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研究生: 羅晨欣
Lo, Chen-Hsin
論文名稱: 軸向自調節徑向磁通渦電流制動器之建模與實驗驗證
Modeling and Experimental Validation of an Axially Self-Adjusting Radial-Flux Eddy Current Brake
指導教授: 歐峯銘
Ou, Feng-Ming
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2026
畢業學年度: 115
語文別: 中文
論文頁數: 155
中文關鍵詞: 永磁渦電流制動器 、徑向磁通 、自調節機構 、多目標最佳化 、準靜態模型
外文關鍵詞: Permanent magnet eddy current brake, Radial flux, Self-adjusting mechanism, Multi-objective optimization, Quasi-static model
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  • 永磁渦電流制動器具有非接觸制動與低磨耗等特性,但固定幾何參數構型之扭矩–轉速特性受既定磁路與幾何參數限制,難以於運轉過程中依需求調整制動輸出。本研究以直立式軸向自調節徑向磁通渦電流制動器為研究對象,透過離心質量塊、斜坡滑槽與彈簧驅動導體盤軸向位移,在維持徑向氣隙固定之條件下,藉由改變有效軸向重疊長度La調整制動扭矩。研究由目標制動需求出發,以磁等效電路解析模型進行參數篩選,並透過三維有限元素分析取得制動扭矩與軸向電磁力,據以決定機構作動範圍與行程。自調節機構則建立考量離心力、重力、彈簧回復力、接觸摩擦及軸向電磁力之準靜態力學模型,分析升、降速受力差異,並以所需彈簧力差異及回程特徵轉速偏差為雙目標進行參數最佳化,完成磁制動端與自調節機構之耦合設計。
    依400 rpm、1.0 N·m與800 rpm、2.5 N·m之設計工況,選定La=18–22 mm為主要作動範圍,對應 4.0 mm 軸向行程;兩設計點之有限元素制動扭矩與目標值分別相差 2.8 % 與 1.2%。固定Lₐ實驗與有限元素分析呈現一致之扭矩變化趨勢。自調節升速實驗中,400 rpm與800 rpm之制動扭矩分別為1.13 N·m與2.68 N·m,較目標值高出12.6%與7.0%;800 rpm 時軸向位移達3.82 mm,為設計行程之95.4%,顯示原型可隨轉速改變有效軸向重疊長度,進而調整制動扭矩。
    降速實驗則出現回程延遲與停機後殘留位移。將實際彈簧預壓條件及方向相依之等效摩擦參數納入準靜態模型後,可改善降速路徑預測,但仍無法完整描述低轉速回程行為。本研究建立由目標制動需求出發,結合軸向電磁力、直立式機構受力分析與多目標最佳化之整合設計流程,並透過原型實驗驗證自調節構型之可行性,同時指出準靜態模型之預測限制。

    Permanent magnet eddy current brakes (PMECBs) provide non-contact braking with reduced wear, but fixed-parameter configurations have limited torque adjustment capability. This study presents a vertically oriented, axially self-adjusting radial-flux eddy current brake. Centrifugal masses, ramp slots, and springs drive axial conductor displacement, varying the effective overlap length while maintaining a fixed radial air gap. A magnetic equivalent circuit (MEC) model was used for parameter selection, followed by three-dimensional finite element analysis (FEA) to calculate braking torque and axial electromagnetic force. A quasi-static mechanical model accounting for centrifugal force, gravity, spring force, electromagnetic force, and contact friction was developed for multi-objective optimization.
    For target torques of 1.0 N·m at 400 rpm and 2.5 N·m at 800 rpm, an effective axial overlap range of 18–22 mm was selected, requiring a 4 mm stroke. The FEA torque deviations from the targets were 2.8% and 1.2%. Prototype experiments yielded 1.13 and 2.68 N·m, respectively, with a displacement of 3.82 mm at 800 rpm, reaching 95.4% of the designed stroke. Delayed return and residual displacement were observed during deceleration. Revising the spring preload and equivalent friction parameters improved displacement predictions but did not fully reproduce the return behavior. The results demonstrate the feasibility of the proposed design and identify limitations of the quasi-static model.

    摘要 i 誌謝 vii 目錄 viii 表目錄 xii 圖目錄 xiv 符號說明 xvii 第1章 前言 1 1.1 徑向磁制動器 1 1.1.1 徑向磁制動器之分析模型 2 1.1.2 徑向磁制動器文獻回顧 4 1.2 調節型磁制動器文獻回顧 6 1.2.1 外部控制式磁制動器 6 1.2.2 自調節式磁制動器 8 1.3 自調節機構最佳化設計需求 11 1.4 研究動機與目的 12 1.5 論文架構 14 第2章 自調節磁制動器建模 17 2.1 徑向磁制動器解析模型 17 2.1.1 建模假設 19 2.1.2 磁等效電路模型 19 2.1.3 磁路與磁場推導 20 2.2 軸向自調節機構模型 30 2.2.1 自調節機構幾何關係 31 2.2.2 建模假設 34 2.2.3 導體盤軸向力平衡 34 2.2.4 單一質量塊受力與楔形推力 35 2.2.5 所需彈簧力與目標位移 38 2.3 機構與磁制動耦合關係 40 第3章 自調節磁制動器參數訂定與最佳化設計 43 3.1 設計工況與目標制動扭矩訂定 43 3.2 磁制動器初步參數訂定 44 3.2.1 設計限制與參數可行域 45 3.2.2 參數篩選與基準設計 48 3.2.3 有效軸向重疊長度與軸向電磁力模型 51 3.3 自調節機構端參數設計 55 3.3.1 設計變數選定 55 3.3.2 力學、幾何與製造約束條件 56 3.3.3 設計變數搜尋範圍與參數邊界設定 60 3.4 目標函數與最佳化方法 62 3.4.1 目標函數定義 63 3.4.2 多目標參數搜尋設定與流程 64 3.4.3 最佳化穩定性評估 66 3.4.4 Pareto候選解分布 69 3.5 自調節機構參數訂定 71 3.5.1 理論等效線性彈簧 74 3.5.2 市售彈簧選配與響應評估 76 第4章 磁制動端模擬與分析 80 4.1 有限元素模擬流程 80 4.2 COMSOL磁制動有限元素模型 81 4.2.1 幾何模型與材料設定 81 4.2.2 物理場、邊界條件與求解設定 83 4.2.3 網格設定與收斂性分析 84 4.3 模擬結果分析 86 4.3.1 磁場模擬結果分析 86 4.3.2 扭矩模擬結果分析 87 4.3.3 軸向電磁力模擬結果分析 91 4.4 模擬結果與討論 93 第5章 實作與實驗驗證 95 5.1 實驗目的與假設 95 5.2 實驗原型與量測系統 96 5.3 實驗方法 99 5.3.1 實驗平台組裝與檢查 99 5.3.2 轉速控制設定 100 5.3.3 轉速穩定區間判定與統計方法 102 5.3.4 系統基準扭矩建立與量測修正 103 5.4 固定有效軸向重疊長度實驗 104 5.5 自調節實驗 107 5.5.1 自調節位移與扭矩響應 107 5.5.2 自調節位移與制動扭矩之模型與實驗比較 111 5.6 模型差異與影響因素分析 114 5.6.1 等效摩擦參數與力平衡差異分析 114 5.6.2 材料溫度對制動扭矩預測之影響 118 5.7 小結 119 第6章 結論與建議 121 6.1 結論 121 6.2 後續研究建議 123 參考文獻 125

    [1] J. Wang et al., "A review of recent developments in permanent magnet eddy current couplers technology," Actuators, vol. 12, no. 7, 2023, Art no. 277.
    [2] Y. Li, G. Wang, D. Jiang, L. Zhu, and J. Huang, "Review and Recent Developments of Speed Regulation Technology for Energy Conservation Based on Permanent Magnet Adjustable Speed Drive," IEEE Access, vol. 12, pp. 58181–58195, 2024.
    [3] J.-Y. Choi and S.-M. Jang, "Analytical magnetic torque calculations and experimental testing of radial flux permanent magnet-type eddy current brakes," Journal of Applied Physics, vol. 111, no. 7, 2012.
    [4] M.-G. Park, J.-Y. Choi, H.-J. Shin, and S.-M. Jang, "Torque analysis and measurements of a permanent magnet type Eddy current brake with a Halbach magnet array based on analytical magnetic field calculations," Journal of Applied Physics, vol. 115, no. 17, 2014.
    [5] S. Mohammadi, M. Mirsalim, and S. Vaez-Zadeh, "Nonlinear modeling of eddy-current couplers," IEEE Transactions on Energy Conversion, vol. 29, no. 1, pp. 224–231, 2013.
    [6] S. Mohammadi and M. Mirsalim, "Double-sided permanent-magnet radial-flux eddy-current couplers: three-dimensional analytical modelling, static and transient study, and sensitivity analysis," IET Electric Power Applications, vol. 7, no. 9, pp. 665–679, 2013, doi: https://doi.org/10.1049/iet-epa.2013.0050.
    [7] J. Wang and J. Zhu, "A simple method for performance prediction of permanent magnet eddy current couplings using a new magnetic equivalent circuit model," IEEE Transactions on Industrial Electronics, vol. 65, no. 3, pp. 2487–2495, 2017.
    [8] A. Erasmus and M. Kamper, "Analysis for Design Optimisation of Double PM-Rotor Radial Flux Eddy Current Couplers," presented at the 2015 IEEE Energy Conversion Congress and Exposition (ECCE), Montreal, QC, Canada, September 20–24, 2015.
    [9] A. S. Erasmus and M. J. Kamper, "Computationally efficient analysis of double PM-rotor radial-flux eddy current couplers," IEEE Transactions on Industry Applications, vol. 53, no. 4, pp. 3519–3527, 2017.
    [10] X. Yang, Y. Liu, and L. Wang, "An improved analytical model of permanent magnet eddy current magnetic coupler based on electromagnetic-thermal coupling," IEEE Access, vol. 8, pp. 95235–95250, 2020.
    [11] J. Luo et al., "A fully analytical model for the performance prediction of radial permanent magnet eddy current couplers," IEEE Transactions on Energy Conversion, vol. 40, no. 1, pp. 505–514, 2024.
    [12] A. Sinmaz, M. O. Gulbahce, and D. A. Kocabas, "Design and finite element analysis of a radial-flux salient-pole eddy current brake," presented at the 2015 9th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey, November 26, 2015.
    [13] S. Cho, H.-C. Liu, H. Ahn, J. Lee, and H.-W. Lee, "Eddy current brake with a two-layer structure: Calculation and characterization of braking performance," IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1–5, 2017.
    [14] Y. Fan and G. Yang, "Design and analysis of magnetic circuit of permanent magnet eddy current brake," Vibroengineering Procedia, vol. 28, pp. 111–117, 2019.
    [15] L. Ye, D. Li, Y. Ma, and B. Jiao, "Design and performance of a water-cooled permanent magnet retarder for heavy vehicles," IEEE Transactions on Energy Conversion, vol. 26, no. 3, pp. 953–958, 2011.
    [16] S. Mohammadi and M. Mirsalim, "Design optimization of double-sided permanent-magnet radial-flux eddy-current couplers," Electric Power Systems Research, vol. 108, pp. 282–292, 2014.
    [17] M. Gulec, P. Lindh, M. Aydin, and J. Pyrhönen, "Cost minimization of a permanent magnet eddy current brake by multiobjective particle swarm optimization based on nonlinear reluctance network modeling," IEEE Access, vol. 9, pp. 157361–157370, 2021.
    [18] Y. Fan and G. Yang, "Design methodology of permanent magnet eddy current brake and optimization based on the Stackelberg game theory," Vibroengineering Procedia, vol. 55, pp. 226–232, 2024.
    [19] Voith Turbo SMI Technologies GmbH & Co. KG, "Better Braking Made Easy. The New Magnetarder," Voith Turbo SMI Technologies GmbH & Co. KG, Crailsheim, Germany, August 2012.
    [20] R. R. Sattarov, "The Controllable Eddy Current Brakes with Permanent Magnets: Basic Concept," presented at the 2018 X International Conference on Electrical Power Drive Systems (ICEPDS), Novocherkassk, Russia, October 3–6, 2018.
    [21] R. Yazdanpanah and M. Mirsalim, "Analytical study of axial-flux hybrid excitation eddy current brakes," International Journal of Applied Electromagnetics and Mechanics, vol. 47, no. 4, pp. 885–896, 2015.
    [22] R. Yazdanpanah, "Design and analysis of radial-flux hybrid excitation eddy current brake," presented at the 2019 10th International Power Electronics, Drive Systems and Technologies Conference (PEDSTC), Shiraz, Iran, February 12–14, 2019.
    [23] Y. Li, H. Lin, H. Yang, S. Fang, and H. Wang, "Analytical analysis of a novel flux adjustable permanent magnet eddy-current coupling with a movable stator ring," IEEE Transactions on Magnetics, vol. 54, no. 3, pp. 1–4, 2017.
    [24] Z. Li, L. Zhang, B. Qu, H. Yang, and D. Wang, "Evaluation and analysis of novel flux‐adjustable permanent magnet eddy current couplings with multiple rotors," IET Electric Power Applications, vol. 15, no. 6, pp. 754–768, 2021.
    [25] K. Deshan, W. Dazhi, L. Wenhui, W. Sihan, and H. Zhong, "Analysis of a novel flux adjustable axial flux permanent magnet eddy current coupler," IET Electric Power Applications, vol. 17, no. 2, pp. 181–194, 2023.
    [26] D. Kong, D. Wang, Y. Ni, K. Song, Y. Qi, and Y. Li, "Analytical Analysis of a Novel Flux Adjustable Permanent Magnet Eddy Current Coupling with Double-Sided Conductor," Actuators, vol. 12, no. 3, 2023, Art no. 105.
    [27] D. Yun and J.-H. Koo, "Design and analysis of an MR rotary brake for self-regulating braking torques," Review of Scientific Instruments, vol. 88, no. 5, 2017.
    [28] R. Sattarov and D. Garafutdinov, "Simulation of a Self-Regulating Eddy-Current Brakes with Permanent Magnets," presented at the 2021 International Ural Conference on Electrical Power Engineering (UralCon), Magnitogorsk, Russia, September 24–26, 2021.
    [29] C. J. Allington, A. K. Diehl, and B. J. Robertson, "Line dispensing device with eddy current braking for use with climbing and evacuation," United States Patent US8490751B2, 2013.
    [30] C.-F. Wu, "Design and Experiment of Self-Regulating Magnetic Brake for Descent Device," Master's thesis, National Cheng Kung University, Tainan, Taiwan, 2024.
    [31] D.-H. Kim, J.-W. Kim, and S. B. Choi, "Design and modeling of energy efficient dual clutch transmission with ball-ramp self-energizing mechanism," IEEE Transactions on Vehicular Technology, vol. 69, no. 3, pp. 2525–2536, 2020.
    [32] X. Chen, C. Li, Y. Han, B. Yuan, H. Zhang, and P. Hu, "A novel semi-active eddy current damper: design, modeling, and validation," International Journal of Mechanical Sciences, vol. 313, 2026, doi: 10.1016/j.ijmecsci.2026.111344.
    [33] T. Hanne and M. J. Moghaddam, "A review of the evolution of multi-objective evolutionary algorithms," Computers, Materials & Continua, vol. 85, no. 3, pp. 4203–4236, 2025.
    [34] Q. Zhang and H. Li, "MOEA/D: A multiobjective evolutionary algorithm based on decomposition," IEEE Transactions on Evolutionary Computation, vol. 11, no. 6, pp. 712–731, 2007.
    [35] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.
    [36] Y. Matsumoto, S. Yamasaki, and Y. Inoue, "One-degree-of-freedom planar link leg mechanisms design without predetermined trajectory using a genetic algorithm," Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 18, no. 6, pp. JAMDSM0075–JAMDSM0075,2024,doi: 10.1299/jamdsm.2024jamdsm0075.
    [37] Y. Matsumoto, S. Yamasaki, and Y. Inoue, "One-degree-of-freedom planer link leg mechanisms design method for multi objectives through NSGA-II," Mechanical Engineering Journal, vol. 13, no. 1, pp. 25–00278–25–00278, 2026, doi: 10.1299/mej.25-00278.
    [38] N. P. Vu, D. B. Vu, V. T. Dinh, D. Vu, and T. Q. Huy, "Optimizing Two-Stage Gear Design using NSGA-II with MATLAB: Multi-Objective Approach on Mass and Efficiency Trade-Off," Engineering, Technology & Applied Science Research, vol. 15, no. 3, pp. 23586–23591, 2025, doi: 10.48084/etasr.11162.
    [39] X. Fan, L. Yang, X. Zhao, G. Yan, Y. Yang, and H. Zhang, "Multi-objective optimization design of steel cross section of integrated supports and hangers based on NSGA-Ⅱ and MDOS," Journal of Building Engineering, vol. 98, 2024, doi: 10.1016/j.jobe.2024.111317.
    [40] J. Gieras, G. Dawson, and A. Eastham, "Performance calculation for single-sided linear induction motors with a double-layer reaction rail under constant current excitation," IEEE Transactions on Magnetics, vol. 22, no. 1, pp. 54–62, 1986.
    [41] L. Cat Eye Co., "キャットアイエルゴサイザー EC-L3200 取扱説明書," Cat Eye Co., Ltd., 2000.
    [42] J. C. Leask, "Eddy current braking system," United States Patent US 5,254,061, 1993.
    [43] K. Rajkumar, S. Vasudevan, and N. Subbiah, "A Comparative Study on the Brass-Steel Tribo-Pair under Dry and Lubricated Sliding Conditions," Applied Mechanics and Materials, vol. 852, pp. 416–421, 2016.
    [44] C. Panagopoulos, E. Georgiou, and K. Simeonidis, "Lubricated wear behavior of leaded α+ β brass," Tribology International, vol. 50, pp. 1–5, 2012.
    [45] E. Zitzler and L. Thiele, "Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach," IEEE transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999.
    [46] M. Li and X. Yao, "Quality evaluation of solution sets in multiobjective optimisation: A survey," ACM Computing Surveys (CSUR), vol. 52, no. 2, pp. 1–38, 2019.
    [47] C. A. C. Coello and N. C. Cortés, "Solving multiobjective optimization problems using an artificial immune system," Genetic programming and evolvable machines, vol. 6, no. 2, pp. 163–190, 2005.
    [48] M. Zelany, "A concept of compromise solutions and the method of the displaced ideal," Computers & Operations Research, vol. 1, no. 3-4, pp. 479–496, 1974.
    [49] L. Li, G.-L. Yang, and Z.-X. Li, "Magneto-thermal coupling analysis of the permanent magnet eddy current brake under intensive impact load," Vibroengineering Procedia, vol. 28, pp. 177–182, 2019, doi: 10.21595/vp.2019.21026.
    [50] C. Moosbrugger, ASM Ready Reference: Electrical and Magnetic Properties of Metals. Materials Park, OH: ASM International, 2000.

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