一种轴向磁通永磁电机的设计

Analytical Design of an Axial Flux Permanent Magnet In-WheelSynchronous Motor for Electric VehicleC. Versèle1, Z. De Grève1,2, F. Vallée1, R. Hanuise1, O. Deblecker1, M. Delhaye1 and J. Lobry11Electrical Engineering Department – Faculté Polytechnique de Mons2 Belgian National Fund for Research, FNRSBoulevard Dolez, 317000 Mons – BelgiumTel.: +32 / (0)65 – 374123Fax: +32 / (0)65 – 374120E-Mail: christophe.versele@umons.ac.beKeywords«AC machine», «Electric vehicle», «Permanent magnet motor», «Synchronous motor».AbstractThis paper deals with the analytical design of an axial flux permanent magnet (AFPM) in-wheel synchronous motor for electric vehicles (EVs). AFPM motor is a pancake-type high torque density motor that fits perfectly the wheel of an automobile vehicle and that can, thus, be easily and compactly integrated into the wheel. Therefore, AFPM motor seems to be a better choice than radial flux permanent magnet (RFPM) motor for this kind of application. First, a design program of AFPM synchronous motors developed by the authors in Matlab environment is presented and validated by experimental results.This program is very simple to use and useful during the first stage of the design of a new motor in order to evaluate its performances and overall dimensions with reasonable accuracy (although more sophisticated methods, such as Finite Element Analysis (FEA), are required in more advanced phases of the design). In a second time, this program is used to design one of the four in-wheel motors of an urban EV. The results confirm that AFPM motor is a competitive choice for this application. Indeed, it meets all the requirements of the EV and fits perfectly the shape and size of a classical rim of an automobile vehicle wheel. Moreover, the results are compared with those obtained for a more conventional RFPM motor. This comparison shows that AFPM motor is a better choice than RFPM motor for in-wheel motor applications.IntroductionSince Neodymium-Iron-Bore (NdFeB) permanent magnet (PM) materials were invented in 1980’s, PM machines are more and more used in large-scale industrial applications where other types of machines were preferred before. Moreover, this invention gave new possibilities for the use of axial field machines until then very limited in industrial applications. It was also found out that AFPM machines are a better choice or, at least, an alternative in some applications compared to RFPM machines [1] such as in-wheel motors for EV, wheelchair motors, generators dedicated to wind energy application, etc.The concept of in-wheel motors for EVs appeared in the 1990’s and in the last twenty years some attempts have been proposed. Several different types of motors have been considered. In 1994, Caricchi et al. [2] developed a slotless AFPM motor as an in-wheel motor to an electrical scooter. However, the slotless type stator is a strong limitation for traction applications where the motor is subjected to several types of stresses [3]. Then, in 1997, Bernot et al. [4] showed that in-wheel motors are a good solution to motorise heavy electrical vehicles, such as buses, but it leads to use two, four or six motorized wheels and power drives. The motor studied in that paper was a RFPM synchronous one with an inverted structure. In 2001, Tutelea and Ritchie [5] analyzed the design of a four wheels drive system for a small city car using induction motor (IM) with outer rotor. More recently, during the lastdecade, the use of AFPM motors as in-wheel motors has been more and more studied. Liu and Chuang[6] presented, in 2002, a systematic guidance for designing an axial-flux disc-type surface mounted PM motor with single-sided stator windings. That motor was intended to motorize an electric scooter.Then, in 2004, Yang et al. [7] proposed a systematic optimal design methodology on the PM axial-flux brushless dc in-wheel motor and its drive for EVs. The same year, Hackmann and Binder [8] published an interesting comparison between several kinds of motors that may be used as in-wheel motors in street cars. They compared an IM, a PM motor and a transverse flux motor (TFM). They found out that the TFM has the lowest active mass (about 50% of the IM and PM motor) for low speed operation and a comparatively higher torque density. However, the efficiency is higher for the PM motor than IM and TFM. In 2005, Nilssen et al. [9] described the design of an AFPM synchronous motor with concentrated windings for wheelchair applications. In 2007, Yang and Chuang [10] presented the optimal design of an in-wheel motor for small electric passenger cars. In that paper, an axial-flux sandwich-type disc motor was designed with a rotor embedded with NdFeBmagnets and two stator plates. Finally, we cannot conclude this short state-of-the-art (of course non-exhaustive) without emphasizing that AFPM could also be used to motorize light rail vehicles or, even, high speed trains (such as the German train ICE3). For instance, Koch and Binder [11] presented, in 2002, the design of PM synchronous motors for light rail vehicles of about 250 kW. The next year, the realization of an in-wheel PM synchronous motor for a tram was published by Hackmann and Binder [12].In this paper, we focus on the analytical design of an AFPM in-wheel synchronous motor for an urban EV. Indeed, AFPM motor is pancake-type high torque density motor that fits perfectly the wheel of an automobile vehicle and that can, thus, be easily and compactly integrated into the rim. Therefore, AFPM motor seems to be a better choice than RFPM motor for this kind of application. There are many alternatives for the design of AFPM motors [13]: slotted or slotless stator, rotor with interior or surface-mounted PMs, internal or external rotor, numbers of rotors and stators, etc. For our application, a double-sided motor with internal slotted stator and surface-mounted PMs is proposed as the basic design choice essentially motivated by the presence of two air gaps doubling the torque.This contribution is organized as follows. The analytical design of the AFPM motor as well as the design program developed in this work are presented in Section 2 and validated in Section 3. Next, in Section 4, we discuss the use of AFPM motor for in-wheel motors of EVs application and compare the results with those obtained for a more conventional RFPM motor.AFPM motor design procedureFundamental design equationsAnalytical design of AFPM motors is usually performed on the average radius R ave of the machine [1] defined by: 2in out ave R R R += (1) where R in and R out are respectively the inner and outer radius of the machine (see Fig. 1(a)). The use of the average radius as a design parameter allows evaluating motor parameters and performances based on analytical design methods explained in details in the specialized literature (see, e.g., [14]).The air gap flux density B g is calculated using the remanence flux density B r (in the order of 1.2 T for a NdFeB type PM) and the relative permeability μra of the PM as well as the geometrical dimensions of the air gap and the PM (thickness and area) according to: 1r g PM ra PM gPMC B B k k g S l S σμ=+ (2) where g and l PM are respectively the air gap thickness and PM thickness (see Fig. 1(b)); S g and S PM are respectively the air gap area and PM area.with()a ()bFig. 1: (a) Stator and rotor of an AFPM machineand (b) doubled-sided AFPM machine with internal slotted statorIn (2), k σPM (<1) is a factor that takes into account the leakage flux and k C (>1) is the Carter coefficient.On the one hand, the main magnetic flux density in the air gap decreases under each slot opening due to the increase in the reluctance. The Carter coefficient permits to take into account this change in magnetic flux density caused by slot openings defining a fictitious air gap greater than the physical one. It can be computed as follows [14]:C t k t gγ=− (3) where t is the average slot pitch (see Fig. 1(b)) and γ is defined by:4arctan 22b b g g γπ=−⎡⎛⎞⎢⎜⎟⎢⎝⎠⎣ (4)where b is the width of slot opening.On the other hand, in order to obtain an accurate estimation of the air gap flux density and the torque developed by the motor, the factor k σPM is one of the most essential quantities that must be computed. Indeed, the leakage flux has a substantial effect on the flux density within the air gap and PMs [15] and, therefore, on the torque developed by the motor (see (5)). In addition to air gap leakage flux, zigzag leakage flux is another main part of the leakage flux. The zigzag leakage flux is the sum of three portions [15]: the first part of the zigzag leakage flux is short-circuited by one stator tooth, the second part links only part of the windings of a phase and the third part travelling from tooth to tooth does not link any coil. Note that, in this paper, an analytical model developed by Qu and Lipo [15] for the purpose of the design of surface-mounted PM machines is used to compute the factor k σPM . This model permits to express this factor in terms of the magnetic material properties and dimensions of the machine. It is thus very useful during the design stage.Assuming sinusoidal waveform for the air gap flux density and phase current, the average electromagnetic torque T of a double-sided AFPM motor can be calculated by:332()g in out d d T B A R k k π=− (5)where A in is the linear current density on the inner radius of the machine and k d is the ratio between inner and outer radii of the rotor disk. It should be noticed that, for a given outer radius and magnetic and electric loading, the factor k d is very important to determine the maximum torque developed by the motor [16]. Figure 2 reports the per-unit (p.u.) electromagnetic torque with respect to k d . One can remark that the maximum value of the torque is reached for k d ≈ 0.58.Fig. 2: Per-unit electromagnetic torque T p.u versus k dFinally, the electromagnetic power P can be calculated by the product of torque and rotational speedΩr of the motor:r P T =Ω (6)Design procedureThe proposed design procedure is divided into several steps and requires some imposed parameters,viz., the outer radius of the motor, the factor k d , the air gap thickness, the number of stator slots, thenumber of poles, the current density, data related to materials, etc. All these parameters must bechosen in accordance with the desired motor performances and must respect all the constraintsimposed by the application. In the first step, the PM thickness is determined by (2) to get a specific airgap flux density (0.85 T is a reasonable choice for a double-sided AFPM motor) considering noleakage flux (k σPM =1). Once the PM thickness is known, the factor k σPM , which is function of thisthickness, can be determined and the air gap flux density is recalculated. If this flux density is lowerthan the specified value, the PM thickness is increased. So, an iterative procedure permits to determinethe PM thickness needed to get the specified air gap flux density taking into account the leakagefluxes. Next, the electromagnetic torque and power developed by the motor are computed. In thefollowing, all the losses (copper losses, eddy currents losses and losses in PM) are estimated as well asthe efficiency of the motor. After that the weight and overall dimensions of the motor are determined.Finally, some electrical parameters of the motor are calculated such as the stator resistance (R s ) and thedirect (L d ) and quadrature (L q ) axes inductances. Note that the computations are performed with adesign program developed by the authors in Matlab environment and based on the above-describedfundamental design equations.Advantages and limitations of the design procedureDuring the first phases of the design of a new motor, it is very interesting to quickly estimate itsperformances and overall dimensions. In this regard, an analytical model of the motor is perfectlysuited and gives results in a fast way. Such a model is used in the design procedure discussed in thispaper. Therefore, the design program developed by the authors permits to design a new motor veryquickly. This is its first advantage. It should be emphasized that, as shown in the next section, theresults of this design are given with a reasonable accuracy.In addition to be simple to use, another advantage of such a design program is that it is very useful tostudy the influence of some design parameters on the performances and overall dimensions of themotor. So, some design alternatives can be rapidly confirmed or eliminated if, e.g., they do not respectthe constraints imposed by the application under consideration. Moreover, such a study can be alsovery helpful to estimate the optimal value of some parameters that must be chosen to design the motor(e.g. the air gap thickness, the value of the factor k d , etc.). Note that the difficulty to find this optimalvalue for some parameters comes from the fact that, firstly, a tradeoff must be found between multiple conflicting objectives and, secondly, in some applications, some constraints must be respected.The main limitation of the design program is a lack of accuracy in some cases like a PM shape higher complexity, viz. when the magnet occupation ratio varies along the radius of the rotor [1]. This lack of accuracy arises from the reduction of the 3D design problem to a 2D plane design problem performed on the average radius of the machine.It should also be noticed that the most accurate method to predict the performances of an AFPM motor is a 3D FEA but it is often too much time consuming to perform. Therefore, the design program presented in this contribution is very useful during the first phases of the design to determine the geometry of the motor as well as estimate its performances although more sophisticated methods, such as 2D or 3D FEA, are required in more advanced phases of the design.Note that, in this paper, the magnet occupation ratio is considered as constant along the radius of the rotor and, therefore, this limitation is not taken into account in the design of the AFPM motor.Experimental resultsIn order to validate the design program presented in this paper, analytical and experimental results are compared. To do so, the proposed design process is applied to a 5.5 kW, 4000 rpm AFPM motor. The calculated motor parameters are then compared with parameters obtained by classical tests (test at dc level, no-load test, etc.) performed on an existing AFPM pump motor. All the results are reported in Table I. As can be seen, very small differences are obtained between the analytical and experimental results, whatever the parameters. According to this validation method, one can conclude that the proposed analytical design process gives reasonable results in this particular case and can be used to design an in-wheel motor for EVs in the next section.Application to the design of an in-wheel AFPM motor for EVsEVs requirementsIn order to determine the requirements, in terms of power and torque, of one of the four in-wheel motors (considering an EV driven by four in-wheel motors), a computer model of an EV traction system is presented in this subsection and added to the AFPM motor design program.The road load on the vehicle consists of three forces [10]: (1) the rolling resistance F r , (2) the aerodynamic drag force F a and (3) the climbing force F c which are expressed [17] as:r r v F f M g = (7)2w 0.5()a f D F A C v v ρ=+ (8)()sin c v F M g α= (9)where f r is the rolling resistance coefficient (which is an empirical coefficient depending on the road-tire friction), M v is the mass of the vehicle, g is the earth gravity acceleration, ρ is the air density, A f is the frontal area of the vehicle, C D is the coefficient of aerodynamic resistance (that characterizes the shape of the vehicle), v is the vehicle speed, v w is the component of the wind speed in the vehicle moving direction and α is the road angle (deduced from the road slope).Table I: Analytical and experimental results forthe 5.5 kW, 4000 rpm AFPM pump motor Parameters Analytical results Experimental resultsR s (dc-resistance) 0.45 Ω 0.423 ΩL d 0,129 H 0,117 HL q 0,127 H 0,117 HT 13.97 Nm 15.04 NmP 5.85 kW 5.5 kWAccording to Newton’s second law, the total tractive effort F t required to reach the desired acceleration a and to overcome the road load is:t v r a c F M a F F F =+++ (10) Once the total tractive effort is computed, it is simple to determine the total torque T t and power P t required to be produced by the four in-wheel motors. Those can be expressed as:t t wheel T F R = (11)t t wheel P T =Ω (12)where R wheel is the drive wheels radius (a typical value for the wheels of an urban vehicle is 33 cm) and Ωwheel is the rotational wheels speed.Based on the specifications of an urban EV presented in Table II (take from literature, see, e.g., [18])and on the above-described computer model of the EV traction system, the requirements of one in-wheel motor can be easily computed. All the results are presented in Table III.Note that, in addition to provide its requirements, the in-wheel motor must also respect some constraints. The main constraints are the total mass of each of the four in-wheel motors M (imposed by the maximal authorized “unsprung” wheel mass) and the imposed outer radius of the motor R out (imposed by the rim of the wheel). Those are also specified in Table II and III.Study of the influence of some parameters on the AFPM motor designIn this subsection, the influence of some parameters on the AFPM motor design and performances are discussed. More precisely, it is found interesting to study two specific parameters (the factor k d and the air gap thickness g ) because they must be chosen to design the AFPM motor.Referring to Fig. 2, an intuitive choice for the factor k d is a value around 0.6 in order to maximize the torque, and, hence, the power developed by the motor. However, this factor has also a great influence on the total mass of the motor. Indeed, the stator and rotor disks are heavier when the ratio between the inner and outer radii of these disks is smaller. So, in order to minimize the mass, a larger value of the factor k d should be chosen. As shown in [16], the maximum value of the torque to mass ratio is reached for a value of the factor k d around 0.9. Consequently, the value of the factor k d could be chosen either to maximize the torque or to minimize the mass of the motor. However, more often, the most favourable motor design results from a compromise value [16]. So, a value between 0.75 and 0.85 will be adopted in this contribution. Indeed, it constitutes a good tradeoff between the two objectives (viz. maximum torque and minimum mass).Table II: EV specificationsTable III: Requirements of one in-wheel motor Parameters ValuesTorque > 107 NmPower > 8.7 kWMass of the motor < 43.125 kg Parameters Values Rolling resistance coefficient f r 0.015 Mass M v 1150 kg Frontal area A f 2.5 m² Coefficient of aerodynamic resistance C D 0.32 Desired speed v 13.9 m/s (50 km/h) Road slope 10% Desired acceleration a 1 m/s² Rim diameter 14’’The results of the AFPM motor design (with an air gap thickness of 1 mm) are shown in Fig. 3 for several values of k d. As can be seen in Fig. 3(b), only values greater than or equal to 0.8 satisfy the constraint on the mass of the motor. Therefore, in order to respect this constraint and to maximize the torque developed by the motor, a value of 0.8 for the factor k d will be assumed in this paper.Another important parameter to study is the air gap thickness. The influence of this parameter on the PM thickness, mass of the motor, specific power (power to mass ratio) and efficiency are shown in Fig. 4. Note that the results are obtained with a PM thickness determined to obtain an air gap flux density of 0.85 T. One can easily remark that the air gap thickness must be the smallest possible in order to minimize the PM thickness as well as the mass of the motor while maximizing the specific power and efficiency of the motor. An air gap thickness of 1 mm will be considered in this paper as a basic design choice.Fig.3: Influence of the factor k d on (a) the torque and (b) the mass of the motorFig.4: Influence of the air gap thickness on the (a) PM thickness,(b) mass of the motor, (c) specific power and (d) efficiencyResults of the AFPM in-wheel motor for EVs designFinally, the design of one of the four AFPM in-wheel motors of the urban EV above-described is performed. A rim diameter of 14’’, an air gap thickness of 1 mm, a factor k d of 0.8 and an air gap flux density of 0.85 T are here considered. All the results are presented in the second column of the Table IV. Note that the requirements of the EV are reminded in the fourth column for the purpose of comparison. Comparing the results of these two columns, one can conclude that it is possible to design an AFPM in-wheel motor that meets all the requirements and respects the constraints.As a final point, comparing the results of the second and third columns of the Table IV, one can also conclude that AFPM motor is a better choice than RFPM motor for in-wheel motor applications. Indeed, the AFPM motor has a bigger specific power and a better efficiency than the RFPM one which, moreover, does not respect the mass constraint. Note that the results of the third column of the Table IV come from a RFPM motor design program not yet published and developed by the authors.A rim diameter of 14’’ and an air gap length of 1 mm are also considered in order to compare with the results of the AFPM motor.Table IV: AFPM and RFPM in-wheel motorsParameters AFPM motor RFPM motor RequirementsTorque 219.5 Nm 207.6 Nm > 107 NmPower 9.24 kW 8.74 kW > 8.7 kWMass of the motor 41.58 kg 55.24 kg < 43.125 kgSpecific power 222.24 W/kg 158.16 W/kg -Rim diameter 14’’ 14’’ -Efficiency 89.8 % 77.8 % -ConclusionIn this paper, a design program for AFPM motor developed by the authors in Matlab environment and validated by experimental results has been presented. This program has two major advantages. Firstly it is very simple to use and, secondly, it is very useful during the first phases of the design of a new motor in order to evaluate the performances and the overall dimensions of an AFPM motor with reasonable accuracy although more sophisticated methods, such as 2D or 3D FEA, are required in more advanced phases of the design. The program is then used to design one of the four in-wheel motors of an urban EV. In comparison with RFPM motor solution, the results confirm that AFPM motor is a competitive choice for this application. Indeed it meets all the requirements of the EV and fits perfectly the shape and size of a classical rim of an automobile vehicle wheel.Future work aims at optimizing the in-wheel AFPM motor. To do so, the authors plan to use multiobjective optimization evolutionary methods in order to maximize the torque and power developed by the motor as well as its efficiency and minimize its total mass while ensuring the satisfactions of a number of constraints.References[1] A. Parviainen, M. Niemelä and J. Pyrhönen, “Analytical, 2D FEM and 3D FEM Modelling of PM Axial Flux Machine”, Proceedings of the 10th Power Electronics and Application Conference, EPE 2003, Toulouse, September 2003.[2] F. Caricchi, F. Crescimbini, E. Fedeli and G. Noia, “Design and construction of a wheel directly coupled axial flux PM prototype for EV’s”, Conference Records of the 29th IEEE Industry Application Society Annual Meeting, IAS 1994, Denver, October 1994.[3] F. Profumo, Z. Zhang and A. Tenconi, “Axial Flux Machines Drives: A New Viable Solution for Electric Cars”, IEEE Transactions on Industrial Electronics, Vol. 44, No. 1, February 1997.[4] F. Bernot, L. Gonthier, S. D. Bocus, S. Elbaroudi, A. 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