本研究主要探討四輥系軋機的彈性變形分析，利用影響係數法以及莫爾積分法，考慮在軋延過程中軋制載荷、彎輥力和支反力的作用下，支承輥以及工作輥之間的彈性變形，並且假設輥間接觸壓力之初值，利用迭代法進而求出真實輥間接觸壓力。其中輥間接觸壓力是參考四輥軋機軋制帶材力學模型的計算，推導支承輥以及工作輥軸線的總撓度，將計算得到的相關係數代入位移協調方程式，再利用工作輥之力與力偶平衡方程，一起化簡代入影響係數矩陣進行運算求解。求解的方式可利用高斯消去法，求解出新的輥間接觸壓力，再將新的輥間接觸壓力與上一次的結果進行誤差比對，最後將新的輥間接觸壓力取代初始輥間壓力，並且再次利用高斯消去法重新計算影響係數矩陣，直到輸出的輥間接觸壓力之誤差位於設定的允許範圍之內。
而工作輥表面壓扁量的計算，可利用半空間模型分析來進行求解，首先假設軋制壓力沿金屬變形區長度呈均勻分布，計算出軋件上一點對於工作輥表面以及中心的壓扁量，接著再計算出軋件上一點對於工作輥表面之壓扁量，最後將兩者進行相減即可得到工作輥表面壓扁量之結果。
本論文藉由開發應用於冷軋製程之輥系彈性變形的分析模型，利用迭代法可以快速計算出支承輥以及工作輥之間的輥間接觸壓力，其計算速度超越有限元素法之模型分析計算，期望能對於鋼廠於冷軋製程中，加速輥間接觸壓力的掌握，並且能夠得到更加精確的數值，進而達到於製程中鋼帶的出口板形能夠快速調整並且控制的技術。

This study mainly discusses the elastic deformation analysis of roller system for a four-roll mill. By using the influence coefficient method and the Mohr integral method, the effect of the rolling load, the bending force, and the reaction force of the support roll and the work roll are numerically calculated for the rolling process. The iterative method used to determine the actual contact pressure and deflection between the working rollers, backup roller, and rolling strip under the mechanical model of the rolling strip of the four-high mill, when the initial value of the contact pressure is applied on the rollers to produce elastic deformation. Substituting the relative coefficient into the equation of compatibility, the equivalent equation are used repeatedly to obtain the influence coefficient matrix until solution converged. The solve method used by Gaussian elimination to determine the new contact pressure between rollers. Hence, the error of the contact pressure is under allowable range.
The deflection of the work roll surface were solved by half-space model analysis. First, assuming the rolling pressure on metal deformation is evenly distributed along the length of the area, the pointwise deflection on the work roll surface relative to the center is calculated; then, the subtraction the value from the deflection on the work roll surface obtained the numerical results.
In this study, by developing the analytical model of the elastic deformation on roll system, the contact pressure between the backup roll and the work roll can be rapidly calculated in cold rolling process by the iterative method. Because the speed of calculation in this study exceeds extremely the analysis of the finite element method, it is expected that this accurate mode for obtained contact pressure is applied to control the strip shape of the steel during the cold rolling process.

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