本論文主要在於研發一套高效率的線拋光方法，用以進行精密拋光。此拋光系統主要由一施力機構、工件、以及帶狀拋光墊所組成。經由適當的操控，該施力機構可在拋光墊與工件接觸處產生任意的壓力分布，而調整加工率分布。該加工特性結合形狀誤差補償策略將可工件上的表面誤差精確的移除，而提升工件精度。

　　文中利用有限元素法進行模擬分析，建立出施力分布與壓力分布的關係。透過現象的觀察與分析，找出適當的設計參數，建立出施力分布與壓力分布之間的數學關係式。當希望的壓力分布給定時，施力分布將透過解聯立方程式或最小平方誤差法來求解。並且探討不同波長的效應，與不同振幅波動波長的效應。並透過重現性、負載分布與加工率關係及工件轉速與加工率關係實驗來探討與驗證此拋光法的可行性與特性。

　　經由模擬與實驗得到四個結論。第一：凹、凸、平三種曲面皆可透過施力機構在拋光墊與工件接觸處得到壓力分布；第二：建立出施力分布與壓力分布的方程式；第三、根據Shannon sampling theorem可以滿足制動器數目對應波長變化的負載分布；第四、實驗證實該法具有高重現性。透過拋光墊的壓力分析，得到最佳的設計參數來建立施力分布與壓力分布的數學關係式。並且依據Shannon sampling theorem來分析得到在固定的制動器數目下所會造成負載分布。透過實驗可知拋光方法具有高重現性，且加工率會隨著工件轉速越高而變大；加工率也隨著負載增大而變大。

This study aims to develop a precision polishing system with high machining rate efficiency. The system is mainly composed of a loading mechanism, a work piece and a polishing pad with belt-shape. The loading mechanism is to generate a specific pressure distribution between the pad and the work surface.　Such a pressure distribution is to render the machining rate distribution, along the contact zone between pad and work surface, capable of compensating the work surface error.　With the capability of accurately removing the work surface error left by the previous machining method, this polishing system can improve the form precision of work and become an effective high precision machining tool.
In this thesis, the relation between the applied loadings and the pressure distribution were established by the finite element method.　A linear model described this relation with the applied loading as the input and the desired pressure distribution as the output. The unknown coefficients of the model were then derived from the simulation data by the finite element method. When a desired pressure distribution was given, the applied loadings could be solved from the model by either the simultaneous equation method or the least squared error method.　A main issue to investigate in the study was to examine whether a pressure distribution with an arbitrary wavelength spectrum could be obtained by the proposed scheme. A detailed analysis about the effect of wavelength in pressure distribution on the precision of loading estimation was done.
Four conclusions could be made from the study.
1.The proposed polishing system can be applied to a free surface with either concave or convex geometrical features
2.The proposed linear model can suggest proper loadings to generate desired pressure distribution with good precision if the wavelength of pressure distribution is large enough.
3.The Shannon sampling theorem can be used to give a qualitative description of the properness of the model in generating a desired pressure distribution.
4.The proposed polishing method has a high machining repeatability when the operating condition is well controlled.

謝誌 I
目錄 II
圖索引 V
表目錄 VIII
中文摘要 IX
ABSTRACT X
第ㄧ章　緒論 １
1.1　研究動機與方法 １
1.2　拋光的特性 ４
1.3　現有拋光法之回顧 ５
1.4　內容介紹 ６
第二章　自由曲面之拋光系統設計 7
2.1　自由曲面拋光方法概念 7
2.1.1　拋光加工法的加工行為須具高重現性 7
2.1.2　高效率拋光 7
2.1.3　加工區域的加工率分布需具可控制性 9
2.2　前一代可變壓力之線拋光法之設計 9
2.3　新一代可變壓力之線拋光法 10
2.3.1　自由曲面拋光法要件 10
2.3.2　可變壓力之線拋光設計概念 12
第三章 凹凸平不同曲面的基本特性分析 15
3.1 　凸的曲面之壓力分布 15
3.2 　凹的曲面之壓力分布 16
3.3 平的曲面之壓力分布 16
第四章　拋光墊的特性分析 18
4.1　壓力分布現象之探討 18
4.2　施力分布與壓力分布關係建立 22
4.2.1　壓力疊加法 22
4.2.2　泰勒展開式方法 23
第五章　拋光墊的壓力分析 26
5.1　不同波長的實際壓力分布與希望得到的壓力分布比較 26
5.1.1　Shannon sampling theorem對應不同波長的誤差 26
5.1.2　兩種關係式對波長變化的比較 28
5.1.3　雙波長的壓力分布探討 28
5.2　不同滾柱參數及拋光墊參數能接受的最小波長 29
5.2.1　小振幅波動波長得到可接受的最小波長 30
5.2.2　大振幅得到可接受的最小波長 31
第六章 拋光特性之實驗分析 33
6.1　實驗規劃 33
6.2　實驗與量測設備 34
6.2.1　實驗設備簡介 34
6.2.2　實驗材料實驗設備簡介 34
6.3　實驗結果與討論 35
第七章　總結與未來展望 36
7.1　各章節之總結 36
7.2　未來展望 37

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