預估修正法於金屬板金成形最佳化料片設計之研究

Study of Predictor-Corrector Methods for Optimum Blank Design of Sheet Metal Forming

吳銘宗(Ming-Tsung Wu)

指導教授 ： 葉豐輝

淡江大學/工學院/機械與機電工程學系博士班/博士(2007年)

https://doi.org/10.6846/TKU.2007.00403

摘要

本文研究乃針對金屬板材沖壓成形於方杯與圓杯成形製程中料片幾何輪廓最佳化之分析，使用顯性有限元素法進行數值模擬，並配合流線法、真實應變法、可行逐步二次規劃方法(FSQP)與適應性網路模糊推論系統(ANFIS)四種最佳化理論進行料片幾何輪廓之預測，以節省以往利用試誤法及反覆實驗所浪費的時間。為求數值模擬與最佳化理論之驗證，依其不同形式成形條件與限制，設計不同形式之實驗模具，以驗證數值模擬其成形後之料片內緣與外緣幾何輪廓尺寸、沖頭負荷與衝程之關係、工件厚度分佈…等結果。經由數值分析與實驗結果比較，可證實顯性有限元素法分析可正確模擬成形過程及成形後料片之變形的狀況。再者其最佳化理論之適應性網路模糊推論系統乃是四者中最能有效且快速求得最佳化料片的理論，則可作為模具設計與加工製程時尋求最佳化方式的參考。
最後於微小尺寸沖壓成形中，為了減少產品之研發時程，也導入CAE/CAD的技術，冀希以電腦模擬來代替耗時的實作測試，並針對微成形之重要參數(尺寸效應及應力應變曲線)作探討比較。在尺寸效應中將料片厚度與晶粒大小導入材料應力應變構成式中，並以數值求解方式尋求適當之猜測值，以期使透過單一修正式就能預測同材料不同料片厚度與不同晶粒大小之應力應變曲線。透過文獻結果比對發現，其導入尺寸效應因子之應力應變構成式與單純應力應變構成式的誤差皆在容許範圍內，故可證明其修正式之可靠性，並依其修正式中給定不同料片厚度與不同晶粒大小來預估其各成形後各相關之資料，則可提供微小成形相關研究之參考。

關鍵字

流線法 ； 真實應變法 ； 適應性網路模糊推論系統 ； 微成形 ； 金屬成形 ； 最佳化料片 ； 尺寸效應.

並列摘要

This thesis discusses the optimization analysis of the blank geometry profile in square cup and cylindrical cup of the metal forming. Using the explicit dynamic finite element method to carry on the numerical simulation, cooperate with streamline method, true strain method and adaptive network fuzzy inference system(ANFIS) three optimization theory to predict the shape of optimum blank. With this way, can be save a lot of time than using “Try and Error” and repeating experiments. In order to ask the verification of the numerical simulation and optimization theory, that to design the multi-form experiment mould in accordance with the condition and restriction of the multi-formly forming. After it made forming in order to verify the numerical simulation relation between reason the geometry measurement of the blank, the loading of the punch and stroke and the thickness distribute of the blank. Compare via number value between analysis and experimental result, shows that explicit dynamic finite element could correctly simulation of situation during forming process of blank form comparing numerical analysis data and experimental data. The adaptive network fuzzy inference system of the optimization theory is the best to can effective and fast to get the optimization of the blank. Moreover, it can to supply optimization reference when making process and designing mold.
Finally, it reduces the research and development of products channel into the technology of CAE/CAD in the micro cylindrical cup, that wish to substitute for testing in fact consuming time with computer simulation. Then probe into comparing to the important parameter of micro forming (size effect and stress-strain curve). Channel the thickness of the blank and grain size into material stress strain equation in size effect, and ask the way of solving to seek the proper conjecture value with number value. In the hope of making can predict stress-strain curve of the different material thickness and different grain size with the material through the single revising type. Than comparison between the error of size effect factor equation and simple stress strain equation form all in permitting range through result, so can provable revise equation dependability. And whether it give in accordance with revising type different material thickness and different grain size definitely estimate it each relevant materials after forming in advance coming, can offer the reference of relevant micro forming.

並列關鍵字

Nelder-Mead Method ； Stream Line Method ； True Strain Method ； ANFIS ； Micro Forming ； Metal Forming ； Optimum Blank ； Size Effect.

參考文獻

19.K. Schweizerhof and J. O. Hallquist, “Explicit Integration and Contact Formulation for Thin Sheet Metal Forming,” VDI, BERICHTE, pp.405-439.

65.陳世傑，〝微小圓杯引伸成形分析與料片最佳化之研究〞，碩士論文，淡江大機械與機電工程學系，2006年。

1.D. M. Woo, “On the Complete Solution of the Deep Drawing Problem,” International Journal of Mechanical Sciences, Vol. 10, pp.89-94, 1968.

2.N. M. Wang, “Large Plastic Deformation of a Circular Sheet Caused by Punch Stretching,” Journal of Applied Mechanics, Vol. 37, pp.431-440, 1970.

3.S. Kobayashi, C. H. Lee and S. N. Shah, “Analysis of Rigid-Plastic Deformation Problems by the Matrix Method,” Journal Japan Society for Technology of Plasticity, Vol. 14, pp.770-784, 1973.