本論文主要在提出新的刀具運動策略，提昇液動壓拋光法(Hydrodynamic Polishing process; HDP)
對於小波長形狀誤差的補償能力，使該法能成為超高精度的加工技術。研究中針對軸對稱分佈的
工件表面輪廓，提出數種不同的刀具停留時間規劃法，同時對提出的各種法則進行電腦模擬，預
測工件表面的殘餘誤差。由不同法則所得到的模擬結果，可以初步分析不同規劃方式的可行性，
以及各法則對於小波長誤差的移除能力，並藉由給定的評估標準，分析各法則的限制並釐清各法
則的適用性。
研究的結果顯示，在所提的數種策略中，最佳化刀具停留時間規劃法可以有效改善波長接近
加工帶尺寸的誤差，且工件表面除了靠近外圍的區域，均能得到不錯的加工精度。對於波長更小
的誤差，最佳化法僅能提供有限的改善，且靠近工件外圍邊界區的誤差也只能做有限的改善而無
法透過該法則加以完全移除。

In this thesis, several machining strategies to remove axially symmetric form error with small wavelength
by Hydrodynamic Polishing process (abbreviated as HDP) were proposed.
Three strategies were proposed progressively in the study so as to remove axially symmetric form error
with small wavelength. The first and second tactics were based on a basic algorithm, say, directly solving of a
set of simultaneous equations. In the first strategy, a set of simultaneous equations was constructed by relating
the total machining action of each dwelling point to the corresponding initial error. Subsequently, a set of dwelling
time was obtained by directly solving the simultaneous equations. The second strategy evaluates solutions in a
similar way like the first one but more restrictions were concerned in solution evaluation. The third strategy is
an optimal based method. A set of dwelling time was obtained by minimizing an objective function with given
constraints.
A series of computer simulations were conducted to estimate the residual error and examine the validity of
the strategies. From the computer simulation, the first and second strategies were confronted with negative-time
problem, so that merely limited improving of form precision was obtained. The proposed optimal strategy was
shown to have high potential for improving the machining precision by the HDP process. Based on the proposed
strategies, a better form precision of the work surface with small wavelength can be obtained.

謝誌…………………………………………………………………………I
中文摘要 …………………………………………………………………II
英文摘要…………………………………………………………………III
目錄 ………………………………………………………………………IV
圖索引 ……………………………………………………………………VI

第一章 緒論………………………………………………………… 1
1.1 前言………………………………………………………… 1
1.2 液動壓拋光法……………………………………………… 3
1.3 研究動機與目的…………………………………………… 4
1.4 內容介紹…………………………………………………… 5

第二章 液動壓拋光法加工特性及軸對稱誤差補償原理 …………6
2.1 液動壓拋光法加工原理…………………………………… 6
2.2 加工率穩定性 …………………………………………… 7
2.2.1 潤滑特性的影響 …………………………………7
2.2.2 刀具表面特性及工件曲率效應的影響 …………8
2.2.3 工件材質的影響 …………………………………9
2.3 軸對稱形狀誤差補償……………………………………… 9
2.3.1 軸對稱形狀誤差補償的原理及數學模式 ………10
2.3.2 加工誤差 …………………………………………13

第三章 刀具停留時間直接規劃法 ……………………………… 14
3.1 刀具停留時間直接解法 ………………………………… 14
3.1.1 策略原理及數學模式 ………………………… 14
3.1.2 電腦模擬分析 ………………………………… 16
3.1.3 負時間成因探討 ……………………………… 17
3.2 修正刀具停留時間直接解法 …………………………… 19
3.2.1 策略原理 …………………………………………19
3.2.2 數學模式………………………………………… 21
3.2.3 電腦模擬分析…………………………………… 23
3.3 結果討論 ………………………………………………… 27
第四章 最佳化刀具停留時間規劃法 …………………………… 28
4.1 策略原理及數學模式 ………………………………… 28
4.2 電腦模擬分析 ………………………………………… 30
4.2.1 幾何特性的影響 ……………………………… 31
4.2.2 界外點的影響 ………………………………… 34
4.2.3 遞迴法則的原理與應用 ……………………… 36
4.3 小波長形狀誤差補償探討 ……………………………… 41
4.4 結果討論 ………………………………………………… 44

第五章 結論 ……………………………………………………… 45

參考文獻 ………………………………………………………………47

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