本文將電腦輔助製造軟體所轉出之刀具路徑資料，再與電腦輔助分析前處理軟體之工具設定與料片邊界條件做結合。採用動顯函有限元素法進行單點增量成形數值分析，以瞭解工件在成形歷程中所發生的厚度分佈、應力與應變分佈，及成形負荷變化。並設計一組含拉伸扣緣之圓柱形壓料板與夾具，經由數控銑床進行單點增量成形實驗，用以驗證本文有限元素數值分析程式之可靠性。
   經由數值模擬與實驗結果比較得知，當設定不同工具轉速與工件進給速率進行45度圓錐杯成形時，於工具轉軸靜止，且工件進給速率為800 mm/min時，成形效果最佳。當工件進給速率遞增時，於錐杯底部圓弧角處的厚度有明顯薄化現象。橢圓錐杯的長軸與短軸分別與拉伸扣緣之距離不同，導致長軸傾斜壁所得的厚度分佈優於短軸。若提高工件進給速率，將可改善短軸傾斜壁之厚度分佈。當圓錐杯與橢圓錐杯隨著傾斜角增加，將導致板材厚度引薄，並使等效應力、等效應變，及成形負荷隨之遞增。成形後工件的最佳表面粗糙度分別為0.30 μm與0.34 μm，隨著傾斜角與加工深度增加，成形工件之表面粗糙度值就愈大。
   本文採用的加工條件分別為螺旋線漸進式刀具路徑、工具轉軸靜止、提高工件進給速率，與注入冷卻潤滑液等，可提升圓錐杯與橢圓錐杯之成形性，並顯著改善工件之表面粗糙度，而數值分析結果皆可合理的模擬實驗結果，故本文之電腦輔助分析程式，皆可合理的預測單點增量成形製程。

In this study, the toolpath data exported from a computer aided manufacturing software are combined with the tool settings and material sheet boundary conditions of a computer aided analysis pre-processing software. A dynamic explicit finite element method is adopted for numerical analysis of single point incremental forming to predict the thickness distribution, stress and strain distribution, and changes in forming load during the forming process of workpieces. A set of cylindrical blankholder and binder with drawbead is designed, and a single point incremental forming experiment is conducted using a CNC milling machine to verify the reliability of the finite element numerical analysis program adopted in this study.
   By comparing the results from numerical simulation and experiments, it is evident that when different tool spindle speeds and workpiece feed rates are set to 45˚ circular cone cup forming, the forming effect is optimal if the tool spindle is stationary and workpiece feed rate is 800 mm/min. When the feed rate of the workpiece increases, the thickness at the arc corner at the bottom of the circular cone cup is significantly decreased. The distances from the long axis and short axis of the elliptical cone cup to the draw beads are different. Thus, the thickness distribution of inclined wall along the long axis is better than that along the short axis. If the workpiece feeding rate is increased, then the thickness distribution of the inclined wall along the short axis can be improved. As the inclination angles of the circular cone cup and elliptical cone cup increase, the thickness of the sheet material and the equivalent stress, equivalent strain, and forming load simultaneously increase. The optimal surface roughness of the formed workpieces is 0.30 μm and 0.34 μm. As the inclination angle and processing depth increase, the surface roughness of the formed workpieces increases.
   The processing conditions adopted in this study involve spiral progressive tool path, stationary tool spindle, increasing workpiece feed rate, and injecting cooling lubricant. These processing conditions can improve the formability of a circular cone cup and elliptical cone cup and significantly improve the surface roughness of workpieces. The numerical analysis results can reasonably simulate the experiment results. Therefore, the computer aided analysis program adopted in this study can reasonably predict single point incremental forming processes.

中文摘要	I
英文摘要	III
目    錄	V
圖表索引	VIII
第一章 緒論	1
1.1前言	1
1.2研究動機與目的	2
1.3文獻回顧	4
1.4論文之構成	17
第二章 基本理論	19
2.1基本假設	19
2.2 Updated Lagrangian Formulation之虛功率原理方程式	19
2.3單點增量成形製程中應力與應變	21
2.3.1圓周方向	23
2.3.2板厚方向	23
2.3.3子午線方向	24
2.3.4軸對稱圓錐杯旋轉對稱平面應變	25
2.4 殘餘高度、工具轉速與進給速率	29
2.5單點增量成形之成形性	31
2.6表面粗糙度	32
第三章 有限元素分析	34
3.1動顯函有限元素法	34
3.1.1有限元素近似解	34
3.1.2節點之內力、外力及慣性力	36
3.1.3運動方程式	37
第四章 不同輪廓錐杯之成形實驗與數值分析	38
4.1實驗設備	38
4.2實驗原理與步驟	45
4.3 數值模擬分析	51
4.4邊界條件	54
4.5材料參數	55
4.6數值模擬與實驗結果之比較	55
4.6.1工具轉速與工件進給速率對 圓錐杯厚度分佈
     之比較	56
4.6.2 銑削方向對 圓錐杯厚度分佈之比較	65
4.6.3工具轉速與工件進給速率對 圓錐杯厚度分佈
     之比較	66
4.6.4工具轉速與工件進給速率對橢圓錐杯厚度分佈
     之比較	69
4.6.5 圓錐杯於不同傾斜角之厚度、等效應力與等效應變
     之分佈	77
4.6.6 橢圓錐杯於不同傾斜角之厚度、等效應力與等效應變
     之分佈	86
4.6.7 不同輪廓錐杯成形負荷之比較	91
第五章 加工條件於不同輪廓錐杯表面粗糙度之比較	97
5.1表面粗糙度與冷卻潤滑液	97
5.2實驗步驟	99
5.3不同輪廓錐杯量測後表面粗糙度之比較	101
5.3.1 銑削方向對圓錐杯表面粗糙度之比較	102
5.3.2 冷卻潤滑液對不同輪廓錐杯表面粗糙度之比較	106
5.3.3 工具轉速與工件進給速率對不同輪廓錐杯
     表面粗糙度之比較	111
第六章 結論與未來展望	119
6.1 結論	119
6.2 未來展望	121
參考文獻	122
符號索引	131
圖2-1  物體變形前後及內部應力之不連續曲面	20
圖2-2  單點增量成形平面應變示意圖[2]	22
圖2-3  單點增量成形薄殼元素示意圖[2]	23
圖2-4  旋轉軸對稱拉伸BC斷面示意圖[2]	...26
圖2-5  殘餘高度示意圖[52]	30
圖2-6  單點增量成形横剖面示意圖	32
圖2-7  中心線平均粗糙度示意圖	33
圖4-1  單點增量成形電腦輔助分析流程圖	39 
圖4-2  實驗設備之整體系統配置圖	41
圖4-3  單點增量成形製程夾具配置圖	41
圖4-4  直徑8 mm半球頭工具	42
圖4-5  單點增量成形夾具之底板	42
圖4-6  單點增量成形夾具之壓料板	43
圖4-7  單點增量成形之料片直徑150.0 mm	43
圖4-8  單點增量成形夾具之固定方式	44
圖4-9  利用尋邊器校正夾具之底板	44
圖4-10 單點增量成形料片位置校正	47
圖4-11 單點增量成形Z軸方向校刀	47
圖4-12 單點增量成形加工前再次確認	48
圖4-13 水溶性太古油潤滑液	48
圖4-14 CNC線切割機	48
圖4-15 CNC線切割完成二分之一片圓錐杯	49
圖4-16 CNC線切割完成四分之一片橢圓錐杯	49
圖4-17  圓錐杯厚度量測之位置圖	49
圖4-18  圓錐杯厚度量測之位置圖	50
圖4-19 橢圓錐杯沿著長軸方向厚度量測之位置圖	50
圖4-20 橢圓錐杯沿著短軸方向厚度量測之位置圖	50
圖4-21 工件厚度量測	51
圖4-22 圓錐杯之螺旋線漸進式刀具路徑	52
圖4-23 橢圓錐杯之螺旋線漸進式刀具路徑	52
圖4-24 半球頭工具與料片之網格分割	53
圖4-25 單點增量成形料片網格分割及邊界條件設定	54
圖4-26  圓錐杯單點增量成形X軸方向成形負荷圖	57
圖4-27  圓錐杯單點增量成形Y軸方向成形負荷圖	57
圖4-28  圓錐杯單點增量成形Z軸方向成形負荷圖	58
圖4-29  圓錐杯實體厚度分佈區域	58
圖4-30  圓錐杯數值模擬厚度分佈區域	59
圖4-31 工具轉速為400 rpm與工件進給速率100 mm/min
       對 圓錐杯厚度分佈之比較	60
圖4-32 工具轉軸靜止於工件進給速率800 mm/min
       對 圓錐杯厚度分佈之比較	62
圖4-33 工具轉軸靜止於工件進給速率1700 mm/min 
       對 圓錐杯厚度分佈之比較	62
圖4-34 工具轉軸靜止於工件進給速率3600 mm/min 
       對 圓錐杯厚度分佈之比較	63
圖4-35 工具轉軸靜止於工件進給速率5400 mm/min
       對 圓錐杯厚度分佈之比較	63
圖4-36 不同工具轉速與工件進給速率對 圓錐杯厚度
       分佈之比較	64
圖4-37 順銑與逆銑對 圓錐杯之厚度分佈之比較	66
圖4-38  圓錐杯實體厚度分佈區域	68
圖4-39 工具轉軸靜止於工件進給速率800 mm/min
       對 圓錐杯厚度分佈之比較	69
圖4-40 橢圓錐杯輪廓形狀示意圖	70
圖4-41 橢圓錐杯實體厚度分佈區域	71
圖4-42 工具轉速400 rpm與工件進給速率100 mm/min
       對橢圓錐杯沿著長軸方向的厚度分佈之比較	72
圖4-43 工具轉速400 rpm與工件進給速率100 mm/min
       對橢圓錐杯沿著短軸方向的厚度分佈之比較	73
圖4-44 工具轉軸靜止於工件進給速率800 mm/min
       對橢圓錐杯沿著長軸方向的厚度分佈之比較	74
圖4-45 工具轉軸靜止於工件進給速率800 mm/min
       對橢圓錐杯沿著短軸方向的厚度分佈之比較	75
圖4-46 不同工具轉速與工件進給速率對橢圓錐杯沿著
       長軸方向的厚度分佈之比較	76
圖4-47 不同工具轉速與工件進給速率對橢圓錐杯沿著
       短軸方向的厚度分佈之比較	76
圖4-48  圓錐杯數值模擬B、C、D三處示意圖	77
圖4-49  圓錐杯數值模擬B、C、D三處示意圖	78
圖4-50  圓錐杯數值模擬最薄厚度之俯視圖	80
圖4-51  圓錐杯數值模擬最薄厚度之等角圖	80
圖4-52  圓錐杯數值模擬最大等效應力之俯視圖	81
圖4-53  圓錐杯數值模擬最大等效應力之等角圖	81
圖4-54  圓錐杯數值模擬最大等效應變之俯視圖	82
圖4-55  圓錐杯數值模擬最大等效應變之等角圖	82
圖4-56  圓錐杯數值模擬最薄厚度之俯視圖	83
圖4-57  圓錐杯數值模擬最薄厚度之等角圖	83
圖4-58  圓錐杯數值模擬最大等效應力之俯視圖	84
圖4-59  圓錐杯數值模擬最大等效應力之等角圖	84
圖4-60  圓錐杯數值模擬最大等效應變之俯視圖	85
圖4-61  圓錐杯數值模擬最大等效應變之等角圖	85
圖4-62 橢圓錐杯數值模擬長軸與短軸B、C、D三處示意圖	87
圖4-63 橢圓錐杯數值模擬最薄厚度之俯視圖	88
圖4-64 橢圓錐杯數值模擬最薄厚度之等角圖	89
圖4-65 橢圓錐杯數值模擬最大等效應力之俯視圖	89
圖4-66 橢圓錐杯數值模擬最大等效應力之等角圖	90
圖4-67 橢圓錐杯數值模擬最大等效應變之俯視圖	90
圖4-68 橢圓錐杯數值模擬最大等效應變之等角圖	91
圖4-69 工具轉軸靜止於工件進給速率100 mm/min 
       對 圓錐杯成形負荷圖	92
圖4-70 工具轉速800 rpm與工件進給速率100 mm/min
       對 圓錐杯成形負荷圖	93
圖4-71 工具轉軸靜止於工件進給速率100 mm/min 
       對 圓錐杯成形負荷圖	93
圖4-72 工具轉速800 rpm與工件進給速率100 mm/min
        對 圓錐杯成形負荷圖	94
圖4-73 工具轉軸靜止於工件進給速率100 mm/min
       對橢圓錐杯成形負荷圖	95
圖4-74 工具轉速800 rpm與工件進給速率100 mm/min 
       對橢圓錐杯成形負荷圖	95
圖5-1  表面粗糙度測定儀品名Mitutoyo型號Sj-410	98
圖5-2  潤滑油的品名為Brugarolas型號Bestril 630系列	98
圖5-3  太古油的品名為Valid Supercut型號500系列	99
圖5-4  建立圓錐杯、橢圓錐杯刀具路徑流程	100
圖5-5  圓錐杯八個點量測位置圖	100
圖5-6  橢圓錐杯八個點量測位置圖	101
圖5-7  單點增量成形逆銑示意圖	103
圖5-8  單點增量成形順銑示意圖	103
圖5-9  工具轉軸靜止於逆時針工件進給速率100 mm/min
       之表面	105
圖5-10 工具轉軸靜止於順時針工件進給速率100 mm/min
       之表面	105
圖5-11 工具轉速400 rpm與逆時針工件進給速率100 mm/min
       之表面	105
圖5-12 工具轉速400 rpm與順時針工件進給速率100 mm/min
       之表面	106
圖5-13 Brugarolas Bestril 630潤滑油注入方式	107
圖5-14 單點增量成形後潤滑油由黃色變成黑色	108
圖5-15 加工時潤滑油溫度量測	108
圖5-16 Valid Supercut 500水溶性太古油注入方式	109
圖5-17 不同潤滑液對 圓錐杯表面粗糙度之比較	110
圖5-18 不同潤滑液對橢圓錐杯表面粗糙度之比較	110
圖5-19 工具轉軸靜止於不同工件進給速率對 圓錐杯
       表面粗糙度之比較	113
圖5-20 量測橢圓錐杯八個點的表面粗糙度值	114
圖5-21 工具轉軸靜止於不同工件進給速率對橢圓錐杯
       表面粗糙度之比較	114
圖5-22 工具轉速與工件進給速率對橢圓錐杯(一) 
       表面粗糙度之比較	115
圖5-23 工具轉速與工件進給速率對橢圓錐杯(二)
       表面粗糙度之比較	116
表2-1  單點增量成形製程的應力與應變狀態	28
表4-1  亞崴科技綜合切削中心機AWEA-AF650規格表	40
表4-2  圓錐杯於不同傾斜角的厚度、等效應力及
       等效應變之比較	79
表4-3  橢圓錐杯於不同傾斜角的厚度、等效應力及
       等效應變之比較	87
表4-4  Z軸方向成形負荷之比較	96
表5-1  潤滑油的性質	99
表5-2  太古油的性質	99
表5-3  電腦輔助製造軟體Master Cam螺旋線漸進式
       刀具路徑設定	102
表5-4  不同輪廓錐杯表面粗糙度	117
表5-5  參考文獻相對應表面粗糙度	118

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