本研究使用魚骨圖篩選梯形扳手之設計參數，利用最佳化理論針對延長使用年限、成本降低、操作安全與操作便利性多目標進行最佳化設計。首先選定手柄外徑、手柄彎曲半徑、手柄斜角與手柄內徑四個設計因子，進而透過3D繪圖軟體建構梯形扳手之實體模型，利用有限元素分析軟體觀察梯形扳手承受彎矩時之應力分布狀況，再以田口法與反應曲面法設計達到減少應力集中值與質量輕量化的最佳參數組合。經由比較分析結果顯示反應曲面法能夠得到全域區域之最佳解，而田口方法只能得到局部區域的較佳解。最後使用多目標反應曲面法來進行最佳化分析，結果顯示當其梯形扳手最佳尺寸組合為手柄外徑22.4 mm、手柄內徑14.0 mm、手柄斜角40.0 度與手柄彎曲半徑31.0 mm時，其最佳全域等效應力為154.00 MPa、最小質量為0.66 kg，最大應力值比單目標反應曲面法增加3.66 %、比田口方法減少2.92 %，最小質量比反應曲面法增加4.55 %、比田口方法增加3.03 %。

This study select design parameters of the new spanner using fishbone diagram and optimization theory for multi-objective optimization design in relation to increase of service life, cost down, handling safety and handling convenience. The first, four chosen design factors external diameter of handle、bend radius of handle、bevel angle of handle and inner diameter of handle are used to create the new spanner model via 3D drawing software. Finite element analysis software show the disposition of stress when the new spanner is bearing a bending moment. Design target for decrease stress concentration and mass lightweight are applied to Taguchi methods and Response surface methodology.
The results indicates the Taguchi methods only get local region batter values, but Response surface methodology can get global region optimization values. The final, we use multi-objective response surface methodology to find the optimization design. The results show the optimization global region equivalent tress was 154.0 MPa and minimum mass was 0.66 kg when external diameter of handle was 22.4 mm , bend radius of handle was 31.0 mm, bevel angle of handle was 40.0 deg and inner diameter of handle was 14.0 mm. The maximum stress increase by 3.66% and the minimum mass increase by 4.55% in comparison with Single-objective Response surface methodology. The optimization stress decrease by 2.92% and the minimum mass increase by 3.03% in comparison with Taguchi methods.

中文摘要 ............................................................................................................... iii
ABSTRACT ............................................................................................................... iv
誌謝 ................................................................................................................ v
目錄 ............................................................................................................... vi
表目錄 ............................................................................................................. viii
圖目錄 ................................................................................................................ x
第一章 緒論 ........................................................................................................ 1
1.1 研究動機與目的 .................................................................................... 1
1.2 文獻回顧 ................................................................................................ 3
第二章 研究內容及方法 .................................................................................. 13
2.1 研究內容 .............................................................................................. 13
2.2 研究方法及步驟 .................................................................................. 14
第三章 理論及實驗設計法 .............................................................................. 15
3.1 有限元素法分析(Finite Element Method) .......................................... 15
3.2 田口方法(Taguchi Methods) ................................................................ 19
3.2.1 3k因子設計(3k Factorial Design).................................................. 22
3.2.2 直交表(Orthogonal Array) .......................................................... 23
3.2.3 訊噪比(S/N Ratio) ....................................................................... 25
3.2.4 變異數分析 ................................................................................. 28
3.3 反應曲面法 .......................................................................................... 30
3.3.1 反應曲面設計 ............................................................................. 31
3.3.2 線性迴歸模型(Linear Regression Model) .................................. 37
3.3.3 多目標最佳化 ............................................................................. 38
第四章 結果與討論 .......................................................................................... 42
4.1 魚骨圖因子選定 .................................................................................. 42
4.2 梯形扳手材料及邊界條件之設定 ...................................................... 45
4.3 以梯形扳手全域等效應力望小建構反應曲面數學模型 .................. 50
4.4 以梯形扳手總質量望小建構反應曲面數學模型 .............................. 57
4.5 利用田口方法建立梯形扳手全域等效應力望小分析 ...................... 64
4.6 利用田口方法建立梯形扳手總質量望小分析 .................................. 67
4.7 分析與結果 .......................................................................................... 70
4.7.1 梯形扳手全域等效應力分析結果 ............................................. 70
4.7.2 梯形扳手總質量分析結果 ......................................................... 71
4.7.3 多目標反應曲面法分析結果 ..................................................... 72
第五章 結論及未來研究方向 .......................................................................... 79
5.1 結論 ...................................................................................................... 79
5.2 未來研究方向 ...................................................................................... 80
參考文獻 .............................................................................................................. 81

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