傳統交通工具是使用石油作為驅動力，隨著全球暖化日漸嚴重，近年來，以電代替石油逐漸成為全球科技發展的趨勢。永磁馬達(Permanent Magnet Motor)具有高效率、高功率密度等優勢，為電動車的理想馬達。為了實現高轉矩低轉速的性能，馬達通常需要搭配減速齒輪組，然而齒輪箱會使效率降低且噪音增加。永磁游標馬達(Permanent Magnet Vernier Motor, PMVM)能以非接觸式磁齒輪效應電機提供解決變速箱問題的方案；另外其簡單的結構以及高轉矩密度，近年來也受到許多的關注。
本文以永磁游標馬達之理論基礎進行設計，並在PMVM上加入庶極(Consequent Pole, CP)以減少磁鐵用量，但是庶極的結構使氣隙磁通密度不平衡而產生偶次諧波，使轉矩漣波變高、鐵損升高等不良影響。本文提出消除庶極永磁游標馬達(CP-PMVM)固有的反電動勢偶次諧波，並以磁障引導磁通走向，使性能上升9.8%。經由全模型最佳化使磁鐵用量與一般游標馬達相比下降23%。最後透過測試原型機對設計與模擬進行驗證。

Traditional vehicles rely on petroleum as their primary source of power. However, due to the increasing severity of global warming, there has been a global trend towards replacing petroleum with electricity in recent years. Permanent magnet motors have emerged as ideal motors for electric vehicles because of their high efficiency and power density. To achieve high torque at low speeds, motors are typically combined with gearboxes. Nevertheless, gearboxes can reduce efficiency and increase noise. The Permanent Magnet Vernier Motor (PMVM) offers a solution to the gearbox issue through the non-contact magnetic gear effect. In addition, its simple structure and high torque density have attracted significant attention in recent years.
This paper focuses on the design of the PMVM based on its theoretical foundation. A consequent pole structure is introduced to reduce the amount of magnetic used. However, the consequent pole structure leads to an unbalance magnetic flux density in the air gap, resulting in increased torque ripple and iron losses due to even order harmonics. This paper proposes a method to eliminate the inherent even harmonics in the Consequent Pole Permanent Magnet Vernier Motor (CP-PMVM) and guides the magnetic flux using magnetic barriers, resulting in a 9.8% improvement in performance. Through comprehensive model optimization, the amount of magnetic usage is reduced by 23% compared to a conventional vernier motor. Finally, the theoretical calculations are validated through testing on a prototype machine.

[1]產業價值鏈資訊平台，電動車輛產業產業鏈簡介，[Online]. Available： https://ic.tpex.org.tw/introduce.php?ic=A300
[2]Roland Irle, Global EV Sales for 2022. [Online]. Available： https://www.ev-volumes.com/country/total-world-plug-in-vehicle-volumes/
[3]交通部統計查詢網，[Online]. Available： https://stat.motc.gov.tw/mocdb/stmain.jsp?sys=100
[4]金屬中心，電動車驅動馬達發展現況，黃得晉，[Online]. Available： https://www.mirdc.org.tw/FileDownLoad/IndustryNews/2014612145710426.pdf
[5]Caty Fairclough, Analyzing the Structural Integrity of an Induction Motor with Simulation. [Online]. Available：
https://www.comsol.com/blogs/analyzing-the-structural-integrity-of-an-induction-motor-with-simulation/
[6]C.C. Hwang, C.M. Chang, S.P. Cheng, C.K. Chan, C.T. Pan, and T.Y. Chang, “Comparison of performances between IPM and SPM motors with rotor eccentricity,” Journal of Magnetism and Magnetic Materials, vol. 282, pp. 360-363, 2004.
[7]X. Zhang, H. Yang, Y. Li, and S. Niu, “Comparative Study of Novel Dual-Stator Machines Having Different Biased PM Configurations,” IEEE Transactions on Magnetics, vol. 58, no. 2, pp. 1-6, 2022.
[8]P. M. Tlali, R. -J. Wang, S. Gerber, C. D. Botha, and M. J. Kamper, “Design and Performance Comparison of Vernier and Conventional PM Synchronous Wind Generators,” IEEE Transactions on Industry Applications, vol. 56, no. 3, pp. 2570-2579, 2020.
[9]O. Barth, “Harmonic piezodrive — miniaturized servo motor,” Journal of Mechanical Engineering, vol. 29, no. 1, pp. 96-98, 1993.
[10]B. N. Wang, L. Zhou, H. Y. Wang, and C. Lin, “Analytical Modeling and Design Optimization of a Vernier Permanent Magnet Motor,” IEEE Energy Conversion Congress and Exposition, Vancouver, BC, Canada, pp. 4480-4485, 2021.
[11]B. Kim, “Design of a direct drive permanent magnet vernier generator for a wind turbine system,” IEEE Transactions on Industry Applications, vol. 55, no. 5, pp. 4665-4675, Sept./Oct. 2019.
[12]Z. S. Du, and T. A. Lipo, “Cost-effective high torque density bi-magnet machines utilizing rare Earth and ferrite permanent magnet,” IEEE Transactions Energy Conversion, vol. 35, no. 3, pp. 1577-1584, Sep. 2020.
[13]R. Qu, D. Li, and J. Wang, “Relationship between magnetic gears and Vernier machines,” in proceeding of International Conference on Electrical Machines and Systems, Beijing, China, 2011, pp. 1-6.
[14]F. Wu, and A. M. EL-Refaie, “Permanent magnet Vernier machines： A review,” in proceeding of XIII International Conference on Electrical Machines, Alexandroupoli, Greece, 2018, pp. 372-378.
[15]G. Kronacher, “Design performance and application of the Vernier resolver,” The Bell System Technical Journal, vol. 36, no. 6, pp. 1487-1500, Nov. 1957.
[16]C. H. Lee, “Vernier motor and its design,” IEEE Transactions on Power Apparatus and Systems, vol. 82, no. 66, pp. 343-349, June 1963.
[17]K. Atallah, and D. Howe, “A novel high-performance magnetic gear,” IEEE Transactions on Magnetics, vol. 37, no. 4, pp. 2844-2846, July 2001.
[18]T. Zou, D. Li, R. Qu, D. Jiang, and J. Li, “Advanced high torque density PM Vernier machine with multiple working harmonics,” IEEE Transactions on Industry Applications, vol. 53, no. 6, pp. 5295-5304, Nov.-Dec. 2017.
[19]Y. Kataoka, M. Takayama, Y. Anazawa, and Y. Matsushima, “Output Characteristics of a Surface Permanent Magnet-type Vernier Motor - Comparison of Test Results and Calculation,” in proceeding of International Power Electronics Conference, Hiroshima, Japan, 2014, pp. 3801-3808.
[20]A. Toba, and T. A. Lipo, “Generic torque-maximizing design methodology of surface permanent-magnet Vernier machine,” IEEE Transactions on Industry Applications, vol. 36, no. 6, pp. 1539-1546, Nov.-Dec. 2000.
[21]H. Kakihata, Y. Kataoka, M. Takayama, Y. Matsushima, and Y. Anazawa, “Design of surface permanent magnet-type vernier motor,” in proceeding of 15th International Conference on Electrical Machines and Systems, Sapporo, Japan, pp. 1-6, 2012.
[22]J. Zhu, Y. Zuo, H. Chen, J. Chen, and C. H. Lee, “Deep-investigated analytical modeling of a surface permanent magnet vernier motor,” IEEE Transactions on Industrial Electronics, vol. 69, no. 12, pp. 12336-12347, Dec. 2022.
[23]D. Li, R. Qu and T. A. Lipo, “High-Power-Factor Vernier Permanent-Magnet Machines,” IEEE Transactions on Industry Applications, vol. 50, no. 6, pp. 3664-3674, Nov.-Dec. 2014.
[24]Y. Yu, Y. Pei, and F. Chai, “Power Factor Analysis in Spoke-Type Permanent Magnet Vernier Motors with Different Slot–Pole Combinations for In-Wheel Direct Drive,” IEEE Transactions on Transportation Electrification, vol. 9, no. 1, pp. 642-655, 2023.
[25]N. Arish, “Electromagnetic Performance Analysis of Linear Vernier Machine with PM and HTS-Bulk. Physica C: Superconductivity and its Applications,” vol.579. pp. 1353751. 2020.
[26]M. Ardestani, N. Arish, and H. Yaghobi, “A New HTS Dual Stator Linear Permanent Magnet Vernier Machine with Halbach Array for Wave Energy Conversion,” Physica C: Superconductivity and its Applications. vol.569. pp. 1353593. 2019.
[27]N. Arish, F. Marignetti, and M. Yazdani-Asrami, “Comparative Study of a New Structure of HTS-Bulk Axial Flux-Switching Machine,” Physica C: Superconductivity and its Applications. vol.584. pp. 1353854. 2021.
[28]N. Baloch, B.-I. Kwon, and Y. Gao, “Low-cost high-torque-density dual-stator consequent-pole permanent magnet Vernier machine,” IEEE Transactions on Magnetics, vol. 54, no. 11, pp. 1-5, Nov. 2018.
[29]T. W. Ching, K. T. Chau, and W. Li, “Power factor improvement of a linear Vernier permanent-magnet machine using auxiliary DC field excitation,” IEEE Transactions on Magnetics, vol. 52, no. 7, Jul. 2016.
[30]Y. Kataoka, M. Takayama, Y. Matsushima, and Y. Anazawa, “Design of surface permanent magnet-type Vernier motor using Halbach array magnet,” in proceeding of 18th International Conference on Electrical Machines and Systems, Pattaya, Thailand, 2015, pp. 177-183.
[31]S. Sakamoto, Y. Yokoi, T. Higuchi, and Y. Miyamoto, “A study on rotor design of consequent-pole permanent magnet machines,” in proceeding of 23rd International Conference on Electrical Machines and Systems, Hamamatsu, Japan, 2020, pp. 1600-1603.
[32]D. Li, R. Qu, J. Li, and W. Xu, “Consequent-pole toroidal-winding outer-rotor Vernier permanent-magnet machines,” IEEE Transactions on Industry Applications, vol. 51, no. 6, pp. 4470-4481, Nov.-Dec. 2015.
[33]Z. Chen, J. Wang, and L. Zhou, “Design and Analysis of Permanent Magnet Vernier Motors for Downhole Applications,” in proceeding of IEEE 1st China International Youth Conference on Electrical Engineering, Wuhan, China, 2020, pp. 1-6.
[34]C. M. Spargo, B. C. Mecrow, and J. D. Widmer, “Application of fractional slot concentrated windings to synchronous reluctance machines,” in proceeding of International Electric Machines & Drives Conference, Chicago, IL, USA, 2013, pp. 618-625.
[35]Z. Chen, J. Wang, Z. Hu, J. Xiao, L. Zhou, and H. Wang, “Design of Consequent Pole Permanent Magnet Vernier Motor for Downhole Electric Drilling System,” in proceeding of IEEE 4th Student Conference on Electric Machines and Systems, Huzhou, China, 2021, pp. 1-6.
[36]H. Wang, S. Fang, H. Yang, H. Lin, D. Wang, Y. Li, and C. Jiu, “A novel consequent-pole hybrid excited Vernier machine,” IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-4, Nov. 2017.
[37]Y. Yu, Y. Pei, L. Chen, F. Chai, and G. Han, “Design and comparative analysis of consequent pole rotor configurations in PM vernier motors for in-wheel drive application,” in proceeding of 22nd International Conference on Electrical Machines and Systems, Harbin, China, 2019, pp. 1-6.
[38]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 Transactions on Magnetics, vol. 47, no. 10, pp. 4215-4218, Oct. 2011.
[39]H. Zhou, W. Tao, C. Zhou, Y. Mao, G. Li, and G. Liu, “Consequent pole permanent magnet vernier machine with asymmetric air-gap field distribution,” IEEE Access, vol. 7, pp. 109340-109348, 2019.
[40]Y. Fan, Y. Mei, and Q. Zhang, “Torque ripple reduction of outer rotor permanent magnet Vernier machine with concentrated winding” in proceeding of International Conference on Electrical Machines, Gothenburg, Sweden, 2020, pp. 543-549.
[41]J. Ma, B. Xu, Q. Wu, C. Luo, Q. Lin, and Y. Fang, “Design of a Chamfered Structure on Consequent-Pole Vernier Permanent-Magnet Machine,” Energies. vol. 15, no. 20, pp. 7780. 2022.
[42]H. Gorginpour, “Design modifications for improving modulation flux capability of consequent-pole vernier-PM machine in comparison to conventional vernier-PM machines,” Scientia Iranica. vol. 27. no.6. pp. 3150-3161. 2020.
[43]T. A. Lipo, Introduction to AC Machine Design, Wiley Online Books, 2017, ch2.
[44]B. Kim, and T. A. Lipo, “Operation and design principles of a PM vernier motor”, IEEE Transactions on Industry Applications, vol. 50, no. 6, pp. 3656-3663, Nov.-Dec. 2014.
[45]J. Rens, R. Clark, S. Calverley, K. Atallah, and D. Howe, “Design, analysis and realization of a novel magnetic harmonic gear,” in proceeding of 18th International Conference on Electrical Machines, Vilamoura, Portugal, 2008, pp. 1-4.
[46]簡伸翰，應用於電動滑板車之輪鼓式游標永磁馬達設計與實驗，國立成功大學電機工程學系碩士論文，2021。
[47]M.-H. Hwang, H.-S. Lee, and H.-R. Cha, “Analysis of Torque Ripple and Cogging Torque Reduction in Electric Vehicle Traction Platform Applying Rotor Notched Design,” Energies. no. 11. pp. 3053. 2018.
[48]D. K. Kana Padinharu, G. J. Li, Z. Q. Zhu, M. P. Foster, D. A. Stone, A. Griffo, R. Clark, and A. Thomas, “Scaling Effect on Electromagnetic Performance of Surface-Mounted Permanent-Magnet Vernier Machine,” IEEE Transactions on Magnetics, vol. 56, no. 5, pp. 1-15, May 2020.
[49]J. Li, K. Wang, F. Li, S. S. Zhu, and C. Liu, “Elimination of even-order harmonics and unipolar leakage flux in consequent-pole PM machines by employing N-S-Iron–S-N-Iron rotor,” IEEE Transactions on Industrial Electronics, vol. 66, no. 3, pp. 1736-1747, Mar. 2019.
[50]陳政，井下電動鉆具庶極永磁游標電機設計研究，華中科技大學電氣工程碩士學位論文，2021。
[51]S. Arslan, O. Gurdal and S. Akkaya Oy, “Design and optimization of tubular linear permanent-magnet generator with performance improvement using response surface methodology and multi-objective genetic algorithm,” Scientia Iranica, pp.3053-3065. 2020.
[52]P. Sreeraj, and T. Kannan, “Modelling and Prediction of Stainless Steel Clad Bead Geometry Deposited by GMAW Using Regression and Artificial Neural Network Models. Advances in Mechanical Engineering,” Advances in Mechanical Engineering, vol 4. 2021.
[53]S. Das, and S. Tesfamariam, State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning. ArXiv, vol. abs/2202.06416, 2022.
[54]S., Timothy, M. Timothy, K. John, and M. Farrokh, Comparison Of Response Surface And Kriging Models For Multidisciplinary Design Optimization. American Institute of Aeronautics and Astronautics, vol.98, 1998.
[55]Response Surface Methodology (RSM) Types. [Online]. Available： https://www.mr-cfd.com/response-surface-methodology-rsm-types/
[56]林昇甫、徐永吉，遺傳演算法及其應用，五南圖書出版，2009。
[57]Magnet INNUOVO, 2021, [Online]. Available：http://www.magnet-innuovo.com/product/16839.htm