Basic Experiments for High-Torque, Low-Speed Permanent Magnet Synchronous Motor and a Technique for Reducing Cogging Torque

Transcription

1 Basic Experients for High-Torque, Low-Speed Peranent Magnet Synchronous Motor and a Technique for educing Cogging Torque Kouichi Sato, Jung-Seob Shin, Takafui Koseki and Yasuaki Aoyaa Φ Abstract -- Fully integrated electric propulsion systes are gaining popularity in both coercial and ilitary sectors. Propulsion otor anufacturers are investigating new direct drive solutions for use in electric ships. These applications require otors with high torque output at low speeds. Such requireents were the otivation for the design of a new PMSM with a novel topology. Firstly, this paper describes an efficient odel of a otor used for high thrust at low speed. Secondly, the authors analyze the theory for otor s behavior. To copare the theoretical result, characteristics of the proposed otor have been tested. The cogging torque has been a serious proble. Therefore, an analytical odel of the cogging torque has been derived for calculating and reducing it. An appropriate skew angle can be designed based on the odel. authors had an experient on the characteristic of suggested otor. II. FUNDAMENTALS OF NEW MOTO DESIGN Index Ters--peranent agnet synchronous otor (PMSM), transverse flux achine (TFM), tunnel actuator (TA), cogging torque, skew I. INTODUCTION As coercial autootive, aerospace, and railway industries were affected by rising fuel costs a couple of years ago, the arine industry has recently endeavored to create ore fuel-efficient, cost-effective drive systes. During the last 15- years, fully electrified propulsion (EP) systes have been gaining popularity and capturing ost of the arket growth in sectors such as cruise ships, passenger ferries, oil and gas transport vessels, and erchant and special order ships [1]-[]. Several different types of otors are currently in use or have been proposed for application in ship propulsion. The authors took particular interest in a Peranent Magnet Synchronous Motor (PMSM) solution because of the possibility of higher thrust, less coplicated design, and lower aintenance. Due to the short pole pitch characteristic of certain types of PMSM designs, these achines can have high torque at low speeds, which is particularly beneficial in a arine application. Transverse Flux Motor (TFM) designs have short pole pitch and high torque characteristics, but TFM are plagued by low power factor []-[4]. In order to iprove on previous designs, the authors developed a theoretical odel of a transverse flux PMSM and subsequently built and tested the prototype of a new design. The authors also adapted the basic flux path idea present in the Tunnel Actuator (TA), a linear PMSM produced by Hitachi, to perfor in a rotary application. Also, in order to decrease the cogging torque that has a negative effect on behavior of a PMSM, the authors suggested the techniques with skew to reduce the cogging torque. Finally, to copare the theoretical result, the This work was supported by MT-Drive and Japan Society for the Prootion of Science. Kouichi Sato, Jung-Seob Shin and Takafui Koseki are with Departent of Electrical Engineering and inforation systes, School of Engineering, The University of Tokyo, 7--1, Hongo, Bunkyo-ku, Tokyo , Japan (e-ail: kouichi@koseki.t.u-tokyo.ac.jp). Yasuaki Aoyaa is with Hitachi eseach Laboratory, Hitachi, Ltd., Ibaraki-ken, Japan. 1 (a) (b) Fig. 1: Transverse Flux Machine The transverse flux achine takes advantage of a -D flux path to increase torque production without having to trade off between electrical or agnetic loading as with radial and axial flux achines. But, the TFM described by Weh, et. al. and later iproveents on that design have such coplex anufacturing requireents that they are ipractical for industrial production. This coplex design can be seen in Fig. 1(a)-(b). Ultiately, the low power factor characteristic of transverse flux achines becoes an obstacle against this type of achine attaining a high real power to volue ratio. For exaple, olls-oyce Ltd. anufactured a TFM for arine propulsion that was capable of large thrust but had power factor ratings of less than.7 [6]. When exaining the field of direct drives for another otor with a siilar flux path configuration but a high power factor, the authors found Hitachi's Tunnel Actuator for linear drive applications [5]. This drive has the advantages of easy assebly, thin peranent agnet and high resultant pereability and a agnetic flux path that is transverse. The TA suffered fro large flux leakage due to the close position of the arature poles and the

2 configuration of the flux path in alternating poles. The authors thought that by placing only poles with flux in the sae direction next to each other and spacing the further apart to increase agnetic isolation. The following sections will show the details of new direct drive design. A. The Model The basic unit of our odel was one pole of the achine. One pole consists of a stator C-core. The winding is wrapped around the back of the C, and the peranent agnets on the rotor are accelerated through the air gap to generate thrust. An illustration of the one-pole odel is in Fig.. The input to the odel is the arature current I a. B a is the arature flux density and B f is the flux density contributed by the field agnets. As I a changes, the polarity of B a also fluctuates, which pulls the alternating polarity agnets through the air gap, creating thrust. The oveent of the agnets through the arature flux field also induces an internal EMF. only cores were used per phase. The rotor was constructed in a siilar fashion by placing alternating polarity agnets on a rotor backing at a set angular separation. In the prototype, there were 6 peranent agnets, thus 18 pole pairs. It is iportant to note that because the flux lines in adjacent stator cores of the sae phase point in the sae direction and there is a large physical separation between phases, the authors expected negligible flux leakage. (a) Stator Cores Fig. : One-Pole Model Diagra [7] Fig. shows how the rotor would be propelled through the consecutive air gaps of several poles connected in phase by their arature winding. The self-induced voltage and thrust contributed by each pole would be superiposed to create the total contribution of one phase. The phases of the achine could then be connected to the operator's convenience. The C-cores of each phase would be placed at balanced angular separation around the axel to create the outer radius of the achine. (b) otor Fig. 4: Layout of the Prototype Motor Model [7] Fig. 5-6 is detailed parts of the prototype otor and the full test bench involved directly connecting a PMSM load otor to the prototype. The prototype was driven directly in generator ode. The prototype was connected to an inverter to be controlled for dynaic testing. This test bench accurately represents the typical case of an industrial client, where the otor supplier will have only general knowledge about the loading conditions applied to their product [7]. Fig. : Flux Path through C-Core and otor [7] B. Creation of the Prototype and Test Bench The prototype design was created by taking a nuber of unit odel C-cores and arranging the radially to create a full stator. In Fig. 4(a)-(b), this idea is drawn up with - phases and 4 stator cores per phase. In the actual prototype, Fig. 5: Detailed Parts of the Prototype Motor [7]

3 L V AC I test V test Fig. 6: A Full Version of the Prototype Motor Model [7] III. FUNDAMENTAL EXPEIMENT In order to verify how our design otor would behave, experients easuring the fundaental characteristics of the prototype otor were prefored. To easure easily, the authors considered 1 core per one phase in the experient. A. Arature esistance Measureent By using DC-voltage drop test, arature resistance was easured. Fig. 7 shows the test circuit. Arature winding resistance is calculated fro applied DC voltage V DC and the current I. Three values of arature resistance (U, V, W phase) were easured. The experiental result is shown in Fig. 8. DC Voltage [V] V DC 1 V A Fig. 7: DC-Voltage Drop Test Circuit I Arature Winding u v w Current [A] Fig. 8: Arature esistance Measureent As the experiental result shows, voltage was alost proportional to current and three arature resistances were corresponded. Average of three resistances is expressed as (1). u + v + w = =.79 [Ω] (1) B. Self-Inductance Measureent By using AC source V AC and test resistance test, selfinductance was easured Fig. 9 shows the test circuit. Fig. 9: The Test Circuit for Measuring Self-Inductance As shown in Fig. 9, the test resistance was connected with the arature winding in the series, and the effective voltages, the phase differences of the test resistance and AC source were observed by oscilloscope. By using two effective voltages and the phase deference, AC resistance and selfinductance L can be obtained. was obtained in DC easureent. However, was considered as a variable to obtain AC resistance accurately. Equations to obtain and L are ()-(). VAC test sinθ L = () πf Vtest V AC = cosθ 1 test () Vtest f is frequency (1~5 [Hz]) of AC source, and θ is a value converted fro the phase deference. Based on these equations and the experiental result, and L were calculated. The result is shown in Fig Self-Inductance [H] esistance [Ω] L1 L L Fig. 1: Self-Inductance Measureent Fig. 11: AC esistance Measureent 1 and L 1 are the value when there is nothing in gap. and L are the value when peranent agnet is under the C- core in the air gap. Also, and L are the value when stainless (etal between peranent agnets) is under the C- core in the air gap. Although 1 and were alost corresponded, L 1 and L depended on each pattern. and L

4 are unstable values especially in low frequency. In this pattern, the prototype otor was not stable and the experient was perfored holding the rotor by hand. AC resistance was larger than DC resistance. The authors guessed that the reason was due to the skin effect caused by AC coponent. However, since and L don t alost depend on frequency except for and L, it can be considered that the experient was good result. Theoretically, since the authors assued that there was nothing in the air gap when calculating L, L 1 was used. Average of L 1 is expressed as (4). L = L 1 =.4 [H] (4) C. Open Circuit Test U N W V V u V w V v W U otated by Using the Driving Motor Fig. 1: The Test Circuit for Measuring Self-Induced Voltage Self-induced voltage was easured by open circuit test. In this test, rotating speed could be controlled by connecting the prototype otor to the driving otor. And, self-induced voltage is easured by rotating the driving otor changing speed. Fig. 1 shows the test circuit. As shown in Fig. 1, the arature side was opened and the neutral point N was connected by distributed cable. In the experient, rotating the prototype otor by driving otor, the effective voltages and the phase differences of each phase voltage were easured by oscilloscope. The test result is given in Fig Effective Voltage [V] Fig. 1: Effective Voltage in the Open Circuit Test V Vu Vv Vw Phase Difference [degree] U-V U-W V-W Fig. 14: Phase Difference in the Open Circuit Test Theoretically, the effective voltage is proportional to frequency, and the phase differences of each phase is 1 [degree]. As shown in Fig. 1, three effective voltages were proportional to frequency and the values were alost corresponding with each frequency. When Frequency is 5 [Hz], averaged effective voltage is expressed as (5). Vu + Vv + Vw V rs = =.81 [V] (5) As shown in Fig. 14, the phase differences of each phase were fallen in error within about 5% of 1 [degree]. IV. COMPAISON OF THEOETICAL AND EMPIICAL DATA By easuring fundaental characteristics, the arature winding resistance, self-inductance L and self-induced voltage V rs were gained. By using these values, the authors estiated specifications that indicate perforance of the otor at noinal operating point. Assuing the condition when d-axis current is controlled to zero, they are expressed one phase equivalent circuit in Fig. 15 and phasor diagra of voltages and currents in Fig. 16. Based on these figures, the authors calculated specifications : output P, torque T, power factor cosθ, efficiency η, and force density D. P = V rs I rs (6) P P T = = p (7) ω πf Vrs + Irs cosθ = (8) ( Vrs + Irs ) + ( XIrs ) Vrs η = (9) Vrs + Irs T D = (1) rs In (6)-(1), I rs is the current to be applied to the arature winding and p is pole pairs of peranent agnet. X is inductive reactance and r is average rotation radius, and S is cross-sectional area of pole. Table I shows the theoretical and epirical values for each paraeter of the prototype otor. I rs V S jx V rs Fig. 15: One Phase Equivalent Circuit 4

5 q d jxi rs w p I rs l g Arature Core V s θ V rs l x Fig. 16: Phasor Diagra of Voltages and Currents (I d = ) TABLE I COMPAISON OF THEOETICAL AND EMPIICAL Specification Theoretical Epirical Value Value Winding esistance :.19 [Ω].79 [Ω] Self-Inductance : L.444 [H].4 [H] Self-Induced Voltage : V rs 4.9 [V].81 [V] Output : P 46.9 [W] 6. [W] Torque : T.69 [N].8 [N] Power Factor : cosθ.99.9 Efficiency : η.8.76 Force Density : D 9.9 [kn/ ].9 [kn/ ] Frequency : f 5 [Hz] 5 [Hz] As shown in Table I, the values of resistance and inductance in the experient were larger than those in the theory. Therefore, actual specifications of the prototype otor were saller than theoretical values. Table I shows each paraeter at frequency 5 [Hz]. However, the prototype otor did not rotate soothly and caused rattling noise at low frequency. In fact, the prototype otor could not rotate as a synchronous otor ode. V. COGGING TOQUE EDUCTION As the authors entioned in previous section, the prototype otor could not rotate soothly. The authors thought the reason that the prototype otor did not rotate well could be the cogging torque. The cogging torque is caused by the reluctance change between the stator teeth and agnet poles on the rotor. This is a characteristic of a PMSM often observed. The cogging torque causes excessive noise and harful vibration to the achine itself, and in any serious cases, a echanical resonance ay occur which result in serious troubles. In any applications, the cogging torque has becoe an iportant design specification to be carefully treated. The cogging torque calculation and reduction ethod will be, therefore, discussed in this section. A. Analytical Method to Calculate the Cogging Torque There are any ethods to calculate the cogging torque such as energy ethod, virtual work ethod, Maxwell tensor ethod etc [8]. Based on the energy ethod, the cogging torque can be calculated fro the energy variation with the angle of rotation. In order to siplify calculation of the cogging torque, the authors have considered one poleone core in the prototype odel. The basic concept is considered without the flux leakage as illustrated in Fig. 17. d l g Flux Line Fig. 17: The Siplified Flux Line in the Air Gap PM In Fig. 17, l g is the air gap length excepted agnet's height l, d and w p are width and depth of both arature core and peranent agnet, and x is the length away fro the initial position that agnet was below arature core vertically. Considering that agnet is in the initial position, the reluctance and flux density B in the air gap are followed respectively, lg l = + (11) μs μs Hcl μhcl B = = (1) S lg + l μ is pereability of the air gap, H c is the coercivity of agnet and S is the surface area of agnet. Considering that agnet is in x away fro the initial position, the reluctance x and flux density B g_x in the air gap are followed respectively, x + lg l x = + (1) μs μs Hcl μ Hcl B g x = = _ (14) xs x + lg + l The total agnetic co-energy U t in the air gap is followed as, B B g _ x Ut = Ua + Ub = V + Vg (15) μ μ U a is the agnetic co-energy in the agnet when agnet is in the initial position. It is assued that U a is always constant. U b is the agnetic co-energy in the gap at x away fro the initial position. V, V g are the volue of agnet and air gap. Therefore, the cogging torque F can be calculated as follows, Ut x F = = 4μ dwplg Hc l (16) x x + l ( x + l + l ) B. Method to educe the Cogging Torque According to different applications and considerations of technical and econoical factors, various cogging torque reduction ethods can be eployed, including Slot or agnet skewing (Fig. 18), Magnet pole shape optiization and Stator slot opening width optiization etc [8]. In particular, skewing has been well recognized as a practical technique to reduce the cogging torque of PMSM. In this paper, the authors calculated the cogging torque as a g g 5

6 function of skewing angle of the agnets. Considering the skewing, the cogging torque is expressed as (17). 4μwplg F = 1 A x + d + l g ( Hcl cosθ ) xdθ + l{ A B} θ { B + l } { A+ l } 1 = θ, B = x dθ + l g (17) were copleted in experient. Also, the fundaental characteristics of the prototype otor were estiated analytically and copared with experient values. However, soe epirical values are estiated based on, L, V rs by equations that the authors have used to calculate theoretical data because the prototype otor could not be rotated as synchronous otor ode. The authors thought the reason that prototype otor did not rotate well could be the cogging torque. In Section III, in order to solve the proble, the cogging torque was calculated as a function of skewing angle of the agnets. By an appropriate skewing, the cogging torque can be reduced to half theoretically. The new odel, i.e., the second odel, is being fabricated. In particular, the nuber of arature core, winding, and pole were changed in order to gain a higher torque than first odel. Skewing was also considered in order to decrease the cogging torque. Fig. 18: Skew Angle Considering the geoetric structure, the authors decided the skew angle θ as 4 [deg]. According to variation of skew angle, the cogging torque is shown in Fig. 19. When not considering skewing, the cogging torque was 51 [N] and its peak value was at.6 [] fro the initial position. In 4 [degree], although it was not eliinated perfectly, the cogging torque was 8 [N] and its peak value was at 1.8 [] fro the initial position. The cogging torque decreased to alost half by skewing. Cogging Torque [N] ] θ= -5 θ=4-6 Displaceent [] Fig. 19: Cogging Torque per a Pole Depending on Skew Angle VII. ACKNOWLEDGMENT We would like to thank MT-Drive (MTD) and Japan Society for the Prootion of Science (JSPS) for their friendly support to this research. VIII. EFEENCES [1] Boran, J., Sharan, B., "Electric Propulsion of Passenger Ships and Other Vessels," Trans. IarE, pp , 16 Nov [] ABB, "ABB Marine eferences," Center of Excellence Cruise & Ferries: ABB Oy, Helsinki, Finland, Deceber 6. [] Harris, M.., Pajooan, G.H., Abu Sharkh, S.M., "The Proble of Power Factor in VPM(Transverse-Flux) Machines," IEEE Conference on Electrical Machines and Drives 1997, Publication No. 444, IEEE, Sept [4] Weh, H, Hoffan, H, Landrath, J, "New Peranent Magnet Excited Synchronous Machine with High Efficiency at Low Speeds," Proceedings of the International Conference on Electrical Machines, [5] Ki, HJ, Nakatsugawa, J, Sakai, K, Shibata, H, "High-Acceleration Linear Motor, "Tunnel Actuator"," The Magnetics Society of Japan, Vol. 9, No., pp 199-4, 5. [6] Husband, S.M., Hodge, C.G., "The olls-oyce Transverse Flux Motor Developent," Electric Machines and Drives Conference, Vol., pp , IEEE,. [7] G. Patterson, T. Koseki, Y. Aoyaa, K. Sako,"Siple Modeling and Prototype Experients for a New High-Thrust, Low-Speed Peranent Magnet Disk Motor," Proc. 1th International Conference on Electrical Machines and Systes, Tokyo, Japan. Nov 9. [8] Z. Guo, L. Chang, Y. Xue, "Cogging torque of peranent agnet electric achines: an overview," Canadian Conference Electrical and Coputer Engineering, CCECE '9, pp , 9. VI. CONCLUSIONS This paper proposed a new evolution in the developent of the transverse flux type peranent agnet otor. A new idea for a low-speed, high-torque peranent agnet otor was proposed. The authors reviewed the initial transverse flux concept and two adaptations of the TFM topology. In Section II, a new design of the proposed otor was described as a odification of the TFMs. It has a siple flux topology that allows for siplified linear odeling of the otor characteristics. The fundaental easureents of the prototype's open circuit voltage arature ipedance and self-induced voltage 6