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研究生: 翁睿哲
Weng, Ruey-Jer
論文名稱: 半固態鎂合金壓鑄充填模擬及界面熱傳導係數之量測
Mold Filling Simulation and Interfacial Heat Transfer Coefficient Measurement for the Die Casting of Semi-solid Magnesium Alloy
指導教授: 黃文星
Hwang, Weng-Sing
學位類別: 博士
Doctor
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2008
畢業學年度: 96
語文別: 中文
論文頁數: 88
中文關鍵詞: 充填模擬等位函數法界面熱傳導係數半固態
外文關鍵詞: mold filling simulation, level set method, Interfacial Heat Transfer Coeffcient, semi-solid
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  • 近年來半固態製程越來越受到重視,和壓鑄相比,半固態製程有許多的優點,如更均 勻的微組織,更少的孔洞及較佳的機械性質。然而半固態流體複雜的流變性使得半固態流 體的流動行為和液態金屬非常的不同,所以傳統鑄造上的經驗及為傳統鑄造所發展的模擬 系統皆無法應用在半固態製程上。因此,為了減少製程上試誤的過程,發展一個能模擬半 固態充填行為的模擬系統是必須的。同時,近年來因為產品的輕量化的趨勢,所以 AZ91D 鎂合金被大量的使用在 3C 產品上,尤其是在亞洲市場。因為半固態製程的優點,目前有許 多產品已改以半固態製程生產,所以本研究的工作之一即是發展一個能模擬 AZ91D 鎂合金 半固態充填的模擬系統。另外,為了提升現有凝固解析系統的準確度,正確的熱物參數也 非常重要,所以本研究的另一個工作就是量測 AZ91D 鎂合金和 SKD61 模具材料之間的界 面熱傳導係數。

    本研究開發的模擬系統,在速度和壓力的求解上是採用 SOLA 的數值技術,同時以 power law 模型來計算半固態流體的表現黏度(apparent viscosity),在自由液面的追蹤上 則是採用等位函數法(Level Set Method)。本研究同時進行一系列不足量充填實驗來驗證 本研究所發展的模擬系統。比較結果顯示,模擬和實驗的結果具有一致性,同時對於本研 究測試案例的製程條件(將 AZ91D 鑄錠加熱到 575 ?C 並以0.5 m/s 的射出速度充填)而言, 適合的 power law 的常數分別為 n 設定為 -0.85,m 設定為 100(P a · s0.15)。

    在界面熱傳導係數的量測方面,本研究量測了不同固相率(22 %, 45 % 和 60 %)鎂合金 及不同壓力(4.9 MPa,9.8 MPa 和 14.7 MPa)下半固態鎂合金於冷卻過程中界面熱傳導係數 的變化。研究顯示,液態鎂合金其界面熱傳導係數(h)隨溫度的變化可分為四個階段,於第 一階段,h 值隨溫度上升並於 560 ?C 到達 3000 W/m2K ,第二階段 h 值開始下降於 525 ?C 達到 2200 W/m2K,第三階段 h 值又再上升並於 430 ?C 達到 2500 W/m2K,最後為第 四階段,h 值又再次下降直到鑄錠完全固化。半固態鎂合金界面熱傳導係數隨溫度變化的趨 勢和液態鎂合金不同,缺少第三階段 h 值上升的部分,同時隨著固相率增加,h 值有增加 的趨勢。在加壓的部分,對於固相率 60 % 的鎂合金而言,加壓到 4.9 MPa 和 9.8 MPa 的 結果很類似,h 值都是在 5000 W/m2K 到 7000 W/m2K 變動,而加壓到 14.7 MPa 於 520 ?C 可得到本研究最大的 h 值 13000 W/m2K。

    Semi-solid metal casting is gaining more interest in the casting industry. Compared with the conventional pressure die casting process, semi-solid casting has some distinct advantages such as a more homogeneous microstructure, less porosity and improved mechanical properties. However, the complex rheology involved in the casting of semisolid metal alloys can result in very different flow behavior. Those simulation tools developed for traditional casting process can’t be applied to this process. In order to speed up the product development progress, a simulation system for semi-solid process is then desired. In addition to mold filling simulation, solidification analysis is also very important. Nevertheless, an accurate solidification model needs to know accurate thermal—physic properties. Therefore, there are two works in this study, one is to develop a mold filling simulation system for semi-solid processes, and the other is to measure interfacial heat transfer coefficient for AZ91D semi-solid magnesium alloy and SKD61 mold during solidification.

    For semi-solid process mold filling simulation, a program based on SOLA and Level Set Method has been developed to predict the filling of semi-solid AZ91D magnesium alloy for die-casting process. Power law model was used to describe the constitutive behavior of semi-solid metal slurry. Different constants of power law model were tested in the simulation system, and a series of short-shots experiments was conducted to validate the simulation results. The experimental results and simulation results were comparable. These results also showed that n set -0.85 and m set 100(Pa ¢ s0.15) are suitable inputs in the power law equation for mold filling simulation of semi-solid AZ91D magnesium alloy with a piston speed of 0.5 m/s and feedstock temperature of 575 C.

    For the interfacial heat transfer coefficient measurement, the experiments were conducted with different solid fractions (22%, 45%, and 60%) of AZ91D. At the solid fraction of 60%, the experiments were also conducted under three different pressures II (4.9MPa, 9.8MPa, and 14.7MPa) in order to investigate the effects of pressure on heat transfer coefficient. The heat transfer coefficient values at various solid fractions and different pressures were obtained and compared. The results obtained from this study indicate that the profiles of heat transfer coefficients for semisolid AZ91D magnesium alloy with different solid fraction have similar tendency. And the heat transfer coefficient profile are different for liquid and smisolid AZ91D. The heat transfer coefficient profile of liquid AZ91D can be divided into four stages, while the heat transfer coefficient profiles of semisolid AZ91D lack the third stage. Furthermore, heat transfer coefficient would increase with increasing solid fraction during solidification process and increase with increasing operating pressure.

    中文摘要· · · · · · · · · · · · · · · · · · · · · · · · I 英文摘要· · · · · · · · · · · · · · · · · · · · · · · · II 目錄· · · · · · · · · · · · · · · · · · · · · · · · · · · V 表目錄· · · · · · · · · · · · · · · · · · · · · · · · · · VIII 圖目錄· · · · · · · · · · · · · · · · · · · · · · · · · · IX 符號說明· · · · · · · · · · · · · · · · · · · · · · · · XII 第1 章緒論· · · · · · · · · · · · · · · · · · · · · · 1 1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . 1 1.2 半固態製程. . . . . . . . . . . . . . . . . . . . . . 1 1.3 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . 2 1.4 研究目的與內容. . . . . . . . . . . . . . . . . . . 3 第2 章理論基礎· · · · · · · · · · · · · · · · · · · · 5 2.1 模流充填的數學模式. . . . . . . . . . . . . . . . . 5 2.1.1 控制方程式. . . . . . . . . . . . . . . . . . 5 2.1.2 本質方程式. . . . . . . . . . . . . . . . . . 6 2.1.3 自由表面的處理. . . . . . . . . . . . . . . 7 2.1.4 邊界條件. . . . . . . . . . . . . . . . . . . 8 2.2 以逆推法(Inverse Method)量測界面熱傳導係數 . . . 9 2.2.1 利用猜測的h值計算溫度分布. . . . . . . .. . 10 2.2.2 潛熱釋放. . . . . . . . . . . . . . . . . . . 10 2.2.3 修正猜測的h值. . . . . . . . . . . . . . . . 11 第3 章數值方法· · · · · · · · · · · · · · · · · · · · 16 3.1 系統的分割與變數的設置. . . . . . . . . . . . . . . 16 3.2 控制方程式的差分化. . . . . . . . . . . . . . . . . 16 3.2.1 動量方程式的差分化. . . . . . . . . . . . . 17 3.2.2 連續方程式的差分化. . . . . . . . . . . . . 18 3.2.3 壓力和速度的修正. . . . . . . . . . . . . . 18 3.3 自由表面追蹤的數值處理. . . . . . . . . . . . . . . 19 3.3.1 等位函數運動方程式的離散. . . . . . . . . 19 3.3.2 等位函數的初始化. . . . . . . . . . . . . . 20 3.3.3 Extension Velocity . . . . . . . . . . . . . 21 3.3.4 Narrow Band Level Set . . . . . . . . . . . 21 3.4 穩定度的要求. . . . . . . . . . . . . . . . . . . . . 22 3.5 計算的流程. . . . . . . . . . . . . . . . . . . . . . 23 第4 章實驗方法與步驟· · · · · · · · · · · · · · · · 30 4.1 不足量充填實驗. . . . . . . . . . . . . . . . . . . 30 4.2 界面熱傳導係數的量測. . . . . . . . . . . . . . . . 31 4.2.1 實驗裝置. . . . . . . . . . . . . . . . . . . 31 4.2.2 實驗步驟. . . . . . . . . . . . . . . . . . . 31 第5 章結果與討論· · · · · · · · · · · · · · · · · · 42 5.1 半固態鎂合金模流充填模擬. . . . . . . . . . . . . 42 5.1.1 系統測試. . . . . . . . . . . . . . . . . . . 42 5.1.2 實際案例分析. . . . . . . . . . . . . . . . 43 5.1.3 power law 模型. . . . . . . . . . . . . . . 43 5.1.4 不同n 值對充填型態的影響. . . . . . . . . 44 5.1.5 不同m 值對充填型態的影響. . . . . . . . . 45 5.1.6 不足量充填實驗. . . . . . . . . . . . . . . 46 5.1.7 邊界條件的影響. . . . . . . . . . . . . . . 46 5.2 界面熱傳導係數的量測. . . . . . . . . . . . . . . . 47 5.2.1 液態AZ91D 鎂合金之界面熱傳導係數. . . . 47 5.2.2 不同固相率對界面熱傳導係數的影響. . . . . 47 5.2.3 不同壓力對界面熱傳導係數的影響. . . . . . 48 第6 章結論· · · · · · · · · · · · · · · · · · · · · · 77 參考文獻· · · · · · · · · · · · · · · · · · · · · · · · 79 附錄A 動量方程式之詳細差分式· · · · · · · · · · · · 83

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