Dimensioning of a permanent magnets motor with double rotor for electric vehicle

Transcription

1 SETIT th International Conference: Sciences of Electronic, Technologies of Inforation and Telecounications arch 5-9, 007 TUISIA iensioning of a peranent agnets otor with double rotor for electric vehicle. Chaieb, S. Tounsi, R. eji and F. Sellai aboratoire d Electronique et des Technologies de l Inforation -ETI- Ecole ationale d Ingénieurs de Sfax B.P. W, 3038 Sfax Tunisie. chaieb_ed@yahoo.fr, souhir.tounsi@enis.rnu.tn, rafik.neji@enis.rnu.tn, faycal@sellai.co Abstract The applications of the electric otors in transport require a broad range of operation at constant power. To answer this requireent, we have studied a structure of achine with double rotor. Indeed, the total torque delivered is the su of torques supplied by the two rotors. This article describes, then a design ethodology of a peranent agnets otor with double rotor, radial flux and strong starting torque for electric vehicles. This work consists, of the analytical diensioning of the otor by taking into account several constraints of operation followed by a odelling by the finite eleent ethod and a Coparison between a otor with double rotor and a otor with one rotor. Key words: peranent agnet, electric otor, diensioning, electric vehicle ITROUCTIO Aong the range of the electric otors, the choice a otor of the traction for electric vehicle is vast and delicate task. A wide range of otors exists with their intrinsic qualities and defects such as: the asynchronous otor, the synchronous otor, the variable reluctance otor and the peranent agnets otors. In electric otors application related to electric vehicle, fundaental selection criteria are considered: the power-to-weight ratio, the efficiency and the production cost. Our choice has focused on the peranent agnets otor with double rotor, guided not only by these criteria but also by reduced bulk and by the strong starting torque developed. The ain objective of this work is the sizing of the strong starting torque otor by the analytical ethod and by the finite eleents ethod. The configuration of the otor is characterized by a relation ship between the nuber of teeth and the nuber of poles pairs directly bound to the space percentage occupied by the slots copared to that occupied by the inserted tooth. The figure () represents a peranent agnets otor with double rotor.. Analytical diensioning of the otor.. Configuration The otor with double rotor is coposed of two stators and two rotors. Each stator contains four poles pairs and six ain teeth. Between two ain teeth an inserted tooth is added to iprove the wavefor and reduce the flux leakages. Each phase winding is ade up of four coils diaetrically opposed. Figure. Configuration of peranent agnets otor with double rotor Three design ratios define the otor s structure []:

2 The first coefficient is the ratio β of the angular width of a agnet a by the pole pith p a () β p The second coefficient is the ratio R ldla of the ain tooth angular width A tooth by the angular width of a agnet. A R ldla tooth () a It adjusts the size of the ain tooth and has a strong influences on the electrootive force. The last coefficient R did is the ratio of the inserted tooth A toothi by a ain tooth A tooth. It fixes the inserted tooth size. i R did (3) The size of the inserted tooth is optiised by the finite eleent ethod in order to reduce leakage flux and ripple torque [,3,4]... Analytical estiate of the electrootive force related to a stator and a rotor. The electrootive force is deduced fro the flux derivative, its necessary then to be able to express the flux in versus agnets position. [5,6] The flux leakage between the air-gap and the stator is neglected and the agnetic induction is supposed to be perfectly rectangular on the air-gap. With these assuptions, for a stator. the in coning flux in a coil can be put in the following for: [7] θ+ ϕb Be ( θ).ds Be( θ).ds (4) coil s θ Where Be, in the agnetic induction in the air-gap. The electrootive force can be given by the following equation [8]: n ef bn.( θ) T 4 θ0+ T/ with: bn E ( θ) ( θ) dθ (5) T θ0 T a and θ The first haronic of the electrootive force in a stator deduced and expressed as follows: ef () t 8 β R ldla sph Ω B e ( p Ω t ) β With: -, otor length -, Stator diaeter - sph, nuber of spire per phase - P, nuber of pole pairs The total electrootive force of the otor is then expressed as follows: ( t) ef 8 sph Be β β Rldla Ω p Ω 8 + sph Be β β Rldla Ω pω ( t) ( t) The otor electric constant is deduces and given by the following expression: Ke + sph sph Be Be.3. The otor diensioning β β R β β R The agnet height fixes the flux density level in the airgap.this paraeter is given by applying the apere law for a axial covering a agnet and a ain tooth. The flux created by agnets is coposed of the leakage flux between agnets and the flux in stator and rotor H a and H a represent the agnet height of the interior and external rotor µ a Be e Ha Be (9) Br Kfu and µ a Be e Ha Be (0) Br Kfu With - µ a is the agnet relative pereability - B r is the agnets reanent induction - K fu is coefficient of flux leakages - e, is the air-gap thickness - H enc and H enc represent respectively the slot height of the interior stator and the exterior stator. ldla ldla (6) (7) (8) - -

3 H enc sph In d δk e enc () H enc sph In d δk e enc () Where - d is the nuber ain teeth - K r is the filling coefficient of slots - enc is the slots width Figure. The otor heights of various constituting eleents To avoid the deagnetisation, the current of phase ust be below I ax I ax p 3µ 0. I ax p 3µ 0. sph sph. Bc.Kfu.e B[ + α.(ta 0)] Bc).Ha Bc.Kfu.e B[ + α.(ta 0)] Bc).Ha. µ a µ a (3) (4) With b c is the iniu flux density allowed in the agnet and µ 0 is the pereability of the air.4. iaeter of the otor The external diaeter of the otor is expressed by the following forula: ex + e+ (h cr a cs d + ers+ e+ h a With: - H cs and H cr are respectively the stator yoke thickness and rotor yoke thickness - h a, is the agnet height - H d, is the ain tooth height. - e rs, is the vacuu between rotor one and stator two.5. Power-to-weight ratio of the otor The power-to-weight ratio of the otor P (W/Kg) is defined by the ratio of the electric power by the total ass: cr ) (5) P e P (6) tot The total ass of the otor ( tot ) is the su of asses of the statoric teeth ( ds ), of the inserted teeth ( di ), of the stator yoke ( cs ), of the copper ( cu ), of the agnets ( ai ) and of the rotor yoke ( cr ): tot ds + di + ai + cs + cr + cu (7) + ds + di + ai + cs + cr + cu ds and ds represent respectively the teeth ass of the interior stator and the exterior stator. A ds tooth ds d e e ) ( Hd) vt (8) d e e (9) ) ( Hd) vt With: - d, is the total nuber of ain teeth. - vt, is the density of etal sheets cs and cs represent respectively the ass of the interior and exterior stator yoke (0) e e cs Hd Hd - Hcs..vt () e e cs Hd Hd Hcs..vt cu and cu represent the ass of the copper 3 In sph sp cu δ vc () 3 In sph sp cu δ vc (3) Where: - sp, is the average length of a spire - δ, is the current density adissible in the notches - I n, is the rated current of the otor - vc, is the copper density ai and ai represent the ass of the interior and external agnets. + e + e ai a + Ha) ( ) va (4) + e + e ai p a + Ha) ( ) va (5) With va, is the agnets density, cr and cr represent the ass of the interior and exterior rotor yoke

4 + e + e cr + Ha + Hcr) ( + Ha) (6) vt + e + e cr Ha Hcr) ( Ha) (7) vt ds and ds represent the ass of the inserted teeth of the interior and exterior stator. A A ds Adenti di (9) Adent ds denti di (8) dent. odelling by finite eleents The studied otor is rotated at its noinal speed at no load. In these conditions, the siple tension corresponds to the ef. The representation of the lines of field, obtained by siulation and represented on the following figure (3). Figure 5. Flux through three phases of the exterior stator The figures (6) and (7) represent the electrootive forces fors at the level of the three phases followed the alientation of the otor by a balanced current three-phase syste Figure 6. Electrootive forces at load of the interior stator Figure 3. ines of fields for an initial position For different positions of the rotor in versus the stator, the incoing flux obtained by the achine winding is represented on the figures (4) and (5). Figure 7. Electrootive forces at load of the exterior stator Figure 4. Flux through the three phases of the interior stator The ef at load is identical to ef at no load because the agnetic reaction of arature is weak. The electrootive force at no load is supposed to be equal to the electrootive force at load (arature reaction neglected) the electroagnetic torque of the otor is given by the following expression [9,0]. 3 3 T e ( θ) Ei(t) Iphi(t) + Ei(t) Iphi(t) (30) Ω i Ω i - 4 -

5 Where, E i and I phi are respectively the electrootive force and a phase current The electroagnetic torques produced by the two rotors and the total torque of the achine are represented by the following figures. If we ake a coparison between the results obtained by calculation of the ass and the Power-to-weight ratio of the two otors for the sae application and in identical state of use (fig 0 and fig ) Figure. 8. Electroagnetic torques of the interior and exterior rotor Figure 0. ass of a otor with one rotor and of a otor with double rotor Figure 9. Electroagnetic torque of the otor The average value of the torque reaches the value fixed by analytical calculations, which validates this analytical diensioning ethod. 3. Coparison between a otor with double rotor and a otor with one rotor The following table presents the ass and the power-toweight ratio of a otor with double rotor and a otor with one rotor for a variation of power of 9 kw to 95 kw. Table. ass and Power-to-weight ratio of the otors otor with double rotor otor with one rotor Power (kw) Torque otor () ass (kg) Power-to-weight ratio (kw/kg) Figure. Power-to-weight ratio of a otor with one rotor and of a otor with double rotor We shows the advantage of a otor with double rotor copared to that with only one rotor on the level of powerto-weight ratio for the strong powers, this explains the benefit of ug a otor with double rotor in the field of the electric traction. 4. Conclusion The study consists in diensioning a otor with double rotor of strong starting torque for an electric vehicle. Firstly an analytical sizing of the achine was carried out. Secondly a odeling by finite eleents in dynaics to validate the wavefor strongly depending on the achine geoetry as well as the electroagnetic torque delivered by the otor. Finally a coparison between the otor with double rotor and the otor with one rotor. REFERECES [] BRISSET S., GIO F., BROCHET P.: "anufacturing cost reduction in brushless C otors" ICE00, 6-8 août à Bruges-Belgique, C: ICE

6 [] TOUSI S., GIO F., BRISSET S., BROCHET P., EJI R.: "esign of an axial flux brushless C otor for electric vehicle. " ICE00, 6-8 August, Bruges-Belgiu, C: ICE0-58. [3] A. CAVAGIO, F. PROFUO, A. TECOI " Axial flux achines: structures and applications" Electro otion 00 pp5-4, Bologna, June 9-0, 00 [4] J. AA G,. BARRIE C "Peranent-agnet achines with powdered Iron Cores and pressed windings" Transaction on industry applications. Vol.36? 4. July/August 000. [5] Z.ZHAG, F.PROFUO and A.TECOI "Analysis and Experiental Validation of Perforance for an Axial Flux Peranent agnet Brushless C otor with Powder Iron etallurgy Cores ": agna Physics publishing and Clarendon Press, Oxford, 994 [6] F. SAHI, A.. TUCKEY, and A.J.A. VAEPUT: "The design of a high speed flywheel ounted axial-flux peranentagnet achine" ICE 000. pp [7] TOUSI S., EJI R., GZARA. and SEAI F: Cost Reduction of Peranent agnet Synchronous otor with Axial Flux. ICE-04 (6th International Conference on Electrical achines), 5-8 Septeber, Cracow-Poland. [8] TOUSI S., EJI R., SEAI F.: "esign of a radial flux peranent agnet otor for electric vehicle." EPE 003.PP.5. [9] IQBA HUSAI and OHAA S. ISA: "esign, odelling and Siulation of an Electric Vehicle Syste". SAE TECHICA SERIES International Congress and Exposition etroit, ichigan arch -4, 999 Reprinted Fro: Advances in Electric Vehicle Technology (SP-47). [0] S.HUAG, J.UO, F.EOARI, T. A. IPO A general approach to sizing power density equation for coparison of electrical achines, IEEE Trans. I.A.998, vol.34, n, pp