### 博碩士論文 110323006 詳細資訊

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(Mathematical Modeling of Five-axis CNC Machining Based on Duplex Helical Method for Spiral Bevel Gears)

 ★ 應用調諧顆粒阻尼器於迴轉式壓縮機振動抑制之研究 ★ 應用離散元素法與多體動力學於齒輪傳動系統動力分析模型之建立 ★ 不同氣體負載下雙螺桿壓縮機動力響應及振動頻譜特徵之預測 ★ 新型魯氏真空泵轉子齒形之參數化設計及性能評估 ★ 以CNC內珩齒機進行螺旋齒輪齒面拓樸修整之研究 ★ 雙螺桿壓縮機變導程轉子齒間法向間隙之數值計算方法及其三維幾何模型驗證 ★ 不同工作條件下冷媒雙螺桿壓縮機之轉子受力分析及動載響應預測 ★ 應用多體動力學及離散元素法於具阻尼顆粒齒輪及軸承系統抑振之研究 ★ 具齒廓修形內嚙合非圓形齒輪創成之方法建立與其傳動誤差分析 ★ 雙螺桿壓縮機於CFD仿真模擬之三維幾何簡化方法建立 ★ 航空發動機齒輪箱傳動系統之強度分析與改善 ★ 電動車差速齒輪傳動系統之動載分析與性能評估 ★ 指狀銑刀安裝偏差對真空泵螺桿轉子加工精度影響之研究 ★ 以CNC內珩齒機加工具鼓形之錐狀齒輪之研究 ★ 應用阻尼顆粒於旋轉機械之振動抑制及動平衡設計 ★ 考量氣體負載下迴轉式壓縮機動態負載分析模型之建立

Because of the complex shape and various calculation methods associated with spiral bevel gears, beginners often find it challenging to comprehend. Therefore, this study aims to develop a comprehensive mathematical model for the design and manufacturing of spiral bevel gears. In the research, is based on inverse kinematics to establish a mathematical model for face-milling of spiral bevel gears and applied to CNC cutting machines, starting from the coordinate system of universal gear cutting machines. However, due to the mysterious mechanical settings for cutting of Spiral gears, particularly the duplex helical cutting method, which is less revealed in the literature, this study, based on disclosed fundamental mechanical principles, research for a duplex helical cutting method to create a mathematical model for spiral bevel gears. Subsequently, the model is implemented on a vertical five-axis CNC machine, and the accuracy of the calculated tooth surface model is confirmed through validation. To promptly evaluate tooth contact outcomes for assessing tooth surface performance, the generated spiral bevel gear model is employed to create an approximate tooth surface model within the gear simulation software KISSsoft. Following this, simulations for tooth surface load contact are conducted. Furthermore, finite element tooth contact simulations are utilized to validate the accuracy of the contact simulation results obtained from KISSsoft.

★ 面銑式加工
★ 雙面雙切削法
★ 負載接觸模擬
★ KissSoft

★ Face-milling
★ Duplex helical method
★ Tooth contact analysis
★ Five-axis CNC machine
★ KissSoft

ABSTRACT ii

1-1 前言 1
1-2 文獻回顧 4
1-3 研究目的與動機 6
1-4 論文架構 7

2-1 傘齒輪之幾何設計 9
2-2 傘齒輪之幾何參數 13
2-3 總結 18

3-1 面銑式刀盤模型之建立 19
3-2 面銑式泛用加工座標系統之建構 24
3-3 應用立式五軸CNC加工機座標系統之建構 29
3-4 相對共軛齒面模型之建立 33
3-5 總結 36

4-1 假想產形輪 38
4-2 平頂假想產形輪 39
4-3 錐形假想產形輪 43
4-4 基於雙面雙切削法創成傘齒輪 53
4-5 總結 55

5-1 螺旋傘齒輪模型參數範例 57
5-2 傘齒輪齒面拓樸網格點之劃分 66
5-3 螺旋傘齒輪模型之驗證 66

6-1 KISSsoft傘齒輪之數學模型 76
6-2 KISSsoft近似齒面模擬模型之建立 77
6-3 KISSsoft負載齒面接觸模擬實驗 81
6-4 有限元素等效齒面模型之比對 88

7-1 總結 95
7-2 未來展望 96

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