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A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

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A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor Journal of Asian Electric Vehicles, Volume 8, Number 1, June 2010 A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor Mohamed Chaieb 1, Naourez Ben Hadj 2, Jalila Kaouthar Kammoun 3, and Rafik Neji 4 1 Electrical Engineering Department, University of Sfax, [email protected] 2 Electrical Engineering Department, University of Sfax, [email protected] 3 Electrical Engineering Department, University of Sfax, [email protected] 4 Electrical Engineering Department, University of Sfax, [email protected] Abstract Currently, the permanent magnet motors PMM represent an attractive solution in the electric traction field, thanks to their higher performances than other electric motors. In this context, this work represents an analytical study and validation by the finite element method of two configurations, the radial flux permanent magnet syn- chronous motors with exterior rotor PMSMER and with interior rotor PMSMIR. This paper is divided into two sections: In the first section, we represent the analytical study based on electromagnetic law of the two structures PMSMER and PMSMIR. In the second section, we represent a comparative study of the two structure perform- ances. Keywords 2. MODELLING OF THE TWO PMM STRUC- permanent magnet motors design, radial flux, finite TURES element method, modelling, performance 2.1 Structural data The motors structure allowing the determination of 1. INTRODUCTION the studied geometry is based on three relationships. Considering the large variety of electric motors, such The ratio β is the relationship between the magnet an- as asynchronous motors, synchronous motors with gular width La and the pole-pitch Lp. This relationship variable reluctances, permanent magnet motors with is used to adjust the magnet angular width according radial or axial flux, the committed firms try to find the to the motor pole-pitch. best choice of the motor conceived for electric vehicle L field. β = a (1) There are different criteria of selection in order to Lp solve this problem such as the power-to-weight ratio, π the efficiency and the price. The traction electric mo- Lp = (2) tor is specified by several qualities, such as the flex- P ibility, reliability, cleanliness, facility of maintenance, The ratio Rldla is the relationship between the angular silence etc. Moreover, it must satisfy several require- width of a principal tooth and of the magnet angular ments, for example the possession of a high torque width. This ratio is responsible for the regulation of and an important efficiency [Zire et al., 2003; Gasc, the principal tooth size which has a strong influence 2004; Chan, 2004]. on the electromotive force form. In this context, The PMM is characterized by a high Adent efficiency, very important torque, and power-to- Rldla = (3) weight, so it becomes very interesting for electric La traction. The rotor of the PMM supports several con- The Rdid ratio is the relationship between the principal figurations interesting for the magnets mounted on tooth angular width and the inserted tooth angular surface. width Adenti. This relationship fixes the inserted tooth In the intension, to ensure the most suitable and judi- size. cious choice, we start by a comparative study between Adent the two structures, then, we implement a methodology Rdid = (4) of design based on an analytical modelling and on the La electromagnetism laws. 1363 M. Chaieb et al.: A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor 2.2 Geometrical structures of the PMSMIR and the • Time of starting td = 4 s PMSMER • Outside temperature tex = 40 °C This part is devoted to an analytical sizing allowing • Maximum motor power Pmmax = 21,635 kW calculation of geometrical sizes of the two PMM con- • Winding temperature tb = 95 °C figurations which are the PMSMER and the PMSMIR. • Base speed of the vehicle Vb = 30 km/h Figure 1 represents the PMSMER and the PMSMIR • Maximum Speed of the vehicle Vmax = 100 km/h with the number of pole pairs is 4 and a number of • Load factor of the slots kr = 0, 44 principal teeth is 6, between two principal teeth, an • Acceptable density of current in the slots δ = 7 A/ inserted tooth is added to improve the form of wave mm2 and to reduce the leakage flux [Hadj et al., 2007]. The slots are right and open in order to facilitate the inser- 2.3.2 Constants specific to materials tion of coils and to reduce the production cost. The The motor is composed by a diversity of materials type of winding is concentric; each winding of phase specified as follows: is made up of two diametrically opposite coils [Mag- • Remanent magnetic induction of the magnets Bm = nussen et al., 2005; Bianchi et al., 2003; Libert and 1,175 T Soulard, 2004]. • Induction of demagnetization Bc = 0,383 T • Magnetic induction in teeth data base = 0,9 T Magnets • Relative permeability of the magnets μ = 1,05 H/m Slots a • Coefficient of mechanical losses k = 1 % Stator yoke m • Resistivity of copper with 95 °C R = 17,2 10-9 Ωm Rotor yoke cu • Coefficient of variation of the copper resistivity α = Principal Teeth Inserted Teeth 0,004 • Density of the electrical sheets Mvt = 7850 kg Fig. 1 Radial flux permanent magnet motors with ex- • Density of magnets Mva = 7400 kg terior rotor and interior rotor • Density of copper Mvc = 8950 kg • Coefficient of quality of the sheets Q = 1,100 2.3 Analytical sizing of the two motors structures • Density of copper Mvc = 8950 kg The analytical study of motor sizing is based on the schedules conditions parameters, the constant charac- 2.3.3 Expert data terizing materials, the expert data and the configura- The expert data are practically represented by three tion of the two motors. This Sizing motor approach is sizes which are, the magnetic induction in the air gap represented as follows: Be, the magnetic induction in the stator yoke Bcs and the magnetic induction in the rotor yoke Bcr. It should 2.3.1 The schedules data conditions be noted that the zone of variation of these three • Electric vehicle mass M = 1000 kg parameters varies between 0,2 to 1,6 T [Hadj et al., • Angle of starting ad = 3 ° 2007]. Schedule data conditions Analytical model Geometrical parameters Specific constants to materials Expert data Finite element method Electromagnetic parameters Full load flux 1 Structural data 0,008 Full load flux 2 0,006 Full load flux 3 0,004 ) b 0,002 W ( 0 x u l 20 40 60 80 100 F -0,002 -0,004 -0,006 -0,008 Rotor position (°) Data identified by the finite element method Fig. 2 Sizing motor approach 1364 Journal of Asian Electric Vehicles, Volume 8, Number 1, June 2010 2.3.4 Structural data Dm e For the two configurations, we adopted the same Sd Aenc Lm (10) number of pole pairs P = 4, with an air gap thickness 2 equivalent to 2mm, With a relationship β equal to 0,667 The inserted tooth section: Sdi and Rldla equal to 1,2. Dm e S Adenti Lm (11) di 2 2.3.5 Data identified by the finite element method Kfu is the flux leakage coefficient of the PMSMIR The slot section: Se which is fixed to 0,95 whereas for the PMSMER, fuK D e 1 2 D e is equal to 0,98. Between the principal tooth angular m m (12) Se Aenc Lm Adent Adenti Lm 2 2 N 2 width Adent and the inserted tooth angular width Adenti, d we define a ratio didR equal to 0,2. with Lm is the motor length. 2.4 Geometrical sizes The teeth height Hd of the PMSMIR is expressed by Geometrical parameters of the two structures motors equation 13 with Nsph is the number of turns per phase are defined in Figure 3. and In is the rated current. Hd specific to the PMSMIR is expressed: 3 4 2 N .I D + e D + e 1 2 sph n m m (13) 5 5 Hd = + − 2 1 Nd δKrAenc 2 2 4 3 Hd specific to the PMSMER is expressed: 2 1 : The magnet height, h a Nsph.In Dm - e Dm - e 2 : The slots height and the tooth height, he, hd Hd (14) δ 3 : The rotor yoke height, hcr Nd KrAenc 2 2 4 : The stator yoke height, hcs 5 : The air gap thickness, e The stator yoke thickness Hcs is obtained by applica- Fig. 3 PMSMER and PMSMIR parameters tion of the flux conservation theorem. B S H d d (15) 2.4.1 Stator geometrical sizes of the PMSMIR cs 2LmBcs The slot average width: Lenc Stator yoke Dm + e + Hd Lenc = Aenc (5) 2 The principal tooth section: Sd Rotor yoke Dm + e Sd = Adent Lm (6) 2 Fig. 4 Application of the theorem of the flux conser- The inserted tooth section: Sdi vation Dm + e Sdi = Adenti Lm (7) 2 The slot section: Se 2.4.3 The rotor geometrical sizes of the two struc- tures Dm + e 1 2 Dm e S A L = e = enc m Adent Adenti Lm (8) The expression of the magnet height Ha is the same 2 2 Nd 2 one in the two structures; it is obtained by the applica- tion of the Ampere theorem: 2.4.2 Stator geometrical sizes of the PMSMER (16) Hdl = Σ ni Haha + ehe = 0 The slot average width: Lenc contour Dm e Hd The remanent induction of the magnet M(Ta) at Ta °C is Lenc Aenc (9) 2 defined by: The principal tooth section: Sd 1365 M.
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