energies

Article Electromagnetic Design and Losses Analysis of a High-Speed Permanent with Toroidal Windings for Pulsed

Yuan Wan, Shumei Cui *, Shaopeng Wu and Liwei Song

School of Electrical Engineering and Automation, Harbin Institute of Technology, No. 2 Yikuang Street, Nangang District, Harbin 150080, China; [email protected] (Y.W.); [email protected] (S.W.); [email protected] (L.S.) * Correspondence: [email protected]; Tel.: +86-0451-86402089

Received: 31 December 2017; Accepted: 2 March 2018; Published: 6 March 2018

Abstract: The configuration of conventional high-speed Permanent Magnet Synchronous Motors (PMSMs) is usually long and thin, with overlong axial end winding lengths, which is not suitable for those applications that place severe restrictions on the axial length, such as pulsed . This paper first studied the key design aspects of a flat-structure high-speed PMSM. The toroidal- windings, low-conductivity material of the retaining sleeve, large airgap and segmentation of were studied to reduce the axial length of the motor. The division of the and the employment of a non-magnetic outer stator were used to improve overall performance. Then the losses of the prototype were calculated and the factors having an influence on the losses were also investigated, after which, their effects on the total loss were evaluated. The total loss could be effectively reduced by the decrease of strand number of conductors and the division of stator, while only being slightly reduced by epoxy resin pole fillers. Metal-stack pole fillers have the same effect on the reduction of loss as epoxy resin, while maintaining the good thermal-conductivity of metal. In addition, the influence of the carrier of the inverter on the losses was analyzed, and it was found that high carrier frequency was helpful to reduce rotor losses. Finally, a small-scale prototype was manufactured and the experimental results were provided.

Keywords: high-speed PMSM; toroidal winding; copper loss; iron loss; rotor loss; carrier frequency

1. Introduction Pulsed alternators are widely considered for driving electromagnetic . Utilizing a primary motor to accelerate the high-speed rotor of the pulsed alternator to store the mechanical energy, it can discharge several megampere currents in a few milliseconds [1,2]. To reduce the axial length of the power, the prime motor should be designed as a flat structure [3]. Nowadays surface-mounted PMSMs are increasingly used for high-speed applications, because of the merits of simple structure and high-strength of the rotor [4,5]. The number of poles is usually designed as two or four to reduce the iron losses at high operating frequency [6]. With conventional lap windings, the overlong axial length of the end windings is unavoidable for motors of a small number of poles. This will not only result in an increase of the volume, but also problems of rotor dynamics. It will cause excessive acoustic noise emissions, high bearing loss, and even catastrophic failure of the system for a slender rotor, when the operating speed of the rotor exceeds the critical speed [7,8]. Toroidal windings have been used to reduce the axial length of the motor [9], but slotting on the outer edge of the stator will decrease the heat-dissipation capability of the motor. Besides, the windings in the outer slots increase the copper loss, which will further increase the heat dissipation difficulty. In addition, the retaining sleeves are designed thicker to improve the rotor strength, in order

Energies 2018, 11, 562; doi:10.3390/en11030562 www.mdpi.com/journal/energies Energies 2018, 11, 562 2 of 21 to withstand the high decelerations encountered during the discharge of pulsed alternator [10,11]. This will cause a huge heat dissipation challenge for the rotor due to the poor cooling conditions of the rotor [12,13], so it’s necessary to study the electromagnetic design of high-speed PMSMs with flat structures and optimize the losses. The proximity and skin losses of the windings should be considered in high-frequency machines. Two-dimensional (2-d) analytical models were proposed to analyze the proximity losses for Permanent Magnet (PM) machines in high-speed operation [14]. The AC loss was much bigger than the DC copper loss. Induced by PWM excitation, the higher-frequency harmonic current will further increase the proximity loss. The influence of PWM on the proximity loss was analyzed for a PM brushless AC machine. The results showed that the skin and proximity losses were significantly increased, and this was confirmed both by theoretical calculations and experiments [15,16]. To predict the iron loss of high-frequency machines accurately, an iron loss model of the elliptical field was proposed, which can take the rotating magnetization into consideration [17,18], but it’s difficult to acquire the corresponding loss coefficients for the rotating magnetization model. Hence, an improved loss separation model, based on the two equivalent orthogonal alternating flux density components by using only alternating loss data, was then proposed. Based on the improved model, the no-load iron losses in the was predicted with satisfactory accuracy [19]. The electromagnetic losses of the rotor, consisting of the eddy-current losses of the magnets, retaining sleeve and pole fillers, make up a small portion of the total loss of the motor. But the heating problem of the rotor becomes even worse for the rotor wrapped with the carbon-fiber composite sleeve and powered by PWM inverter, because of the poor property of thermal conductivity and the increased rotor loss [20,21]. 2-d FEA and analytical field analysis methods were used to calculate the rotor losses. The technologies of magnet segmentation, new sleeve materials and structures were developed to reduce the eddy-current losses of the rotor [22–25]. The influence of the carrier frequency of the PWM inverter on the rotor loss was investigated by 3-d FEA method to improve the accuracy of the calculation [26]. In this paper, the key design features of a flat-structure high-speed PMSM were first studied, and a prototype with toroidal windings was designed. Then the copper loss, iron loss, rotor eddy-current losses of the prototype were calculated, based on the advanced methods, respectively, and the factors having an influence on the losses were also investigated. After that, their effects on the total loss were evaluated. Moreover, the influence of the carrier frequency of the PWM inverter on the losses was analyzed. Eventually, a small-scale prototype was manufactured and the experimental results were provided to verify the theoretical analysis.

2. Electromagnetic Design The rated parameters of the prototype were 300 kW, 12,000 rpm. It was used to accelerate a 50-MJ alternator. The main dimensions of prototype can be expressed as [6]:

0 2 6.1 P Di Le f = 0 · (1) αpKNmKdp ABδ n

0 0 where Di is the inner diameter of the stator, Lef is the effective length, P is the apparent power, ap is the effective pole arc coefficient, KNm is the air-gap flux factor, Kdp is the stator winding factor, A is the electric loading, Bδ is the airgap flux density, nN is the rated speed. Tangential speed of the rotor is a key criterion for the high-speed motor. It is generally restricted by the mechanical strength of the material of the rotor core. The centrifugal force at the outer edge of the rotor is expressed as: 2 2 2 ρν = ρω Dr /4 ≤ [σ] (2) where ρ is the density, v is the tangential speed at the outer edge of the rotor, [σ] is the allowable stress of the rotor. The terms ω, Dr are the angular velocity and outer diameter of the rotor, respectively. Energies 2018, 11, 562 3 of 21

According to the allowable stress of the rotor core, the maximum diameter can be determined and Di can also be acquired. According o Equation (1):

1 Le f ∝ (3) Bδ

The eddy-current loss of the rotor is caused by the asynchronous magnetic field of the airgap with respect to rotor, which results from the airgap permeance variation due to stator slotting, space harmonics of winding distribution and time harmonic components of the current. The eddy-current loss in the sleeve or magnets can be expressed as [23]:

∞ 1 2 3 P = ∑ Bk ωkπrmhLe f (4) k=1 ρ where P is the eddy-current loss of the sleeve or magnets, ρ is the resistivity of the sleeve or magnets, rm and h are the mean radius and thickness of the sleeve or magnets, respectively, Bk is the amplitude of harmonic flux density at the region of sleeve or magnets, ωk is the relative speed between harmonics and rotor, k is the order of the harmonic. When all the dimensions of the cross-section for the prototype are fixed, the percentage of each harmonic flux density in the airgap flux density is certain, regardless of the value of the airgap flux density, so the eddy-current loss of the rotor can be further written as:

2 Ploss ∝ Bδ Le f (5) where Ploss is the eddy-current loss of the rotor. The loss density of the rotor can be expressed as:

4P = loss 2 ρloss 2 ∝ Bδ (6) πDr Le f where ρloss is the loss density of the rotor. The maximum allowable loss density of the rotor is limited with the given cooling method. ρloss ≤ ρmax (7) where ρmax is the maximum allowable loss density of the rotor. When the rotor loss density is higher than the allowable value, Bg should be decreased to reduce the rotor loss density, which will cause the increase of the axial length and decrease of the power density. Material of sleeve, airgap length and segment number of magnets were analyzed to reduce the axial length.

2.1. Windings Double-layer lap windings are widely used in high-speed PMSMs, but they usually have long end windings. Toroidal windings were considered as a way to reduce the axial length of the motor, since they were like toroids around the stator, the axial length of the end windings could be made very short. Concentrated windings were also considered for the shorter length of end windings. The configurations of windings are shown in Figure1a–c, respectively. 35WW250 and B20AT1500 were analyzed for the design of the prototype to reduce the high-frequency iron loss. Figure1d shows the curves plotted of the iron loss versus flux density for the two materials, with the of 400 Hz and 1000 Hz. It can be seen that the iron loss of 35WW250 was much higher than B20AT1500, at the same frequency and flux density. Normally, a value of 31 W/kg was given as an acceptable limit for silicon steel sheet [27]. Beyond this limit, the cooling of the metal core poses a problem. Within this limit, the largest value of flux density is about 0.5 T, at the 1000 Hz level for 35WW250, but which is too low for the motors. For this reason it is usually used in low and medium frequency motors. In contrast, the largest value of flux density is about 0.8 T at the 1000 Hz level for B20AT1500. The B-H curves of the two materials were given in Figure1e. Energies 2017, 10, x FOR PEER REVIEW 4 of 21 toroidal windings, and case 4 used concentrated windings. It can be seen the axial length of windings of case 1 was 290 mm, which was longer than case 2–4 of 180 mm, decreased by 37.9%. 35WW250 was used as the stator materials for the first two cases, and it was replaced by the low-loss silicon Energiessteel sheet2018 ,of11 ,B20AT1500 562 for cases 3 and 4. As can been seen, the volume of case 2 was reduced4 of by 21 7.1% compared to case 3 by replacing 35WW350 with B20AT1500.

Figure 1. ConfigurationsConfigurations of, (a) double-layer lap windings;windings; (b) toroidaltoroidal windings;windings; ((c) concentratedconcentrated windings; Characteristics of, ((dd)) ironiron loss;loss; ((ee)) B-HB-H ofof 35WW25035WW250 andand B20AT1500.B20AT1500.

Table 1. Specifications of the four designs of the prototype. Within the limit of the iron loss density, four designs of the prototype were provided in Table1. Do is the outerCases diameter of the stator.1 Case 1 used double-layer2 lap windings, 3 case 2 and 3 used 4 toroidal windings,Poles and number case 4 used concentrated 4 windings. It 4can be seen the axial length 4 of windings 10 of case 1 was 290Slot mm, number which was longer than 36 case 2–4 of 180 36 mm, decreased by 37.9%. 36 35WW250 was 15 used as theRated stator Frequency materials (Hz) for the first two 400 cases, and it was 400 replaced by the low-loss 400 silicon steel 1000 sheet of B20AT1500 for cases 3 and 4.Double-layer As can been seen, the volume of case 2 was reduced by 7.1% compared to Toroidal Toroidal Concentrated case 3Winding by replacing type 35WW350 withlap B20AT1500. windings windings windings windings Do of stator (mm) Table 1. Specifications 490 of the four 560 designs of the prototype. 520 450 Di of stator (mm) 294 294 294 294 MaterialsCases of stator 35WW250 1 35WW250 2 B20AT1500 3 B20AT1500 4 EffectivePoles length number (mm) 480 4 80 4 80 10 98 Slot number 36 36 36 15 AxialRated length Frequency (mm) (Hz) 400 290 400 180 400 180 1000 180 2 3 Double-layer lap Concentrated Heat loadingWinding type(A /m ) 175.3 Toroidal 178.3 windings Toroidal windings 179.3 178.68 EMF (V) windings 216.4 220.1 220.8 windings 220 Do of stator (mm) 490 560 520 450 RatedDi of power stator (mm) (kW) 294 300 294 300 294 300 294 300 RatedMaterials current of stator (A) 35WW250 472.1 35WW250 480.2 B20AT1500 474.5 B20AT1500 496 Effective length (mm) 80 80 80 98 AxialEfficiency length (mm) 98.45% 290 98.44% 180 180 98.77% 18096.36% HeatPower loading factor (A2/m 3) 0.9822175.3 178.30.9672 179.3 0.9763 178.68 0.9554 Power densityEMF (V) (kW/kg) 2.1914216.4 220.11.8841 220.8 2.2605 220 2.5884 Rated power (kW) 300 300 300 300 Iron loss density Rated current (A) 472.130.59 480.229.14 474.5 26.88 496 30.14 (W/kg)Efficiency 98.45% 98.44% 98.77% 96.36% 0.9822 0.9672 0.9763 0.9554 Power density 2.1914 1.8841 2.2605 2.5884 A 2-d(kW/kg) time-stepping FEA method was used to analyze the electromagnetic performance of the prototype.Iron lossThe density iron loss was calculated by the classic loss separation model of Bertotti, as seen in 30.59 29.14 26.88 30.14 (W/kg) Equation (8). Here, Kh, Kc, Ke, are coefficients of loss, eddy-current loss, and excess loss for the silicon steel sheet, respectively. f and Bm are the alternating frequency and amplitude of the A 2-d time-stepping FEA method was used to analyze the electromagnetic performance of the prototype. The iron loss was calculated by the classic loss separation model of Bertotti, as seen in Equation (8). Here, Kh, Kc, Ke, are coefficients of hysteresis loss, eddy-current loss, and excess loss for the silicon steel sheet, respectively. f and Bm are the alternating frequency and amplitude of Energies 2018, 11, 562 5 of 21 the magnetic flux density. By curve fitting the iron loss characteristics of the materials provided in Figure1d, the loss coefficients are found to be 269.8, 0.403, 0.3965 for 35WW250, while they are 115.51, 0.211, 0.8441 for B20AT1500. Figure2a–d show the FE meshes and the distributions of the flux lines and densities for the four prototypes. More leakage flux lines were observed between the poles of case 4 than theEnergies other 2017 three, 10, x FOR cases, PEER as REVIEW well as in the slot openings. The flux density of case 3 was higher5 of 21 than case 2 onmagnetic the basis flux of density. similar By value curve of fitting the averagethe iron loss iron characteristics loss density. of the Figure materials2e shows provided the in iron Figure losses for the four1d, prototypes. the loss coefficients With low-loss are found silicon to be 269.8, steel 0.403 sheet,, 0.3965 the for iron 35WW250, loss of casewhile 3 they was are smaller 115.51, 0.211, than case 2. The iron0.8441 loss offor case B20AT1500. 4 wasthe Figure highest 2a–d show among the theFE meshes four cases and owingthe distributions to the high of the operating flux lines frequency.and The irondensities loss densities for the four were prototypes. calculated More in Table leakage1. Theflux lines radial were flux observed densities between in the the middle poles of of case the 4 airgap than the other three cases, as well as in the slot openings. The flux density of case 3 was higher than were plotted in Figure2f, and the waveforms were highly distorted. Harmonic spectrum images case 2 on the basis of similar value of the average iron loss density. Figure 2e shows the iron losses correspondingfor the four to the prototypes. radial flux With density low-loss were silicon provided steel sheet, in the Figure iron loss2g. of As case can 3 bewas seen, smaller the than amplitude case of the working2. The harmonic iron loss of flux case density4 was the of highest case 4among was lower the four than cases the owing other to the cases high with operating the same frequency. thickness of magnet,The because iron loss of thedensities fact that were there calculated was morein Table leakage 1. The radial flux betweenflux densities the in poles the middle and in of the the slot airgap openings. Besides,were more plotted high-frequency in Figure 2f, harmonicsand the waveforms were included were highly in casedistorted. 4, ranging Harmonic from spectrum 2000 toimages 11,000 Hz, which wouldcorresponding have resulted to the radial in eddy-current flux density losswere inprovided the rotor. in Figure As aresult, 2g. As thecan be eddy-current seen, the amplitude losses of case of the working harmonic flux density of case 4 was lower than the other cases with the same thickness 4 were much higher than the first three cases as shown in Figure2h. And it became the dominant loss of magnet, because of the fact that there was more leakage flux between the poles and in the slot of motor,openings. which will Besides, have more resulted high-frequency in overheating harmonics problems. were included In addition, in case both 4, ranging the efficiency from 2000 and to power factor of11,000 case Hz, 4 were which lower would than have theresulted other in threeeddy-current cases asloss shown in the rotor. in Table As a 1result,. With the the eddy-current same material for the stator,losses of the case power 4 were density much higher of case than 2 the was first lower threethan cases caseas shown 1, while in Figure case 2h. 3 wasAnd it lower became than the case 4, due to thedominant increased loss mass of motor, of the which outer will teeth have for resulted the cases in overheating with toroidal problems. windings. In addition, In contrast, both thethe power density ofefficiency a similar and high-speedpower factor of PMSM case 4 were of a 1.12lower MW, than the 18,000 other rpm three was cases 1.4 as shown kW/kg in (6).Table Consequently, 1. With the same material for the stator, the power density of case 2 was lower than case 1, while case 3 was four poleslower and than toroidal case 4, windingsdue to the increased were chosen mass of for the the outer prototype. teeth for the Lap cases windings with toroidal are notwindings. suitable for those applicationsIn contrast, the that power have density any strict of a similar requirement high-speed on PMSM the axial of a 1.12 length MW, of18,000 the rpm motor was for 1.4 thekW/kg long end windings.(6). Even Consequently, though concentrated four poles and windingstoroidal windings have short were endchosen windings, for the prototype. they are Lap typically windings not are suitable for the applicationnot suitable for due those to higher applications eddy-current that have lossany strict of the requirement rotor. on the axial length of the motor for the long end windings. Even though concentrated windings have short end windings, they are typically not suitable for the application due∂ to higher2 2eddy-current1.5 1.5 loss of the rotor. piron = kh f Bm + kc f Bm + ke f Bm (8) =+∂ 2 2 + 15.. 15 (8) pkfBkfBkfBiron h m c m e m

(a) (b)

(c) (d)

Figure 2. Cont.

Energies 2017, 10, x FOR PEER REVIEW 6 of 21

Energies 2018, 11, 562 Case 1 Case 2 Case 1 Case6 2 of 21 5Energies 2017, 10, x FOR PEER REVIEW 6 of 21 Case 3 Case 4 1.0 Case 3 Case 4

4 (T) 0.5 Case 1 Case 2 Case 1 Case 2 5 3 Case 3 Case 4 1.0 Case 3 Case 4 0.0 (T)

4 2 0.5 3

Iron loss (kW) -0.5 0.0

1

2 Airgap flux density

0 Iron loss (kW) -0.5-1.0 1 0 30 60 90 120 150 180

0.0 0.5 1.0 1.5 2.0 2.5 Airgap flux density Mechanical angle (degree) 0 Time (ms) -1.0 0.0 0.5 1.0 1.5 2.0 2.5 0 30 60 90 120 150 180 (e) Mechanical angle(f) (degree) Time (ms) (e) (f) Case 1 Case 2 0.8 10 Case 1 Case 1Case 3Case 2 Case 4 0.8 10 Case Case 2 1 (kW) Case 3 Case 4 0.6 8 Case 2 (kW) 0.6 Case 3 8 Case Case 4 3 0.4 Case 4 6 0.4 6 44 0.2 0.2 22 Airgap flux density(T) flux Airgap Airgap flux density(T) flux Airgap 0.0 0.0 0 0 2000 4000 6000 8000 10000 12000 Eddy current loss of rotor 0

0 2000 4000 6000 8000 10000 12000 Eddy current loss of rotor Frequency(Hz) 0.00.51.01.52.02.5 Frequency(Hz) 0.00.51.01.52.02.5Time (ms)

(g) (Timeh) (ms) (g) (h) Figure 2. FEA models of prototypes with the distribution of flux lines and densities of, (a) Case 1 FigureFigure 2. (15,226 FEAFEA trianglemodels models elements, of of prototypes prototypes time step: with with 2.5 × the10 the−6 distriS); distribution (b) butionCase 2 (26,136 of of flux flux triangle lines lines elements,and and densities densities time step: of, of, 2.5( (aa ))× Case Case 1 1 −6 (15,226(15,226 triangle triangle10−6 S); (c )elements, elements,Case 3 (26,136 time time triangle step: step: el2.5ements, 2.5 × 10× − 106time S); step:(bS);) Case (2.5b) × Case 102 −(26,1366 S); 2 (d (26,136) Case triangle 4 triangle(15,107 elements, triangle elements, timeelements, step: time 2.5 step: × −6 −7 −6 102.5−6 ×S);10 (ctime) CaseS); step: ( c3) (26,1365 Case × 10 3 S); triangle (26,136 (e) Calculated triangle elements, (FEM) elements, time iron step: loss; time 2.5(f) step: radial× 10−6 2.5flux S);× (densitiesd10) CaseS); in4 ( (15,107thed) Casemiddle triangle 4 of (15,107 airgap; elements, triangle (g) harmonic spectrum− of7 radial flux density; (h) rotor eddy-current loss. timeelements, step: time5 × 10 step:−7 S);5 (e×) Calculated10 S); (e) (FEM) Calculated iron (FEM)loss; (f) iron radial loss; flux (f) radialdensities flux in densities the middle in the of airgap; middle of airgap; (g) harmonic spectrum of radial flux density; (h) rotor eddy-current loss. (g) harmonic2.2. Stator Structurespectrum of radial flux density; (h) rotor eddy-current loss.

2.2. Stator StructureThe distribution of flux lines of the prototype with toroidal windings at rated load was shown 2.2. Statorin StructureFigure 3a. Some leakage flux lines can be seen around the outer slots. So the flux circuit was TheThemodified distribution by the of ofwindings flux flux lines in the of outer the prototype slots of the stator, with andtoroidal it will windings have resulted at at inrated the degradation load was shown of electromagnetic performance. Thus, the stator of the prototype was divided into two parts: inner inin Figure Figure 33a.a. Some leakageleakage fluxflux lineslines cancan bebe seenseen aroundaround thethe outerouter slots.slots. SoSo thethe fluxflux circuitcircuit waswas stator and outer stator shown in Figure 3b. modifiedmodified by the windings in in the the outer outer slots slots of of the the stator, stator, and it will have resulted in the degradation ofof electromagnetic performance. Thus, Thus, the the stator stator of of the the prototype prototype was divided into two parts: inner statorstator and and outer stator shown in Figure 33b.b.

Figure 3. (a) Distribution of flux lines of undivided stator with toroidal windings; (b) cross-section of divided stator and distribution of flux lines with outer stator of non-magnetic material.

Figure 3. (a) Distribution of flux lines of undivided stator with toroidal windings; (b) cross-section of Figure 3. (a) Distribution of flux lines of undivided stator with toroidal windings; (b) cross-section of divided stator and distribution of flux lines with outer stator of non-magnetic material. divided stator and distribution of flux lines with outer stator of non-magnetic material.

The inner stator was exactly the same with the conventional stator both in the structure and function, the outer stator was made of non-magnetic materials to solve the problem of flux leakage Energies 2018, 11, 562 7 of 21 Energies 2017, 10, x FOR PEER REVIEW 7 of 21

The inner stator was exactly the same with the conventional stator both in the structure and and functioned only for placement of the windings. Aluminum alloy (al-alloy) and epoxy glass cloth function, the outer stator was made of non-magnetic materials to solve the problem of flux leakage laminate sheet were successively considered for the manufacture of the outer stator. The distribution and functioned only for placement of the windings. Aluminum alloy (al-alloy) and epoxy glass cloth of the flux lines of the prototype, with a non-magnetic outer stator at rated load, was also shown in laminate sheet were successively considered for the manufacture of the outer stator. The distribution Figureof the2b. flux The lines problem of the of prototype, the leakage with flux a non-magn around theetic outer outer slots stator was at approximatelyrated load, was solved.also shown So thein influenceFigure of 2b. windings The problem in the of outer the leakage slots on flux the around electromagnetic the outer slots performance was approximately of the prototype solved. could So the be ignored.influence From of the windings calculations in the done,outer theslots power on the factor electromagnetic was increased performance from 0.9672 of the to 0.9761prototype and could 0.9729 for thebe ignored. outer stator From of the al-alloy calculations and epoxy done, glass the clothpower laminate factor was sheet, increased respectively. from 0.9672 to 0.9761 and 0.9729 for the outer stator of al-alloy and epoxy glass cloth laminate sheet, respectively. 2.3. Retaining Sleeve 2.3.In Retaining order to Sleeve shield the harmonic magnetic field in the rotor, an eddy current will be induced in the retainingIn order sleeveto shield and the magnet, harmonic resulting magnetic in field eddy-current in the rotor, losses. an eddy Based current on thewill above be induced 2-d FEA in methods,the retaining the influences sleeve and of themagnet, conductivity resulting of in the ed retainingdy-current sleeve losses. on Based the losseson the of above the sleeve 2-d FEA and magnetsmethods, are illustratedthe influences in Figure of the4 a,b,conductivity with the thicknessof the retaining of the sleevesleeve beingon the 10 losses mm. of The the conductivity sleeve and of themagnets magnets are wasillustrated 6.25 × in10 Figure5 S/m. 4a,b, As canwith be the seen, thickness the eddy-current of the sleeve lossbeing of 10 the mm. sleeve The firstconductivity increases proportionallyof the magnets with was the 6.25 conductivity, × 105 S/m.when As can conductivity be seen, theis eddy-current lower than 4loss× 10 of6 theS/m, sleeve and first then increases decreases withproportionally the conductivity. with the The conductivity, reason is that wh theen conductivity shielding effect is lower of thethan harmonic 4 × 106 S/m, magnetic and then field decreases of the sleevewith first the increases conductivity. with conductivity,The reason is sothat that the the shield eddying current effect of of the the harmonic sleeve increases magnetic proportionally field of the withsleeve conductivity, first increases whereas with conductivity, the resistance so of that the the sleeve eddy decreasescurrent of the proportionally sleeve increases with proportionally conductivity, consequently,with conductivity, the eddy-current whereas the loss resistance of the sleeve of the (product sleeve decreases of the square proportionally of the current with and conductivity, resistance) increasesconsequently, proportionally the eddy-current with the loss conductivity. of the sleeve When (product the of conductivity the square of is the higher current than and 4 ×resistance)106 S/m, increases proportionally with the conductivity. When the conductivity is higher than 4 × 106 S/m, the the harmonic magnetic field is completely shielded, the shielding effect of the sleeve no longer increases harmonic is completely shielded, the shielding effect of the sleeve no longer increases with conductivity, so the induced current can be viewed as constant, whereas the resistance still with conductivity, so the induced current can be viewed as constant, whereas the resistance still decreases proportionally with conductivity, so the eddy-current loss decreases with the conductivity. decreases proportionally with conductivity, so the eddy-current loss decreases with the conductivity. The changes of the eddy-current loss of the magnets with respect to conductivity are very little, The changes of the eddy-current loss of the magnets with respect to conductivity are very little, when when conductivity is lower than 105 S/m, because of the poor shielding effect of the harmonic conductivity is lower than 105 S/m, because of the poor shielding effect of the harmonic magnetic field magneticof the sleeve. field of As the the sleeve. shielding As effect the shieldingof the sleeve effect increases of the with sleeve conductivity, increases the with harmonic conductivity, magnetic the harmonicfield penetrating magneticfield into penetratingthe magnets into decreases, the magnets so the decreases, eddy-current so the loss eddy-current of magnets then loss ofdecreases magnets thengreatly. decreases The greatly.loss of the The magnets loss of can the be magnets ignored can with be conductivity ignored with ranges conductivity larger than ranges 4 × 10 larger6 S/m, thansince 4 6 × 10theS/m, harmonic since magnetic the harmonic field magneticpenetrating field into penetrating magnets has into been magnets completely has beenshielded. completely shielded.

250 104 103 200

Carbon fiber (W)

(W) 2 Carbon fiber 10 150 1 Ti-alloy

10 Ti-alloy 100 0 Ni-alloy 10 Ni-alloy

Sleeve Loss -1 50 10 Magnets Loss 10-2 0 -1 0 1 2 3 4 5 6 7 10 10 10 10 10 10 10 10 10 10-1 101 103 105 107 Sleeve conductivity (S/m) Sleeve conductivity (S/m) (a) (b)

Figure 4. Influences of conductivity of the sleeve materials on (a) sleeve loss; (b) magnet loss. Figure 4. Influences of conductivity of the sleeve materials on (a) sleeve loss; (b) magnet loss. Nickel alloy (Ni-alloy), titanium alloy (Ti-alloy) and carbon fiber are three typical materials for useNickel with alloythe retaining (Ni-alloy), sleeve titanium at present, alloy they (Ti-alloy) are mark anded in carbon the figures. fiber areIt can three be seen typical that materials the magnet for uselosses with the of the retaining rotor with sleeve Ni-alloy at present, and Ti-alloy they are sleeve marked are inabout the figures.half of that It can of bethe seencarbon that fiber the sleeve, magnet lossesbut of the the sleeve rotor losses with Ni-alloy are 20 times and Ti-alloymore than sleeve that are of the about carbon half offiber that sleeve. of the The carbon rotor fiber loss sleeve, with Ni- but the sleevealloy or losses Ti-alloy are sleeve 20 times is about more three than times that ofmore the than carbon stator fiber loss, sleeve. which The will rotor cause loss the with overheating Ni-alloy or Ti-alloyof the motor. sleeve To is reduce about the three rotor times loss more density, than the stator airgap loss, flux whichdensities will should cause be the decreased overheating according of the motor.to Equation To reduce (6). the With rotor the loss inner density, diameter the of airgap the st fluxator densitiesfixed, the shouldaxial length be decreased of the motor according will be to Equation (6). With the inner diameter of the stator fixed, the axial length of the motor will be increased Energies 2018, 11, 562 8 of 21 to maintain the output and the density will be decreased. As a result, the low-conductivity carbon-fiber was beneficial improving the torque density and decreasingthe axial length of the motor, and so was chosen as the material of the retaining sleeve.

2.4. Airgap Table2 presents the performances of the prototype with the airgap length of 1, 2, 3, 4 mm, calculated by 2-d FEA method. In order to maintain the rated output, the thickness of the magnets was increased with the increase of the airgap length. As can be seen, the corresponding thicknesses of magnets were 16, 18, 20, 22 mm, respectively.

Table 2. Electromagnetic performance of the prototype with different airgap length.

Cases 1 2 3 4 Airgap length (mm) 1 2 3 4 Magnet thickness (mm) 16 18 20 22 EMF (V) 220.9 220 219.3 217.6 Power (kW) 300 300 300 300 Rated current (A) 477.4 475.2 474.2 475 Torque ripple 3.8 3.5 3.1 2.5 Efficiency 98.06% 98.28% 98.40% 98.46% Power factor 0.9733 0.9753 0.9767 0.9741 Loss density of magnets (W/m3) 314.88 213.46 149.65 111.85 Loss density of sleeve (W/m3) 1803.68 976.03 582.53 364.77 Intensity of PM utilization (kg/kW) 0.022 0.0243 0.0266 0.0288

The distributions of the radial airgap flux density at the surface of the rotor, in no-load and rated-load conditions, were shown in Figure5a,b. The root mean square (RMS) values of the radial airgap flux density were almost identical, with different lengths of the airgap. The no-load (EMF) and rated current were also almost the same, as shown in Table2. Besides, the flux density distributions showed a characteristic dip in correspondence to each slot opening. As the airgap length increased, the dip became smaller, which meant the harmonic flux density caused by the stator slotting was reduced. Moreover, the amplitude of harmonic flux density, due to space harmonics of winding distribution and time harmonic components of the armature current, would also decrease with the increasing the airgap length, because of the increase of the magnetic resistance in the airgap. Figure5c shows the harmonic spectrum images corresponding to Figure5b. The fundamental amplitudes were almost the same, while the amplitudes of the harmonics decreased with the airgap length, which agreed well with above analysis. According to Equation (4), the eddy-current loss of the rotor loss could be reduced. The eddy-current losses of the carbon fiber sleeve and magnets induced by the harmonic flux density were plotted in the Figure5d. Both the sleeve and magnet losses decreased with the length of the airgap. The loss densities were computed and decrease with the airgap length, shown in Table2. The cooling capacity was limited for a certain rotor, so the loss density would be within the maximum allowable value, otherwise the rotor will have overheated. With the given length of airgap, the flux density of the airgap would have to be decreased in order to reduce the rotor loss density according to Equation (6), when it exceeds the maximum allowable value, and which will in turn increase the volume of the motor in Equation (1). Alternatively, the loss densities could also be reduced by an increase of the airgap length and thickness of the magnets, without affecting the volume. However, there was the dilemma that the intensity of PM utilization was greatly increased, as shown in Table2. As a comparison, it was 0.0167 kg/kW for a similar motor as illustrated in [6]. Besides, a thicker sleeve was called for in order to ensure the rotor strength remained the same, which will have further increased the difficulty of dissipation of heat for the rotor. Therefore, the increase of the airgap length is helpful to improve the torque density, and to decrease the axial length of a high-speed motor with flat structure, but at the expense of consuming more magnets. Finally, a 2-mm airgap was chosen for the prototype. Energies 2018, 11, 562 9 of 21 EnergiesEnergies 2017 2017, 10, 10, x, xFOR FOR PEER PEER REVIEW REVIEW 9 of 921 of 21

B =0.5347 T (1 mm) B =0.5343 T (2 mm) Bδ=0.5347δ T (1 mm) Bδδ=0.5343 T (2 mm) B δB=0.5213δ=0.5213 T (1T (1mm) mm) Bδ=0.5191 Bδ=0.5191 T (2 T mm) (2 mm)

B B=0.5338δ=0.5338 T T (3 (3 mm) mm) BBδ=0.5329=0.5329 T (4 mm) B δB=0.518=0.518 T (3T (3mm) mm) Bδ=0.5169 B =0.5169 T (4 T mm) (4 mm) 1.01.0 δ δ 1.01.0 δ δ (T) (T) (T) (T) 0.50.5 0.50.5

0.0 0.0 0.0 0.0

-0.5 -0.5 -0.5 -0.5 Airgap flux density Airgap flux density Airgap flux density density Airgap flux Airgap flux density Airgap flux density -1.0 -1.0 density Airgap flux -1.0 0 20 40 60 80 100 120 140 160 180 -1.00 20 40 60 80 100 120 140 160 180 0 20 40Mechanical 60 80 angle 100 120(deg) 140 160 180 0 20Mechanical 40 60 80angle 100 (deg) 120 140 160 180 Mechanical angle (deg) Mechanical angle (deg) (a) (b) (a) (b) 0.8 1 mm 1500 0.8 21 mmmm 1500 Retaining sleeve Magnets Retaining sleeve 0.6 32 mmmm 1200 1200 Magnets 0.6 43 mmmm 900 4 mm 0.4 900 0.4 600 0.2 600 0.2 300 Eddy-current losses (W) losses Eddy-current 300 0.0 0 Eddy-current losses (W) losses Eddy-current 0.0 density(T) flux of Amplitude 1 3 5 7 9 1117192123253133353739 1234 Harmonics 0 Airgap length (mm) Amplitude of flux density(T) flux of Amplitude 1 3 5 7 9 1117192123253133353739 1234 Harmonics(c) Airgap(d) length (mm) Figure 5. Distribution( ofc) radial airgap flux densities at the surface of the rotor with(d different) thickness Figure 5. Distribution of radial airgap flux densities at the surface of the rotor with different thickness of magnets (a) at no load; (b) at rated load; (c) harmonic spectrum of the radial airgap flux density at Figure 5. Distribution of radial airgap flux densities at the surface of the rotor with different thickness of magnetsrated load; (a) at (d no) eddy-current load; (b) at losses rated of load; retaining (c) harmonic sleeve and spectrum magnets versus of the airgap radial length airgap at fluxrated density load. at ratedof load;magnets (d) eddy-current(a) at no load; losses(b) at rated of retaining load; (c) sleeve harmonic and spectrum magnets versusof the ra airgapdial airgap length flux at rateddensity load. at rated load; (d) eddy-current losses of retaining sleeve and magnets versus airgap length at rated load. 2.5. Segmentation of Magnets 2.5. Segmentation of Magnets 2.5. SegmentationCircumferential of Magnets and axial segmentations of permanent magnets were analyzed to reduce the Circumferentialeddy-current loss andof magnets, axial segmentations based on the 3-d offinite permanent element (FE) magnets model in were Section analyzed 3.2. The tovariations reduce the of magnetCircumferential loss with theand number axial segmentations of circumferential of permanentand axial segments magnets were were plotted analyzed in Figure to reduce 6a,b. the eddy-currenteddy-current loss loss of magnets,of magnets, based based on on the the 3-d 3-d finite finite element element (FE) (FE) modelmodel in Section 3.2.3.2. The The variations variations of magnetof magnet loss loss with with the the number number of of circumferential circumferential and and axial axial segments segments werewere plottedplotted in Figure 66a,b.a,b. 150 150 (W) (W) 150 100150

100

(W) (W) 10050

100

Magnets Loss Magnets Loss 50 500 024681012 Magnets Loss

Magnets Loss 0 5 10 15 20 50 Number of circumferential segmentations Number of axial segmentations (a) 0 (b) 0 5 10 15 20 024681012 FigureNumber 6. (a) Eddy-current of circumferential losses segmentations of magnets versus circumferentialNumber segmentation of axial segmentations number; (b) eddy- current losses of magnets(a) versus axial segmentation number. (b)

Figure 6. (a) Eddy-current losses of magnets versus circumferential segmentation number; (b) eddy- FigureAs 6. the(a) Eddy-currentnumber of circumferential losses of magnets and versus axial circumferentialsegments increases, segmentation the magnet number; loss decreases (b) eddy- current losses of magnets versus axial segmentation number. currentgradually. losses It means of magnets the airgap versus flux axial density segmentation can be increased number. with the increase of the segment number of magnets, within the maximum allowable loss density of the rotor. With the fixed diameter of the stator,As thethe numberaxial length of circumferential of the motor willand beaxial decreased segments with increases, the segment the magnetnumber. loss When decreases the gradually.Ascircumferential the number It means number of the circumferential airgap of segments flux density is and larger can axial thbean increased segments 15, the loss with increases, change the increase becomes the of magnet thevery segment small loss as decreases number the gradually.of magnets, It means within the the airgap maximum flux density allowable can beloss increased density of with the the rotor. increase With ofthe the fixed segment diameter number of the of magnets,stator, within the axial the maximumlength of allowablethe motorloss will density be decreased of the rotor. with With the thesegment fixed diameternumber. ofWhen thestator, the thecircumferential axial length of thenumber motor of willsegments be decreased is larger with than the 15, segmentthe loss number.change becomes When thevery circumferential small as the number of segments is larger than 15, the loss change becomes very small as the number increases. Energies 2018, 11, 562 10 of 21

The loss of magnets circumferentially divided into 20 segments is nearly 35.1% of that not segmented. Energies 2017, 10, x FOR PEER REVIEW 10 of 21 Likewise, the loss change becomes very small as the number increases, when the axial number of segmentsnumber is larger increases. than The six. loss The of lossmagnets of the circumferentially magnets that was divided axially into divided 20 segments into 12is nearly segments 35.1% is of nearly 11.9%that of thatnot segmented. not segmented. Likewise, Nevertheless, the loss change the magnetsbecomes very cannot small be as divided the number into increases, too small when size, the because it is probablyaxial number fragile of segments during the is larger process than of six. assembly. The loss Thus,of the magnets considering that was the manufacturingaxially divided into feasibility, 12 the magnetssegments were is nearly circumferentially 11.9% of that not divided segmented. into five Nevertheless, segments, the and magnets the magnet cannot loss be divided was reduced into by 19.1%too compared small size, with because that it of is the probably non-segmented. fragile during Though the process the axial of assembly. segment Thus, of the considering magnets was the very manufacturing feasibility, the magnets were circumferentially divided into five segments, and the effective to reduce their eddy-current loss, the axial divisions were not implemented for the prototype magnet loss was reduced by 19.1% compared with that of the non-segmented. Though the axial in order to simplify the manufacturing process. segment of the magnets was very effective to reduce their eddy-current loss, the axial divisions were not implemented for the prototype in order to simplify the manufacturing process. 2.6. Electromagnetic Performances The2.6. Electromagnetic configuration Performances of the prototype is provided in Figure7a and the specifications are listed in Table3. PoleThe fillers configuration were assembled of the prototype between is theprovided magnets in Figure to improve 7a and the the strength specifications of the are rotor. listed The in disks wereTable used 3. to Pole fix fillers the magnets were assembled axially. between The waveform the magnets of theto improve rated torque the strength was shownof the rotor. in Figure The 7b. The torquedisks were ripple used was to fix about the magnets 1%. The axially. waveforms The wa ofveform the lineof the back rated EMF, torque at nowas load, shown were in Figure shown in Figure7b.7 c.The The torque total ripple harmonic was about distortion 1%. The (THD) waveforms was of about the line 0.84%. back TheEMF, waveforms at no load, were of rated shown currents in wereFigure shown 7c. in The Figure total7 harmonicd. The THD distortion of the (THD) current was curveabout was0.84%. only The aboutwaveforms 0.44%, of rated hardly currents with any harmonicswere shown component. in Figure Thus, 7d. theThe prototypeTHD of the showed current goodcurve electromagneticwas only about 0.44%, performance. hardly with any harmonics component. Thus, the prototype showed good electromagnetic performance.

Retaining sleeve 300 Magnets AVG=239N⋅m Rotor ) 275 m ⋅ N ( 250

Windings 225 Torque Torque

Disks 200 Outer stator 180 185 190 195 200 Pole fillers Inner stator Time (ms) (a) (b)

800 1000

400 500

0 0

-400 Current (A) -500 (V)

-800 -1000 0.0 0.5 1.0 1.5 2.0 2.5 198 199 200 Time (ms) Time (ms) (c) (d)

Figure 7. (a) Configuration of the prototype; (b) waveform of the rated torque; (c) waveforms of no- Figureload 7. line(a) back Configuration EMF; (d) waveforms of the prototype; of rated current. (b) waveform of the rated torque; (c) waveforms of no-load line back EMF; (d) waveforms of rated current. Table 3. Specifications of the prototype. Table 3. Specifications of the prototype. Parameters Value Parameters Value Poles number 4 Thickness of sleeve (mm) 10 Parameters Value Parameters Value Slots Number 36 Thickness of Magnet (mm) 18 PolesDo numberof outer stator (mm) 4 570 Effective Thickness length of sleeve (mm) (mm) 80 10 Slots Number 36 Thickness of Magnet (mm) 18 Do of outerDi of stator outer (mm) stator (mm) 570 490 Material Effective of inner length stator (mm) 35WW250 80 Di of outerDi of stator inner (mm) stator (mm) 490 294 Material Material of outer of inner stator stator Al-alloy 35WW250 Di of innerAirgap stator length (mm) (mm) 294 2 Material Material of retaining of outer sleeve stator Carbon Al-alloyfiber Airgap length (mm) 2 Material of retaining sleeve Carbon fiber

Energies 2018, 11, 562 11 of 21

Energies 2017, 10, x FOR PEER REVIEW 11 of 21 3. Analysis of Losses and Evaluation of Effects of Influencing Factors 3. Analysis of Losses and Evaluation of Effects of Influencing Factors 3.1. Copper Loss 3.1. Copper Loss The AC loss of the windings is greatly dependent on the density of the magnetic field and the frequencyThe atAC the loss location of the ofwindings the windings. is greatly As dependent the density on of the the density magnetic of fieldthe magnetic is considerable field and stronger the infrequency the iron core at the slots, location whereas of the very windings. small As in thethe air,dens theity innerof the slotmagnetic windings field is and considerable end-windings stronger losses in the iron core slots, whereas very small in the air, the inner slot windings and end-windings losses need to be calculated separately. The toroidal windings were divided into three parts: the windings in need to be calculated separately. The toroidal windings were divided into three parts: the windings the inner slots (inner-slot-wingdings), the windings in the outer slots of stator (outer-slot-wingdings), in the inner slots (inner-slot-wingdings), the windings in the outer slots of stator (outer-slot- and the remaining part of the windings (end-windings), shown in Figure8a. The strand number wingdings), and the remaining part of the windings (end-windings), shown in Figure 8a. The strand of each conductor was 15. The 2-d FEA models of conductors in one inner slot, outer slot and end number of each conductor was 15. The 2-d FEA models of conductors in one inner slot, outer slot and windingsend windings were builtwere andbuilt meshed and meshed as Figure as Figures8b–d. 8b–d. Based Based on the on models, the models, the copper the copper losses losses of the of the three partsthree were parts calculated were calculated and are and given are ingiven Table in4 Table, respectively, 4, respectively, with the with outer the statorouter stator material material of silicon of steelsilicon sheet, steel al-alloy sheet, andal-alloy epoxy and glass epox clothy glass laminate. cloth laminate. It can be It seencan be that seen the that end-windings the end-windings loss accounts loss foraccounts the majority for the of themajority copper of loss the for copper the prototype. loss for the Compared prototype. with Compared the outer statorwith the material outer ofstator silicon steelmaterial sheet, theof silicon copper steel loss wassheet, decreased the copper by 226.4 loss W,was about decrease 10.4%,d afterby 226.4 replacement W, about of the10.4%, outer after stator materialreplacement with al-alloyof the outer or epoxy stator glass material cloth with laminate. al-alloy And or theepoxy AC glass copper cloth loss laminate. was 17.4%, And larger the AC than thecopper DC loss. loss was 17.4%, larger than the DC loss.

Figure 8. (a) Coil segments for toroidal windings; FEA models and meshes the conductors of, (b) Figure 8. (a) Coil segments for toroidal windings; FEA models and meshes the conductors of, (b) inner- inner-slot winding; (c) outer-slot winding; (d) end winding. slot winding; (c) outer-slot winding; (d) end winding.

Table 4. Copper loss with different materials of outer stator. Table 4. Copper loss with different materials of outer stator. Material of Outer Stator Silicon Steel Sheet Al-Alloy/Epoxy Glass Cloth Laminate Inner-slot-wingdingsMaterial of Outer Stator loss (W) Silicon 531.5 Steel Sheet Al-Alloy/Epoxy 531.5 Glass Cloth Laminate Inner-slot-wingdingsOuter-slot-wingdings loss loss (W) (W) 531.5 531.5 305.1 531.5 Outer-slot-wingdingsEnd-windings loss loss (W) (W) 1106 531.5 1106 305.1 End-windingsTotal copper loss loss (W) (W) 2169 1106 1942.6 1106 Total copper loss (W) 2169 1942.6 With the outer stator material of al-alloy or epoxy glass cloth laminate, the leakage magnetic fieldWith in the outer statorslot caused material by ofthe al-alloy windings orepoxy is comparable glass cloth to laminate,that in the the air, leakage so the magnetic outer-slot- field inwindings the outer loss slot was caused included by the in windings the end-windings is comparable loss for to thatthe following in the air, analysis. so the outer-slot-windings The variation of losscopper was includedloss with inrespect the end-windings to strand number loss forof thethe followingconductors analysis. was investigated The variation under of sinusoidal copper loss voltage and 8-kHz carrier-frequency PWM excitations, and then compared with DC loss as well, with respect to strand number of the conductors was investigated under sinusoidal voltage and 8-kHz shown in Figure 9. The strand number of the conductors ranges from 15 to 150, so the corresponding carrier-frequency PWM excitations, and then compared with DC loss as well, shown in Figure9. diameters of the wire are from 2.26 mm to 0.71 mm, maintaining the same section area for the The strand number of the conductors ranges from 15 to 150, so the corresponding diameters of the conductors. It can be seen that the copper loss powered by PWM excitation is much higher than sine wire are from 2.26 mm to 0.71 mm, maintaining the same section area for the conductors. It can be excitation. The copper loss will be largely underestimated, without taking proximity and skin losses seeninto that consideration. the copper loss powered by PWM excitation is much higher than sine excitation. The copper loss will be largely underestimated, without taking proximity and skin losses into consideration.

Energies 2018, 11, 562 12 of 21 Energies 2017, 10, x FOR PEER REVIEW 12 of 21

1000 1500 Sine Sine 800 PWM PWM DC 1450 DC 600 1400 Loss (W) Loss 400 Loss (W)

200 1350 0 50 100 150 0 50 100 150 Strands Strands (a) (b)

2400 Sine PWM 2200 DC

2000

Loss (W) Loss 1800

0 50 100 150 Strand number (c)

Figure 9. Influences of the strand number of conductors on (a) inner-slot-windings loss; (b) end- Figurewindings 9. Influences loss; (c) oftotal the copper strand loss, number under sine of conductors voltage and on8 k( acarrier-frequency) inner-slot-windings PWM excitations, loss; (b) end- windingscompared loss; with (c) total DC loss copper as well. loss, under sine voltage and 8 k carrier-frequency PWM excitations, compared with DC loss as well. Under the sinusoidal voltage excitation, the copper loss decreases with the increase of strand Undernumber the and sinusoidal the change voltage slows excitation,down gradually. the copper The copper loss decreases loss for the with slot-in-windings the increase ofwas strand decreased by 216.5 W, about 68.7%, while the end-windings loss will have been decreased by 43 W, number and the change slows down gradually. The copper loss for the slot-in-windings was decreased about 3.1%, and the total copper loss will have been decreased by 15.4%, when the strand number by 216.5 W, about 68.7%, while the end-windings loss will have been decreased by 43 W, about 3.1%, increases from 15 to 150. The reduction of the copper loss is mainly contributed by the slot-in- and thewindings. total copper The change loss will of copper have been loss is decreased very small by and 15.4%, can be when ignored, the strandwhen the number strand increasesnumber is from 15 to 150.larger The than reduction 55. Under of the the PWM copper excitation, loss is the mainly influence contributed of increasing by the strand slot-in-windings. number on the Thecopper change of copperloss is loss more is veryobvious. small And and the can change be ignored, of copper when loss theis still strand large number even when is larger the strand than number 55. Under is the PWMlarger excitation, than 55. the The influence copper loss of increasing for the inner-slot-win strand numberdings onwill the have copper been lossdecreased is more by obvious.199 W, about And the change32.2%, of copper while lossthe end-windings is still large even loss will when have the been strand decreased number by is 25 larger W, about than 55.1.8%, The and copper the total loss for the inner-slot-windingswindings loss will have will been have decreased been decreased by 11%, by when 199 the W, strand about 32.2%,number while increases the from end-windings 55 to 150. loss will haveTherefore, been decreasedthe copper loss by 25can W, be aboutfurther 1.8%, reduced and by the decreasing total windings the strand loss number willhave of the been conductors decreased under PWM excitation. by 11%, when the strand number increases from 55 to 150. Therefore, the copper loss can be further reduced3.2. byIron decreasing Loss the strand number of the conductors under PWM excitation.

3.2. Iron LossThe magnetization of the stator core consists of alternative magnetization and rotating magnetization. Most of the traces of magnetic flux lines are distorted elliptically rotating flux. The Theclassic magnetization loss separation model of the of statorEquation core (8) was consists based ofon the alternative alternative magnetization magnetization and and widely rotating magnetization.used in low-frequency Most of the motors traces for ofaccuracy magnetic results. flux However, lines are it may distorted underestimate elliptically the iron rotating loss in flux. The classichigh-frequency loss separation machines, model so the ofimprov Equationed model (8) was built based as shown on the in alternative [18]: magnetization and widely used in low-frequency motors for accuracy results. However, it may15.. underestimate 15 the iron nn  αα 2 k 1 T dB() t dBθ () t loss in high-frequencypkkfBBkkfBB=++++⋅+() machines, so() the improved()22 model wase built as shownr in [18]: dt iron h kmaj k min c kmaj k min 0 (9) == 8. 763363 T dt dt kk11  n   n    1.5 1.5 = α + α + ( )2 2 + 2 + ke · 1 R T dBr(t) + dBθ (t) piron ∑ khk f Bkmaj Bkmin ∑ kc k f Bkmaj Bkmin 8.763363 T 0 dt dt dt (9) Here,k=1 Br and Bθ are the radialk=1 and circumferential components of the elliptically rotating flux density vector, and Bkmaj and Bkmin are the harmonic amplitudes of Br and Bθ, k is the harmonic order. Here, Br and Bθ are the radial and circumferential components of the elliptically rotating flux density vector, and Bkmaj and Bkmin are the harmonic amplitudes of Br and Bθ, k is the harmonic order. On the basis of the improved iron loss model, the iron losses of the prototype were computed, as shown Energies 2018, 11, 562 13 of 21 in Table5, with the outer stator material of silicon steel sheet, al-alloy and epoxy glass cloth laminate, respectively. The iron loss is thus the least with the use of silicon steel sheet as outer stator material.

Table 5. Losses of stator with different materials of outer stator.

Outer Stator Material Silicon Steel Sheet Al-Alloy Epoxy Glass Cloth Laminate Iron loss (W) 1795 1901 1909 EnergiesOuter 2017 stator, 10, lossx FOR (W) PEER REVIEW / 1083 0 13 of 21 Shell loss (W) 2583 953 1366 On theTotal basis loss of (W) the improved iron 4378loss model, the iron 3937losses of the prototype were 3275 computed, as shown in Table 5, with the outer stator material of silicon steel sheet, al-alloy and epoxy glass cloth laminate, respectively. The iron loss is thus the least with the use of silicon steel sheet as outer stator Due to the alternative leakage flux formed by the outer-slot-windings, additional eddy-current material. losses would be induced in the metal housing, as well as the outer stator of al-alloy. With a 20-mm Due to the alternative leakage flux formed by the outer-slot-windings, additional eddy-current thicknesslosses stainless would be steel induced housing, in the themetal losses housing, in the as well housing as the and outer outer stator stator of al-alloy. were With also calculateda 20-mm in Table5thickness by 3-d FEAstainless method. steel Figurehousing, 10 thea shows losses thein the 3-d housing FE mesh and model outer ofstator the prototype,were also calculated which is 1/8in of the wholeTable region5 by 3-d due FEA to method. the symmetry. Figure 10a Figure shows 10 theb shows3-d FE mesh the distribution model of the ofprototype, eddy current which generatedis 1/8 in theof outer the whole stator region and due shell to the with symmetry. the al-alloy Figure outer 10b shows stator. the As distribution can be seen of eddy in Tablecurrent5, generated the housing loss isin highestthe outer with stator the and outer shell with stator the made al-alloy of outer silicon stator. steel As sheet. can be Althoughseen in Table no 5, eddy-current the housing loss loss is generatedis highest in the with outer the outer stator stator of epoxy made glassof silicon cloth steel laminate, sheet. Although the housing no eddy-current loss is still loss huge. is generated Considering the poorin the thermal outer stator conductivity of epoxy ofglass epoxy cloth glass laminate, cloth the laminate, housing the loss losses is still arehuge. impossible Considering to bethe dissipated poor thermal conductivity of epoxy glass cloth laminate, the losses are impossible to be dissipated by by water-cooling of the housing. By contrast, the housing loss with the outer stator of al-alloy is lowest, water-cooling of the housing. By contrast, the housing loss with the outer stator of al-alloy is lowest, and the outer stator loss can be conducted quickly to the housing. Therefore, al-alloy was thought to and the outer stator loss can be conducted quickly to the housing. Therefore, al-alloy was thought to be thebe wisest the wisest choice choice of materialof material for for the the outer outer stator. stator.

J(A/m2) 4.49×106 Symmetry 3.19×106 6 plane 3.89×10 3.59×106 3.29×106 2.99×106 2.69×106 2.39×106 2.09×106 1.79×106 1.49×106 1.19×106 8.99×105 5.99×105 2.99×105 (a) (b)

Figure 10. (a) 3-d FE mesh model (360,409 tetrahedron element, time step: 5 × 10−6 S); (b) Distribution Figure 10. (a) 3-d FE mesh model (360,409 tetrahedron element, time step: 5 × 10−6 S); (b) Distribution of eddy-current density in the shell and outer stator with outer stator material of al-alloy. of eddy-current density in the shell and outer stator with outer stator material of al-alloy. Table 5. Losses of stator with different materials of outer stator. 3.3. Eddy-Current Loss of the Rotor Outer Stator Material Silicon Steel Sheet Al-Alloy Epoxy Glass Cloth Laminate The eddy-currentIron loss losses (W) of the rotor were1795 also analyzed 1901 based on the 1909 above 3-d FE model to take Outer stator loss (W) / 1083 0 account of the influences of the variation of the eddy current of the rotor along the axial direction. Shell loss (W) 2583 953 1366 With al-alloy pole fillers,Total loss the (W) distributions 4378 of the eddy-current 3937 density on the 3275 sleeve, magnets and pole fillers were provided for the one-eighth model in Figure 11a–c. Several rings of the eddy current can be observed3.3. Eddy-Current on these components. Loss of the Rotor The density of the current is lower on the ends than middle. Due to the good conductivityThe eddy-current of al-alloy, losses the of densitythe rotor of were current also analyzed of the filler based is higheron the above than the3-d FE sleeve model and to take magnets. Ti-alloy,account stainless of the steelinfluences (s-steel) of the and variation epoxy of resin the ed weredy current also considered of the rotor asalong candidates the axial todirection. reduce the eddy-currentWith al-alloy loss pole of the fillers, fillers. the As distributions can be seen of inth Tablee eddy-current6, the filler density losses on are the a littlesleeve, different, magnets asand given for thepole three fillers metal were fillers.provided The for rotor the one-eighth eddy-current model loss in Figure is least 11a–c. with Several epoxy rings resin of the pole eddy fillers. current But the thermalcan conductivitybe observed on of these resin components. pole fillers The is poor, density so of it the is not current helpful is lower for heaton the dissipation ends than middle. in the rotor. Due to the good conductivity of al-alloy, the density of current of the filler is higher than the sleeve and magnets. Ti-alloy, stainless steel (s-steel) and epoxy resin were also considered as candidates to reduce the eddy-current loss of the fillers. As can be seen in Table 6, the filler losses are a little different, as given for the three metal fillers. The rotor eddy-current loss is least with epoxy resin pole fillers. But the thermal conductivity of resin pole fillers is poor, so it is not helpful for heat dissipation in the rotor. With the advantageous property of mechanical strength and thermal conductivity, metal

Energies 2018, 11, 562 14 of 21

With the advantageous property of mechanical strength and thermal conductivity, metal materials are Energies 2017, 10, x FOR PEER REVIEW 14 of 21 competitive as pole fillers. To reduce the eddy-current loss of the metal pole fillers, and to maintain the beneficialmaterials are properties competitive of metal,as pole metalfillers. To stack reduce technology the eddy-current was employed. loss of the Themetal configuration pole fillers, and of the metal-stackto maintain pole fillerthe beneficial was exhibited properties in Figure of 8metal,d. It wasmetal made stack up technology of thin sheets was of employed. metal, which The were gluedconfiguration under compression of the metal-stack with a high-temperature pole filler was exhibited adhesive in Figure to achieve 8d. It thewas axialmade resistivity. up of thin sheets The losses of theof pole metal, fillers which constructed were glued byunder 2-mm compression s-steel stack with and a high-temperature 1-mm, 2-mm al-alloy adhesive stack to achieve were computedthe axial in Tableresistivity.6. As a result, The losses the eddy-current of the pole fillers loss ofconstr poleucted fillers by could2-mm bes-steel ignoredin stack and the 1-mm, 2-mm 2-mm s-steel al-alloy stack and 1-mmstack al-alloy were stack. computed The in total Table eddy-current 6. As a result, loss the of eddy-current the rotor was loss close of pole to fillers that of could the rotorbe ignoredin with epoxy resinthe fillers. 2-mm With s-steel 2-mm stack s-steel and 1-mm stack, al-alloy the distributions stack. The total of eddy-current the eddy-current loss of density the rotor and was vectors close to were that of the rotor with epoxy resin fillers. With 2-mm s-steel stack, the distributions of the eddy-current shown in Figure 11e,f. The eddy-current densities were largely reduced, and the current that flows density and vectors were shown in Figure 11e,f. The eddy-current densities were largely reduced, axiallyand was the almostcurrent eliminated.that flows axially was almost eliminated.

J(A/m2) 2 J(A/m ) 2 5 6 J(A/m ) 4.94×10 1.40×10 7 5 6 1.37×10 4.28×10 1.22×10 7 5 6 1.19×10 3.62×10 1.03×10 7 5 5 1.00×10 2.97×10 Symmetry 8.41×10 6 5 5 Symmetry 8.21×10 2.31×10 plane 6.54×10 6 5 5 plane 6.39×10 1.65×10 4.67×10 6 4 5 4.56×10 9.91×10 2.80×10 6 4 4 2.74×10 3.32×10 9.35×10 5 2 0 9.14×10 3.15×10 2.70×10 3 Symmetry plane 2.25×10

(a) (b) (c)

(d) (e) (f)

Figure 11. Distributions of eddy-current density of (a) sleeve; (b) magnets; (c) pole filler; (d) Figureconfiguration 11. Distributions of the metal-stack of eddy-current pole filler; density distributions of (a) sleeve; of ( (eb) )eddy-current magnets; (c) density; pole filler; (f) eddy-current (d) configuration of thevectors metal-stack in the metal-stack pole filler; pole distributions filler. of (e) eddy-current density; (f) eddy-current vectors in the metal-stack pole filler. Table 6. Eddy-current losses of rotor with different pole fillers. Table 6. Eddy-current losses of rotor with different pole fillers. Material of Pole Fillers Sleeve Loss (W) Magnet Loss (W) Filler Loss (W) Total (W) Al-alloy 491.2 130.3 43.2 664.7 Material of Pole Fillers Sleeve Loss (W) Magnet Loss (W) Filler Loss (W) Total (W) Ti-alloy 504.7 133.9 42.1 680.7 Al-alloyS-steel 491.2500.3 130.3128.6 58.1 43.2 687 664.7 Ti-alloyEpoxy resin 504.7 504.7 133.9 126.2 42.10 630.9 680.7 2-mmS-steel s-steel stack 500.3 499.3 128.6 128.5 0.64 58.1 628.4 687 Epoxy resin 504.7 126.2 0 630.9 1-mm al-alloy stack 499.1 128.4 1.7 629.2 2-mm s-steel stack 499.3 128.5 0.64 628.4 2-mm al-alloy stack 498.6 128.6 7.6 634.8 1-mm al-alloy stack 499.1 128.4 1.7 629.2 2-mm al-alloy stack 498.6 128.6 7.6 634.8 3.4. Evaluation of Influencing Factors on Total Loss

3.4. EvaluationAccording of Influencing to the above Factors studies on of Total the electromagne Loss tic losses, the effects of the influencing factors (such as strand number of conductors, division of stator and employment of non-magnetic outer Accordingstator, material to the of pole above fillers,) studies on the of total the electromagneticloss were concluded losses, in Figure the effects 12. Theof stator the was influencing undivided, factors (suchthe as strand strand number number was of 15, conductors, and al-alloy division pole fillers of were stator employed and employment for the original of non-magnetic prototype. The outer stator,strand material number of pole was fillers,)increased on to the 55 totalfor the loss first were case. concluded The stator was in Figure divided 12 and. The al-alloy stator was was used undivided, as the strandthe outer number stator was for case 15, and 2. Case al-alloy 3 was pole the sum fillers of werethe above employed two methods. for the originalAnd the 2-mm prototype. s-steel The stack strand numberpole was fillers increased were adopted to 55 for for case the 4 first on basis case. of The case stator 3. Here, was the divided stator loss and includes al-alloy the was iron usedloss of as the

Energies 2018, 11, 562 15 of 21 outer stator for case 2. Case 3 was the sum of the above two methods. And the 2-mm s-steel stack pole fillers were adopted for case 4 on basis of case 3. Here, the stator loss includes the iron loss of the inner Energies 2017, 10, x FOR PEER REVIEW 15 of 21 stator, the eddy-current losses of the outer stator and housing. The rotor loss includes eddy-current lossesEnergiesthe in inner the 2017 sleeve, stator,, 10, x FOR the magnets, PEEReddy-current REVIEW fillers, losses and frictionof the oute lossr stator of the and rotor housing. [28]. ItThe can rotor be loss seen includes that the 15eddy- totalof 21 loss couldcurrent be decreased losses in bythe 5.3%sleeve, by magnets, only increasing fillers, and the friction strand loss number of the ro oftor the[28]. conductors, It can be seen 8.8% that bythe only the inner stator, the eddy-current losses of the outer stator and housing. The rotor loss includes eddy- divisiontotal of loss the could stator be anddecreased use of by an 5.3% al-alloy by only outer incr stator.easing the By strand a combination number of ofthe the conductors, two methods, 8.8% the current losses in the sleeve, magnets, fillers, and friction loss of the rotor [28]. It can be seen that the total lossby only would division be decreased of the stator by and 11.8%. use of And an al-allo totaly loss outer can stator. be further By a combination decreased of by the only two 0.7%methods, with the total loss could be decreased by 5.3% by only increasing the strand number of the conductors, 8.8% use ofthe the total 2-mm loss would s-steel be stack decreased pole fillers,by 11.8%. but And it is tota meaningfull loss can befor further the rotor,decreased due by to only the 0.7% poor with thermal bythe only use ofdivision the 2-mm of the s-steel stator stack and pole use offillers, an al-allo but ity is outer meaningful stator. By for a thecombination rotor, due of to the the two poor methods, thermal conductivity of the carbon fiber sleeve. theconductivity total loss wouldof the carbonbe decreased fiber sleeve. by 11.8%. And total loss can be further decreased by only 0.7% with the use of the 2-mm s-steel stack pole fillers, but it is meaningful for the rotor, due to the poor thermal conductivity of the carbon fiber sleeve. Copper loss Stator loss Rotor loss 8000 -5.3% Copper loss Stator-8.8% loss-11.8% Rotor-12.5% loss 8000 6000 -5.3% -8.8% -11.8% -12.5% 6000 4000 Losses (W) Losses 4000 2000 Losses (W) Losses 2000 0 Origin case 1 case 2 case 3 case 4 0 Figure 12. Evaluation of influencing factors on the total loss. Figure 12. EvaluationOrigin of case influencing 1 case 2 factors case 3 on case the total4 loss. 3.5. Influences of Carrier FigureFrequency 12. Evaluation of PWM Inverter of influencing on the factorsLosses on the total loss. 3.5. Influences of Carrier Frequency of PWM Inverter on the Losses 3.5. InfluencesPowered ofby Carrier the PWM Frequency inverter, of PWM lots ofInverter harmonic on the components Losses of the current will be generated, Poweredwhich will by result the in PWM an increase inverter, of the lots electromagnetic of harmonic losses. components With the of carrier the current frequencies will of be 8, generated,12, 16 whichand will 20Powered result kHz, inthe by an copperthe increase PWM loss, ofinverter, stator the electromagnetic loss lots and of harmonic rotor eddy-current losses. components With loss the of carrierofthe the current optimized frequencies will beprototype, generated, of 8, 12, at 16 and which will result in an increase of the electromagnetic losses. With the carrier frequencies of 8, 12, 16 20 kHz,rated the load, copper were loss, calculated stator in loss Figure and 13, rotor respectively eddy-current. It can lossbe seen of thethat optimizedthe total loss prototype, was increased at rated andlargely 20 bykHz, the the PWM copper inverter, loss, andstator the loss corresponding and rotor eddy-current increasing percentages loss of the were optimized 36.1%, prototype,25.3%, 18.9% at load,rated were load, calculated were calculated in Figure in 13 Figure, respectively. 13, respectively It can. beIt can seen be that seen the that total the total loss loss was was increased increased largely by theand PWM 14.8%, inverter, compared and with the sinusoidal corresponding excitation. increasing As the carrier percentages frequency were increases, 36.1%, the 25.3%, total loss 18.9% was and largelygradually by theclose PWM to that inverter, of the and sinusoidal the corresponding excitation. increasing The copper percentages loss and were stator 36.1%, loss 25.3%,were a 18.9% little 14.8%, compared with sinusoidal excitation. As the carrier frequency increases, the total loss was anddifferent 14.8%, as compared the carrier with frequency sinusoidal increased, excitation. but As th thee variation carrier frequency of rotor eddy-current increases, the loss total was loss verywas graduallygraduallyhuge. close As the close to carrier that to of thatfrequency the of sinusoidal the increased sinusoidal excitation. from excitati 8 kHz Theon. to The copper20 kHz, copper lossthe totalloss and lossand stator willstator loss have loss were been were a decreased little a little different as thedifferentby carrier 21.3%. frequencyas Meanwhile, the carrier increased, the frequency reduction but increased, of the rotor variation loss but accounted the of variation rotor for eddy-current 17%, of rotor and eddy-currentthe lossreductions was veryloss of the was huge. copper very As the carrierhuge.loss frequency and As thestator carrier increased loss frequency contributed from increased 8 kHz1.5% toand from 20 2.8%, kHz,8 kHz respectively. the to 20 total kHz, loss the Therefore, total will loss have willthe been haverotor decreased been loss decreasedcould by be 21.3%. Meanwhile,byreduced 21.3%. thelargely Meanwhile, reduction by the theof increase reduction rotor loss of ofthe accounted rotor carrier loss accountedfrequency, for 17%, for andwhich 17%, the wasand reductions thevery reductions helpful of the to of copper reducethe copper lossthe and statorlosstemperature loss and contributed stator rise loss of 1.5%the contributed rotor, and but 2.8%, its1.5% effects respectively. and on 2.8%, coppe respectively. Therefore,r and stator the Therefore,losses rotor were loss the not could rotor as high beloss reducedas couldthe rotor be largely reduced largely by the increase of the carrier frequency, which was very helpful to reduce the by theloss. increase of the carrier frequency, which was very helpful to reduce the temperature rise of the temperature rise of the rotor, but its effects on copper and stator losses were not as high as the rotor rotor, but its effects on copper and stator losses were not as high as the rotor loss. loss. Copper loss Stator loss Rotor loss 10000 36.1% Copper loss 25.3% Stator loss Rotor loss 18.9% 14.8% 100008000 36.1% 25.3% 80006000 18.9% 14.8%

60004000 Losses (W) 40002000 Losses (W) 20000 8k 12k 16k 20k sine 0 Carrier frequency(Hz) 8k 12k 16k 20k sine Figure 13. Influences of the carrierCarrier frequencies frequency(Hz) of the PWM inverter on the losses. Figure 13. Influences of the carrier frequencies of the PWM inverter on the losses. Figure 13. Influences of the carrier frequencies of the PWM inverter on the losses.

Energies 2018, 11, 562 16 of 21

Energies 2017, 10, x FOR PEER REVIEW 16 of 21 4. Experiments A4. 60Experiments kW, 12,000 rpm small-scale prototype was manufactured based on the above studies. Toroidal windingsA were 60 kW, used, 12,000 and rpm the small-scale axial length prototype of the endswas manufactured of toroidal windings based on wasthe above made studies. very short, as shownToroidal in Figure windings 14a,b. were By used, calculation, and the axial the axiallength length of the ofends toroidal of toroidal windings windings was was reduced made very by 30.5% comparedshort, as with shown double-layer in Figure 14a,b. lap windings.By calculation, Carbon the axial fiber length retaining of toroidal sleeve windings was mounted was reduced outside by of the magnets30.5% compared shown inwith Figure double-layer 14c,d. A lap photograph windings. Carbon of the fiber complete retaining experimental sleeve was mounted setup was outside shown in Figureof 14thee. magnets The prototype shown in wasFigures connected 14c,d. A photograph with dynamometer of the complete though experimental a universal setup coupling. was shown WT1800 in Figure 14e. The prototype was connected with dynamometer though a universal coupling. WT1800 power analyzer was used to record the test results. power analyzer was used to record the test results.

Pt100 Pt100 Pt100

(a) (b)

(c) (d)

Dynamometer

Prototype

Motor controller Temperature patrol instrument

(e)

Simulation Test Simulation Test 300 200 200 100 100

(V) 0 0

EMF -100 Current (A) -100 -200

-300 -200 0246810 0246810 Time (ms) Time (ms) (f) (g)

Figure 14. Configurations of (a,b) stator of the prototype; (c) rotor with magnets mounted; (d) rotor Figureafter 14. retainingConfigurations sleeve mounted; of (a,b) ( statore) a photograph of the prototype; of the complete (c) rotor experimental with magnets setup; mounted; waveforms (d of) rotor after( retainingf) no-load sleeveback EMF; mounted; (g) rated (e )current a photograph of prototype of the at 6000 complete rpm. experimental setup; waveforms of (f) no-load back EMF; (g) rated current of prototype at 6000 rpm. Energies 2018, 11, 562 17 of 21

The prototype was tested to 14,000 rpm with no load. Due to a limit put on the speed of the dynamometer, the prototype was only tested to 6000 rpm with load. The waveform of no-load back EMF of prototype driven by dynamometer at 6000 rpm was shown in Figure 14f. It agreed well with the simulation result. With the carrier frequency of 8 kHz of the inverter, the waveform of the rated current at 6000 rpm was tested, and shown in Figure 14g, and it also agreed well with the simulation result. So the electromagnetic performance of the prototype can be verified. The losses of the small-scale prototype were analyzed on the basis of the above studies. Then loss densities of each part were calculated and mapped to the 3-d FEA model for thermal analysis. The convection-heat-transfer coefficients for the water jacket, airgap, surfaces of the internal end-space, such as end-windings, stator, sleeve and rotor core, were obtained by means of CFD method. The distribution of the temperature calculated by the FEA model were shown in Figure 15a,b, in which the prototype was operated at rated torque and 6000 rpm, powered by the inverter of 8 kHz, with the ambient temperature at 22 ◦C. As can be seen, the predicted maximum temperature was on the rotor. The temperature of the windings in the inner slot was about 1 ◦C higher than that in the outer slots. The highest temperature of the magnets was 110.44 ◦C. To verify the losses and temperature rise, the test setup for the small-scale prototype was fabricated. The temperature rises of the stator and the windings in the inner slots and outer slots were tested by 3 pre-set Pt100 RTDs for the prototype, which were in the middle of one inner slot and one outer slot, as well as in the deep hole of the stator, respectively, shown in Figure 14a. But it was difficult to test the temperature rise of the rotor directly. It was finally predicted by the calculation of the temperature rise of the magnets, by means of the no-load back EMF tested, after the temperature was stable. The no-load EMF can be expressed as:

E0 = 4.44 f kdpkNM Nφδ0 (10) where, N is the number of turns in series in one phase, φδ0 is the airgap flux at no load. f, N, kdp, kφ can be known for the prototype. 0 bm0Br Am φδ0 = 0 (11) σ0 0 where, b m0 and σ0 are the operating point of the magnets and magnetic leakage factor at no load, respectively, which also can be known for the prototype. Br is the of PM material, Am is the cross-sectional area of the flux in one pole. By Equations (10) and (11), the no-load EMF could also expressed as: E0 ∝ Br (12)

Br is related with temperature and can expressed as:

 IL  B = [1 + (t − 20)∂ ] 1 − B (13) r br 100 r20 where, αbr, IL are the coefficients of temperature and irreversible loss of PM materials. Br20 is the remanence of PM material at 20 ◦C. They can be known from the Manufacturer. t is the temperature of magnets. E0 is related with temperature due to Equations (12) and (13). Therefore, the temperature of the magnets can be predicted by means of the no-load EMF. With the carrier frequency of 8 kHz of the inverter, the temperature rises of the prototype were tested at 6000 rpm with different load rates in Figure 15c. The highest temperature rise appeared at the magnets, and the temperature rise of the windings in the outer slots was a bit lower than that in the inner slots, which was in accordance with thermal analysis. As the load rate increased, the difference of the temperature rise between rotor and stator was smaller due to the increase of copper loss. The comparison between test and simulation of temperature rises of the magnets and windings in the Energies 2018, 11, 562 18 of 21 inner slot was shown in Figure 15d. The test and simulation results showed good accordance, so the Energies 2017, 10, x FOR PEER REVIEW 18 of 21 analysis of the losses for the toroidal-windings motor can be verified.

Temperature(℃) Temperature(℃) 114.71 96.42 108.13 91.78 101.55 87.15 94.971 82.51 88.392 77.88 81.812 73.24 75.232 Windings 68.653 ℃ ℃ 62.073 Temperature( ) Temperature( ) 110.44 55.494 92.35 106.68 48.914 90.38 88.41 102.93 42.334 86.43 99.17 35.755 84.46 95.42 29.175 82.49 91.66 22.596 Stator Magnet (a) (b)

Magnets Windings in inner slots Magnets(Simulation) Magnets(Test) Stator Windings in outer slots Windings(Simulation) Windings(Test) 90 90 80 80 ℃ ℃ () 70 70 60 60 50

50 40 40 30 30

20 Temperature rise ( ) Temperature rise rise Temperature 20 10 20 40 60 80 100 20 40 60 80 100 Load rate (%) Load rate (%) (c) (d)

Magnets(4k) Windings(4k) Stator(4k) Simulation Test Magnets(8k) Windings(8k) Stator(8k) 100 100 80 ℃

℃ 80 () 60 60 40 40 20 20 Temperature rise( ) Temperature rise 0 0 s s s r 2000 3000 4000 5000 6000 gnet ding ding Stato Ma r win r win Speed (rpm) Inne Oute (e) (f)

Figure 15. Distribution of temperature rise of, (a) entire prototype; (b) different components of the Figureprototype; 15. Distribution (c) variation of of temperature the tested temperature rise of, (a rises) entire with prototype; load rates at (b 6000) different rpm; (d) components comparison of of the prototype;the test ( cand) variation simulation of temperature the tested temperature rises; (e) comparison rises with of the load tested rates temperature at 6000 rpm; rises (d between) comparison the of the testcarrier and frequencies simulation of temperature 4 kHz and 8 rises;kHz; ( (fe) )comparison comparison of ofthe the test tested and simulation temperature temperature rises between rises the carrierwith frequencies carrier frequencies of 4 kHz of and4 kHz. 8 kHz; (f) comparison of the test and simulation temperature rises with carrier frequencies of 4 kHz. In order to clarify the influence of the carrier frequency on the rotor losses, the temperature rises of the prototype, under the carrier frequencies of 4 kHz and 8 kHz, were tested and compared at 50% In order to clarify the influence of the carrier frequency on the rotor losses, the temperature rises load, respectively, shown in Figure 15e. As the speed increased, the temperature rise of the magnets of thewas prototype, greatly influenced under the by carrier the carrier frequencies frequency. of The 4 kHz temperature and 8 kHz, rise were of the tested magnets and was compared decreased at 50% load,by respectively, 34.6%, compared shown the in carrier Figure frequency 15e. As theof 4 speedkHz with increased, 8 kHz at the 6000 temperature rpm. The influences rise of the on magnetsthe was greatlytemperature influenced rises of bythe the windings carrier and frequency. stator were The not temperature as high as on rise the of magnets. the magnets According was to decreased the by 34.6%, compared the carrier frequency of 4 kHz with 8 kHz at 6000 rpm. The influences on the Energies 2018, 11, 562 19 of 21 temperature rises of the windings and stator were not as high as on the magnets. According to the above studies, rotor loss was decreased by 39.7%, when the carrier frequency increases from 8 kHz to 16 kHz (the ratios of the carrier wave are also 20 and 40). With the same change of rotor loss, the rotor loss of the prototype at the speed of 6000 rpm under the carrier frequency of 4 kHz can be acquired, based on the known losses of carrier frequency of 8 kHz (the ratios of the carrier wave were also 20 and 40, respectively). Then the temperature rise were analyzed and compared with the test results in Figure 15f, which were in good agreement. So the influences of the carrier frequencies on the rotor losses can also be confirmed.

5. Conclusions This paper provides the key design features of a flat-structure high-speed high-power PMSM for pulsed alternators. The toroidal-windings were used to reduce largely the axial length of the motor. The problem of leakage flux lines around the outer slots was solved by the division of stator and the use of non-magnetic material on the outer stator. Low-conductivity material of the retaining sleeve, the large airgap, the large number of segments of the magnets were together investigated to achieve the decrease in the axial length and improve the power density of a high-speed motor with flat structure. The electromagnetic design was verified by the test of a small-scale prototype. The copper loss, iron loss and rotor loss of the toroidal-windings PMSM prototype were calculated, respectively, and the influencing factors on the losses were analyzed. The effects of the influencing factors on the total loss were then evaluated. By increasing the strand number of the conductors, the copper loss could be effectively reduced, and the total loss could be decreased by 5.3% for the prototype. By the division of the stator and the use of non-magnetic materials on the outer stator, the stator loss and copper loss could both be effectively reduced; thus, the total loss could be decreased by 8.8%. By the combination of these two methods, the total loss could be decreased by 11.8%. Replacing the aluminum alloy pole fillers with epoxy resin, the rotor loss could be decreased, and as a consequence, the total loss could be decreased by 0.7%, which is significant for the rotor. The employment of the 2-mm stainless steel stack or 1-mm aluminum alloy stack pole fillers will have had the same effect on the reduction of rotor loss as epoxy resin fillers, while maintaining the good thermal-conductivity properties of metal. The calculation of the losses was confirmed by tests of the temperature rise in the small-scale prototype. Powered by the PWM inverter, the rotor was great influenced by the carrier frequency, whereas its influences on the losses of windings and stator were not as high as on the magnets. The employment of a high carrier frequency inverter was very helpful to decrease the rotor loss. The comparisons of the tested temperature rises in the small-scale prototype, between the carrier frequencies of 4 kHz with 8 kHz, showed the same results.

Author Contributions: Yuan Wan and Shumei Cui contributed equally to the research work described in this paper. Yuan Wan conducted the main work of design, simulation and experiments, while supervised by Shumei Cui. Shaopeng Wu reviewed and improved the paper by proofreading the paper for the correction of sentence structure and grammar. Liwei Song provided technical feedback and suggestions throughout the research. Conflicts of Interest: The authors declare no conflict of interest.

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