單螺桿壓縮機轉子對之幾何設計及加工方法之建立

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姓名

張銘哲(Ming-Zhe Zhang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

單螺桿壓縮機轉子對之幾何設計及加工方法之建立
(Establishment of Design and Manufacture Methods on Rotor Pairs for Single-Screw Compressors)

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至系統瀏覽論文 (2026-8-30以後開放)

摘要(中)

單螺桿壓縮機(Single screw compressor, SSC)是由一單螺桿轉子及與其嚙合之兩星輪(Star wheel)在密閉機殼中運轉，達到吸氣、壓縮及排氣功能，現今已廣泛應用於空調製冷、國防軍事領域。然而星輪齒面易磨損、製造困難及加工精度低等因素，往往是此種壓縮機待解決之問題。有鑑於此，本文建立單螺桿轉子對之齒面創成數學模型，產生直線包絡嚙合對(Line envelope meshing pair, LEMP)與圓柱包絡嚙合對(Column envelope meshing pair, CEMP)的嚙合齒面，並提出提升星輪齒面接觸面域之最佳化方法，以改善單螺桿壓縮機之磨耗情形。為了找出單螺桿轉子對之最佳設計參數，本研究透過均勻設計法(Uniform design)和ISIGTH軟體建立徑向基函數(Radial basis function, RBF)之近似模型，以探討控制因子對於接觸面域之影響；接著，基於RBF模型以內點懲罰函數法進行最佳化，並比較最佳化前後接觸面域之改善程度。此外，根據單螺桿轉子對幾何模型建立相對應加工刀具之數學模型，並經由泛用加工座標系統與CNC加工機台座標系統之加工運動一致性，推導出各加工軸運動方程式，亦透過VERICUT軟體進行虛擬CNC機台切削模擬，最後確認數值計算結果與切削模擬結果是否吻合，以驗證本文提出理論模型之正確性。

摘要(英)

A single screw compressor (SSC) comprises a main screw rotor and two star wheels. It is widely used in many fields, including air compression, refrigeration and defense industry. However, the factors such as the abrasion on the star wheel teeth, difficulty in manufacturing and low-accuracy in machining process are often an important issue to be solved. This study establishes a mathematical model to design geometries of the main screw rotor and the star wheels. The design methods of line envelope meshing pair (LEMP) and column envelope meshing pair (CEMP) are developed. A numerical method is proposed to enhance the contact area and improve the tooth wear problem. Moreover, this study aims to propose a novel manufacturing method for star wheels and main screw rotor of single screw compressors based on a CNC machine with the cutter. The geometric models of two kinds of rotors and the cutter design are constructed firstly, and then the rotor profiles are generated by the cutter according to a relative motion coordinate system established based on the novel CNC machine. The motion equation of each machining axis is derived for cutting the line- and column-sided tooth profiles of star wheels and main screw rotor. In addition, the cutting simulations are performed and the normal profile deviation of tooth side profile for two rotors is analyzed to verify the effectivity of the proposed theoretical models.

關鍵字(中)

★ 單螺桿壓縮機
★ CNC加工機
★ 接觸面域
★ 切削模擬
★ 法向齒廓誤差

關鍵字(英)

★ single screw compressor
★ CNC machine
★ contact area
★ cutting simulation
★ normal profile deviation

論文目次

摘要 I
ABSTRACT II
謝誌 III
圖目錄 VII
表目錄 X
符號對照表 XI
第1章緒論 1
1-1 研究背景 1
1-2　文獻回顧 3
1-3　研究動機與目的 5
1-4　論文架構 5
第2章轉子幾何模型建立與星輪接觸面域計算 7
2-1　單螺桿壓縮機之轉子對數學模型建立 7
2-1-1　星輪齒廓種類 7
2-1-2　直線包絡嚙合對 8
2-1-3　圓柱包絡嚙合對 15
2-2　星輪齒面之接觸面域計算 18
2-3　轉子幾何參數對圓柱星輪齒面的接觸面域之影響 19
2-3-1　均勻設計試驗法 19
2-3-2　徑向基函數 22
2-3-3　平均絕對誤差百分比 23
2-3-4　近似模型之影響指數 23
2-3-5　接觸面域之最佳化設計 24
第3章星輪之創新加工數學模型建立 27
3-1　泛用加工座標系統之建立 27
3-2　盤式銑刀之刃口幾何設計 28
3-3　五軸CNC加工機座標系統建立 32
3-4　泛用座標系統與機台座標系統之參數關係 34
3-5　星輪虛擬切削模型之建立 35
第4章螺桿之創新加工數學模型建立 37
4-1　飛刀之刃口幾何設計 37
4-2　飛刀創成螺桿工件之泛用座標系統建立 46
4-3　五軸CNC加工機座標系統建立 48
4-4　泛用座標系統與機台座標系統之參數關係 49
4-5　螺桿之虛擬切削模型建立 50
4-6　法向齒廓誤差分析 51
4-6-1　法向齒廓誤差分析流程與簡介 51
4-6-2　法向齒廓誤差分析方法 52
第5章數值範例 53
5-1　直線包絡嚙合對創生、切削模擬及模型驗證 53
5-1-1　直線包絡嚙合對之加工範例 53
5-1-2　單線星輪之法向齒廓誤差分析 57
5-1-3　直線包絡嚙合對的螺桿齒槽之法向齒廓誤差分析 59
5-2　圓柱包絡嚙合對創生、切削模擬及模型驗證 61
5-2-1　圓柱包絡嚙合對之加工範例 62
5-2-2　圓柱星輪齒廓之法向齒廓誤差分析 68
5-2-3　圓柱包絡嚙合對的螺桿齒槽之法向齒廓誤差分析 70
5-3　圓柱星輪之齒面接觸面域最佳化設計 72
5-3-1　控制因子與近似模型之影響 73
5-3-2　最佳化之結果分析與探討 74
第6章總結與未來展望 76
6-1　總結 76
6-2　未來展望 77
參考文獻 78
附錄 80
附錄一　單線星輪之切削誤差比對 80
附錄二　圓柱星輪之切削誤差比對 81
附錄三　粗加工LEMP螺桿之切削誤差比對 82
附錄四　精加工LEMP螺桿之切削誤差比對 83
附錄五　粗加工CEMP螺桿之切削誤差比對 84
附錄六　精加工CEMP螺桿之切削誤差比對 85
附錄七　VERICUT切削模擬 86
附錄八　加工單螺桿轉子對之NC程式 90
作者介紹 94

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指導教授

吳育仁(Yu-Ren Wu)

審核日期

2021-8-25

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