線接觸車削加工真空泵變導程螺桿轉子之研究

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姓名

曾玟鈞(WEN-CHUN TSENG) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

線接觸車削加工真空泵變導程螺桿轉子之研究
(A Study on Applying Line-contact Turning to Manufacture Variable-pitch Screw Rotors of Vacuum Pumps)

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至系統瀏覽論文 (2029-1-30以後開放)

摘要(中)

螺旋式真空泵（screw vacuum pump）是利用一對嚙合的螺桿轉子之間的封閉齒腔來抽送空氣，以達到所需的真空度，其廣泛應用於工業、半導體產業、化學化工產業和生物科技。在真空泵中，螺桿轉子可分為定導程和變導程兩種類型，相較於定導程螺桿轉子，變導程螺桿轉子具有更優越的壓縮性能和更高的設計彈性。然而，由於變導程轉子的輪廓會受到導程變化的影響，進而使其瞬間接觸線也會隨著導程的變化而有所改變，使成型磨無法用於變導程轉子上，因而提高變導程螺桿轉子的加工難度。過去，變導程螺桿轉子的精加工通常是使用CNC數控與傳統車刀，通過多次點接觸的方式加工變導程螺桿轉子的齒面。本研究提出利用線接觸的方式加工變導程螺桿轉子的齒面，由於是透過線接觸的方式加工，於加工時經由一次軸向進給就可完成一側齒面的加工，達到更精確、更有效率的加工方式。首先，建立變導程螺桿轉子的泛用加工座標系統，並基於變導程螺桿轉子的齒形輪廓在任意旋轉角度下，幾何都維持不變，由這項原則取螺桿轉子的齒形輪廓做為刃口線幾何。接著透過數值計算軟體求解變導程螺桿轉子後，將結果與標準轉子進行比較，以驗證模型的正確性。此外，還使用有限元素軟體和均勻設計法來探討刀具斷屑槽對於切削產生的切屑影響。

摘要(英)

The screw vacuum pump utilizes a pair of interlocking screw rotors within a closed chamber to evacuate air and achieve the desired level of vacuum. It is widely used in industries such as manufacturing, the semiconductor industry, chemical processing, and biotechnology. In vacuum pumps, the screw rotors can be categorized into fixed-pitch and variable-pitch types. Compared to fixed-pitch screw rotors, variable-pitch screw rotors exhibit superior compression performance and greater design flexibility. However, due to the variation in pitch, the profile of variable-pitch screw rotors is influenced by changes in pitch, causing the instantaneous contact line to also change with the variation in pitch. This renders the use of form grinding impractical for variable-pitch rotors, thereby increasing the difficulty in the machining of variable-pitch screw rotors.
In the past, precision machining of variable pitch screw rotors typically involved the use of CNC (Computer Numerical Control) and conventional turning tools, processing the variable pitch screw rotor through several times point contacts. In contrast to the traditional method, this study proposes a machining technique utilizing a line contact approach for the tooth profile of variable pitch screw rotors. Compared to traditional machining methods, this approach completes the entire tooth profile with a single axial feed, achieving a more precise and efficient machining process.
Firstly, a general machining coordinate system for variable-pitch screw rotors is established. Based on the principle that the tooth profile of variable-pitch screw rotors remains unchanged at any rotational angle, the tooth profile of the rotor is used as the cutting edge geometry. Subsequently, numerical calculations are performed using software to solve for the variable-pitch screw rotor, and the results are compared with a standard rotor to validate the model′s accuracy. Additionally, finite element software and uniform design methods are employed to investigate the influence of tool chip grooves on the chips produced during cutting.

關鍵字(中)

★ 螺桿轉子
★ 變導程
★ 線接觸
★ 有限元素軟體(FEM)
★ 均勻設計法

關鍵字(英)

★ Screw Rotor
★ Variable Pitch
★ Finite Element Analysis
★ Experimental Design Method

論文目次

摘要 i
Abstract ii
謝誌 iv
目錄 v
圖目錄 viii
表目錄 xi
符號對照表 1
第1章緒論 3
1-1 前言 3
1-2 文獻回顧 6
1-3 研究目的 7
1-4 論文架構 8
第2章變導程螺桿轉子數學模型之建模 9
2-1 轉子齒面數學模型 9
2-2 變導程曲線設計 12
2-2-1 線性變導程曲線設計 12
2-2-2 非線性變導程曲線設計 14
2-3 雙螺桿變導程轉子之間隙計算 15
2-3-1 齒間間隙計算 15
2-3-2 間隙調整 17
2-4 線接觸刀具數學模型之建立 18
2-5 變導程轉子之泛用加工坐標系統建立 20
2-6 車削刀具設計 23
2-6-1 斷屑裝置 24
2-7 本章結論 25
第3章多軸數控加工機數學模型 26
3-1 CNC多軸加工機座標建立 26
3-2 泛用加工座標系統與機台座標系統之參數關係 28
3-3 基於機台模擬轉子輪廓 29
3-4 本章結論 30
第4章數值範例 31
4-1 齒間間隙 31
4-2 線性變導程螺桿轉子範例 35
4-2-1 MATHEMATICA數值計算軟體之計算結果 36
4-3 非線性變導程螺桿轉子範例 38
4-3-1 MATHEMATICA數值計算軟體之計算結果 40
4-4 本章結論 41
第5章刀具斷屑槽幾何分析 42
5-1 切削模擬 42
5-1-1 模型建立 42
5-1-2 有限元素模型之建立 43
5-1-3 網格劃分 44
5-1-4 材料本構模型 45
5-1-5 切削模擬結果 47
5-2 刀具斷屑槽幾何之影響 49
5-2-1 均勻實驗法 49
5-3 模擬結果與數據 50
5-4 應用ISIGHT建立近似模型 51
5-5 近似方程式建立 55
5-5-1 近似模型結果之最佳解 58
第6章總結與未來展望 59
6-1 總結 59
6-2 未來展望 60
參考文獻 61
附錄一 64
作者介紹 69

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指導教授

吳育仁(Yu-Ren Wu)

審核日期

2024-1-29

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