簡易檢索 / 詳目顯示

研究生: 洪湘閔
Hung, Hsiang-Min
論文名稱: 混合型步進馬達之頓轉轉矩分析及實測
Detent Torque Analysis and Experimental Measurement of Hybrid Stepper Motors
指導教授: 蔡明祺
Tsai, Mi-Ching
黃柏維
Huang, Po-Wei
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 93
中文關鍵詞: 混合型步進馬達頓轉轉矩齒槽轉矩極對數比有限元素分析
外文關鍵詞: hybrid stepper motor, detent torque, cogging torque, pole ratio, finite element analysis
相關次數: 點閱:3下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 步進馬達具有結構簡單、控制容易及定位精度高等優點,廣泛應用於自動化設備與精密定位系統。其中,頓轉轉矩(Detent Torque)為步進馬達在未通電狀態下所產生的轉矩,其特性會影響馬達的定位能力與運轉表現。然而,頓轉轉矩與永磁馬達齒槽轉矩(Cogging Torque)皆源自於轉子與定子間磁阻隨位置變化所產生的轉矩,因此兩者在特性與名稱上容易混淆。基於此,本研究以兩相混合型步進馬達為研究對象,釐清齒槽轉矩與頓轉轉矩特性差異,並探討頓轉轉矩週期特性與主要諧波成分。
    本研究首先透過電機極對數比(Pole Ratio)概念,建立齒槽轉矩與頓轉轉矩分類方式,並針對既有量測平台所取得正、逆轉轉矩資料進行整理與處理,以取得頓轉轉矩波形,進一步以 Two-Port 形式描述量測系統與數學模型之間的對應關係。此外,本研究利用 Ansys Maxwell 建立有限元素模型,並與理論分析及實際量測結果進行比較。

    Stepper motors are widely used in automation equipment and precision positioning systems because of their simple structure,straightforward control, and high positioning accuracy. This study investigates the detent torque of a two-phase hybrid stepper motor to clarify the differences between detent torque and cogging torque and analyze the periodic characteristics and dominant harmonic components of detent torque.
    The pole ratio concept is introduced to describe the spatial relationship between the rotor and stator magnetic fields and to establish a classification framework for these two torque characteristics. The periodic characteristics of detent torque are further analyzed based on the motor tooth configuration, tooth-pitch angle, and Fourier representation. Clockwise (CW) and counterclockwise (CCW) torque data obtained from an existing measurement platform are processed to extract the detent torque waveform, while a two-port representation is used to describe the relationship between the measurement system and the mathematical model. In addition, a finite-element model is established in ANSYS Maxwell and compared with the theoretical and experimental results.
    The results show that the fourth harmonic is the dominant component in both the measured and simulated detent torque responses. The finding demonstrate that the proposed analysis framework can effectively characterize the primary periodic behavior of detent torque and establish a correspondence among theoretical analysis, finite-element simulation, and experimental measurements.

    中文摘要 I Abstract II 致謝 XV 目錄 XVII 表目錄 XX 圖目錄 XXI 符號表 XXIII 第一章 緒論 1 1.1 研究動機 1 1.2 文獻回顧 2 1.2.1 齒槽轉矩與頓轉轉矩形成機制與特性 2 1.2.2 極對數比定義與應用 3 1.2.3 頓轉轉矩數學模型 4 1.2.4 頓轉轉矩量測方法 5 1.2.5 Two-Port 系統描述方法 6 1.3 研究目的 7 1.4 論文架構 8 第二章 步進馬達架構與頓轉轉矩分析 10 2.1 混合式步進馬達介紹 10 2.1.1 步進馬達分類 10 2.1.2 混合式步進馬達結構 11 2.1.3 步進馬達方塊圖 14 2.2 磁通調制與極對數比概念 15 2.3 電機極對數比分析 18 2.4 頓轉轉矩週期性與數學模型 21 2.5 步進馬達齒距角與頓轉轉矩位置關係 23 2.5.1 齒距角分析 23 2.5.2 頓轉轉矩相對位置關係 24 2.6 齒槽轉矩特性分析 27 2.6.1 齒槽轉矩平衡位置分析 27 2.6.2 齒槽轉矩週期與諧波分析 28 2.7齒槽轉矩與頓轉轉矩比較 31 第三章 頓轉轉矩模擬與結果分析 33 3.1 有限元素模擬建立 33 3.2 模擬條件 34 3.3 模擬結果 35 3.4 模擬頻譜分析 36 第四章 實測結果與分析 39 4.1 頓轉轉矩量測平台 39 4.1.1 雙馬達系統動態方程式推導 40 4.1.2 系統模型方塊圖 41 4.1.3 量測平台架構總覽 42 4.1.4 量測平台各元件功能說明 43 4.2 量測流程與資料處理 47 4.2.1 實測平台量測流程 47 4.2.2 量測資料處理方式 48 4.3 頓轉轉矩實測結果 50 4.3.1 CW與CCW原始量測結果 50 4.3.2 頓轉轉矩計算結果 51 4.3.3 頻譜分析 52 4.4 實測與模擬比對 55 4.4.1 頓轉轉矩波形比較 55 4.4.2 頻譜分析結果比較 57 第五章 結論與未來建議 59 5.1 結論 59 5.2 未來建議 60 參考文獻 62

    [1] Julia Jansson and Charlotte Radahl, “Torque Estimation Algorithms for Stepper Motor,” Department of Electrical Engineering Chalmers University of Technology Gothenburg,Sweden, 2018.
    [2] J. Gao, Z. Xiang, L. Dai, S. Huang, D. Ni and C. Yao, "Cogging Torque Dynamic Reduction Based on Harmonic Torque Counteract," in IEEE Transactions on Magnetics, vol. 58, no. 2, pp. 1-5, Feb. 2022.
    [3]黃品樺,「永磁游標電機考量鐵損與齒槽轉矩建模」,國立成功大學電機工程學系碩士論文,2023年。
    [4] B. Henke, O. Sawodny, S. Schmidt, and R. Neumann, “Modeling of hybrid stepper motors for closed loop operation,” IFAC Proceedings Volumes, vol. 46, no. 5, pp. 177 – 183, 2013.
    [5]「齒槽轉矩如何被測量出來的」,工業傳動共享平台,2022年1月24日,https://motor.eetrend.com/content/2022/100557278.html.
    [6] E. V. C. Sekhara Rao, P. V. N. Prasad, "Torque Analysis of Permanent Magnet Hybrid Stepper Motor using Finite Element Method for Different Design Topologies," International Journal of Power Electronics and Drive System (IJPEDS), vol. 2, no. 1, pp. 107–116, Mar. 2012.
    [7] “Two-port network,” Wikipedia.Apr.23, 2024.Retrieved May 24, 2024,
    From Two-port network - Wikipedia.
    [8] Ming’s Blogger,「步進馬達介紹」,2013年5月8日, https://ming-shian.blogspot.com/2013/05/blog-post_8.html
    [9]台灣東方馬達股份有限公司,「步進馬達的基本特性」,https://www.orientalmotor.com.tw/service/tech/stepping_motor03/,檢索時間:2024年9月。
    [10]徐鈺涵,「步進馬達驅動晶片分析與馬達建模」,碩士論文,國立成功大學電機工程學系,2023年。
    [11]張啟洋,「交流馬達建模與分析」,碩士論文,國立成功大學機械工程學系,2023年。
    [12]張啟洋,「 Modeling of PMSM 」,簡報,國立成功大學馬達科技中心,2024年。
    [13]程明,「電機氣隙磁場調制統一理論及應用」,機械工業出版社,2021年。
    [14] Faiz, Jawad, et al. "Single stator‐single rotor permanent magnet Vernier machine topologies for direct‐drive applications: Review and case study." International Transactions on Electrical Energy Systems 31.12 (2021)
    [15]王漢祺,「數位孿生應用於永磁馬達快速特性量測系統」,碩士論文,國立成功大學機械工程學系,2024年。
    [16] M. Kant, Les actionneurs électriques pas à pas. Paris, France:Éditions Hermès, 1989.
    [17] C.Studer, A.Keyhani, T. Sebastian and S.K. Murthy. “Study of cogging torque in permanent magnet machines.” IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty-Second IAS Annual Meeting, vol.1, pp.42-49,1997.
    [18] The MathWorks, Inc., “makima,” MATLAB Documentation, Natick, MA,USA.[Online].Available:https://www.mathworks.com/help/matlab/ref/makima.html.Accessed: May. 10, 2026.
    [19] J. Wanjiku, M. A. Khan, P. S. Barendse and P. Pillay, "Influence of Slot Openings and Tooth Profile on Cogging Torque in Axial-Flux PM Machines," in IEEE Transactions on Industrial Electronics, vol. 62, no. 12, pp. 7578-7589, Dec. 2015.
    [20] T. -S. Hwang and J. -K. Seok, "Observer-Based Ripple Force Compensation for Linear Hybrid Stepping Motor Drives," in IEEE Transactions on Industrial Electronics, vol. 54, no. 5, pp. 2417-2424, Oct. 2007.
    [21] S. Abduh, S. Karunanithi, and T. Nur, “Analysis of the Cogging Torque Reduction in Permanent Magnet Generators for a Very Low Wind Speed,” Energies, vol. 15, no. 19, p. 7182, 2022.
    [22]許乃文,「具雙機械端口之磁性齒輪電機建模研究及具步進馬達應用」,國立成功大學電機工程學系碩士論文,2024月1月。
    [23] Y. Xie, Y. Zhuang, C. Wu and F. Cao, "Comprehensive Suppression Method of Mechanical Resonance and Disturbance in Servo System," 2024 14th Asian Control Conference (ASCC), Dalian, China, pp. 1854-1859, 2024.
    [24] N. Matsui, M. Nakamura and T. Kosaka, "Instantaneous torque analysis of hybrid stepping motor," in IEEE Transactions on Industry Applications, vol. 32, no. 5, pp. 1176-1182, Sept.-Oct. 1996.
    [25] M. Cheng, Z. Ma, W. Hua, B. Wang, and Z. Wang, "Research Progresses and Prospects of General Airgap Field Modulation Theory for Electrical Machines," Proceedings of the CSEE, vol. 45, no. 4, pp. 1220-1236, Feb. 20, 2025.
    [26] J. Zhou, M. Cheng, H. Wen, X. Yan, M. Tong and W. Wang, "Modeling and Suppression of Torque Ripple in PMSM Based on the General Airgap Field Modulation Theory," in IEEE Transactions on Power Electronics, vol. 37, no. 10, pp. 12502-12512, Oct. 2022.
    [27] H. Qiu, W. Yu, C. Yang, and R. Yi, “Influence of different rotor magnetic circuit structure on the performance of permanent magnet synchronous motor,” Archives of Electrical Engineering, vol. 66, no. 3, pp. 583–594, 2017.
    [28] A. Masmoudi and A. Elantably, "A simple assessment of the cogging torque in a transverse flux permanent magnet machine, IEEE International Electric Machines and Drives Conference, pp. 754-759, 2001.
    [29]蔡明祺,「 槽極配 」,簡報,國立成功大學馬達科技中心,2025年。

    QR CODE