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研究生:陳宏原
研究生(外文):Hong-Yuan Chen
論文名稱:往復移動式表面加熱之導螺桿熱傳分析
論文名稱(外文):Heat transfer analysis of ballscrew with oscillatory surface heating
指導教授:洪振益洪振益引用關係
指導教授(外文):Chen-I Hung
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:59
中文關鍵詞:導螺桿往復式表面加熱格林函數
外文關鍵詞:oscillatory surface heatingGreen’s functionballscrew
相關次數:
  • 被引用被引用:4
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導螺桿在機械加工機中為一常見驅動機構,其作用是將旋轉運動轉變為直線運動。現今導螺桿多為滾珠式導螺桿,此類導螺桿摩擦係數較低,但長時間運轉後仍會產生溫升,進而影響到定位精確性。本研究以數值模擬及解析解兩種方法建立出導螺桿溫升模型,並探討溫升之發展情形。

本文模擬導螺桿在不同進給速度之溫升,並以熱像儀量測導螺桿表面溫度。對導螺桿而言螺帽相當於一熱源,因螺帽進行往復移動,故此為移動熱源問題,在數值模擬中因無法直接處理移動項,故以變動邊界處理移動熱源條件;然而在解析解中則可直接考慮熱源移動所產生的效應,其中解析解的推導方式中採用具系統化的Green’s Function來推導。

與實驗相比,數值模擬與解析解之結果與實驗數據相當吻合。此外,由計算結果可知在初期導螺桿之溫升約略呈線性,隨著運轉時間的拉長,溫升速率會漸緩。而由解析解則可進一步得知導螺桿的表面軸向溫度分布則會逐漸呈現鐘形,其溫度的最高點在往復移動區的中央部份。另一方面由徑向溫度分布可發現導螺桿表面與軸心間溫度差幾乎相同,可視為溫差僅會隨著軸向變化。
A lead-screw is a common driving mechanism in machine tools, and it translates rotational motion to linear motion. Nowadays a ballscrew is usually used instead of a lead-screw. This kind of screw has smaller friction coefficient, but under long time running there is still temperature rise on the ballscrew. The temperature rise will induce thermal expansion and affect the positioning accuracy. This study uses numerical simulation and analytical solution to construct temperature rising model of ballscrew, and investigates the development of temperature rising.

This study simulates temperature rise of ballscrew under different feed rates, and the surface temperature of ballscrew is measured by infrared thermograph. For a ballscrew the nut is regard as a heat source, and it’s a moving heat source problem because the nut reciprocates on the ballscrew. In numerical simulation the moving heat source cannot be handled directly, so it is treated as a variable boundary condition. However, it can be considered directly in analytical solution, and systematic Green’s Function is used to derive analytical solution.

Compared with experimental data, numerical results and analytical solutions show good agreement. Besides, from the computational results the tendency of temperature rise of ballscrew is approximately linear in the beginning; however, it slows down as the operating time getting longer. And further, from analytical solutions, the surface axial temperature distribution of ballscrew grows like a bell, where the highest temperature appears at the center of heating region. On the other hand, radial temperature distribution shows that the surface temperature and axis temperature of ballscrew are almost the same, and it can be seen as the temperature rise varies along axial direction only.
中文摘要...................................................................................................I
英文摘要................................................................................................. II
誌謝........................................................................................................IV
目錄......................................................................................................... V
表目錄...................................................................................................VII
圖目錄................................................................................................. VIII
符號說明...............................................................................................XII
第一章 緒論............................................................................................ 1
1-1 研究動機與目的........................................................................ 1
1-2 文獻回顧.................................................................................... 4
1-3 研究流程.................................................................................... 7
1-4 本文架構.................................................................................... 8
第二章 理論分析.................................................................................... 9
2-1 物理模型.................................................................................... 9
2-2 數學模型.................................................................................. 11
2-3 數值模擬.................................................................................. 12
2-4 解析解...................................................................................... 14
VI
第三章 結果與討論.............................................................................. 21
3-1 格點驗證.................................................................................. 21
3-2 數學模型驗證.......................................................................... 22
3-3 參數探討.................................................................................. 26
第四章 結論與未來展望...................................................................... 28
4-1 結論.......................................................................................... 28
4-2 未來展望.................................................................................. 29
參考文獻................................................................................................ 30
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[5]廖子恩, “滾珠螺桿溫昇熱變位量測之研究,”國立中正大學機械工程研究所碩士論文, 2000.

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[8]魏進忠, “單螺帽雙圈滾珠螺桿在預負荷及潤滑作用條件下運動機制與機械性能的理論分析及實驗印證, ”國立成功大學機械工程學系博士論文, 2003.

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