2622 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 Analysis of Winding MMF and Loss for Axial Flux PMSM With FSCW Layout and YASA Topology Qixu Chen , Deliang Liang , Senior Member, IEEE, Shaofeng Jia , Member, IEEE, Qiji Ze, and Yibin Liu Abstract—This article takes 12-slot/10-pole axial flux permanent magnet (PM) synchronous machine (AFPMSM) with fractionalslot concentrated windings and yokeless and armature (YASA) topology as the research object. Winding magnetomotive force (MMF) of three-phase double-layer layout is analyzed by three kinds of methods, which are star diagram method, winding function method, and holographic spectrum method. The analysis results of finite-element method (FEM) show that the three methods are effective and consistent in analyzing winding MMF. Comparative analysis of iron loss density and B–H magnetizing curves of four typical iron materials are studied. B–H hysteresis loops of silicon steel sheet and soft magnetic composite are measured by magnetizing and measuring equipment to validate iron core per unit mass. The three-dimensional FEM is used for analyzing eddy-current loss in PMs considering radial segmentation. Finally, an AFPMSM prototype is manufactured adopting YASA topology and segmented PM. Load experiments show that solid–liquid coupling computational fluid dynamics model can precisely predict temperature distribution of AFPMSM. Improved cooling jacket is beneficial to afford large current load. Index Terms—Axial flux permanent magnet (PM) synchronous machine (AFPMSM), fractional-slot concentrated winding (FSCW), holographic spectrum, loss of iron core and PM, star graph, winding function, winding magnetomotive force (MMF). I. INTRODUCTION HE axial flux permanent magnet (PM) synchronous machine (AFPMSM) is applied to high-performance electric vehicles (EV) due to high power density and high torque density [1]. However, cases such as low-voltage high-current operation conditions and flux density saturation problem cause a huge challenge to motor heat dissipation at overload case. Scholars have made active explorations and studies. Oxford YASA Motors Inc. developed a high power density AFPMSM with yokeless and segmented armature (YASA) topology, oil T Manuscript received September 3, 2019; revised January 10, 2020 and March 3, 2020; accepted March 10, 2020. Date of publication March 17, 2020; date of current version April 24, 2020. Paper 2019-EMC-1093.R2, presented at the 2018 IEEE Energy Conversion Congress and Exposition, Portland, OR, USA, Sep. 23–27, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. This work was supported in part by the National Natural Science Foundation of China under Project 51677144 and in part by the State Key Laboratory of Electrical Insulation and Power Equipment. (Corresponding author: Deliang Liang.) The authors are with the Shaanxi Key Laboratory of Smart Grid, State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail: xianjiaotong2014@163.com; dlliang@xjtu.edu.cn; shaofengjia@mail.xjtu.edu.cn; ze.3@osu.edu; ybliuxjtu2015@126.com). Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2020.2981445 immersion cycle cooling, and soft magnetic composite (SMC) stator iron core. [2], [3]. Authors in [4]–[6] carried out important research in the aspects of magnetic flux density versus magnetic field intensity (B–H) curve characteristics of SMC material, comparison between Si steel core and SMC core, and its application in AFPMSM. A variety of fractional-slot concentrated-winding (FSCW) winding layout ranging from single-layer winding to multilayer winding are studied by star graph method (SGM) in [7]–[9]. Its disadvantage is that SGM usually takes a long time to obtain magnetomotive force (MMF) results. Multilayer or multiphase windings can realize eddy current loss reduction in PMs [7]–[9]. Winding MMF theory was deduced by winding function method (WFM), which was used to analyze three-phase double-layer (TP-DL) and double-TP-DL (DTP-DL) winding in [10]. However, the distribution of winding function and winding MMF were not derived in detail. In addition, permanent magnet synchronous machine (PMSM) with FSCW includes a large amount of time and space harmonics, which generates eddy current loss in PMs. Eddy current loss reduction in PMs had received more and more attention. Authors in [11]–[13] presented an analytical solution of eddy current loss calculation using electric circuit network, which is compared with the finite-element method (FEM). Rotor loss reduction of interior PMSM with FSCW layout can be realized by the circumferential and axial segmentation of PMs of interior PMSM [14], [15]. The study emphasis of these literatures is mainly on theoretical derivation and simulation; experiment verification is almost neglected. The first task of this article is to develop the holographic spectrum method (HSM) to analyze the winding MMF under the given winding layout, and to analyze the difference and relationship between HSM and WFM. Compared with the traditional analysis methods, HSM and WFM have the advantages of easy program implementation, fast calculation speed, and high precision. The second task of this article is to develop a novel AFPMSM. Focusing on improving efficiency, power density, and torque density, an external rotor AFPMSM is developed in this article, which brings great challenges to design and manufacturing. For FSCW, the spatial harmonics of the MMF cause PM eddy current losses. In order to reduce eddy current loss, PM of radial segmentation process and epoxy coating is studied under the given winding layout. The comparison experiment of core loss provides the basis for material selection. Because the core of YASA topology brings a reduction in heat capacity, the 0093-9994 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY 2623 Fig. 1. TP-DL winding with 12s10p combination. (a) Star graph. (b) Winding layout. (c) Unfolded winding layout. improved channel design improves convective heat dissipation coefficient on the surface, which is beneficial to heat dissipation of the core and winding. Finally, an AFPMSM prototype with 12-slot/10-pole combination is manufactured. No-load and load experimental platforms are established. No-load back EMF wave, load current wave, line voltage wave, and infrared thermal imaging are measured to validate the proposed methods and liquid–solid coupling model. II. WINDING MMF ANALYSIS It takes a long time to analyze the winding MMF by the traditional tooth MMF SGM and the FEM. Winding MMF of a 12-slot/10-pole combination and TP-DL winding layout is emphatically analyzed with HSM and WFM in this section. A. Winding MMF Analysis With SGM According to the winding distribution as shown in Fig. 1, the basic idea of tooth MMF star diagram method is that winding MMF generated by a single coil of each phase is obtained first, then the resultant winding MMF of each phase is derived, and finally, the resultant winding MMF of the three windings is finished. TP-DL winding layout with 12-slot/10-pole combination is adopted in this article. Star graph of tooth MMF is given in Fig. 1(a). TP-DL winding distributions of 12-slot/10-pole combination are shown as Fig. 1(b) and (c). According to the SGM, the normalized resultant winding MMF distribution is given in Fig. 2(a). Its Fourier decomposition of winding MMF is given as Fig. 2(b). The fifth harmonic is taken as fundamental wave for 12-slot/10-pole winding configuration. The total harmonic distortion (THD) of winding MMF can be defined as follows [16]: 2 2 2 ∞ (1) (7) (6n±1) F̂mag + F̂mag + F̂mag THDSta MMF = n=2,3 (5) F̂mag (1) (1) (5) (7) (11) (13) where F̂mag , F̂mag , F̂mag , F̂mag , F̂mag are 1st, 5th, 7th, 11th, and 13th harmonic amplitude, respectively. For 12-slot/10-pole Fig. 2. Winding MMF using star diagram. (a) Winding MMF. (b) Harmonic magnitude distribution. combination, harmonic distortion rate (THD) of TP-DL winding reaches 79.8%. B. Winding MMF Analysis With WFM Winding functions NA (θ), NB (θ), NC (θ) of each phase are given as ⎧ NA (θ) = NA1 (θ) + NA2 (θ) ⎪ ⎪ ⎪ ⎪ ∞ ⎪ 4Nc vπ π ⎪ ⎪ ⎪= vπ sin 12 cosv θ − 12 ⎪ ⎪ v=1,3,5,··· ⎪ ⎪ ∞ ⎪ ⎪ 4Nc vπ 11π ⎪ + ⎪ vπ sin 12 cosv θ − 12 ⎪ ⎪ v=1,3,5,··· ⎪ ⎪ ⎪ ⎪ N (θ) = −NB1 (θ) + NB2 (θ) ⎪ ⎪ B ⎪ ∞ ⎪ ⎨ 4Nc vπ 7π =− vπ sin 12 cosv θ − 12 . (2) v=1,3,5,··· ⎪ ∞ ⎪ ⎪ 4N vπ 3π c ⎪ ⎪ + ⎪ vπ sin 12 cos v θ − 4 ⎪ v=1,3,5,··· ⎪ ⎪ ⎪ ⎪ NC (θ) = NC1 (θ) − NC2 (θ) ⎪ ⎪ ⎪ ⎪ ∞ ⎪ 4Nc vπ π ⎪ ⎪ = ⎪ vπ sin 12 cosv θ − 4 ⎪ ⎪ v=1,3,5,··· ⎪ ⎪ ∞ ⎪ ⎪ 4Nc vπ 5π ⎪ − ⎩ vπ sin 12 cosv θ − 12 v=1,3,5,··· Each phase has two groups of coils. Take phase A as an example—no. 1 coil and no. 7 are classified into group 1, no. 6 coil and no. 12 are classified into group 2. Phase B and phase C are similar to phase A, which corresponds with the winding layout in Fig. 1(b) and (c). Winding function distribution of the three phases is given in Fig. 3(a)–(c). The three phase currents are defined as √ ⎧ ⎪ ⎨ iA (t) = √2I1 cos(ωt + ϕ0 ) (3) iB (t) = 2I1 cos(ωt + ϕ0 − 2π/3) . ⎪ √ ⎩ iC (t) = 2I1 cos(ωt + ϕ0 + 2π/3) Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2624 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 Fig. 4. Resultant winding MMF with winding function. respectively, as shown in Fig. 4, defined by Fsum (θ, t) = FA (θ, t) + FB (θ, t) + FC (θ, t) √ ∞ 12 2Nc I1 2 vπ = sin sin (vθ−ωt−ϕ0 ). vπ 12 v=1,−5,7,··· (5) C. Winding MMF Analysis With HSM Element motor number t is the greatest common divisor (GCD) between slot number Q and pole pairs p. Therefore, slot number of element motor Qt and pole pairs of element motor pt are defined as (6). For the double-layer FSCW and Qt = 6K(K is natural number), holospectrum D(vt ) and composite winding factor Dpu (vt ) are defined as (7) in the following: Fig. 3. Winding function of 12s10p TP-DL winding. (a) Phase A. (b) Phase B. (c) Phase C. (6) t = GCD(Q, p) Qt = Q/t pt = p/t ⎧ sin(kπ/6)·[1−cos(kπ)] π c ⎪ D(υt ) = 2N ⎪ Qt sin kpt Qt sin(kπ/Qt ) ⎪ ⎪ ⎪ ⎨ j ( π2 −kpt Qπ −k π6 +k Qπ ) t t × e sin(kπ/6)·[1−cos(kπ)] π ⎪ Dpu (υt ) = 3 sin kpt Qt ⎪ Qt sin(kπ/Qt ) ⎪ ⎪ ⎪ ⎩ j ( π2 −kpt Qπ −k π6 +k Qπ ) t t ×e k = M od(υt X, Qt ) 1 ≤ υt ≤ Qt − 1, 1 ≤ k ≤ Qt − 1 (7) where I1 is the amplitude of phase current (A) and ϕ0 is the initial phase angle. Winding MMF of each phase can be expressed by ⎛ √ ∞ 4 2Nc I1 FA (θ, t) = sin2 vπ vπ 12 ⎜ v=1,3,5,··· ⎜ ⎜ sin (vθ + ωt + ϕ0 ) ⎜ ⎜ + sin (vθ − ωt − ϕ0 ) ⎜ √ ∞ ⎜ 4 2Nc I1 ⎜ FB (θ, t) = sin2 vπ vπ 12 ⎜ v=1,3,5,··· ⎜ ⎛ ⎞ ⎜ sin vθ + ωt + ϕ0 − 2(v+1)π ⎜ (4) 3 ⎜ ⎝ ⎠ ⎜ + sin vθ − ωt − ϕ0 − 2(v−1)π ⎜ 3 ⎜ √ ∞ ⎜ 4 2N I 2 c 1 ⎜ FC (θ, t) = sin vπ vπ 12 ⎜ ⎜ ⎛ v=1,3,5,··· ⎞ ⎜ ⎜ sin vθ + ωt + ϕ0 + 2(v+1)π 3 ⎝ ⎝ ⎠ 2(v−1)π + sin vθ − ωt − ϕ0 + 3 where Nc is turns per coil, X is slot number of moment vector, vt is harmonic order, and k is remainder of vt X/Qt . Winding factor kwv and phase angle ϕv of vth harmonic are given by ⎧ v=0 ⎪ ⎨ 0, sin vπ(q+L) −cos(vπ)sin vπ(q−L) ) ( vyπ 6q 6q (8) kwv = sin 6q · 2q sin(vπ/(6q)) ⎪ ⎩ v = 1, 2, . . . , 6q − 1 π π π ϕv = − vy − v (q + L − 1) , v = 0, 1, 2, . . . , 6q − 1 2 6q 6q (9) where Nc is the number of turns per coil. According to the following equation, the resultant winding MMF is the vector sum of the three phase winding MMFs, where q is the slot number per pole per phase. For three-phase ac motor, its three-phase current is set as iA , iB , iC , and winding MMFs of phase A, phase B, and phase C Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY 2625 TABLE I COMPOSITE WINDING FACTOR kwvt AND PHASE ϕvt (RAD) Note: υt : Harmonic order, k: Harmonic order of element motor, ϕvt_A : Phase angle of A (rad), ϕvt_B : Phase angle of B (rad), ϕvt˙C : Phase angle of C (rad). are defined as [17] ⎧ ⎪ fA (x) = iAπQ ⎪ ⎪ ⎪ k=1,···Q−1 ⎪ ⎪ l=0,1,··· ,∞ ⎪ ⎪ ⎪ l=0,k=0 ⎪ ⎪ ⎪ ⎨fB (x) = iBπQ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ fC (x) = iCπQ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ k=1,···Q−1 l=0,1,··· ,∞ l=0,k=0 k=1,···Q−1 l=0,1,··· ,∞ l=0,k=0 DkA lQ+k ks(lQ+k) sin ((lQ + k) x + ϕkA ) DkB lQ+k ks(lQ+k) sin ((lQ + k) x + ϕkB ) DkC lQ+k ks(lQ+k) sin ((lQ + k) x + ϕkC ) Fig. 5. (10) The composite winding MMF f(x) of three-phase ac winding is the vector superposition of phase A, phase B, and phase C, and its general expression is defined as f (x) = fA (x) + fB (x) + fC (x) . Amplitude and phase. (a) Winding factor kwvt . (b) Phase angle ϕvt . . (11) The vth harmonic phase angle ϕv for the three phases are given by ⎧ ⎧ k=0 ⎨ π/2, ⎪ ⎪ π π 1 L−1 ⎪ ⎪ − kp y − k( + ϕ (v) = t kA ⎪ 2 Qt 6 Qt )π, ⎪ ⎩ ⎪ ⎪ k = M od(Xν, Q) ⎪ ⎪ ⎧ ⎪ ⎪ −5π/6, k = 0 ⎨ ⎨ 2π ϕkB (v) = π2 − kpt y Qπt − k( 16 + L−1 Qt )π + k 3 , . (12) ⎪ ⎩ ⎪ ⎪ k = M od(Xν, Q) ⎪ ⎧ ⎪ ⎪ ⎪ π/6, k=0 ⎨ ⎪ ⎪ π π 1 L−1 2π ⎪ ⎪ − kp y − k( ϕ (v) = t kC ⎪ Qt 6 + Qt )π − k 3 , ⎩ ⎩2 k = M od(Xν, Q) Its calculation results of winding factor and phase angle for 12-slot/10-pole combination are given in Table I. According to (8) and (9), winding factor and phase-angle distribution of vth-order harmonic are shown as Fig. 5. Winding MMF distribution per phase is calculated by (10), which is given in Fig. 6(a)–(c), respectively. Resultant winding MMF distribution is given in Fig. 7. By comparison among SGM, WFM, and HSM, we find that the analytical results of the three methods have good agreement with FEM as shown in Fig. 8. Similarity: The winding MMF derived by HSM and WFM have a common characteristic, which is always step wave fitted by Fourier series. Differences: WFM is a bottom-up approach. Starting from the winding functions generated by a pair of conductors (kth, kth + 6); then, the winding function and winding MMF of each phase are derived, and finally, the resultant winding MMF is given. HSM is a top-down method, the winding coefficients and phase angles considering the vth harmonic are calculated; then, holospectrum and composite winding factor are deduced, and finally, the winding MMF of each phase and their resultant winding MMF are obtained according to the winding layout. HSM and WFM have the advantages of fast calculation speed and high precision. In addition, HSM and WFM can be extended to solve the winding MMF and harmonic distribution of multilayer multiphase winding. III. LOSS ANALYSIS The stator current can produce subharmonics for FSCW, which consequently result in eddy current loss in PMs. It can cause a high temperature rise and even lead to local demagnetization of PM. Winding MMF of 12-slot/10-pole TP-DL winding is analyzed in Section II. An AFPMSM with the above-mentioned pole-slot combination is designed in this article. In this section, three-dimensional (3-D) magnetic field distribution and loss characteristics are discussed in detail, which mainly involve stator iron core loss, eddy-current loss in PMs, and bearing loss. An external rotor AFPMSM model adopts double-rotor single-stator topology in this article, which is composed of rotor, stator, shell, and resolver applied to the large electric motorcycle Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2626 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 Fig. 8. Winding MMF with FEM method. Fig. 9. AFPMSM. (a) Model. (b) Prototype. (c) Application object (large motorcycle). Fig. 6. Phase winding MMF with HSM. (a) Phase A. (b) Phase B. (c) Phase C. Fig. 7. Resultant winding MMF with HSM. as shown in Fig. 9. Each separated stator iron is connected to the stator hub using bolt. Stator hub designs liquid coolant channel including inlet and outlet. YASA topology means that stator yoke iron core is removed. In other words, iron core loss and weight of stator yoke are eliminated. Therefore, the efficiency and power density are improved. Spacer bar is installed between two adjacent PMs in order to fix PM, which results in different pole-arc coefficients for each Fig. 10. Air gap flux density distribution along radial and circumferential direction. (a) Two-dimensional distribution of different layers. (b) Threedimensional distribution. slice in the circumferential direction. Air gap flux density of a slot pitch in radial direction is given in Fig. 10. Shape difference between torus sample and actual stator iron core results in the uneven distribution of flux density. In addition, Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY 2627 Fig. 12. Flow chart of iron core loss calculation. Fig. 13. Magnetic saturation flux density of different materials. Fig. 11. Flux density distribution of single stator tooth. (a) Two-dimensional distribution of different layers. (b) Three-dimensional distribution. stator tooth flux density is different in the circumferential and radial direction as shown in Fig. 11. A. Calculation and Experiment of Iron Core Loss Classic Bertotti separation model was used to calculate iron core loss [18], [19]. The effect of the alternate current (ac) magnetization is only considered, which ignores the direct current (dc) component of the magnetic flux density. Iron core loss Pv (unit: W/m3 ) at operating frequency f of sinusoidal magnetic flux density can be calculated by α 2 1.5 +Kc f 2 Bm +Ke f 1.5 Bm (13) Pv = Ph +Pc +Pe = Kh f Bm where Pv , Ph , Pc , and Pe are the iron core loss, hysteresis loss, classic eddy-current loss, and additional eddy-current loss, respectively. Bm , f, and α are the ac flux density component amplitude, frequency, and coefficient α = 2, respectively. Kh , Kc , and Ke are the coefficients of the magnetic hysteresis loss, classic eddy current loss, and additional loss, respectively. At least three groups’ flux density B–power loss P (BP) curve data about magnetic flux density versus iron core loss per mass need to be provided at frequencies f = 100, 200, 400, and 1000 Hz. Coefficients Kh , Kc , Ke can be obtained by solving the following equation: 2 1.5 + K2 B m P v = K1 B m where K1 = Kh f + Kc f 2 and K2 = Ke f 1.5 . (14) The values of the coefficients K1 , K2 are derived, which satisfy the minimum value of the quadratic expression (i) (i) = min minf K1 , K2 Pv(i) − i (i) (i)2 K1 B m + (i) (i)1.5 K2 B m 2 (15) where Pvi , Bmi are the ith point data (Pvi , Bmi ) of the iron core loss BP curve. The classic eddy current loss coefficient Kc , loss coefficient Kh , Ke can be calculated by Kc = π 2 · σ · d2 /6, Kh = (K1 − Kc f02 )/f0 , Ke = K2 /f01.5 (16) where f0 is the test frequency of the loss curve, σ is conductivity, and d is thickness of a sheet of silicon steel. The iron loss coefficient Kh , Kc , Ke are obtained by (14)–(16), and brought into (13); thus, the iron loss Pv can be evaluated [20]. Flow chart of core loss calculation is given in Fig. 12. Magnetic saturation flux density of several kinds of magnetic materials is shown in Fig. 13. Thin-gauge silicon steel, conventional silicon steel, and SMC Somaloy series are at the same level from the point of the saturation flux density. However, the trend of the iron core loss density at f = 2 kHz, B = 0.05 T is as follows: Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2628 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 Fig. 14. DC magnetization curve and iron core loss density. (a) DC magnetization curve of different materials (B–H curve). (b) Iron core loss density (W/kg) at f = 50 Hz. (c)–(e) Iron core loss density (W/kg) at f = 100, 200, 400, and 1000 Hz. Thin-gauge silicon steel < conventional silicon steel < SMC Somaloy series. The main advantage of Fe-based amorphous alloy Metglas 2605SA1 is that it has lower core loss density than that of the silicon steel and SMC Somaloy, but its saturation flux density is at a relatively low level. DC magnetization curve and iron core loss density for different materials and different frequencies are shown in Fig. 14(a)–(f). Somaloy provided by Höganäs Corporation is an isotropic, high-resistive SMC material for electromagnetic applications. The unique characteristic is the 3-D flux properties. Both silicon steel and SMC material have high saturation flux density (the saturation induction flux density of Somaloy 10003P approaches B = 2.46 T at H = 304535 A/m, which is from Höganäs Corporation product data), which are helpful to reduce the volume. However, the disadvantage of the SMC material is that its iron core loss is higher than that of silicon steel sheet 35WW270 from Wugang Inc data. B–H magnetic hysteresis loops at Bmax = 1 T and different frequencies are measured by magnetizing and measuring equipment provided by Laboratorio Elettrofisico Engineering Srl. as shown in Figs. 15 and 16. Similarly, we can also get iron core losses per unit mass at specified flux density and frequency, and derive the three loss coefficients Kh , Kc , Ke according to (13)–(16). We can find that hysteresis loops widen with increasing frequency, which shows that iron core losses are proportional to the area of the hysteresis loops based on the measured data. Measured Fe-Si N.O and Somaloy 700-1P sample are given in Fig. 17. B–H magnetizing curves and iron core density curves are measured based on the above-mentioned analysis in Fig. 18. We can see that coercive force Hc of SMC Somaloy 700-1p is obviously larger than Fe-Si N.O. (silicon steel sheet) from measured data. Limited by the output power of magnetizing Fig. 15. Fe-Si N.O sample test. (a) Measure platform. (b) Measure data. Fig. 16. Somaloy 700-1P sample test. (a) Measure platform. (b) Measure data. and measuring equipment, the turns of SMC sample are much more than that of Fe-Si N.O in order to obtain the same MMF F. In other words, the relative magnetic permeability of SMC Somaloy 700-1p is far less than that of that of Fe-Si N.O. as explained in Table II and the following: F = N i = Bl/μ Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. (17) CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY Fig. 17. Test sample. (a) Fe-Si N.O. (b) Somaloy 700-1P. 2629 Fig. 19. Flux density and iron core density. (a) Magnetic flux density magnitude (T). (b) Stator iron core loss (W/m3 ). Fig. 20. Transient iron core loss under the condition of f = 400 Hz and no current excitation. Fig. 18. Measured B–H magnetic hysteresis loop curves at different frequencies. (a) Fe-Si N.O. (b) SMC Somaloy 700-1p. TABLE II IRON CORE MATERIAL PARAMETERS where MMF F is the product of ampere current I and turns N; B, μ, and l are flux density, magnetic permeability, and length of magnetic path, respectively. The oriented ultra-thin silicon steel sheet GT-100 from Nippon Kinzoku’s products can significantly reduce the core loss with sheet thinning from 0.23 to 0.05 mm, and at the same time, keep high saturation flux density (B = 1.95 T at H = 3225 A/m), which is beneficial to obtain higher efficiency and save energy. Ferrite and conventional silicon steel sheet are still widely used in industrial products and home electronics for cost considerations. Amorphous alloy are widely used in high-frequency transformers with very low iron core loss, but the low saturation flux density restricts its application (for example, saturation induction flux density of 2605SA1 from Metglas, Inc series is only 1.56 T). Magnetic flux density magnitude and iron core loss are analyzed by 3-D FEM in Fig. 19. Density, conductivity, and saturation flux density of four kinds of iron core materials are shown in Table II. Stator iron core losses follow the rule that the lower the value of iron core loss density, the smaller the value of iron core loss for different materials as shown in Fig. 20. Hysteresis loss coefficient of Somaloy 10003P has the highest value (Kh = 583.2 W/m3 ) among the four kinds of materials. It may lead to relatively long convergence time to reach steady state. Therefore, iron core loss density (unit: W/kg) comparisons of four kinds of materials are made under the condition of Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2630 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 TABLE III IRON CORE LOSS AND IRON CORE DENSITY AT F = 400 Hz, Bave = 1 T Fig. 21. Ohmic loss density and eddy current density. (a) PM ohmic loss (W/m3 ). (b) Eddy current density magnitude (A/m2 ). Mat1: SMC1000-3P, Mat2: 2605SA1, Mat3: 35WW270, Mat4: GT-100 frequency f = 400 Hz and average iron core flux density Bave = 1 T as shown in Table III. B. Eddy Current Loss in PMs For PMSM with FSCW operating at high frequency, PM eddy current loss minimization is very important because of the challenge associated with heat removal as well as PM demagnetization risks. The value of the skin depth δ pm declines with the increase of the frequency f (f ࣔ 0) [21] ρpm (18) δpm = πfr,v μ0 μr,pm where the relative permeability of PM μr,pm is 1.05; the PM resistivity ρpm is 1.5 × 10−7 m/S; the vacuum permeability μ0 is 4π × 10−7 H/m. Induced rotor frequency fr,v is the vth space harmonic frequency as shown in v (19) fr,v = f sgnv − p where f is supply frequency; sgnv is sign function of the vth space harmonic, v is harmonic order, and p is pole pair number. Eddy current loss Peddy is related with eddy current density Jeddy and volume conductivity σ. Average eddy current loss Peddy˙ave in a period of time T are calculated as [21] 2 Peddy = Jeddy /σdV , Jeddy = jωσA V 1 ⇒ Peddy_ave = T T 1 σE dV dt = T T 2 0 V 2 Jeddy /σdV 0 dt V (20) where ω is angular frequency, σ is the conductivity of the volume, and A is the magnetic vector potential. Permeance harmonic produced by slotting effect and winding MMF harmonic produced by FSCW winding layout can cause eddy current in PMs. Equation (21) can adapt these two cases. Eddy current loss calculation of laminated iron core can be used to calculate the eddy current loss in PMs [22]. The PM loss Fig. 22. Transient eddy current loss in PMs considering radial segmentation and rated load. considering unsegmented and segmented PM in radial direction is given as ⎧ 2 2 2 2 ⎨ PPM_unseg = VPM π f Bm WPM Unsegmented PM 6ρPM 2 2 2 2 ⎩ PPM_seg = VP M π f Bm WPM Segmented PM 6ρPM Nseg (21) where PPM_unseg is unsegmented PM loss, PPM_seg is segmented PM loss, VPM is volume of PM, f is frequency, Bm is working flux density, WPM is width of PM, ρPM is electrical resistivity, and Nseg is the number of segmentation. PM ohmic loss, eddy current density magnitude with segmented PM are analyzed by 3-D FEM in Fig. 21. It is shown that eddy current losses in PMs decrease significantly with increasing segmentation number in radial direction as shown in Fig. 22. C. Friction Loss in Bearing Machining and assembly errors result in different bilateral air gap lengths δ 1 and δ 2 , which produce large axial load on bearing. Levels of rotor dynamic balance accuracy G2.5 and G6.3 are usually adopted to measure inevitably residual unbalanced mass. Residual unbalanced mass produces radial centrifugal force effects on bearing. Friction loss in bearing is caused by combined axial load Fa , radial load Fr , and gravity of rotor Mg ΔM = 2πn eper M 1000G , eper = , ω= 2r n/10 60 Fr = ΔM rω 2 = 5.48e−5 GM n Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. (22) (23) CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY 2631 TABLE IV AFPMSM DIMENSIONS AND PARAMETERS Fig. 23. Model equivalence. (a) AFPMSM. (b) Unfolded LPMSM. where ΔM is the residual unbalanced mass (g), eper is degree of unbalance (g.mm/kg), G is balancing precision grade (G = 2.5 or 6.3), n is speed (r/min), and Fr is centrifugal force along radial direction (N). The 3-D AFPMSM model is unfolded into 3-D LPMSM for the calculation of axial thrust Fa as shown in Fig. 23. We assume that one-sided air gap length δ 1 is less than the other side air gap length δ 2 (that is δ 1 < δ 2 ). Axial thrust Fa acting on the bearing is given by Fa = pSm 2 2 Bδ1 − Bδ2 μ0 (24) where p is number of pole pairs, Sδ is air gap area, μ0 is air permeability, Bδ1 and Bδ2 are the flux density corresponding to each side air gap. Closed magnetic circuit is composed of PM, stator iron, and back iron, which can be simplified as a combination of PM and iron. The air gap flux density Bδ is calculated by (25) and (26) in the follow in the following: ⎧ ⎨ φm = Bm Sm = σBδ Sδ , Bδ = μ0 Hδ B m = B r − μ 0 μ r Hm (25) ⎩ F m = Hm L m = K r H δ δ Bδ = B r Sm μr Kr δSm /Lm + σSδ TABLE V AFPMSM LOSS VALUE (26) where Φm is main magnetic flux, Bm is magnetic density of PM at working point, Sm is cross-sectional area of main magnetic flux, Hm is magnetic field intensity of PM at working point, σ is leakage coefficient, Bδ is air gap flux density, Sδ is air gap area (Sδ = Sm ), Fm is main flux linkage, Hm is main magnetic field strength, Lm is thickness in magnetizing direction, Kr is reluctance coefficient (Kr = 1.2), Hδ is air gap magnetic field strength, δ is length of air gap, Br is remanent magnetic density (Br = 1.25 T), μ0 is vacuum permeability (μ0 = 4π∗1e−7 H/m), and μr is relative permeability (μr = 1.05). Rotor weight Mg, radial load Fr , and axial load Fa are borne by two bearings. We assume that the center of rotor mass locates at the middle line between two bearings. The total load Fsum for each bearing can be expressed by Fsum = 0.5 (M g + Fr )2 + Fa2 . (27) We assume that the air gap unevenness is set as 30%.The load value of single bearing is approximately calculated as Fsum = 180 N·m. So, the value of friction loss Pbea = 2.6 W. Friction loss Pbea of bearing is defined as [22] Pbea = 0.5μΩFsum Dbea (28) where μ is the coefficient of friction (μ = 0.0015 for deep groove ball bearing, μ = 0.002–0.0024 for angular contact ball bearing), Ω is angular speed (n = 3800 r/min, Ω = 398 rad/s), Dbea is inner diameter of bearing (Dbea = 0.03 m). Main parameters of AFPMSM are given in Table IV. Table V gives the loss values for the heat generation applied to AFPMSM. IV. COMPUTATIONAL FLUID DYNAMICS (CFD) MODEL AND SIMULATION Losses obtained in Section III are heat sources, which are applied to AFPMSM components in the form of heat generation rates. In order to calculate the temperature distribution of AFPMSM, a liquid–solid coupling model is built with CFD in this section. The forced water-cooling scheme in stator hub is adopted for improving the power density. The fluid can be modeled using 3D CFD tools to compute the convective heat transfer coefficients between solid wall and fluid surface, which are necessary for reducing computational burden. The velocity of inlet is given by v = Q/A (29) where v is the velocity of the liquid coolant, Q is the flow of liquid coolant, and A is the cross-sectional area of water channel. Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2632 Fig. 24. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 Velocity vector. (a) Original. (b) Improved. Fig. 26. CFD model and its result. (a) Three-dimensional liquid–solid coupling model. (b) Simulation result. Fig. 25. Convective heat transfer coefficient. (a) Original. (b) Improved. Thermal conductance between inner wall of stator hub and liquid coolant is represented as [23] 0.14 1/3 de 1/3 v 1.86Re1/3 Pr Re < 2200 wa L υwa N uwa = 0.8 0.4 0.023Rewa Pr Re > 2200 (30) Rewa = v de 2ab =v υwa υwa (a + b) hwa = N uwa λwa De (31) (32) where N uwa is the Nusselt number of liquid coolant, Rewa is the Rayleigh number of liquid coolant, Pr is the Prandtl number, de is the equivalent diameter, L is the path length of water channel, a is the width of water channel, b is height of water channel, υwa is kinematic viscosity coefficient of liquid coolant, hwa is convective heat transfer coefficient of liquid coolant, and λwa is thermal conductivity of liquid coolant. Traditional equations (30)–(32) are frequently used to calculate the convection heat transfer coefficient hwa of liquid. However, convection heat transfer coefficient hwa is different, because the changing cross-sectional area along the waterway path results in the change of velocity and convection heat transfer coefficient hwa as shown in Figs. 24 and 25. The inlet velocity is 5 m/s. Therefore, the average convection heat transfer coefficients obtained by CFD simulations can be used to amend the empirical formula. In order to study the temperature distribution of AFPMSM, CFD model of liquid–solid coupling is established by GAMBIT, and its temperature distribution is obtained by FLUENT as shown in Fig. 26(a) and (b), respectively. The water jacket in the stator hub can take away most of the heat. We can see from Fig. 26(b) that the temperature of stator winding and stator iron core reach the highest value ranging Fig. 27. Parts and assembly. (a) Unsegmented PM. (b) Radial-segmented PM. (c) Segmented stator tooth iron. (d) Stator. (e) Assembly. (f) Measurement of air gap flux density. from 96.9–101 ˚C. Due to the adoption of the radial-segmented PM, the temperature rise of PM is obviously suppressed. V. AFPMSM MANUFACTURE AND EXPERIMENT In order to verify the analysis result of Section IV, a 12slot/10-pole AFPMSM prototype is designed and manufactured. No-load and load experimental platforms are established to evaluate the machine performance in this section. A. AFPMSM Manufacture and Assembly AFPMSM adopts double-rotor single-stator architecture. Rotor eddy current losses in AFPMSM mainly include loss of rotor core and PM. In order to reduce the eddy loss in PMs, two methods, including unsegmented PM covered with epoxy resin coating in Fig. 27(a) and radial segmented PM in Fig. 27(b) Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY Fig. 28. Fig. 29. 2633 No-load test. (a) Platform. (b) No-load back-EMF wave at 1000 r/min. Fig. 30. 100 A. Wave of load current and line voltage at n = 1000 r/min and Ia = Fig. 31. 120 A. Wave of load current and line voltage at n = 1000 r/min and Ia = AFPMSM load test platform. are adopted. Each separate stator core with coiling process is developed in Fig. 27(c). Three thermocouples are located in the slotting winding of each phase in Fig. 27(d). The AFPMSM assembly process is finished in Fig. 27(e). A teslameter is used to measure the air gap flux density and the leakage flux of back iron of rotor in Fig. 27(f) [24]. B. AFPMSM No-Load Test No-load test platform of AFPMSM include AFPMSM, asynchronous motor, and controller. YASA structure can realize a very small slotting opening. The advantage is brought that the harmonic components of EMF are weakened and the measured waveform of no-load back EMF is improved. Voltage probes of the oscilloscope are responsible for gathering the no-load back EMF wave as shown in Fig. 28(a) and (b) [24]. C. AFPMSM Load Test A load testing platform is established including controller, AFPMSM, dynamometer, and host computer control system in Fig. 29, where the temperature measurements of AFPMSM are carried out using a thermocouple and an infrared thermal camera device. Wave of load current and line voltage at n = 1000 r/min is given in Figs. 30 and 31. Thermocouple temperature sensors are located into each phase slot winding for measuring the winding temperature and iron core temperature. The temperature measurements of rotor and shell are made by using an infrared thermal camera device. Surface temperature measurement is obtained by an infrared thermal imager in Fig. 32. The comparison result between CFD simulation and measurement is shown in Table VI. Simulation results of CFD have a good consistency with the experimental results. Fig. 32. Infrared thermal image at f = 316 Hz, Ia = 200 A. (a) Load platform. (b) Thermal image. TABLE VI COMPARISON OF CFD AND MEASUREMENT VI. CONCLUSION The analysis results show that WFM and HSM are fast and effective methods to analyze the winding MMF and its harmonic distribution. A 12-slot/10-pole external rotor AFPMSM prototype with YASA topology and radial segmentation PM is developed in this article. Radial-segmented and epoxy-coated Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. 2634 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 56, NO. 3, MAY/JUNE 2020 PM can obviously reduce eddy current loss in PMs. The comparison experiment of core loss provides the basis for material selection. The improved channel design improves the convective heat dissipation coefficient on the water jacket surface, which can make up the increasing heat generation rate of iron core. Load experiments verify that the AFPMSM prototype can bear large current load and maintain relatively low temperature rise, which can provide design guidance for other researchers. ACKNOWLEDGMENT The authors would like to thank Höganäs for their SMC samples. The authors would also like to thank Small Elephant Electric Technology Co. Ltd. for their help during the experimental tests. REFERENCES [1] M. Aydin, “Axial flux surface mounted permanent disc motors for smooth torque traction drive applications,” Ph.D. dissertation, Univ. Wisconsin– Madison, Madison, WI, USA, 2004, pp. 396–425. [2] T. J. Woolmer C. Gardner, and J. Barker, “Electric machine—Overmoulding construction,” U.S. Patent 2013/0147291 A1, Jun.13, 2013. [3] T. J. Woolmer and M. D. McCulloch, “Analysis of the yokeless and segmented armature machine,” in Proc. IEEE Int. Elect. Mach. Drives Conf., May 2007, pp. 704–708. [4] B. Zhang, T. Seidler, R. Dierken, and M. 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Hou, Theory of Space Discrete Fourier Transform and the Holospectrum Analysis of Winding in AC Electrical Machines. Beijing, China: Waterpub Press, 2017, pp. 174–180. [18] D. Lin., P. Zhou, W. N. Fu., Z. Badics, and Z. J. Cendes, “A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis,” IEEE Trans. Magn., vol. 40, no. 2, pp. 1318–1321, Mar. 2004. [19] S. H. Han, T. M. Jahns, and Z. Q. Zhu, “Analysis of rotor core eddy current losses in interior permanent-magnet synchronous machines,” IEEE Trans. Ind. Appl., vol. 46, no. 1, pp. 196–205, Jan./Feb. 2010. [20] Magnetic Materials Part 6: Methods of Measurement of the Magnetic Properties, British European Std BSEN60404-6-2003, 2003. [21] H. Vansompel, P. Sergeant, and L. Dupre, “A multilayer 2-D-2-D coupled model for eddy current calculation in the rotor of an axial-flux PM machine,” IEEE Trans. Energy Convers., vol. 27, no. 3, pp. 784–791, Sep. 2012. [22] J. Pyrhönen, T. Jokinen, and V. Hrabovcová, Design of Rotating Electrical Machines, 2nd ed. Hoboken, NJ, USA: Wiley, 2018, pp. 445–451. [23] Q. X. Chen, Z. Y. Zou, and B. G. Cao, “Lumped-parameter thermal network model and experimental research of interior PMSM for electric vehicle,” CES Trans. Elect. Mach. Syst., vol. 1, no. 4, pp. 367–774, Dec. 2017. [24] Q. Chen, D. Liang, S. Jia, Q. Ze, and Y. Liu, “Loss analysis and experiment of fractional-slot concentrated-winding axial flux PMSM for EV applications,” in Proc. IEEE Energy Convers. Congr. Expo., 2018, pp. 4239–4335. Qixu Chen received the bachelor’s degree in mechatronic engineering from the North University of China, Taiyuan, China, in 2007, and the master’s degree in mechatronic engineering from Xidian University, Xi’an, China, in 2010. He is currently working toward the doctoral degree in electric engineering with Xi’an Jiaotong University, Xi’an, China. His research interests include axial flux PMSM design and drive of the electric vehicle. Deliang Liang (Senior Member, IEEE) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 1989, 1992, and 1996, respectively. Since 1999, he has been with the School of Electrical Engineering, Xi’an Jiaotong University, where he is currently a Professor. From 2001 to 2002, he was a Visiting Scholar with Science Solution International Laboratory, Tokyo, Japan. His research interests include optimal design, control, and simulation of electrical machines, and electrical machine technology in renewable energy. Shaofeng Jia (Member, IEEE) received the B.Eng. degree in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 2012, and the Ph.D. degree in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2017. He is currently an Associate Professor with the School of Electrical Engineering, Xi’an Jiaotong University. He is the Author/Co-Author of about 50 IEEE technical papers. His research interests include design and control of novel PM and reluctance machines. Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply. CHEN et al.: ANALYSIS OF WINDING MMF AND LOSS FOR AXIAL FLUX PMSM WITH FSCW LAYOUT AND YASA TOPOLOGY Qiji Ze received the B.S. and Ph.D. degrees in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 2011 and 2018, respectively. He is currently a Postdoctoral Researcher with The Ohio State University and the Soft Intelligent Material Laboratory, Columbus, OH, USA. His research interests include magnetic-responsive soft materials and soft robotics. 2635 Yibin Liu received the B.S. and M.S. degrees in automation and electrical engineering from Lanzhou Jiaotong University, Lanzhou, China, in 2012 and 2015, respectively. He is currently working toward the Ph.D. degree in electrical engineering with Xi’an Jiaotong University, Xi’an, China. His research interests include special transformer design and control. Authorized licensed use limited to: University of Exeter. Downloaded on June 25,2020 at 10:37:13 UTC from IEEE Xplore. Restrictions apply.