摘 要
輥軋加工屬於塑性加工?堶垠n的一環，為提高加工品質、提昇效率及減少能量損耗，對於輥軋加工中的摩擦係數掌握，卻仰賴累積的經驗公式，故為了減少加工不良的次數與降低能源損耗，摩擦係數成為輥軋加工重要的依據。
本研究先從Karman理論的解析，分別探討不考慮加工硬化與加工硬化下輥軋過程中，摩擦係數、縮減率、負荷、力矩、中立點、壓力的關係，然後再由已知負荷、力矩、前向滑動、中立點逆解反求出摩擦係數，壓力分佈的關係。
由研究結果得知，摩擦係數隨著縮減率增加，其值愈大。加工硬化的最大壓力值大於不考慮加工硬化的壓力值。中立點較靠近出口區。不考慮加工硬化逆解所求得摩擦係數的誤差比加工硬化逆解所求的值小。加工硬化下所求得負荷、力矩皆比不考慮加工硬化下的值大。若無量測誤差時，逆解法可較準確的預測摩擦係數，其誤差值在5 ﹪以下。若有量測誤差時，逆解法也可預測摩擦係數。

Abstract
The rolling is an efficient and economical approach for the manufacturing of strip or plate metals, it plays an important role because of its versatility and its high production rate in the manufacture of various products with uniform cross-sectional area. Without the knowledge of the influences of the variables such as friction conditions, material properties, and workpiece geometry on the process mechanics, it will not be possible to design and control the equipment adequately, or to predict and prevent the occurrence of failures.
According to modeling by numerical has become a major tool in rolling research. By using the proper criterion, de-pending upon the production requirements along with the modeling results, the process efficiency, productivity and quality can be increased and the down time of the mill and cost operation can be reduced.
In this study, investigated that it do not consider to work hardening and consider to work hardening during the rolling process from Von Karman theory. We can realize friction coefficient, reduction ratio, rolling force, rolling torque, neutral point, and pressure distribution relation, then from measuring rolling force, torque, neutral point can inverse to solve friction coefficient and pressure distribution. Result that we found the error of direct and inverse solution about rolling friction coefficient was less than 5 %, and the coef-ficient of friction was found to increase with reduction and rolling force and neutral point.

總 目 錄
頁次
封面 i
授權書 ii
論文口試審定書 iii
謝誌 iv
目錄 v
圖目錄 vii
符號目錄 xi
中文摘要 xii
英文摘要 xiii

第一章 緒 論 1
1-1 研究動機 1
1-2 文獻回顧 2
1-3 本文重點 4
1-4 本論文架構 4
第二章 不考慮加工硬化輥軋的理論解析 5
2-1 理論推導的基本假設 5
2-2 直接解法的理論推導 6
2-3 逆解法公式推導 10
第三章 加工硬化輥軋的理論解析 18
3-1 理論推導的基本假設 18
3-2 直接解法的理論推導 19
3-3 逆解法公式推導 23
第四章 結果與討論 30
4-1 不考慮加工硬化的數值解析 30
4-2 加工硬化的數值解析 33
第五章 結論與未來展望 37
5-1 結論 37
5-2 未來展望 38
參考文獻 80

參考文獻
【1】 Siebel, E., Berichile des Walzwerksausschusses, Verein deustcher Eisenhuttenleute, No.37, 1924, See Also Stahl und Eisen, 1925, Vol. 45, p.1563.
【2】 Von Karman, Th.“On the Theory of Rolling” Zeitschrift fur ange-wandte Mathematik und Mechanik, Vol.5, 1925, p.138-141.
【3】 Hitchock, J.H.“Elastic Deformation of Rolls During Cold Roll-ing”A.S.M.E. Report of Special Research Committee on Roll Neck Bearings, June, 1935, p.33-41.
【4】 Nadai, A.”The Forces Required for Rolling Steel Strip under Ten-sion“ Journal of Applied Mechanics, 1939, June, p.a54-a62.
【5】 Orowan, E.“The Calculation of Roll Pressures in Hot and Cold Flat Rolling” Proceedings of the Institution of Mechanical Engineers, 1943, Vol.150, p.150-167.
【6】 Bland, D.R. and Ford, H. “The Calculation of Roll Force and Torque in Cold Strip Rolling with Tensions” Proceedings of the In-stitution of Mechanical Engineers, Vol.159, 1948,p.144-153.
【7】 Hessenberg, W.F., Sims R.B. “The Effect of Tension on Torque and Roll Force in Cold Strip Rolling” Journal of the Iron and Steel In-stitute, June,1951, p.155-164.
【8】 Tong, K., Sachs G. “Roll-Seperating Force and Minimum Thick-ness of Cold-Rolled Strips” Journal of the Mechanical and Physis of Solids, Vol.6, 1957,p.35-46.
【9】 Alexander, J.M., “On the Theory of Rolling”, Proc. Roy. Soc. Lond. A.1972,p.535-563.
【10】 Venter, R., Abd-Rabbo A. ”Modeling of the Rolling Process Part I. Inhomogeneous Deformation Model” International Journal of
Mechanical Science, vol.22, 1980, p.83-92.
【11】 Venter, R., Abd-Rabbo A. ”Modeling of the Rolling Process Part II.Evalution of Stress Distribution in the Rolled Material “ Interna tional Journal of Mechanical Science, Vol.22, 1980, p.93-98.
【12】 Christensen, P., Everflet H. and Bay N. ”Pressure Distribution in Plate Rolling” Annals of the CIRP, Vol. 35, 1986, p.141-146.
【13】 Gunasekera, J.S., Alexander J.M. “Analysis of Rolling” Annals of the CIRP, Vol.36, 1987, p.203-206.
【14】 Wanheim, T., Bay, N. and Petersen, A.S. “A Theoretical Deter-mined Model for Friction in Metal Working Processes”, Wear, Vol.28, 1974, p.251-258.
【15】 Francis, B. Hildebrand, “Methods of Applied Mathematics”, p.119-122.
【16】 Campbell Mcconnell, J.G. Lenard, “Friction in Cold Rolling of a Low Carbon Steel with Lubricants”, Journal of Materials Proc-essing Technology, Vol.99, 2000, p.86-93.
【17】 Rusia, R., “Improvements to Alexander’s Computer Model for Force and Torque Calculations in Strip Rolling Process” Journal of the Material Shaping Technology, Vol.8, 1990, p.167-177.
【18】 Rusia, D., “Review and Evalution of Different Methods for Force and Torque Calculations in Strip Rolling Process” Journal of the Material Shaping Technology, Vol.9, 1991, p.117-125.
【19】 Roberts, William. L., “Cold Rolling of Steel”, Marcel Dekker, Inc., 1978.
【20】 Wusatowski, z.原著,關昌揚譯 ”金屬輥軋學” 徐氏基金會出版, 1974.
【21】 向四海, “輥軋加工中輥輪變形與板材形狀之研究”, 國科會專題研究報告, 1988.
【22】 朱開華, “薄板冷軋之潤滑分析” 台灣大學機械工程研究所碩士論文, 1987.
【23】 余哲良, “冷間壓延潤滑理論之基礎研究”, 中山大學機械工程研究所碩士論文, 1995.
【24】 賴耿陽, “最新冷軋成形集”, 復漢出版社, 1990.
【25】 蘇品書, “Modern Mechanics Compute and Analysis in Materials Process”, 復漢出版社, 1992.