擺線減速機(Cycloidal Reducers)在工業上運用甚廣，具有高減速比、體積小及乘載能力大等特點，本研究的主要目的在於解決傳統機械式擺線齒輪的接觸產生的磨耗問題，以永磁體的磁場耦合代替機械齒輪的嚙合為研究目標。為了降低高速軸的徑向承受力，本文採用擺相斥極性的永磁體排列來當作本研究的分析模型。
以建立擺線齒輪的線速度等式，來探討減速關係。在計算磁轉矩方面，於計算磁通密度分佈的過程中加入偏心條件，得出其基本波值解。在有限元素模擬方面，將擺線齒輪模型以正齒輪運動模式作其靜磁場分析及暫態分析，並評估永磁體展開角角度設計，將其進行諧波分析，進而確定偏心對於磁場調製的影響，以期能得到更佳的傳動性。最後，探討擺線磁性齒輪減速機在失步時所能承受得最大扭矩值，稱其為「滑移扭矩值(Slip Torque)」。
在數學的模型建立基礎上，利用Ansys Maxwell 2D建立擺線磁性齒輪建模計算，並與偏微分解進行對照驗證，實現了對於擺線磁性齒輪減速機的滑移扭矩值的研究。最終，將模擬結果與實測扭矩進行比對，總結了擺線磁性齒輪滑移扭矩值的計算、模擬及實測的結論。

Cycloidal reducers are widely adopted in industry for their high reduction ratio, compact size, and robust load capacity. This research aims to address wear issues associated with traditional mechanical cycloidal gears by proposing a magnetic field coupling approach using permanent magnets. This method seeks to replace mechanical gear meshing with magnetics interaction to mitigate radial bearing force on the high-speed shaft. The configuration employs repelling polarity permanent magnets on both the cycloidal magnetic gear and the outer ring magnetic gear.
The study establishes the linear velocity equation of the cycloidal gear to analyze deceleration relationships. Magnetic torque calculations consider eccentricity conditions to determine the basic wave value of the magnetic flux density distribution. The cycloidal gear model is simulated using finite element analysis in the spur gear motion mode, encompassing static and transient magnetic field analysis. The design of the permanent magnet expansion angle is evaluated, while and harmonic analysis is performed to assess the impact of eccentricity on magnetic field modulation for improved better transmission performance.
Furthermore, the study also investigates the “slip torque,” the maximum torque that the cycloidal magnetic gear reducer can sustain when out of step. Using ANSYS Maxwell 2D, the mathematical model of the cycloidal magnetic gear is established, and its calculations are compared and verified with partial differential decomposition. The study concludes by comparing simulation results with measured torque to summarize the findings on the slip torque value of the cycloidal magnetic gear reducer.

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