中立半徑模式對圓環鍛粗加工上界限解的影響

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黃嘉榮(Chia-Lung Huang) 查詢紙本館藏

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機械工程學系

論文名稱

中立半徑模式對圓環鍛粗加工上界限解的影響
(Effect of Neutral Radius on the Upper-Bound Solution of Upset Forging of Rings.)

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摘要(中)

摘要
本文的目的在於應用變分方法探討中立半徑模式對於上界限解的影響，且視中立半徑於鍛粗過程中為一函數型態，以取代一般將其視為常數的假設。本文首先根據流函數（Stream Function）所定義呈函數型態的動可容速度場及變形場，建立鍛粗加工所需的上界限能量消耗的總功率，其次以變分法（Variational Method）最小化總功率的泛函數以獲得靜可容邊界條件，並應用於求取上界限解。本文所採用之數值解析，係利用IMSL［25］最佳化程式"NCONF"。
為驗證理論分析的妥適性，本文採用圓環及圓盤鍛粗加工的實驗結果［5,6,9,18］和理論計值互做比較及討論。此外，本文亦探討各種加工因素，如摩擦條件（Friction Condition）、高度縮減率（Reduction in Height）對上界限解的影響。本文結果顯示，在考慮中立半徑為一函數型態且滿足靜可容邊界條件下，對於校正曲線、圓環及圓盤桶脹輪廓的預測有較佳的結果。

摘要(英)

Abstract
The objective of this thesis is to investigate the effect of neutral radius on the upper-bound solution of the upset forging of rings using a variational approach. To this end, the neutral radius of the upset ring is considered an explicit function of polynomials during deformation process, and the upper-bound energy equation is formulate in terms of the explicit function as well as the velocity field derived from the theory of stream function. Since the velocity field was considered unknown functions before the upper-bound energy equation is extremized, a variational approach is required. As a result, a set of boundary conditions can be derived. To determine the upper-bound solution, the set of boundary conditions, which include the so-called natural boundary conditions, was imposed in the optimization procedure. In numerical analysis, an optimization program "NCONF" of the IMSL［25］is utilized.
Some experimental results of the upset disks［6,18］and ring［5,9］were employed for discussion and comparison among the theories. It also discussion the effect of working factors, such as the friction condition and the reduction in height on upper-bound solution. From the result we can clearly indicate that the solution in predicting the calibration curve as well as the bulged profiles of the upset disks and ring would be better when it is based on the model of neutral radius considered, and satisfies the natural boundary condition.

關鍵字(中)

★ 鍛粗
★ 自然邊界條件
★ 中立半徑
★ 變分上界限理論
★ 流函數

關鍵字(英)

★ Neutral radius
★ Variational upper-bound method
★ Stream function
★ Natural boundary condition
★ Upset forging

論文目次

目錄
頁次
摘要 Ⅰ
Abstract Ⅱ
目錄 Ⅳ
圖表說明 Ⅶ
符號說明 Ⅹ
第一章緒論
1-1 前言 01
1-2 文獻回顧 01
1-3 研究動機與方法 04
第二章上界限解析
2-1 上界限原理 06
2-2 上界限流函數法 09
第三章圓環鍛粗加工之分析
3-1 基本假設 12
3-2 流函數場的建立 12
3-3 速度場的建立 14
3-4 應變率場的分析 14
3-5 鍛粗加工成形所需的功率消耗 16
3-6 變分法 19
3-7 待定函數及中立半徑的決定 20
第四章數值方法
4-1 數值積分 22
4-2 最佳化求解方法 23
4-3 變形場的建立 23
第五章結果與討論
5-1 校正曲線的比較(Calibration Curve) 26
5-2 圓環桶脹輪廓的比較 26
5-3 中立半徑對圓環桶脹輪廓的效應 27
5-4 圓盤桶脹輪廓比較 28
5-5 VUB及UB對成形能量的影響 29
5-6 摩擦條件與半高度縮減率對內徑縮減率的影響 29
5-7 變分邊界條件對變形場的影響 30
5-8 摩擦條件與半高度縮減率對變形場的影響 31
5-9 半高度縮減率與摩擦條件對應變場的影響 32
5-10 半高度縮減率與摩擦條件對速度場及中立半徑位置的影響 32
第六章結論與建議
6-1 結論 34
6-2 建議 36
參考文獻 37
附錄A 66
附錄B 74
附錄C 75

參考文獻

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指導教授

葉維磬(Wei-Ching Yeh)

審核日期

2005-1-25

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