz1 is the fundamental amplitude of the air-gap the sine of the axial air-gap flux density are the main flux density along the axial direction, and Bz3, Bz5, and rd th parameters to evaluate the feasibility of the magnet Bz7 are the axial magnetic flux densities for the 3 , 5 , th steel in the novel magnet array. Air-gap flux density and 7 harmonic amplitudes, respectively. for the pole angle changes with α at the average radius 4.2 Influence of equal polar angles at the inner (Fig. 7). Changes in the evaluation function for dif- and outer diameters of the air-gap magnetic flux ferent α are shown in Table 4. density Table 4 Values of evaluation functions corresponding to different α As permanent magnet price increases, to main- Angle of the main tain the permanent magnet condition and quality, the Value of the evaluation axial and tangential magnetization of the permanent magnetic pole (°) function (F) 7.25 9.883 magnet can be altered by changing the angle between the main and auxiliary poles and the center line as 9.25 10.734 11.25 11.121 much as possible to increase the air-gap flux density. 13.25 10.941 When the polar angles of the inner and outer diame- 15.25 10.018 ters of the permanent magnet are the same, the inside

420 Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424

1.0 Comparing the optimal conditions of the design of the 11.25° 13.25° Halbach permanent magnet array auxiliary PCB sta-

0.5 9.25° tor pole ratio of the coreless motor, the magnetic flux 15.25° density of the fundamental amplitude increased by 7.25° 14.5%, and the 3rd harmonic content was weakened. 0 30 90 150 210 270 330

Shaded plot Bz −0.5 smoothed Air-gap flux density (T) 1.4643400 1.1740100 0.8836820 −1.0 Electrical angle (°) 0.5933540 0.3030250 0.0126966 Fig. 7 Distribution of air-gap magnetic density at the −0.277632 mean radius of different α −0.567960 −0.858289 −1.148620 Fig. 7 shows that the air-gap flux density reaches −1.438950 its maximum when α=11.25°, i.e., α=β=θ/2. It can also be derived from the values of evaluation function Fig. 8 Distribution of magnetic flux density of the motor F in Table 4, and the fundamental wave has the rotor highest energy ratio. Simulation results show the 1.0 following: Analytic method Finite element method 1. From the synthetic waveform of the axial air- 0.5 gap flux density at the mean radius, the amplitude of the air-gap flux density at α=11.25° is larger than 0 30 90 150 210 270 330 those at α=9.25° and α=13.25°; however, the ad- −0.5 vantage of flux density at α=11.25° is not significant.

2. The evaluation function F, i.e., the funda- Air-gap axial flux density (T) −1.0 mental wave energy ratio, is higher at α=11.25° than Electric angle (°) those at α=9.25° and α=13.25°. Fig. 9 Air-gap flux density waveform We can conclude that when the main pole angle is α=11.25°, i.e., the pole angle of the axial magnetic 100 permanent magnet is equal to that of the tangential magnetized permanent magnet, the air-gap flux den- 80 sity reaches its maximum and the magnetic harmonic 60 component is the smallest. The magnetic flux density distribution on the 40 rotor of the motor is shown in Fig. 8. The maximum

Harmonic content (%) 20 magnetic flux density of the magnet steel is 1.263 T. The analytical results of axial air-gap magnetic flux density and the simulation results are shown in Fig. 9. 0 1 3 5 7 9 11 Harmonic frequency

Fig. 9 shows that the results of the two methods are consistent with a maximum error of 0.037 T. This Fig. 10 Harmonic analysis of the air-gap flux density error is cased by the edge effect of the magnetic field. The fundamental and subharmonic components of the 4.3 Influence of different polar angles at the inner axial air-gap flux density are shown in Fig. 10. and outer diameters of the air-gap magnetic flux In the case of the same permanent magnet, the density fundamental magnitude of the magnetic flux density of the conventional axial magnetic field coreless PM To increase the ratio of the permanent magnetic motor was 0.825 T, and the 3rd and 5th harmonic material, the influence of the shape and distribution of components were 0.065 T and 0.061 T, respectively. the permanent magnet on the air-gap flux density is Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 421 studied, when the inner and outer diameters of the the reduction in the inner diameter in the arc length of permanent magnet, i.e., the center diameters of the the gas can be accounted for. The air-gap flux density permanent magnet, are different. By changing the is effectively increased and the magnetic leakage is center angle of the Halbach permanent magnet in the reduced. The reduction of the polar angle of the axial inner and outer diameters, α1, α2, β1, and β2 are magnetized permanent magnet at the inner diameter changed, and the shape of the Halbach permanent and the increase in the polar angle at the outside di- magnet and the distribution of the magnetic steel are ameter are both approximately 2°. changed as well. Fig. 11 shows the fundamental am- When α1=9.25° and α2=13.25°, the value of plitude of the axial air-gap flux density when the evaluation function F reaches its maximum. The flux center of the permanent magnet is changed at the density distribution is shown in Fig. 12 for the posi- inner and outer diameters. tion of the motor magnetic air-gap at this time.

0.98 0.96 1 0.94 0.92

amplitude (T) 0.90 0 fundamental wave Air-gap flux density 13.25 15.25 11.25 11.25 13.25 Angle at the inner9.25 diameter 7.25 9.25 of the main magnetic pole (°)7.25 −1 360 Angle at the outside diameter 45.00 Axial air-gap flux density (T) 270 40.25 of the main magnetic pole (°) Electrical angle180 (°) 35.50 90 30.75 26.00 Fig. 11 Fundamental amplitude of the air-gap flux density 0 Radial distance (mm) with the center angle

Fig. 12 Air-gap flux density at different radial positions Fig. 11 shows that when α1=9.25° and α2=13.25°, and electrical angles the air-gap flux density of the fundamental amplitude reaches its maximum approximately at 0.973 T. Table As shown in Fig. 12, the air-gap flux density 5 shows the values of evaluation function F when α1 increases and then decreases along the radius direc- and α2 have different values. tion, showing a sinusoidal trend along the circum- ferential direction. In this case, the fundamental Table 5 Values of the evaluation function when α and α 1 2 magnitude of the air-gap flux density and the mag- have different values nitude of each subharmonic wave were compared α (°) α (°) Value of evaluation function (F) 1 2 with the optimum results in Section 4.2. The contrast 7.25 13.25 11.203 diagram at α=11.25° is shown in Fig. 13. 7.25 15.25 11.151

9.25 13.25 11.310 1.0 9.25 15.25 11.136 Result of Section 4.3

13.25 9.25 10.574 0.8 Result of Section 4.2

15.25 9.25 10.477 0.6

0.4

Table 5 shows that when α1=9.25° and α2=13.25°, amplitude (T) the value of evaluation function F reaches its maxi- 0.2 mum. When α1<θ/2 and α2>θ/2, the value of evalua- 0 Axial air-gap magnetic flux density tion function F is larger than the optimization results 0 1 3 5 7 9 in Section 4.2. Thus, for a PCB stator coreless AFPM Harmonic frequency motor with a Halbach permanent magnet array in the Fig. 13 Comparison of the amplitudes of the fundamental axial magnetized permanent magnet and tangential wave with each sub-harmonic magnetized permanent magnet for equal central angle width, the axial magnetized permanent magnet can be Fig. 13 shows that the novel Halbach permanent increased in the outer diameter of the arc length, and magnet array has a larger fundamental harmonic 422 Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 amplitude and a smaller harmonic content compared with the optimal result of the Halbach permanent magnet array with the polar angles including the inner and outer diameters in Section 4.2. The magnetic density distribution of the novel Halbach array is shown in Fig. 14.

Fig. 15 PCB stator prototype and prime mover with a PCB stator

Shaded plot Bz smoothed 1.42725 1.13924 0.851227 0.563216 0.275205 −0.0128061 −0.300817 −0.588828 −0.876839 −1.16485 −1.45286

Fig. 14 Magnetic flux density distribution of the novel Fig. 16 Experimental platform

Halbach permanent magnet array

18 In summary, for a PCB stator AFPM motor with a novel Halbach permanent magnet array to ensure a 15 permanent magnet quantity, the fundamental ampli- 12 tude of air-gap flux density increased by 17.9% compared with the traditional coreless axial motors. 9 Experiments Voltage (V) Compared with the optimal results obtained for the FEM Halbach permanent magnet array with polar angles 6 including the inner and outer diameters described in 3 Section 4.2, the fundamental amplitude of the air-gap 200 250 300 350 400 450 500 550 600 flux density approximately increased by 3%; however, Speed (r/min) the amount of the odd harmonics, especially the three Fig. 17 Comparison between the measured values of harmonics, was reduced. no-load EMF amplitude and the simulation results at different speeds

5 Experiments The PCB stator AFPM motor was driven at a speed of 500 r/min by a coupling. No-load back EMF To verify the feasibility and accuracy of the de- waveform of the PCB stator AFPM motor was sign method and apply the novel Halbach array to measured by an oscilloscope. Experimental results verify the no-load back EMF of the motor, a prototype are shown in Fig. 18a. The dynamic simulation results is required to carry out an experiment. The prototype obtained using a 3D FEM are shown in Fig. 18b. and DC prime mover with a PCB stator are shown in Fig. 18 shows that the experimental and simulation Fig. 15. The test platform is shown in Fig. 16. waveforms basically follow a sinusoidal distribution, In this experiment, we used a power-driven and the two waveforms are in good agreement; 200 W DC motor as the prime mover. The amplitudes therefore, the finite element analysis calculation of the no-load EMF at different speeds were com- model and analysis method established in this study pared with the simulation results (Fig. 17). are reasonable. Wang et al. / Front Inform Technol Electron Eng 2019 20(3):414-424 423

16 permanent magnet motors, in the PCB stator motor, the magnetic flux density increased by 14.5%.

8 In the novel Halbach array, when assuming the magnetic pole’s inner and outer diameters and the polar angle as independent variables, it is appropriate 0 to increase the polar angle at the outer diameter and Voltage ( V ) reduce the polar angle at the inner diameter of the −8 main pole, which can further increase the air-gap flux

(a) density and reduce the magnetic leakage. For the PCB −16 stator AFPM motor designed in this study, this am- 0 7.5 15.0 Time (ms) plitude was approximately 2°, and the fundamental

15 amplitude of air-gap flux density increased by 3%. The simulation results for the motor were in 10 good agreement with the experimental results, 5 showing that the finite element analysis model and the 0 analysis method established in this study are 2.5 5.0 7.5 10.0 12.5 15.0

Voltage ( V ) reasonable. −5

−10 (b) References −15 Cao YJ, Huang RK, Jin L, et al., 2014. Design and analysis of a Time (ms) stator coreless axial-flux permanent magnet machine with

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