Design Considerations and Validation of Permanent Magnet Vernier Machine with Consequent Pole Rotor for Low Speed Servo Applications

Transcription

1 J Electr Eng Technol Vol. 8, No.?: 742-?, ISSN(Print) ISSN(Online) Design Considerations and Validation of Permanent Magnet Vernier Machine with Consequent Pole Rotor for Low Speed Servo Applications Shi-Uk Chung *, Yon-Do Chun **, Byung-Chul Woo **, Do-Kwan Hong ** and Ji-Young Lee ** Abstract This paper deals with design consideration and validation of a new pole-slot combination for permanent magnet vernier machine (PMVM) with consequent pole (CP) rotor especially for extremely low speed servo applications. A 136pole-24slot PMVM with CP rotor is introduced and analyzed by 2D and 3D finite element analysis (FEA) and discussion on experimental validation is also included. Keywords: Consequent pole, Permanent magnet, Vernier machine, Low speed 1. Introduction A lot of researches on different machine topologies have been continually being reported with the rising need of low speed direct drives in various industry areas. A Permanent magnet vernier machine (PMVM) is widely acknowledged as an attractive candidate for low speed applications due to several distinctive features that belong uniquely to this topology such as magnetic gear effect, and low number of windings with high number of poles [1-5]. Even today, new topologies are being studied and introduced based on PMVM topology since PMVM topology still offers design variants. A PMVM which utilize additional slot space for DC field winding for flux control is introduced and characterized for field weakening control [6]. A dual stator structure was also introduced in PMVM topology to increase torque density [7]. Another rotor design using consequent pole (CP) concept was recently introduced and yet to be further investigated [8]. This paper is a continuation of the previous research work on PMVM with CP rotor with a different phase winding arrangement. The most distinctive difference between the former design and the one introduced in this paper is that the proposed configuration in this paper comprises multiple teeth at an equal pitch and each phase is magnetically coupled. The most important topic of this research is to introduce another PMVM topology which can utilize CP rotor structure since the CP rotor configuration needs a special pole-slot combination which suppresses magnetic unbalance caused by the CP rotor [8]. Corresponding Author: Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea (suchung@keri.re.kr) ** Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea. Received: November 3, 211; Accepted: May 13, 213 This paper introduces three major design considerations for PMVM with CP rotor as follows: To avoid magnetic unbalance, it needs special pole-slot combinations which can be numerically expressed as (1) where τ p, N s and N t denote pole pitch, numbers of splitpoles/stator tooth, and numbers of stator teeth, respectively. Flux leakage prevention needs to be carefully considered since magnetic flux flows freely through the entire magnetic circuit. Motor syetry is an important issue related to noise and vibration. γ N τ 2τ 3, τ 3 3 N t 3N s 2 This paper analyzes the proposed PMVM with 2D and 3D finite element analysis (FEA) since no analytical design tool for PMVM has been introduced. 2D and 3D FEA results are also compared with the experimental results in later section. 2. 2D and 3D FEA results Fig. 1 shows the proposed topology which comprises CP rotor of 136 poles and 24 slots at an equal slot pitch unlike the previous design [8]. Detailed dimensions and geometric symbols are listed in Table 1. Field distributions by 2D FEA are shown in Fig. 2 which shows flux flow patterns repeating every 45 mechanical degrees. This may be understood that the proposed PMVM has 8 syetries, however, actual syetry of the proposed PMVM is considered to be 4 due to the CP rotor. The syetry issues will be discussed in this section. Figs. 3(a) and (b) show cogging torque and rated torque computed by 2D FEA, respectively. Considering the torque (1) 742

2 Shi-Uk Chung, Yon-Do Do Chun, Chun Byung-Chul Woo, Do-Kwan Hong and Ji-Young Young Lee Table 1. Proposed PMVM design dimensions and major specifications. Split-pole Lt Lp /U 2 γ V2 /W2 Item(Symbol) Number of poles(np) Number of split-poles/stator tooth(ns) Number of stator teeth (Nt) Stack length(ls) PM width(wm) PM thickness(hm) Chamfer(C) Airgap length(g) Split-pole width(wp) Stator inner hollow diameter(d1) Stator outer diameter(d2) Rotor outer diameter(d3) Tooth length(lt) Split-pole length(lp) Number of turns/coil(n) PM material Rotor/stator lamination material Lamination stacking factor Ph. Resistance(@2 ) DC link voltage Rated current/ph. Rated torque(2d analysis) Rated speed Rated output power D3 W 1 C g /V1 D1 Hm D2 Wm 2τp Wp U1 Fig. 1. Analysis PMVM geometry. geometry Value Br=1.3T, µr=1.5 S Unit % Ohm Vdc Arms Nm RPM W ripple period, the skew angle is.882 mechanical degrees ( 1/3pole-pitch), pitch), which seems to be practically infeasible. infea So, 1. mechanical degree of skewing is chosen for the analysis and prototype. It is shown that low cogging torque (peak value is.24nm even before skewing, which is less than 1.% % of rated torque) and low torque ripple even before skewing (±1.6%). Based on typical FEA results shown in Fig. 3, it can be stated that the proposed PMVM can be applied for low speed servo applications due to low torque ripple and extremely large number poles. Airgap radial force density distribution at rated state is examined to check motor syetry using Maxwell stress method by 2D FEA since CP structure induces high local force and unbalance magnetic pull along with rotor eccentricity [9]. Fig. 3 (c) shows that the proposed topology has rotational syetry every 9 mechanical mech degrees which is structurally more stable compared to the previous design as in [8]. However, this is not easily predictable when observing the flux lines even at rated state. As a result of that, motor syetry has to be carefully considered when implementing mplementing CP rotor since this configuration halves motor syetry when compared to the conventional rotor having alternating polarity of PMs. The stack length of the proposed PMVM is considerably short (stack length=35) and excessive flux leakage can occur from the active parts to the inactive structural steel parts. Therefore, 3D FEA is also performed to calculate no load induced voltage and the overall field distribution. distribution Comparison between 2D and 3D FEA is also performed to compensate computational error which is possibly caused by 2D FEA since 2D FEA cannot fully consider (a) No load state. (b) Rated state. FEA Fig. 2. Field distribution by 2D FEA. 743

3 Design Considerations and Validation of Permanent Magnet Vernier Machine with Consequent Pole Rotor for Low Speed Servo~.6.4 Before skewing After skewing Cogging torque[nm] Rotor structural parts Simplified bearing Torque[Nm] Radial force density[n/ 2 ] (a) Cogging torque. Before skewing( _+ Ripple 1.6%) After skewing( _+ Ripple.7%) (b) Rated torque leakage within the motor. Fig. 4 illustrates no load field distribution considering all steel structure within the motor. For the field computation, all the inactive steel parts are conservatively considered as simple insaturable iron which has a constant relative permeability of 4. Considering the overall field distribution, flux leakage seems to be negligible. Fig. 5 compares no load induced voltage obtained by 2D and 3D FEA. It should be noted that the waveforms are well balanced due to the pole-slot combination and the winding arrangement. However, there 9 27 Mechanical angle[deg.] 3 (c) Radial force distribution at rated state. Fig. 3. 2D FEA results Fig. 4. No load field distribution by 3D FEA considering inactive structural steel parts. No load induced voltage at 12RPM[V] V rms 31.2V rms 27.8V rms -2 2D FEA(Before skewing) -4 2D FEA(After Skewing) 3D FEA Fig. 5. No load induced voltage comparison. is computational difference between 2D and 3D FEA which is about 1.9%. Therefore, it would be reasonable to apply a correction factor of.891 to the 2D FEA results when comparing with the experimental results based on this difference. This correction will be discussed in the following section. 3. Experimental validation 3.1 Prototype and experimental setup Rotor assembly and stator with windings are respectively shown in Figs. 6(a) and (b). When the size of the motor is taken into consideration, it is not difficult to recognize excessively long end winding shown in Fig. 6(b). This was nearly unavoidable due to easier winding insertion in prototyping. This leads to copper loss increase and efficiency decrease at the same time. Fig. 7(a) shows static torque measurement setup where the prototype PMVM is connected to a reduction gear box and excited by external DC current source between Ph.U and Ph.V. A noncontact torque sensor is located between the reduction gear box and the prototype. The static torque was measured every.22 mechanical degrees which corresponds to 15 electrical degrees. The rotation angle was measured with a built in angular encoder of which resolution is 4, division/revolution. Fig. 7(b) shows dynamo test bench for 744

4 Shi-Uk Chung, Yon-Do Chun, Byung-Chul Woo, Do-Kwan Hong and Ji-Young Lee (a) Rotor assembly Reduction gear Fig. 6. Prototype PMVM. (b) Stator winding Induced voltage[v rms ] D_FEA Measurement RPM (a) Linear variation of no load induced voltage. PMVM Torque sensor (a) Static torque measurement setup Load motor (b) Dynamo test bench Fig. 7. Prototype and experimental setup. dynamic torque and efficiency. Torque sensor 3.2 No load induced voltage and static torque measurement PMVM Fig. 8(a) shows linear variation of no load induced voltage measured at several RPMs on the dynamo test bench. Measured no load induced voltage and computed no load induced voltage are compared in Figs. 8(b) and (c), respectively. It can be seen that sinusoidal no load induced voltage is obtainable and the measurement and the analysis agree well each other within 3% differences. Static torque measurement and 3D FEA are compared in Fig. 9 which shows about 2% differences on average value. It should be noted that the waveforms are quite sinusoidal. Therefore, the prototype is expected to have smooth torque characteristic which is required especially for low speed servo applications. It is seen in Fig. 1 that the 2D FEA results simulates much closer to the actual dynamic situation when considering the computation error correction factor which is mentioned in the preceding section. Voltage[V] V/div. (b) Measurement at 12RPM(27.V rms ) (c) 3D FEA at 12 RPM(27.8V rms ) Fig. 8. No load induced voltage comparison between analysis and measurement. Static torque by Ph.U & Ph.V[Nm] Time[msec] 1% of rated current 5% of rated current Symbol : Measurement Line : 3D FEA Fig. 9. Static torque under DC current excitation. However, measured efficiency shown in Fig. 11 is not much satisfactory and the maximum efficiency is measured to be merely around 79%(at output power of 157W) since the prototype has short stack and suffers appreciable flux leakage within the motor as seen in the comparison of 2D and 3D FEA. Moreover, due to the winding insertion issue in prototyping, it suffers considerably higher copper loss than expected. Therefore, a larger and better-made 745

5 Design Considerations and Validation of Permanent Magnet Vernier Machine with Consequent Pole Rotor for Low Speed Servo~ Torque[Nm] D FEA 2D FEA after error correction Dynamo test at RPM exemplary PMVM has been analyzed by extensive 2D and 3D FEA and the validity of the analysis has been experimentally examined for the prototype. Future research on geometry optimization, performance improvement and positioning control capability of the proposed PMVM needs to be followed. Efficiency[%] Current[A rms ] Fig. 1. Torque vs. current characteristics. Fig. 11. Measured efficiency. Table 2. Loss components comparisons at RPM. Item Unit Torque[Nm] Ph. current A rms Copper loss W Core loss W Mechanical loss W Total loss W Output torque Nm Output power W Efficiency(2D FEA) % Efficiency(experiment) % prototype is expected to display higher efficiency in such a low speed region. Table 2 compares loss components obtained by 2D FEA after the correction with ones by the experiment. In the loss computation, PM eddy loss is not considered and the mechanical loss is considered using the value obtained by the experiment. The mechanical loss coefficient turned out to be.1576w/rpm. It can be said that the estimated efficiency after the correction is quite reasonable. 4. Conclusion RPM RPM(2D FEA) RPM 3 35 Value This paper has presented another feasible pole-slot combination of PMVM with CP rotor and its geometric relation has been also mathematically introduced. An References [1] A. Toba, and A. Lipo, Novel dual-excitation permachine, Proc. IEEE IAS manent magnet vernier Annual Meeting, Oct. 1999, Vol. 4, pp [2] A. Toba, and A. Lipo, Generic torque-maximizing design methodology of surface permanent-magnet vernier machine, IEEEE Trans. Ind. Appl., Vol. 36, No. 6, pp , Nov./Dec. 2. [3] E. Spooner, and L. Haydock, Vernier hybrid ma- Power Appl., Vol. 15, chines, in Proc. IEE Electr. No. 6, pp , Nov. 23. [4] J. Li, K.T. Chau, J.Z. Jiang, C. Liu, and W. Li, A new efficient permanent-magnet vernier machine for Wind Power Generation, IEEE Trans. Magn., Vol. 46, No. 6, pp , June 21. [5] S. Niu, S.L. Ho, W.N. Fu, and L.L. Wang, Quanti- vernier permanent magnet tative comparison of novel machines, in IEEE Trans. Magn., Vol. 46, No. 6, pp , June 21. [6] C. Liu, J. Zhong, and K. T. Chau, A novel flux- machine, controllable vernier permanent-magnet IEEE Trans. Magn., Vol l. 47, No. 1, pp , Oct [7] S. Niu, S. L. Ho, W. N. Fu, A novel direct-drive dual-structure permanent magnet machine, IEEE Trans. Magn., Vol. 46, No. 6, pp , June 21. [8] S. U. Chung, J. W. Kim, B. C. Woo, D. K. Hong, J. Y Lee, and D. H. Koo, A novel design of modular three-phase permanent magnet vernier machine with consequent pole rotor, IEEE Trans. Magn., Vol. 47, No. 1. pp , Oct [9] D.G. Dorrell, M.F. Hsieh, and Y.G. Guo, Unin large brushless rare-earth balanced magnet pull permanent magnet motors with rotor eccentricity, IEEE Trans. Magn., Vol l. 45, No. 1, pp , Oct. 29. Shi-Uk Chung He received the B.S., M.S. and Ph.D. degrees in mechanical engineering from Pusan National Uni- South Korea in 1997, versity, Busan, 1999 and 21, respectively. From 22 to 25, he was with Samick THK as a Researcher. Since 25, He has been with Electric Motor Research 746

6 Shi-Uk Chung, Yon-Do Chun, Byung-Chul Woo, Do-Kwan Hong and Ji-Young Lee Center, Korea Electrotechnology Research Institute, Changwon, South Korea, as a Senior Researcher. His research interests include the design and analysis of linear and rotary direct drive electric machines. Yon-Do Chun He received the B.S., M.S. and Ph.D. degrees in electrical engineering from Hanyang University, Seoul, Korea, in 1996, 1998 and 21, respectively. From 21 to 23, he received a Japan Society for the Promotion of Science (JSPS) fellow- ship and he was with the Department of Electrical Engineering at Waseda University as a visiting scholar. From 24 to 211, he was with Mechatronics Research Group, Korea Electrotechnology Research Institute, Changwon, South Korea, as a Senior Researcher. Since 212, he has been with Electric Motors Research Center as a Principal Researcher and Technical Leader. His research interests include the design and analysis of industrial induction machines, permanent-magneand high torque machines machines. Byung-Chul Woo He received the B.S. degree in mechanical engineering from Youngnam University, Gyeongsan, South Korea, in 1989, the M.S. and Ph.D. degrees in mechanical design engineering from Kyungpook National University, Daegu, South Korea in 1991 and 2, respectively. He is currently with Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea, as a Principal researcher and Technical Leader. His research interests include the design and analysis of electric machines and power plants. Do-Kwan Hong He received the B.S, M.S. and Ph. D degrees in mechanical engineering from Dong-A University, Busan, South Korea, in 1998, 2 and 24, respectively. Since 24, He has been with Electric Motor Research Center, Korea Electrotechnology Re- Changwon, South search Institute, Korea, as a Senior Researcher. His research interests include the design, analysis and performance evaluation of ultra-high speed machine, motor-generator for micro gas turbine generator. Ji-Young Lee She received the B.S., M.S, and Ph.D degrees in electrical engineering from Changwon National University, Changwon, South Korea, in 2, 22, and 26 respectively. She is currently with Electric Motor Research Center, Korea Electrotech- Institute, Changwon, nology Research South Korea, as a Senior Researcher. Her research interests include the design and analysis of various electromagnetic devices, permanent-magnet machines and transverse flux machines. 747