本研究主要針對鋼帶在冷軋過程鋼帶寬展(Spread)分佈的探討，探討冷軋過程的寬展機制，並計算冷軋過程中的軋製力、摩擦力、張力及橫向分佈，主要目的為避免軋延後鋼帶產生邊浪或中浪之缺陷造成嚴重的產能損失。本研究探討不同材料的鋼種與板形初始狀態進行冷軋製程的理論分析與數值計算，金屬材料與板形的初始狀態分為板形初始斷面為平直狀態的不鏽鋼帶材(SUS304)、板形初始斷面為邊浪狀態的黃銅帶材(CDA-110)及鋁帶材(AL-6061)，藉由條元理論分析方法與有限元素法進行理論分析與數值計算。本研究藉由條元法分析求解鋼帶在冷軋製程鋼帶之軋製力、摩擦力、張力之橫向分佈，此方法以變形區出口橫向位移為待定參數，根據最小能量原理，使用優化方法求得出口橫向位移的數值解，進而確定變形區內的流動速度場、應變速度場和應力場等，建立條元理論分析模型達到精敏軋延的冷軋製程控制能力。本研究並利用商業套裝軟體有限元素法建立冷軋數值計算模型，進行數值計算分析鋼帶冷軋過程寬度的橫向分佈變化及軋製後寬度值，並與本研究所建立之條元法理論分析模型及實驗量測結果相互驗證。經由本研究之冷軋製程對於鋼材之板形控制，獲得冷軋前後之寬展分佈機制，並建立板形控制快速分析模型，同時利用有限元素法驗證鋼材於冷軋之寬展分佈，以確立進行冷軋製程於理論分析快速運算的正確性，亦採用實驗驗證數值數值計算的分析模型，故本研究藉由理論分析、數值計算與實驗量測完整建構鋼帶於冷軋製程中之板形控制的相關參數，以提升鋼廠冷軋製程現場之板形控制能力。

A finite strip element method is presented for analyzing the three-dimensional deformations and stresses of large cylindrical shell rolling process. In this study, the verification of cold rolling processes on finite strip element method (SEM), finite element method (FEM), and experimental measurement for flatness of stainless steel, aluminum and brass, respectively. The traditional theory of strip rolling is based on plane strain deformation, which ignores the lateral displacement of metal, distribution of thickness deformation, so that the outlet flatness cannot considered according to rolling pressure and front and back tension. FEM numerical calculation has also been widely used for analyzing the rolling process. In cold rolling process, each of these rotations must be divided into a large number of deformation increments, hence the number of increments is several times more than that in other metal forming simulation. In the SEM approach, the uneven distributions of deformations and stresses at the roll gap are taken into account. The rolling deformation zone is divided into a number of strip elements along the width directions. In order to reduce the optimization parameters and improve the computation efficiency, the exit lateral displacement distribution is expressed as linear differential function and third power spline function, respectively. Based on the fundamental principles of plasticity, the three-dimensional deformations and stresses of the deformation zone are formulated. The SEM results can be obtained quickly and easily. The predicted rolling force and average spread of the proposed method are in agreement with the experimental and FEM results.

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