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Nov 13, 2018 - Instead of a classical Halbach array with only radial and axial PMs, the proposed .... 26,182 nodes, 2607 line elements and 13,601 surface elements. ... experiments, with an average deviation of only 4.8%, the results of the ... measured at nearly 39.3 o, in the experimental setup, only 39 o of the load ...
energies Article

Improvement of Tubular Permanent Magnet Machine Performance Using Dual-Segment Halbach Array Minh-Trung Duong 1,2 , Yon-Do Chun 1,2, * and Deok-Je Bang 2 1 2

*

Energy and Power Conversion Engineering, University of Science and Technology, Daejeon 34113, Korea; [email protected] Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon 51543, Korea; [email protected] Correspondence: [email protected]; Tel.: +82-055-280-1490

Received: 15 October 2018; Accepted: 8 November 2018; Published: 13 November 2018

 

Abstract: In this paper, a modification of the dual-segment permanent magnet (PM) Halbach array is investigated to improve the performance of the tubular linear machine, in terms of flux density and output power. Instead of a classical Halbach array with only radial and axial PMs, the proposed model involves the insertion of mig-magnets, which have a magnetized angle shifted from the reference magnetized angles of axial and radial PMs. This structure leads to the elimination of flux leakage and the concentration of flux linkage in middle of the coil; therefore, the output power is increased by 13.2%. Keywords: electromagnetic shock absorber; tubular machine; energy harvesting; Halbach array

1. Introduction Tubular machines are commonly applied in many industrial applications, such as cryocoolers, linear compressors, or refrigerators [1–3]. Recent research activities for energy harvesting in vehicle suspension systems [4–6] or using ocean wave energy [7–9] have proposed a new trend for tubular machines. From a design viewpoint, at a particular volume, increasing the output power is very difficult. L. Zou et al. [10] provide the original design, which is composed of one magnet layer using a Halbach arrangement instead of only axial magnet or radial magnet arrays. In the following step, by using the same Halbach array structure, X. Tang et al. [11] modified the original model with a double layer of permanent magnet; this method eliminates the flux leakage, while concentrating flux density in the middle of the coil. This leads to an eightfold improvement in the output power and a 3.8-fold improvement in the power density compared to the values of the original design. Another technique was studied by Y. Shen, in which mid-magnets whose magnetization angle is shifted from the reference angle of axial and radial magnets are inserted [12]. There are two possible structures—odd-segment and even-segment—and these structures define the number of magnet segments over a pole pitch as an odd or even number. The FEM and analytical results for a 12-slot/10-pole PM brushless machine illustrate that the 3-segment Halbach array exhibits significantly higher fundamental airgap flux density than that of the magnet cylinder, having a traditional Halbach array with two segments. Under the same theory, W. Zhao designed a tubular linear generator for energy harvesting from body motion [13] using an even-segment Halbach array. The eight-segment dual Halbach array is employed in the optimized generator because its magnetic flux density is greater than that of the four-segment array. However, the effects of the odd-segment model were not presented. In this paper, an electromagnetic shock absorber for vehicle energy harvesting using a segment-magnet Halbach array is proposed. Unlike most conventional research [6,7], in which a mechanical shock absorber is replaced with an electrical one, the proposed device is a combination Energies 2018, 11, 3132; doi:10.3390/en11113132

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Electrical components including a magnetic core, winding, and permanent magnet (PM) are attached to the inner and outer frame of the mechanical shock absorber. To validate with the corresponding experiments, a single PM layer, with a coreless model, is designed, fabricated and tested. To avoid the noise caused by the mechanism, experiments are carried out under lower vibration speeds than Energiesof 2018, 3132 2 ofon 10 those the11, previous study [14,15]. In addition, the effects of both the even- and odd-segment PM the tubular generator are investigated and compared with the conventional one. In previous publications, these effects have mostly been investigated for rotating machine. Finite element analysis of both parts. Electrical components including a magnetic core, winding, and permanent magnet (FEA) results show thata under the same operating conditions, a tubular generator using segment(PM) are attached to the inner and outer frame of the mechanical shock absorber. To validate with magnet yields has higher power than that of a generator with the original Halbach array structure by the corresponding experiments, a single PM layer, with a coreless model, is designed, fabricated and 13.2%. In the further study, the optimized dimensions of the PM segments, the magnetized angle, tested. To avoid the noise caused by the mechanism, experiments are carried out under lower and feasibility will be taken into account. vibration speeds than those of the previous study [14,15]. In addition, the effects of both the evenand odd-segment PMwith on the tubularHalbach generator are investigated and compared with the conventional 2. Tubular Machine Classical Array one. In previous publications, these effects have mostly been investigated for rotating machine. Finite element analysis (FEA) results show thata under the same operating conditions, a tubular 2.1. Design Specifications generator using segment-magnet yields has higher power than that of a generator with the original Thisarray section deals by with the design specifications ofoptimized the tubular machine of using thesegments, classical Halbach structure 13.2%. In the further study, the dimensions the PM Halbach array based thefeasibility actual dimensions of ainto commercial the magnetized angle,on and will be taken account. shock absorber in an SUV-Korando car. Analyses using FEM are validated with corresponding experiments. FigureMachine 1 shows the cross-section of the half model and its geometry over one pole pitch, as was 2. Tubular with Classical Halbach Array presented in Reference [14,15]. The overlapping length of the magnet array and coil windings is about 2.1. mm Design Specifications 200 but, fortunately, this value is adjustable by ± 40 mm. That is also the condition for the outer diameter, which bewith flexibly values between mm and 160 mm, while inner This section can deals the chosen design at specifications of the80tubular machine using thethe classical diameter has tobased be aton least mm,dimensions the same asofthe diameter ofshock the damping the mechanical Halbach array the 40 actual a commercial absorber part in anor SUV-Korando car. part [14,15]. Analyses using FEM are validated with corresponding experiments. Due to 1the relative between the coils and and the excited flux density, and with the as aim of Figure shows the position cross-section of the half model its geometry over one pole pitch, was simplifying the drive system, an external circuit is designed with two phases, in which phase 1 is in presented in Reference [14,15]. The overlapping length of the magnet array and coil windings is about series connection with coil 1 and coil 3, and phase 2 is in series connection with coil 2 and coil 4. It is 200 mm but, fortunately, this value is adjustable by ±40 mm. That is also the condition for the outer mandatory to precisely set up chosen the winding directions maximum powerthe [14,15]. Detailed diameter, which can be flexibly at values betweento80achieve mm and 160 mm, while inner diameter specifications of the tubular machine are summarized in Table 1. has to be at least 40 mm, the same as the diameter of the damping part or the mechanical part [14,15].

Back iron Radial PM Axial PM

Insulation PM cover

Coil 4 Coil 3 Coil 2 Coil 1 Coil 4 Coil 3 Coil 2 Coil 1 Coil 4 Coil 3 Coil 2 Coil 1 Coil 4 Coil 3 Coil 2 Coil 1

Phase 2 g

Phase 1

Coil 4 Coil 3 Coil 2 Coil 1

tb

tc

wc

tim

Additional iron layer

Mechanical part

tia tii

Inner iron layer

(a)

(b)

Figure 1. 1. (a,b) (a,b) Half Half cross-section cross-section of of the the single single PM PM layer layer coreless coreless model. Figure model.

Due to the relative position between the coils and the excited flux density, and with the aim of simplifying the drive system, an external circuit is designed with two phases, in which phase 1 is in series connection with coil 1 and coil 3, and phase 2 is in series connection with coil 2 and coil 4. It is mandatory to precisely set up the winding directions to achieve maximum power [14,15]. Detailed specifications of the tubular machine are summarized in Table 1.

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Table 1. Design specifications of the tubular machine with classical Halbach array. Energies 2018, 11, 3132

Item Value Vibration speed (m/s) 0.25 Vibration frequency (Hz) 10 Table 1. Design specifications of the tubular machine with classical Halbach array. Stroke length (mm) 11.25 Value Length, L (mm) Item 243 Vibration speed (m/s) 0.25 Outer diameter, D (mm) 160 10 PM Vibration thickness,frequency tim (mm)(Hz) 26.0 Stroke length (mm) 11.25 Radial PM width, 13.5 Length, L (mm) wrm (mm) 243 Axial PM diameter, width, wD am(mm) (mm) 13.5 Outer 160 thickness, tim (mm) 26.0 PolePM pitch, τp (mm) 27.0 PM thickness, width, wrm t(mm) 13.5 CoilRadial window c (mm) 8.0 Axial PM width, wam (mm) 13.5 CoilPole window width, wc (mm) 12.1 pitch, τp (mm) 27.0 Mechanical air gap, g (mm) 4.3 Coil window thickness, tc (mm) 8.0 Coil window width, (mm) 12.1 Inner iron thickness, tiiw (mm) 1.6 c Mechanical air gap, gtia(mm) 4.3 Added iron thickness, (mm) 16.0 Inner iron thickness, tii (mm) 1.6 Back iron thickness, tb (mm) 5.6 Added iron thickness, tia (mm) 16.0 WireBack diameter, wr (mm) 0.6 iron thickness, tb (mm) 5.6 Number of winding/slot, 180 Wire diameter, wr (mm)turns 0.6 Number of winding/slot, turns 1808 Number of poles, Np Number of poles, N 816 p Number of slots, Ns Number of slots, Ns 16 BackBack ironiron material S20C material S20C ◦ C); PMsPMs material NdFeB—N40SH; B r = 1.26T(at(at °C); µr1.05 = 1.05 material NdFeB—N40SH; Br = 1.26T 2020 µr =

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The relative position between the coils and the excited flux, and the external circuit, are shown The relative position between the coils and the excited flux, and the external circuit, are shown in in the Figure 2. According to References [10,14,16], the maximum output power occurs at the the Figure 2. According to References [10,14,16], the maximum output power occurs at the maximum maximum vibrating speed vmax when the load resistance RL equals the sum of the coil resistance Rc; vibrating speed vmax when the load resistance RL equals the sum of the coil resistance Rc ; this is termed this is termed the full load condition. the full load condition. Phase 1

Flux distribution Coil 4

Coil 3

Coil 2

Rcoil 1

Rcoil 3

Rcoil 2

Rcoil 4

Coil 1

2p

0

Phase 2

RLoad

(a)

RLoad

(b)

Figure2. 2.(a) (a)Coils Coilsand andexcited excitedflux fluxdensity; density;(b) (b) External External circuit. circuit. Figure

Equation(1) (1)shows showsthat thatoutput output power is proportional to the square of radial the radial density, Equation power is proportional to the square of the flux flux density, the the square of the vibrating speed and the volumes of the coil [10,14,15]. square of the vibrating speed and the volumes of the coil [10,14,15]. Pmax = Ve I0 = B2 2r v2 2z σVcoil Pmax = Ve I 0 = B r v z σVcoil

(1) (1)

where Br is the radial flux density, vz is the vibrating speed, σ is the conductivity, and Vcoil is the where Br is the radial flux density, vz is the vibrating speed, σ is the conductivity, and Vcoil is the coil coil volume. volume. The relationship between the peak to peak stroke, the vibrating speed, and the vibrating frequency The relationship the peak to peak stroke, the vibrating speed, and the vibrating is calculated as followsbetween [10,14,15]: frequency is calculated as follows [10,14,15]: √ vmax vrms 2 Strokepeak-to-peak = = (2) vω v rms πf2 max (2) = Stroke peak − to − peak = ω πf where vrms is root-mean-square of the vibration speed, and f is the vibration frequency. addition, the instantaneous ofspeed, one coil at equilibrium position z0 in the whereInvrms is root-mean-square of thevoltage vibration andcentered f is the vibration frequency. regenerative shock absorber is presented as a function of time, position, magnetic flux density B0 ,

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In addition, the instantaneous voltage of one coil centered at equilibrium position z0 in the 4 ofB10 absorber is presented as a function of time, position, magnetic flux density 0, length of the conductor L, sum of the thicknesses H of a radial and an axial PM, suspension velocity and frequency. For the L, 0° sum coil or for thicknesses coil 1, which maximum magnetic flux density, if the length of the conductor of the H has of a the radial and an axial PM, suspension velocity vibration amplitude is small, the voltage is calculated by [10]: ◦ and frequency. For the 0 coil or for coil 1, which has the maximum magnetic flux density, if the

Energies 2018, 11,shock 3132 regenerative

vibration amplitude is small, the voltage is calculated by [10]: jω V0° = B0 L 2 e in sin ωt 2 jω ω − ω + j ζω ω 2 n V0◦ = B0 L n 2 ein sin ωt ωn − ω2 + 2jζωn ω

(3) (3)

90°◦ coil or coil 3 will have a double frequency wave [10]: and a 90 V90◦ °== B B00L V90

2 πV2max πV max sin ωt sin22ωt 2Hω 2 Hω

(4) (4)

The additional is inserted to reduce the inner of the PMs; thisPMs; layer this is composed additionaliron ironlayer layer is inserted to reduce the diameter inner diameter of the layer is of stainless of steel, while steel, the back ironthe is made of aniselectromagnetic material. Bothmaterial. radial PMs andradial axial composed stainless while back iron made of an electromagnetic Both ◦ C and a relative PMs are made of DDP-40SH, which has a relative flux density of B = 1.26 T at 20 and axial PMs are made of DDP-40SH, which has a relative flux r density of Br = 1.26 T at 20 °C permeability µr = 1.05. Windings are wound around and supported by asupported bobbin with number and a relativeofpermeability of µr = 1.05. Windings are wound around and byaatotal bobbin with of turns per slot of 180. a total number of turns per slot of 180. 2.2. Validation with with Experimental Experimental Data 2.2. Validation Data According toReference Reference[10], [10],when whena mid-sized a mid-sized is moving a speed 60 mph a road According to carcar is moving at aatspeed of 60ofmph on a on road class class C, the vibrating frequency of the shock absorber is estimated to be approximately 0.25 m/s. C, the vibrating frequency of the shock absorber is estimated to be approximately 0.25 m/s. Under these Under thesethe conditions, the peak to length peak stroke length and vibratingare frequency are about 11.25 conditions, peak to peak stroke and vibrating frequency about 11.25 mm and 10 mm Hz, and 10 Hz, respectively. These conditions of the stroke length, vibrating speed, and linear frequency are respectively. These conditions of the stroke length, vibrating speed, and linear frequency are considered considered as a standard for the models studied in this paper. When applying the standard conditions, as a standard for the models studied in this paper. When applying the standard conditions, the the maximum average power cantheoretically be theoretically calculated as 76.09 W37.8 andW, 37.8 W, respectively. maximum andand average power can be calculated as 76.09 W and respectively. To prepare for the experiments, a prototype of a single layer coreless model was To prepare for the experiments, a prototype of a single layer coreless model was fabricated fabricated and and installed, as in in the the illustrations illustrations provided provided in in Figures Figures 33 and 4. Unfortunately, Unfortunately, if installed, as and 4. if the the linear linear frequency frequency of of the generator is 10 Hz, the required rotating speed of the sub-motor is 3000 rpm, which exceeds the the generator is 10 Hz, the required rotating speed of the sub-motor is 3000 rpm, which exceeds the limitation of this limitation of this motor; motor; therefore, therefore, measurements measurements were were performed performed at at lower lower vibrating vibrating speeds speeds than than in in the previous study [14,15]. the previous study [14,15].

Figure Prototype. Figure 3. 3. Prototype.

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Figure 4. Experimental Experimental installment. installment.

Figure from Flux 2D, a commercial FEA software. There are showsthe themesh meshelements elementsgenerated generated from Flux 2D, a commercial FEA software. There Figure 55 shows 26,182 nodes, 2607 line elements and 13,601 surface elements. In addition, the number of excellent are 26,182 nodes, 2607 line elements and 13,601 surface elements. In addition, the number of excellent quality quality elements elements is is 99.1%. 99.1%.

Figure 5. Surface the 2D 2D FEA FEA analysis. analysis. Surface mesh mesh elements Figure 5. elements in in the

80 80 60 60

Simulation Simulation Experiment Experiment

40 40 20 20 00 -20 -20 -40 -40 -60 -60 -80 -80 0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20 0.25 0.25 Time Time (s) (s)

(a)

0.30 0.30

0.35 0.35

0.40 0.40

BackEMF EMFon onphase phase22(V) (V) Back

BackEMF EMFon onphase phase11(V) (V) Back

With the assumption that the peak to peak stroke length is fixed at 11.25 mm, Figure 6 presents the back EMF waveforms achieved for the load load resistance resistance when when the the vibrating vibrating speed speed is is 0.125 0.125 m/s, m/s, which equals equals 50% 50%of ofthe thestandard. standard.The Theaverage averagedeviation deviationis is approximately 6.7%. Figure it can which approximately 6.7%. In In Figure 6b,6b, it can be be clearly seen that frequency load 2 isdouble doublethat thatofofload load1;1;this thisphenomenon phenomenon can can be clearly seen that thethe frequency ofof load 2 is be predicted using Equations (3) and (4). Simulation Simulation Experiment Experiment

20 20 15 15 10 10 55 00 -5 -5 -10 -10 -15 -15 -20 -20 0.00 0.00

0.05 0.05

0.10 0.10 Time Time (s) (s)

0.15 0.15

0.20 0.20

(b)

Figure 6. Comparison of of the back EMF on the load resistors obtained from the FEA and and experiment experiment under a vibrating speed of 0.125 m/s: (a) Phase 1; (b) Phase 2. (a)Phase Phase1; 1;(b) (b) Phase Phase 2. 2. under a vibrating speed of 0.125 m/s: m/s: (a)

Figure illustratesthe thepower powervariation variation according to various vibrating speeds under theload full according to various vibrating speeds under the full Figure 77 illustrates load condition. the maximum output voltage well-matched betweenthe theanalyses analyses and and the condition. WhileWhile the maximum output voltage is is well-matched between the experiments, with an average deviation of only of 4.8%, the results the average output power are not experiments, with an average deviation of only of very satisfactory, being around 13.5%. Although the resistance in one phase under full load condition

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60 60 50 50 40 40 30 30 20 20 10 10 0 00.075 0.075

Simulation Simulation Experiment Experiment

0.100 0.100

0.125 0.150 0.175 0.125 speed 0.150 Vibrating (m/s) 0.175 Vibrating speed (m/s)

0.200 0.200

Average output power (W)(W) Average output power

Maximum output power (W)(W) Maximum output power

is measured at nearly 39.3 Ω, in the experimental setup, only 39 Ω of the load resistance can be very satisfactory, being around the resistance in one under fullresistance load condition is is measured at nearly 39.3 Ω, 13.5%. in the Although experimental setup, only 39 phase Ω of the load can be connected. measured at nearly 39.3 Ω, in the experimental setup, only 39 Ω of the load resistance can be connected. connected. 30 30 25 25 20 20 15 15 10 10 5 5 0 00.075 0.075

Simulation Simulation Experiment Experiment

0.100 0.100

(a) (a)

0.125 0.150 0.125 speed 0.150 Vibrating (m/s) Vibrating speed (m/s)

0.175 0.175

0.200 0.200

(b) (b)

Figure 7. Power variation according to vibrating speeds under full load condition: (a) maximum Figure variation according to Figure 7. 7. Power Power according to vibrating vibrating speeds speeds under under full full load load condition: condition: (a) (a) maximum maximum output power; (b)variation average output power. output output power; power; (b) (b) average average output output power. power.

Another noticeable phenomenon is the linear relationship between the output power and the Another noticeable noticeable phenomenon phenomenonisis the the linear linear relationship relationship between between the the output output power power and and the the Another square of the vibrating speed, according to Equation (1). For instance, when the generator is operating square of of the thevibrating vibrating speed, speed, according according to to Equation Equation (1). (1). For Forinstance, instance,when whenthe thegenerator generatorisisoperating operating square at 0.075 m/s, an average power of about 2.78 W can be obtained. The average power under a vibrating at 0.075 0.075 m/s, m/s,an anaverage averagepower powerof ofabout about2.78 2.78W Wcan canbe beobtained. obtained.The Theaverage averagepower powerunder underaavibrating vibrating at speed of 0.15 m/s can be predicted according to the following equation: speed of of 0.15 0.15 m/s m/scan canbe bepredicted predictedaccording accordingto tothe thefollowing followingequation: equation: speed 2

2

Average output power (W)(W) Average output power

 0.15   0. 15 2 2 2 (5) P0.15m/s =P0.075m/s ×  ≈ 11.12(W) .15  2= 2.78 × 0.15 0.15  00.15 0 . 075 0 . 075 (5)(5) ×  × × P0.15m/s =P0.075m/s× 2.78 P0.15m/s = P0.075m/s 2.78 ≈(W) 11.12(W)  = =  ≈ 11.12 .075   00.075  0.0750.075  The measured result at a vibrating speed of 0.15 m/s for the average power is approximately The measured result at a vibrating speed of 0.15 m/s for the average power is approximately measured resultthe at same vibrating 11.46The W, which is nearly as the expectation. m/s for the average power is approximately 11.46 W, is nearly the same as the expectation. 11.46Figure W, which 8 illustrates the power variation according to various load resistances when the vibrating Figure 88 illustrates the power variation according to load resistances when the according to various various load resistances the vibrating vibrating speedFigure is 0.125illustrates m/s andthe thepower peak variation to peak stroke length is 11.25 mm. Both thewhen analysis and the speed is 0.125 0.125m/s m/sand and the peak to peak stroke length ismm. 11.25 mm. Both theand analysis and the speed is the peak to peak stroke length is 11.25 Both the analysis the experiment experiment results present similar trends, with an average deviation of about 13.4%. When the load experiment results present similar trends, with an averageof deviation of about 13.4%. When the load results present similar trends, with average deviation about 13.4%. load resistance resistance equals the sum of the coilan resistance, the average output power When is at itsthe maximum. There resistance sum the coil resistance, the average output power is at its maximum. There equals theequals sum ofthe theexplanations coil of resistance, output power is at its maximum. There are several are several possible for the the average differences between the simulation and the experiment in are several possible explanations for the differences between the and simulation and the experiment in possible explanations for the differences between simulation the experiment in Figures 6–8. Figures 6–8. As illustrated in Figure 3, owing to thethe limitations during manufacturing, the permanent Figures 6–8. Asin illustrated Figure owing to the limitations during manufacturing, the permanent As illustrated Figure 3,in owing to3,the limitations manufacturing, theMoreover, permanent magnets magnets were separated into smaller segments ofduring a solid toroidal shape. when the magnets were separated into smaller segments of a shape. solid toroidal shape. Moreover, when the were separated into smaller segments of a solid toroidal Moreover, when the prototype is being prototype is being measured, errors can occur due to the noise caused by the mechanical system. prototype beingcan measured, occur dueby tothe themechanical noise caused by the mechanical system. measured,is errors occur dueerrors to thecan noise caused However, the accuracy is much better than the previous design for thesystem. corelessHowever, model. the accuracy However, the accuracy much better than design for the coreless model. is much better than the is previous design for the the previous coreless model. 12 12 10 10 8 8 6 6 4 4 2 2 0 0 10 10

Simulation Simulation Experiment Experiment

20 20

30 40 30 40 Load resistance (Ω) Load resistance (Ω)

50 50

60 60

Figure 8. Average power according to various load resistances. Figure 8. Average power according to various load resistances. Figure 8. Average power according to various load resistances.

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3. Tubular TubularMachine Machinewith withDual-Segment Dual-SegmentHalbach HalbachArray Array 3. In this this section, section, aa dual-segment dual-segment Halbach Halbach array array is is applied applied to to the the same same tubular tubular generator generator with with the the In aim of of improving improving the the output output power. power. The The design design specifications specifications with with the the number number of of magnets, magnets, the the sizes, aim sizes, and the magnetized direction are shown in Figure 9 and Table 2. and the magnetized direction are shown in Figure 9 and Table 2.

tp

tp 900

1200

0

45

0

135

900 600

1500

300

-1500 -1200

-300

0

0 1800 0

-135

6.75 (a)

-450 -900

5.4

-900

-600

(b)

Halbach array. array. Figure 9. (a) 4-segment Halbach array; (b) 5-segment Halbach Table 2. Specifications of the magnet segments over one pole pitch. Table 2. Specifications of the magnet segments over one pole pitch. Item Classical Halbach ArrayArray4-Segment Item Classical Halbach 4-Segment 5-Segment 5-Segment Vibration speed (m/s) 0.25 Vibration speed (m/s) 0.25 Vibration frequency (Hz) 10 Vibration frequency (Hz) 10 Stroke length (mm) 11.25 Stroke length (mm) 11.25 Length (mm) 243 Length (mm)(mm) Diameter 160243 Pole pitch, τp (mm) 27 160 Diameter (mm) Number of segments/pole pitch 2 5 Pole pitch, τp (mm) 274 Width of each segment (mm) 13.5 6.75 5.4 Number of segments/pole pitch 2 4 5 Magnetized angle of — 45◦ 30◦ Width of each segment (mm) 13.5 6.75 5.4 mid-magnet Magnetized angle of mid-magnet --45° 30°

Based on the results in Reference [12], instead of applying only axial and radial PMs over one Basedinona the results in Reference instead of applying only axial and radial PMs over one pole pitch classical Halbach array, a[12], number of mid-magnets with different magnetized angles pole pitch in a classical Halbach array, a number of mid-magnets with different magnetized angles are inserted. There are two applicable approaches: even-segment, with an even number of magnets are inserted. applicable approaches: with an even number of magnets over one poleThere pitch,are andtwo odd-segment, with an oddeven-segment, number of magnets over one pole pitch. In the over onedesign, pole pitch, and odd-segment, an odd number of of magnets over oneispole pitch.toInbethe original the pole pitch is τp = with 27 mm, so the number PM segments selected 4 original design, the pole pitch is 𝜏 = 27 mm, so the number of PM segments is selected to be 4 in in the even-segment case and 5 in the odd-segment case. If there is a higher number of segments, the width even-segment case andbecomes 5 in the smaller. odd-segment is a higher number of PM segments, the of each segment In thecase. case If ofthere the odd-segment, the axial with 0◦the of width of each segment becomes smaller. In the case of the odd-segment, the axial PM with 0° of the the magnetized angle is removed [8]. For a fair comparison, the other dimensions, such as the length magnetized is generator, removed [8]. a fair comparison, dimensions, length and diameterangle of the theFor number of turns per the slot,other and the materials,such are as thethe same for and the the generator, number of turns per slot, the materials, the same for the 3 3diameter models. of In addition, in thethe preliminary investigation, the and magnetized angle isare equally divided. models. In addition, preliminary investigation, the magnetized angle is equally divided.with a Figure 10 shows in thethe flux distribution on the 3 different models under a no-load condition, Figure 10 shows the flux distribution on the 3 different models under a no-load condition, vibrating speed of 0.25 m/s, a peak to peak stroke length of 11.25 mm and a linear speed of 10with Hz. a vibratingto speed of 0.25 m/s, peak topower peak is stroke length ofto 11.25 mm and a density linear speed 10 Hz. According Equation (1), theaoutput proportional the radial flux in theofmiddle According to the Equation (1),the the4-segment output power is proportional to the the middle of the coil. In cases of and 5-segment magnet, theradial radialflux fluxdensity densityin increased by of the coil. In the cases of the 4-segment and 5-segment magnet, the radial flux density increased by 6.8% and 5.2%, respectively; therefore, the output power can be expected to increase by around 15%. 6.8%to and respectively; therefore, the output power angle), can be expected to increase byodd-segment around 15%. Due the5.2%, absence of the axial PM (0◦ of the magnetized the flux linkage in the Due to the absence of the axial PM (0° of the magnetized angle), the flux linkage in the odd-segment PM model is slightly higher than that of the even-segment PM model. Figure 11 presents a comparison PM is slightly higher than thatflux of density the even-segment PM model. Figure presents a of themodel three models in terms of the radial in the middle of the coil and the 11 output power. comparison of the three models in terms of the radial flux density in the middle of the coil and the The other characteristics are summarized in Table 3. output power. The other characteristics are summarized in Table 3.

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(a) (a)

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(b) (b)

(c) (c)

0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8

Classical Halbach array Classical Halbach array 4-segments Halbach array 4-segments Halbach array 5-segment Halbach array 5-segment Halbach array

Position (mm) Position (mm)

(a) (a)

Classical Halbach array Classical Halbach array 4-segment Halbach array 4-segment Halbach array 5-segment Halbach array 5-segment Halbach array

100 100 Output Outputpower power(W) (W)

Radial Radialflux fluxdensity densityininthe the middle middleofofcoil coil(T) (T)

Figure 10. Flux Flux distribution distribution on the the three three different different models models under under no-load no-load condition: condition: (a) (a) classical classical Figure Figure 10. Flux distribution onon the three different models under no-load condition: (a) classical Halbach Halbach array;(b) (b)4-segment; 4-segment;(c) (c)5-segment. 5-segment. Halbach array; (b)array; 4-segment; (c) 5-segment.

80 80 60 60 40 40 20 20 0 0 0.10 0.10

0.15 0.15

0.20 0.20 Time (s) Time (s)

0.25 0.25

0.30 0.30

(b) (b)

Comparisonof: (a)4-segment 4-segmentHalbach Halbacharray; array. Figure11. 11.Comparison of:(a) array;(b) (b)5-segment 5-segmentHalbach Halbacharray. array. Figure Table 3. Comparison of three models. Table3.3.Comparison Comparisonof ofthree threemodels. models. Table Items Classical Halbach Array 4 Segment 5 Segment 44 55 Items Classical Halbach array Items Max Classical Segment Segment 0.55 Halbach array Segment 0.59 0.58 Segment Radial flux density (T) RMS 0.36 0.39 0.39 Max 0.55 0.59 0.58 Max 0.55 0.59 0.58 Radialflux fluxdensity density(T) (T) Radial RMS 0.36 0.39 0.39 Maximum induced Phase 1 54.10 0.36 57.98 57.86 RMS 0.39 0.39 Phase11 54.10 57.98 57.86 voltages (V) Phase 2 Phase 17.05 54.10 18.53 19.12 57.98 57.86 Maximuminduced inducedvoltages voltages(V) (V) Maximum Phase22 17.05 18.53 19.12 Phase 17.05 18.53 19.12 Maximum 76.09 87.10 87.38 Output Power (W) Maximum 76.09 87.10 87.38 Average Maximum 37.78 76.09 43.53 43.47 87.10 87.38 Output Power (W) Output Power (W) Average 37.78 43.53 43.47 Average 37.78 43.53 43.47

4. Conclusions Conclusions 4.4.Conclusions In this paper, a tubular permanent magnet machine composed of a novel magnet arrangement is Inthis thispaper, paper,aatubular tubularpermanent permanentmagnet magnetmachine machinecomposed composedof ofaanovel novelmagnet magnet arrangement In proposed and compared with the conventional model in terms of the radial flux density arrangement in the middle is proposed and and compared compared with with the the conventional conventional model model in in terms terms of of the the radial radial flux flux density density in in the the is ofproposed the coil and output power. A prototype of a tubular machine composed of the classical Halbach middle of the coil and output power. A prototype of a tubular machine composed of the classical middle of the coil and output power. A prototype of a tubular machine composed of the classical

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array was fabricated and validated using the FEM analyzed results, which show an average deviation of 13.5% in terms of the output power. Unlike devices that use the classical Halbach array, in the proposed model mid-magnets are inserted, which have a magnetized direction that is shifted from that of the original axial and radial PMs. Based on the FEM analyses, in the cases of 4-segment and 5-segment Halbach arrays, the RMS values of the radial flux density increased by nearly 6.8%, which led to an increase in the average output power of 13.2%. In a further study, the relative dimensions and the magnetized angle between the magnet segments will be optimized. Author Contributions: Investigation, M.-T.D.; Writing-Review & Editing, M.-T.D.; Supervision, Y.-D.C.; Project Administration, D.-J.B. Acknowledgments: This research was supported by the KERI Primary research program of MSIT/NST (No. 18-12-N0102-04). Conflicts of Interest: The authors declare no conflict of interest.

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