TRACING OF MAXIMUM POWER DENSITY POINT FOR AXIAL FLUX TORUS TYPE MACHINES USING GENERAL PURPOSE SIZING EQUATIONS

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1 TRACING OF MAXIMUM POWER DENSITY POINT FOR AXIAL FLUX TORUS TYPE MACHINES USING GENERAL PURPOSE SIZING EQUATIONS M. Ramanjaneyulu Chowdary Dr.G.S Raju Mr.V.Rameshbabu M.Tech power electronics Former BHU Director Assoc, Professor VNRVJIET, Hyderabad Varanasi-1005 VNRVJIET, Hyderabad Abstract-two different external-rotor-internal-stator TORUS type axial flux pm machines can be derived based on the direction of the flux. In the first type of the TORUS machine, magnet driven flux enters stator and travels circumferentially along the stator core while in the second type the flux enters the stator and travels axially along the machine axis of operation. The major differences between the two topologies are the direction of the magnet driven flux, the winding arrangement and the thickness of the stator yoke. In this paper, the sizing equations are derived for both types of TORUS machines. Based on the sizing analysis, optimum design is achieved for minimum ripple torque and maximum torque density. Finally the comparison of the TORUS topologies are made in terms of flux densities, diameter ratio and power densities and the results are illustrated in the paper. in TORUS NS type machine in order to produce torque. II. TORUS TYPE TOPOLOGY STRUCTURES The basic TORUS type machine has one stator sandwiched between two disc-shaped rotors. Figures 1a and 1b show the axial flux surface mounted PM slotted TORUS machine NN and NS types. The major differences between the two TORUS topologies are the arrangement of the magnet polarity, the arrangement of the armature winding and the thickness of the stator yoke. Keywords: Axial flux permanent magnet machines, power density and double sided. T I. INTRODUCTION ORUS concept machines are external rotor and internal stator structures. The stator has a slotted structure with strip wound stator steel. Poly phase windings are placed into slots. The two disc shape rotors carry the axially magnetized arch shaped Neodymium Iron Boron (NdFeB) permanent magnets mounted on the inner surfaces of the rotor discs. Two different TORUS machines, TORUS NN and TORUS NS, can be derived based on the direction of the flux using this structure. In the first type (TORUS NN), magnet driven flux enters the stator and travels circumferentially along the stator core. In the second TORUS type (TORUS NS), the flux enters the stator and travels axially along the machine axis of rotation resulting in theoretically no stator yoke. Moreover, while a back-to-back wrapped winding configuration is used in TORUS NN type machine, short-pitched lap winding configuration is sed Fig. 1. Slotted TORUS concept machine models (a) NN type, (b) NS type The structure of the TORUS NN type machine, winding layout and the flux direction over one pole pair are shown in Figure1a.Thestator current flows in reverse direction in each of the backto-back stator slots. A back-to-back wrapped winding structure has been used in this topology. The back-toback wrapped winding is one in which the windings are wrapped around the stator periphery in much the same manner as the winding of a toroid. TORUSNS type machine is the second type of the TORUS machine as mentioned earlier and two-pole section of the machine is illustrated in Figure1b.Thestator current flows in the same direction in each of the back-to-back stator slots in order to create torque. One of the basic differences between the TORUS NN 1

2 and TORUS NS type machines is the direction and path of the flux. In the TORUS NN type, the N pole of the permanent magnet driven flux enters the stator core through the air gap, travels circumferentially along the stator core, and then goes into the rotor core trough the S pole of the permanent magnets as seen in Figure 1 (a). Fig.. one pole pair of the slotted TORUS machine at the average diameter and flux directions for both NN type NS type structures K p -Electrical power waveform factor K e -Emf factor incorporating winding distribution factor (K w ) and the per portion of the total airgap area spanned by salient poles of the machines (if any) N t -No.of turns per phase The machine and power density for the total volume can be defined as P den = 4 D t L e (3) Where, D t is the total outer diameter of the machine, including the stack outer diameter and the protrusion of the end winding from the iron stack in the radial direction. P R B. Sizing analysis for surface mounted PM slotted TORUS type machines III. SIZING ANALYSIS OF TORUS MACHINES A. Sizing Equations and Torque Density The approach for the general purpose sizing equations has been provided in[4] and[5]. The sizing equations have the following form for axial flux machines(afm)[5]; m1 P R = K m m1 P R = K m K ek i K p K L ηb g A f p 1 λ 1 + λ D o L e K ek i K p ηb g A f p 1 λ 1 + λ D o 3 () Where P R =rated output power of the machine, K = A r =ratio of electrical loading on rotor and stator(without A s a rotor winding,k=0) D o =machine outer surface diameter L e -Effective stack length p-machine pole pairs f-converter frequency m-no.of phases of the machine m 1 -No.of phases of each stator A-Total electric loading B g -Flux density in the air gap η-machine efficiency at full load K L -Aspect ratio coefficient for radial flux machine K -Aspect ratio coefficient for axial flux machine Ratio of electric loading on rotor and stator (without a rotor winding, K =0) K i -Current waveform factor (1) Fig.3 Axial length calculation (Le) for TORUS - NN type machine To find the power density of TORUS NN-Type machine, various parameters needs to be calculated. From the general sizing equations for the axial flux machine, the outer surface diameter can be determined as D o = P R 1 m 1 + K m1 K ek i K p ηb g A f p λ λ The total outer diameter of the machine can be given as, D t = D o Where, W cu is the protrusion of the end winding from the iron stack in the radial direction. The axial length of the machine is, L e = L s + L r + g 1 3 (4) (5)

3 Where, Ls - axial length of the stator, L r - axial length of the rotor and g -air-gap length.the axial length of the stator is, L s = L cs + L ss Where, L cs - axial length of the stator core, L ss - axial length of the stator slot. The axial length of the rotor is, L r = L cr + L PM Where L cr -axial core lengthof rotor disc core, L PM -permanent magnet length (7) (8) C. Calculation of the Protrusion of the end winding (W cu ) from the iron stack. (6) the annular stator is limited by the inner circumference of the stator. A s(rg) = A i r i r g The electrical loading at radius r g is Average electrical loading is, were, R i r g, R o (1) A i = 3 N t I rms R i (13) A s D g = 6 N t I rms (14) J s = I rms A cu (15) A cu -cross sectional area of the stator conductor A s D g = A T cu J s (16) A T cu = 6 N t A cu = A s D g J s (17) Combining (9) (11) and (17) and solving for Wcu, A s D g J s K cu α s = D i D i W cui (18) Fig.4 Radial Section of TORUS-NN Type Machine Let the total area required for the stator teeth, conductors and insulation be: A Tot = D i D i W cui A Tot = D o + W cuo D 0 (9) (10) Let total area occupied by the stator copper (conductors) is: A T cu = A Tot K cu α s (11) The electrical loading at radius rg is the maximum possible number of conductors which can be wound toroidally around Protrusion of the end winding from the iron stack in the radial direction is, W cui = W cuo = D i D i A sd g (19) D o + A sd g D o (0) W cuo = 0.46~0.6 D o p (1).For NS type In TORUS NN type machine the axial length of the stator slot Lss is equal to the protrusion of the end winding. Where, W cui = L ss = D i D i A sd g () 3

4 αs - Ratio of stator teeth portion to the stator pole pitch portion (0.8) Kcu - slot fill factor of the stator winding (0.36) Js - current density of the stator winding (9 A/mm -NN, 6.6 A/mm - S) As - stator electrical loading D. Calculation of Axial length of the stator core Minimal length for mechanical strength for NS type Where, B cs - Maximum flux density in the stator core (1.7T) α i -ratio of the average air-gap flux density to peak air-gap flux density(0.75) L cr = k fb g max D o 1 + λ k d B cs 8p L cs Where, B cr - flux density in the rotor disc core (1.8T) K d -flux leakage factor of the PM machines k d = 1 p 30 = (7) K f - peak value corrected factor of air-gap flux density in radial direction of thedisc rotor (0.9). E.Calculation of permanent magnet length Fig.5 axial cross section Average value of air-gap flux density is, pφ g B avg = 4 D o D i (3) Flux/pole in stator core = Flux density cross sectional area φ cs = B cs R o R i L cs (4) φ cs = g (5) The back-iron support the air-gap flux for NN type, Substituting (4) (5) into (3) we will get, pφ g σ i B g max = 4 D o D i σ i B g max = B cs L cs p D o + D i B cs R o R i L cs = B avg 4 D o D i p L cs = B g max σ i D o 1 + λ B cs 4p (6) Observing from the equation (6), if no of poles increases axial length will decrease. The maximum flux density in the stator core is a limiting constraint based on saturation limit of the soft magnetic material. Equation for the linear section of the B-H characteristics is, B m = μ o μ rec H m + B r (8) By equating MMF across the magnet to the air-gap MMF, H m L pm + H g g = 0 For surface mounted PM machines, B m = B g Subsisting (9) into (8) we will get L PM = μ rb g B r B g k f k d k c g (30) (9) μ r - Recoil relative permeability (1.05), Br - residual flux density of the PM material (1.5 T), K c - carter s factor for stator slot (1.05). For the toroidal stator winding (distributed full pitch windings) the winding factor is K w =1, K i,=. K p =0.5 and K e =. IV.TRACING OF MAXIMUM POWERDENSITY POINT The ratio, λ, and air gap flux density are important design parameters effecting the characteristic in axial flux machines. Hence, the ratio λ and the air gap flux density must be chosen carefully to optimize the axial flux machine performance. Figure 6 shows power density plot as a function of air gap flux density and the ratio λ for TORUS NN type machine. From this plot, the maximum power density (or torque density), which is found as.56 W/cm 3, occurs at an air gap flux density of 0.91 T and the diameter ratio of λ= For that maximum point, the motor 4

5 efficiency is 94.9%. Likewise, maximum power density point can be obtained for TORUS NS type machine and shown in Figure 7. The optimization results for both machines are tabulated in Table I. Fig.6. Power density plot for TORUS NN type machine as a function of airgap flux density (Bg ) and diameter ratio (λ) (PR=00HP, ns=100rpm, p=3, A=600A/cm. TABLE-I OPTIMIZATION OF TORUS NN TYPE AND NS TYPE MACHINES FOR MAXIMUM POWER DENSITY POINT TORUS machine type NN type NS type Maximum power density (MPD) P(den)[w/cm 3 ] Diameter ratio (λ) at MPD point D Air gap flux density at MPD poin Efficiency at MPD point η [%] Fig.7.Power density plot for TORUS NS type machine as a function of air gap flux density(bg)and diameter ratio (λ) (PR=00HP, ns=100rpm,p=3, A=600A/cm). V.CONCLUSION There are several prospects of the AF machine which distinguish it from the conventional RF machine. Firstly it can be designed to possess a higher power-to-weight ratio with substantial saving in core material. Secondly, the AF machine usually has a larger diameter-to-length ratio. AF machine is particularly suitable for multi-pole and low-speed machines. The larger the number of poles, the shorter is the overhang winding at the periphery. A general approach is presented to develop and interpret general purpose sizing and power density equations for both axial and radial flux machines. Sample applications of the sizing and power density equations are utilized to compare the radial and axial flux induction machine. One of the key points of the design of axial flux TORUS concept machines is that the diameter ratio, axial length and air-gap flux density values must be chosen carefully to optimize the machine power density and efficiency. Also, this study points out that to obtain the advantages of axial flux machines, it is essential to operate the AFPM machine drives at high frequencies. Therefore, materials other than common silicon steel, such as powder metals (Soft Magnetic Composite materials) mustbe considered in the construction. A novel electric machine topology is required in Electric vehicles (EV s) to circum vent permanent magnet machine and get the same performance by using the advantage of axial flux motor and segmented core switched reluctance motor. REFERENCES [ 11 T. k Lip and Yue Li, CFMs - A New Family of Electrical Machines,IPEC 95,Japan,April3-7,1995, pp [] T.A. Lip and F.X Wang, Design and Performance of Converter Optimized AC Machines, IEEE Trans. on Industry Applications,vol.IA-0,No. 4 July/Aug~s1t 984, pp [3] S. Huang, J. Luo, F. Leonardi, and T. k Lipo, A General Approach to Sizing and Power Density Equations for Comparison of Electrical Machines, IEEE-IAS Annual Meeting, San Diego, CA Oct pp [4] P. Campbell, Principle of a Permanent Magnet axial fielddcmachine,proc.inst.elec.engg,vol.11no.1,dec1974,pp [5]C.C.Jensen,F.Profimoand T.kLipo, ALow Loss Permanent Magnet Brushless DC Motorutilizing Tape Wound Amorphous Iron, IEEETrans. on Industry Applications, vol.8,no3, May/June. 199, [6]P.Campbell, The magnetic circuit of an axialfield DC electrical machine, IEEE Transactions on Magnetics, Vol.Mag-11, No. 5, Sept. 1975, pp [7] W.S. Leung and J.C.C. Chan, A new design approach for axial-field electrical machines, IEEE Trans. Power App. Syst., vol. PAS-99, July/Aug. 1980, pp