Comparative Study of Air-Cored Axial Flux Permanent Magnet Machines with Different Stator Winding Configurations

Transcription

1 IEEE TRANSACTION ON INDUSTRIAL ELECTRONICS Comarative Study of Air-Cored Axial Flux Permanent Magnet Mahines with Different Stator Winding Configurations B. Xia, J.X. Shen, Member, IEEE, P.C.K. Luk, Member, IEEE, W. Fei, Member, IEEE Abstrat This aer resents a omrehensive analysis and omarison of air-ored axial flux ermanent magnet (AFPM) mahines with different tyes of oil onfigurations. Although oil fator is artiularly more sensitive to oil band width and oil ith in air-ored mahines than onventional slotted mahines, remarkably no omrehensive analytial equations exist. Here new formulae are derived to omare the oil fator of two ommon onentrated-oil stator winding tyes. Then resetive oil fators for the winding tyes are used to determine the torque harateristis, and from that the otimized oil onfigurations. Three-dimensional (3D) FEA models are built to verify the analytial models. Furthermore, overlaing and wave windings are investigated and omared with the onentrated-oil tyes. Finally, a rototye mahine is designed and built for exerimental validations. The results show that the onentrated-oil tye with onstant oil-ith is suerior to all other oil tyes under study. Index Terms Air-ored, axial flux, ermanent magnet, winding onfiguration, oil fator. NOMENCLATURE B Airga flux density d wire Diameter of oer wire E Indued hase voltage h Height of oils I Phase urrent k b Band fator of the oil k Pith fator (k I for Tye I, k II for Tye II) k oil Coil fator (k oili for Tye I, k oili for Tye II) l Ative length of ondutors (l = R o R i ) L a Indutane of armature N Number of ondutors in one oil Number of oles Manusrit reeived November 19, 13; revised Marh 14, 14 and June 3, 14; aeted July 15, 14. B. Xia is with Shool of Engineering, Cranfield University, Cranfield, MK43 AL, UK. ( b.xia@ranfield.a.uk). J. X. Shen is with the College of Eletrial Engineering, Zhejiang University, Hangzhou 317, China ( j_x_shen@zju.edu.n). P. C. K. Luk is with Shool of Engineering, Cranfield University, Cranfield, MK43 AL, UK ( ..k.luk@ranfield.a.uk). W. Fei is with Shool of Engineering, Cranfield University, Cranfield, MK43 AL, UK. ( w.fei@ranfield.a.uk). P u Coer loss P o Outut ower Q Number of oils in one layer Q Number of oil bands for 3-layer wave oils r Cutting radii to the mahine model (R i r R o ) Δr The infinitesimal thikness of the radial slie R a Armature resistane of one hase R e Mean radius of PM oles, (R i +R o )/ R i Inner radius of PM oles R o Outer radius of PM oles S Area of one ondutor ross setion T d Eletromagneti torque develoed by the mahine (T di for Tye I oils, T dii for Tye II and T dw for wave oils) U l Line outut voltage W Width of oil band W m Distane between oil-band midlines in one oil W Width of one oil ith x i The distane between eah ondutor and oilband midline α Filling fator of armature γ the Euler-Masheroni onstant Ω Angular rotating veloity τ Pole ith length θ Radians of one oil band (θ = W / τ ) θ i Radians of one oil band R i θ o Radians of one oil band R o θ m Radians of oil band midline ith Radians of one oil ith θ A I. INTRODUCTION XIAL flux ermanent magnet (AFPM) mahines have the merits of high aset-ratio lanar strutures, omatness and relatively high torque density [1]. As suh, they have reeived inreasing interests in aliations suh as wind ower generation systems [] [5], flywheel energy storage system [6]-[7] and eletri vehiles [8] [11] and airraft [1]- [13]. Air-ored AFPM mahines avoid using any ferromagneti material in the stator, and thus not only redue the overall weight, but also eliminate the assoiated ogging torque and stator ore losses. Due to the growing onerns of energy and environmental issues, wind ower has beome a favorable lean energy

2 IEEE TRANSACTION ON INDUSTRIAL ELECTRONICS resoure. In some rural and remote areas, small-sale off-grid wind ower systems have the artiular aeal in their aliations for owering household eletrial alianes and field monitoring devies. Air-ored AFPM mahines, whih an start with a low torque and oerate with high effiieny, have some of the most suitable harateristis among other mahine tyes. Beause of the mahine s large air ga, no saturation aears in the bak iron, the amount of harmonis is greatly redued, and low armature indutane is ahieved [14] [15]. All these features make it an ideal andidate for small-sale off-grid diret-drive wind ower systems. Comared with distributed windings, onentrated oils have the advantages of shorter end-turn length and simler struture [16]-[17]. Some researh work has shown that onentrated oils have reasonable oil fators with high ole numbers and an redue oer losses, eseially in large ole-number mahine strutures [3], [16]-[18]. With its highaset ratio lanar shae, the AFPM mahine is suitable for larger ole number onfigurations. And onentrated oils suit AFPM mahines for both high effiieny and easy manufature reasons. Other winding tyes, suh as wave winding, multi-layer windings onfigurations, are now also being used in radial flux, axial flux and linear mahines [19] []. For slotted mahines, oils are all laed in the slots. So oil struture is limited by the shae of the slots. As most of the flux goes through stator teeth in slotted mahines, oil fators are mainly deided by oil ith and an be easily alulated and analyzed [3]-[4]. However, for air-ored AFPM mahines, though there is more freedom in designing the layout of stator oils without any slot onstrains, the alulation of oil fator is more omliated. Sine in airored mahines, oils are laed in the airga, and the flux density distributes sinusoidally in the stator along the irumferential diretion. So the indued EMF of one ondutor is different from one another even in the same oil. Thus exet for the oil ith of the windings, oil band width should be taken into onsideration when studying the oil fator. Whilst air-ored winding of the linear mahine is disussed in [5], the alulation of oil fator for AFPM mahines is more omliated beause the oil ith is a funtion of the radius of the rotor. In [1], three onentrated windings onfigurations for air-ored AFPM are omared, but it only analyzes the oil fators based on the mean radius. In [6], onentrated oil with different ole-oil ombinations is analyzed. In this aer, an air-ored AFPM mahine s oil fators with different oil ithes and band widths are omrehensively omared and analyzed. The torque harateristis of mahines with different oil tyes and ole/oil onfigurations are studied. Both analytial methods and 3D FEA models are then develoed in order to evaluate the mahine erformane for different tyes of windings. Also multi-layer winding onfigurations of onentrated and wave windings are also omared with its non-overlaing ounterart. Simulation results show that mahines with onentrated windings have a better erformane. Finally, a Fig. 1. Model of AFPM air-ored mahine with onentrated windings rototye mahine is built and tested to validate the analytial and FEA models. II. COIL FACTOR AND TORQUE CHARACTERISTICS OF CONCENTRATED COILS The external-rotors-internal-stator struture, also alled the TORUS tye, is the most widely used toology of the AFPM mahines. TORUS surfae mounted mahines have advantages of simle strutures, low ost, low noise and smooth torque outut [7], [8]. Double-outer-rotor-singlestator toology for air-ored AFPM mahines is adoted as a vertial diret-drive wind generator in this aer, and the model is illustrated in Fig.1. As analyzed in [9], the indutane of air-ored AFPM mahines is very small omared to the resistane, and thus the influene of indutane is not inluded in the analytial model disussed in this setion. A. Coil Fators of Conentrated Windings There are two tyes of onentrated oils, namely Tye I and Tye II as illustrated in Fig. Sine flux distribution seen by the oil in air-ored mahines is different from that in slotted mahines, the oil fator definition is also different. The angular area ouied by one oil is defined as oil ith θ (in eletrial radians), and the eletrial radians between the midlines of oil band is θ m. For Tye I, the neighbouring oils are losely touhing eah other along the edge of the oils. For Tye II, the neighbouring oils only touh eah other at inner radius R i, and θ m does not hange with utting radius r. For slotted mahines, the oil fator is mainly deided by the oil ith. When the oil ith is 18 eletrial degrees, flux linkage through the oil is maximal, and thus maximal EMF is obtained. However, there would be a redution of the vetor sum omared to the numerial sum of the ondutors in the two oil bands when the oil ith is not 18 eletrial degrees. The oeffiient to reresent the redution is alled ith fator. Also in air-ored mahines, the width of oil band annot be ignored, sine the ondutors in eah oil have hase differene with one another. Thus, there would be a derease in EMF vetor sum sine the ondutors in one oil band are not in hase. The oeffiient to reresent the derease is alled band fator.

3 Fig. 3. Cirumferential setion of D model of ole-ithes. Fig.. Coil layout of two tyes of onentrated oils, Conentrated Tye I, Conentrated Tye II. By emloying a ylindrial setion at different utting radii (r), a ross setion in irumferential diretion is obtained. Only two ole ithes are shown in Fig.3 for larity. First the influene of the oil-band width is onsidered. Assuming the ondutors in one oil-band are distributed evenly, they are symmetri to the midline of the oil band. So the vetor sum of the indued voltage of all ondutors in one oil-band has the same hase angle with the ondutor in the midline. As deited in Fig 4, eah arrow reresents the indued voltage vetor of eah ondutor in one oil-band and has the same amlitude but different hase angles at different irumferential ositions. Then the indued voltage of one ondutor whih is at a distane of x i from the oil-band midline at r an be derived: xi ei ( r) Br r os( ) (1) Hene, the indued voltage of the ondutors in series in one oil-band an be obtained: W / xi e( r) Br r os( ) dxi Thus band fator k b (r), whih indiates the voltage redution due to the width of the oil-band, an be obtained at r as: W / xi B r r os( ) dx i W kb( r) sin (3) B r r W W As one oil-band is onverted into ideal ondutors loated at the midline of the oil-band using the band fator, the oil ith fator at a ertain radius an be alulated as normal slotted windings: m k( r) sin (4) Thus for onentrated Tye I windings, the oil ith fator given by: () Fig. 4. Vetor diagram of indued voltage of ondutors in one oil-band. ( ) sin W W k 1 r (5) The oil ith fator for onentrated Tye II windings is: ( ) sin Wm k r (6) where W r (7) m i o W /Ro i W /Ri So the oil fator an be alulated as follows: k oil1 Ro Ri B r k k dr Ro Ri br r B r dr By alying (3) and (5) to (9), the oil fator for onentrated oil Tye I is obtained: koil1 os o 1 1 o o 3 o i sin o os i o i i Cio sin Sio os Si i os Cii sin os o i Similarly, the oil fator for onentrated oil Tye II is derived as: (8) (9) (1)

4 m sin 3 1 koil sin o 1 1 o 3 o i (11) 1 sin o os sin i o o i 1 1 sin i osi Cio Cii i i where funtions Ci(x) and Si(x) are defined in Aendix. From (1) and (11), we an see that oil fator is deided by the oil ith and oil-band width, and is indeendent of the ole number. Sine the sae for windings at inner radius R i is muh smaller than the outer radius R o, the limitations of oil-band width are θ i θ /. Beause θ diretly indiates the requirement of the sae for a oil, oil ith is hosen as a key variable when analyzing oil fators. The variations of the oil fator of two onentrated tyes against oil ith at different oil-band widths are illustrated in Fig. 5. It an be seen that maximum oil fators are ahieved while oil ithes are between 18-3 eletrial degrees, deending on the width of oil-band. Aording to Equation (5) and (6), when the band midline ith is 18 eletrial degrees, ith fator reahes eak value. Also, based on Equation (8), the wider the oil band, the bigger the oil ith will be. Thus oils with wider bands ahieve maximums at larger oil ith. As oil-band width inreases, the eak value of oil fator dereases for both oil tyes beause of the derease of oil-band fator, whih an be redited from Equation (3). Comared to Tye I winding, the eak value of Tye II dereases muh faster with oil-band width. So, Tye I oils have a higher maximum value of oil fator with the same usage of oer. From oil fator oint of view, oil Tye I should be better than Tye II with the same rotor. B. Torque Charateristis of onentrated oils However, oil fator only reresents the utility ratio of oer oil. Thinner oil-band oil has higher oil fator, but that also means less stator sae is utilised and less ondutors are used to generate torque. Thus the shae and size should be hosen arefully to ahieve higher torque density and lower loss. The main ontribution to the temerature rise of the mahine is oer loss due to the absene of ore loss and eddy urrent. And with the same R o and R i, the volume of the stator is aroximately the same. To kee a onstant temerature rise for stator, oer loss is ket onstant. With the oil fator equations derived, the indued voltage an be alulated: NQBlv Re E koil NQBl k (1) oil 3 3 To alulate the urrent, armature resistane needs to be estimated for Tye I and Tye II: 4 Re NQ RaI u l (13) Q 3 4 Re NQ RaI u l (13) Q 3 mre NQ RaII u l W (14) 3S Then, at a onstant oer loss, hase urrent an be derived as: I I Pu Pu S 3R Ql 4 R W h u u e Pu Pu S 3R l W 4 R / QW h u u m e (15) (16) where α is the filling fator and is usually between.4-.5, aording to manufaturing exeriene: N d / wire W h (17) The torque outut at a given oer loss P u are derived for Tye I (T di ) and Tye II (T dii ) as: 3EI h P W Q T BR l k u di e oil1 u l 4 Re / Q h P W Q T BR l k u dii e oil u l W 4 Re i / (18) (19) In order to investigate the influene of oil onfigurations, assumtion is made suh that the mahine size, magnet usage and oil height as well as filling fator are ket onstant. Thus R o, R i, B, h and α are onstants. Then with different Fig. 5. Coil fator against oil ith for onentrated oils, Conentrated tye I, Conentrated tye II.

5 3 Torque (Nm) Tye I =1 Tye II =1 Tye I = Tye II = Tye I =8 Tye II =8 Tye I =36 Tye II = θi/θ 35 Torque (Nm) 3 5 Tye I =1 Tye II =1 Tye I = Tye II = Tye I =8 Tye II =8 Tye I =36 Tye II = θi/θ Fig. 6. Torque outut against oil band width ratio with different ole numbers for onentrated oils, θ =1 eletri degrees, θ =4 eletri degrees. arameters alied to Equation (18) and (19), the torque outut an be alulated with analytial methods. For three hase mahines, ertain attern of oil arrangement rules should be followed, and windings with oil ithes of 1 and 4 eletrial degrees are the most ommon onfigurations. As shown in Fig. 6, though larger oil-band width redues the oil fator, stator sae will be fully used as more ondutors will generate higher torque with a smaller derease in oil fator. Thus, for Tye I oils, thiker oil band an inrease torque outut. But for Tye II oils, sine oil fator dros muh faster with wider oil band, too wide oils would redue torque outut. Also, due to higher oil fators, oils of 4-eletrial-degree ith have a muh better torque aability than that of 1 eletrial degrees (more than %). And from the omarison of the two tyes of onentrated oils, when oil band width ratio is higher than.35, Tye I oil obtains higher torque density. And Tye I oils an ahieve higher overall maximum torque outut than their ounterarts. In order to maximize torque ability, thiker band width will be adoted and thus Tye I oils resent the better hoie. From Fig. 5, we an see that the value of oil ith to obtain maximum oil fator lies between 5-55 eletrial degrees when θ i /θ.3. For windings with some other ommonly used oil ithes suh as 15, 1, 3 eletrial degrees, under the same oil band width ratio (θ i /θ = onstant) ondition, their oil fators are smaller than that of 4 eletrial degrees aording to (1) and (11). Moreover, distribution fator needs to be onsidered beause more than one oils need to form a hase grou, whih will further redue their oil fators, and thus will redue torque outut. So, Tye I oils with 4 eletrial degrees is the best hoie for onentrated windings. Another way to inrease the outut torque is using higher () Fig. 7. Coil layout of 3 tyes of multi-layer windings, -layer onentrated windings, 3-layer onentrated windings, () 3-layer wave windings. ole numbers. Assuming the total amount of effetive ondutor is ket onstant (N Q/S = onstant), R a dereases with inrease of aording to Equation (13) and (14). That means mahines with higher ole numbers have shorter endwindings, beause the ative art stays the same. As a result, higher urrent an be suorted and the outut is inreased. However, onsidering the manufature of the mahine, higher ole numbers lae greater demands on the fabriation of smaller winding oils and also on the assembly. Flux leakage will be a severe issue if the ole number is too high and the ole ith is too small. Moreover, a small offset of magnet osition would be amlified / times and may ause onsiderable distortion in the flux distribution. Eddy urrent losses in the winding ould be an issue in higher seed aliations. C. Analysis of Multi-Layer Windings Air-ored struture rovides muh more freedom for winding design without slot onstrains. So other oil onfigurations an also be used in air-ored AFPM mahines. The -layer onentrated, 3-layer onentrated and 3-layer wave winding onfigurations are deited in Fig. 7. For -layer or 3-layer onentrated oils, the analytial model is the same with onentrated Tye I oils. So the alulation equations for oil fators and torque are the same with (1) and (18), exet that Q reresents the number of oils er layer for multi-layer windings. For examle, multilayer onentrated windings with oil ith of 1 and 4 eletrial degrees have exatly the same oil fator and torque harateristis as demonstrated in Fig. 5 and 6. In one-layer er hase 3-layer onentrated windings onfiguration, eah oil usually overs a ole ith (if not, there will be a distribution fator for eah oil, whih would

6 Torque (Nm) θi/θ Fig. 8. Comarison of torque between 3-layer onentrated oils with oil ith of 18 eletri degrees and Tye I models. redue the overall oil fator). As illustrated in Fig. 8, 3-layer onentrated winding has higher torque outut with smaller θ i /θ beause of higher oil fator and higher number of oils. With the inrease of oil band width ratio, oil fator dros muh faster than that of Tye I 4-degree winding, and thus higher maximum torque aabilities an be ahieved for Tye I windings. As for 3-layer wave windings, the analytial model is similar to onentrated Tye II oils. So the oil fators of this winding tye an be written the same as (11) and the torque outut T dw an be derived as: h P W Q' T BR l k u dw e oil u l W ml Ri / () For wave windings, all oil-bands are onneted in series to form one layer, so normally Q equals to the number of oles. And the oil-band width limitation is given by: W R / Q' R / (1) i i 3-layer, =1 Tye I =1 3-layer, = Tye I = 3-layer, =8 Tye I =8 3-layer,=36 Tye I =36 Fig. 9. Analytial torque harateristis of wave windings, Torque against oil-band width at different, Torque against oil-band width at different θ m (in eletrial degrees) with =8. So the oil-band width of wave winding is wider than the onentrated ones, whih requires larger room for endwindings. So it is harder to assemble wave winding beause of limited sae in the inner radius area. The torque harateristis of wave windings are illustrated in Fig. 9. With the inrease of the number of oles, higher torque density an be ahieved, and more oer ould be laed in the stator whih further inreases torque outut. And with 18- eletrial-degree midline ith θ m, torque outut is omaratively higher. The maximum value of torque aears when θ i /θ m equals.8. But omared to onentrated Tye I windings, wave windings are inferior for air-ored AFPM mahines. From a theoretial oint of view, multi-layer onentrated and wave winding onfigurations have no advantage over single layer onentrated windings. Moreover, more oil layers would inrease the ost of assembly. Another disadvantage of 3-layer windings (eah for one hase) is the EMF imbalane among 3 layers. Aording to airga flux distribution analysis in [5] and [3], the flux density is higher if the layers are loser to magnets. Thus the bak-emf of the middle layer would be smaller than the other two, and the imbalane will eventually result in large torque riles and vibrations. III. 3D FEA ANALYSIS Due to the intrinsi magneti flux distribution of AFPM mahines, three-dimensional (3D) FEA analysis is always neessary for high reision erformane redition. Although 3D FEA software has beome more oular, 3D FEA simulations are still quite time-onsuming in otimization stages. To redue simulation time and imrove effiieny, it is always neessary to ensure the solution sae is arefully hosen by means of symmetri boundary onditions. A. Conentrated Windings As a onlusion from the analysis of setion II, onentrated windings with higher ole numbers and a oilith of 4 eletrial degrees have better torque harateristis. But AFPM mahines with too many oles will inrease the manufaturing ost. Taking manufaturing issues into aount, the 8-ole-1-oil onfiguration is a more ratial struture with relatively high torque outut. So 3D FEA models with 8 oles are develoed and analyzed. Results between FEA models and analytial models of both Tye I and II windings are omared in Fig. 1. It an be seen that the analytial methods show fair agreements with FEA results. The disreany an be attributed to edge effet not being onsidered in the analytial models. Thus the advantage of imroved mahine erformane of Tye I oils with wider oil-band is validated. B. Multi-layer Windings For multi-layer onentrated onfigurations, their analytial models are the same as Tye I. Thus the torque features are exatly the same with their Tye I ounterarts if the oil ith of the windings is the same. Models of -layer windings with oil ith of 4 eletrial degrees are omared in Fig. 1

7 () (d) () Fig. 1. 3D FEA results of different winding onfigurations, onentrated tye I and II, -layer onentrated, () 3-layer wave winding. with the analytial and FEA methods, and the result reveals that the torque harateristis is aroximately the same with Tye I. So if a winding onfiguration an fit in one layer, it makes no differene to slit it into or 3 layers. The analytial model of 3-layer wave winding is similar to onentrated Tye II winding, but it has muh wider oil bands. As a result, the end-windings of this onfiguration are muh longer than other oil tyes. Thus oer loss is higher and mahine effiieny is redued. These are the main reasons why mahines with wave windings have the worst outut harateristis among all oil onfigurations disussed here. As for the imbalane issues for one-hase-er-layer 3-layer windings mentioned in setion II, the results of FEA models show that the EMF of the middle-layer hase is about 7% lower than the other two. As a ower generator, severe imbalane of 3-hase ower suly will inrease the loss and ause over-heating issues to both the generator itself and other devies onneted to it. Same imbalane roblems an be found in other one-layer-er-hase windings onfigurations. Through the analysis in this setion, it an be seen that the analytial method for oil fator alulation and torque redition agrees reasonably well with the 3D FEA method, and it onfirms that onentrated Tye I oils with a oil ith of 4 eletrial degrees are the best winding onfiguration hoie for air-ored AFPM mahines. (e) Fig. 11. Prototye AFPM mahine and testing rig, assembled mahine, stator dis, () rotor dis, (d) one oil, (e) test rig. IV. EXPERIMENTAL TESTS AND DISCUSSION To ahieve a higher torque outut at aetable fabriation osts, a design with 8 oles and 1 Tye I onentrated oils has been seleted as a rototye mahine for exerimental verifiation of the analytial and FEA models. A dediated test rig is also set u for this. The rototye mahine and its arts (the stator and rotor and winding), together with the test rig, are shown in Fig.11. Due to manufaturing onstrains, width of 13mm is hosen for oil-band. More detailed arameters are listed in Table I. Under laboratory onditions, the generator is installed horizontally and driven by an indution motor through a gear box. A rogrammable frequeny onverter is used to regulate the rotating seed to simulate various wind onditions. The load in the lab is resistive only, with adjustable resistors without aaitane. The resistors are onneted diretly to three hase armature with star onnetion for AC load test, while one resistor is onneted through a 3-hase retifier bridge for DC load test. At first the line voltage is tested at no load, as deited in Fig. 1. FFT analysis of the bak EMF shows that the voltage

8 Bak EMF(V) Line Voltage (V) D FEA Exerimental Eletri Degrees 3D FEA Exerimental Harmoni Orders 9 11 Fig. 1. Bak EMF of FEA model and rototye mahine, line voltage wave form, FFT analysis. Voltage (V) Voltage Current Time (ms) 6 4 Current (A) Voltage (V) - -4 (d) Fig. 13. Voltage and urrent at full load, 3D FEA with 3-hase AC load, 3D FEA with 3-hase retifier bridge, () rototye test with 3-hase AC load, (d) rototye test with 3-hase retifier bridge. () waveform is highly sinusoidal with negligible harmoni omonents, and the error from FEA is less than % omared to exerimental results. This rovides good evidene that only fundamental of the flux is neessary for the analytial method to alulate winding fator and redit the torque erformane Voltage Current Time (ms) 6 4 Current (A) - -4 Line Voltage(V) Line Voltage with DC Load 5 Line Voltage with DC Load Outut Power(W) Fig. 14. Voltage variation with 3-hase AC load and DC load. TABLE I PARAMETERS OF PROTOTYPE MACHINE Parameters Value Parameters Value Rated ower (W) 1 Outer diameter (mm) 35 Rated seed (rm) 3 Inner diameter (mm) 1 Number of oles 8 Height of PM (mm) 7.5 Number of slots 1 Height of oils (mm) 1 Armature filling fator.43 Width of airga (mm) 1.5 Coil ith (ele. degrees) 4 Coilband width (mm) 13 TABLE II COMPARISON BETWEEN ANALYTICAL METHOD AND TESTING RESULTS Prototye Testing Analytial Method 3D FEA Analysis Line EMF (V) R a (Ω) L a (mh) U l (V) I (A) T d (N m) P o (W) of air-ored AFPM mahines. Then the rototye mahine is tested at rated seed with oer loss of 75W. The mahine is onneted to 3-hase AC loads and DC load through a 3-hase retifier bridge searately to test oerating features. Both FEA and testing results are illustrated in Fig. 13. As it is evident, the omutational intensive 3D FEA simulation gives very aurate results. Various seed tests are also arried out to test overall oeration harateristis at full working range. The voltage regulation of the rototye generator is tested at different seeds and loads. As shown in Fig. 14, the roosed mahine oerates stably under different seeds and loads with a good voltage regulation of about 7%. Sine no torque sensor was used in the test, the mehanial loss annot be estimated. Thus aurate effiieny annot be evaluated. But with a oer loss of 75W, low mehanial loss of roughly W, negligible eddy urrent loss and ore loss, it is estimated that the effiieny at full load an be u to 9%. The key features of analytial method, FEA model and rototye mahine are listed in Table II. As exeted, the armature indutane is quite small, and has little effet on the mahine erformane. The bak EMF an be reisely redited, beause the absene of slots simlifies the magneti flux ath. But alulation of stator armature resistane brings about the main error (6.6%) in the analytial model, beause the limited sae for the inner radius area makes it hard to

9 form ideal oils. Contat resistane may also add u the error. The error of magneti torque and ower outut are 4.1% and 4.4% resetively. V. CONCLUSION Different tyes of stator winding onfigurations are analyzed and disussed for air-ored AFPM mahines. Analytial models for onentrated and wave winding are resented to alulate the oil fators and torque harateristis. As the two key variables, the influene of oil band width and oil ith are omared and disussed. Though thiker oil-bands redue the oil fator, they emloy more ondutors to make full use of the magnet. Higher ole numbers also imrove the torque aability, but mahines with too high ole numbers are hard for assembly and would inrease eddy urrent loss in the stator oils. Then, a series of 3D FEA models are develoed to verify the auray of analytial methods. Results from the 3D FEA models show good agreements with analytial methods. Through the omarison among different tye of onentrated oils, multi-layer onentrated and wave windings, it is obvious that onentrated Tye I winding onfiguration with oil ith of 4 eletrial degrees is the best hoie for airored AFPM mahines. For onsiderations of relatively high torque outut and fabriation issues, a 8-ole-1-oil rototye mahine is built and tested. Exerimental results validate the good erformane of the rototye mahine. It also onfirms that the analytial method of oil fator and torque outut is an effiient and aurate way for reliminary design of winding onfigurations and for the redition of the mahine erformanes. VI. ACKNOWLEDGEMENT The work was artly funded by the Engineering and Physial Sienes Researh Counil (EPSRC) within the Vehile Eletrial Systems Integration (VESI) rojet (EP/I38543/1), and The Royal Soiety of United Kingdom. k1 APPENDIX k 1 x sint k1 x Si x dt 1 t k 1 k 1! ost x Ci x dt ln x x t k k! k1 REFERENCES k (18) (19) [1] F. F. Giulii Caoni, G. De Donato, F. 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10 [4] L. Chong, R. Dutta, and M. F. Rahman, "Aliation of Conentrated Windings in Interior Permanent Magnet Mahine," in Pro. Australasian Universities Power Eng. Conf.,. 1-5, De. 7. [5] A. Mohammadour, A. Gandhi, and L. Parsa, "Winding fator alulation for analysis of bak EMF waveform in air-ore ermanent magnet linear synhronous motors," IET Eletri Power Aliations, vol.6, no.5, , May 1. [6] M. J. Kamer, Rong-Jie Wang, and F. G. Rossouw, "Analysis and Performane of Axial Flux Permanent-Magnet Mahine With Air-Cored Nonoverlaing Conentrated Stator Windings,", IEEE Trans. on Ind. Al., vol.44, no.5, , 8. [7] A. Mahmoudi, S. Kahourzade, N.A. Rahim, W.P. Hew, "Design, Analysis, and Prototying of an Axial-Flux Permanent Magnet Motor Based on Geneti Algorithm and Finite-Element Analysis," IEEE Trans. Magn., vol.49, no.4, , Aril 13. [8] M. Aydin, Surong Huang, and T. A. Lio, "Design and 3D Eletromagneti Field Analysis of Non-Slotted and Slotted TORUS Tye Axial Flux Surfae Mounted Permanent Magnet Dis Mahines," in Pro. IEEE Int. Eletri Mah. and Drives Conf. (IEMDC), , 1. [9] J. R. Bumby and R. Martin, "Axial-flux ermanent-magnet air-ored generator for small-sale wind turbines," in Pro. IEE Eletri Power Aliations, vol.15, no.5, , 9 Set. 5. [3] Yunkai Huang, Baoyun Ge, Jianning Dong, Heyun Lin, Jianguo Zhu, Youguang Guo, "3-D Analytial Modeling of No-Load Magneti Field of Ironless Axial Flux Permanent Magnet Mahine," IEEE Trans. Magn., vol.48, no.11, , Nov. 1. Bing Xia reeived the B.S. degree in Eletroni Engineering and the M.S. degree in Eletri Mahines and Aaratus from Zhejiang University, Hangzhou, China, in 8 and 11, resetively. He is urrently ursuing the Ph.D. degree with Eletri Power and Drives Grou, Shool of Engineering, Cranfield University, UK. His urrent researh interests inlude the design and aliations of ermanent-magnet mahines and drives. Patrik Chi-kwong Luk (M'9-SM'8) was born in Hong Kong. He reeived the High Diloma from Hong Kong Polytehni University in 1983, the M.Phil degree from Sheffield University, in 1989, and the Ph.D. degree from the University of South Wales, in 199, all in eletrial engineering. After a brief areer in Hong Kong, he gained the Overseas Researh Students Award to undertake ostgraduate study at Sheffield University in Sine 1988, he had held aademi ositions at the Universities of South Wales and Hertfordshire, U.K. He joined Cranfield University, U.K., in, where he is Chair Professor in Eletrial Engineering and Head of the Eletri Power and Drives Grou in the Shool of Engineering. He has over 14 ubliations and is o-holder of several atents. His urrent researh interests inlude eletrial drives, renewable energy and wireless ower transfer. Currently he holds a visiting rofessorshi at Shanghai Jiaotong University, China. Weizhong Fei (M 1) was born in Zhejiang, China. He reeived the B.Eng. and M.Eng. degrees from Zhejiang University, Hangzhou, China, in 4 and 6, resetively, and the Ph.D. degree from Cranfield University, Shrivenham, U.K., in 1, all in eletrial engineering. From 11 to 1, he was a Researh Assoiate at the University of Sheffield, Sheffield, U.K. Sine 1, he has been with the Shool of Engineering, Cranfield University, where he is urrently a Leturer in Clean Energy Tehnology. His urrent researh interests inlude design and aliations of eletri mahines and drives. Jian-Xin Shen (M 98-SM 3) was born in Huzhou, China, in He reeived the B.Eng. and M.S. degrees from Xi an Jiaotong University, Xi an, China, in 1991 and 1994, resetively, and the Ph.D. degree from Zhejiang University, Hangzhou, China, in 1997, all in eletrial engineering. He was with Nanyang Tehnologial University, Singaore ( ), the University of Sheffield, Sheffield, U.K. (1999 ), and IMRA Euroe SAS, U.K. Researh Centre, Brighton, U.K. ( 4). Sine 4, he has been a rofessor of eletrial engineering at Zhejiang University. He has ublished more than 13 aers and obtained atents. He reeived a Prize Paer Award from the IEEE Industry Aliations Soiety in 3, and a Best Paer Award from EVER-Monao in 1. His main researh interests inlude toologies, ontrol and aliations of ermanent-magnet mahine drives.