快速辊系变形在线计算方法研究

工作辊和支撑辊弹性变形计算是板带轧机板形设定模型的关键,其计算速度与结果精度是当前制约辊系变形在线计算的主要因素。物理建模方面,在传统影响函数法的基础上,通过引入工作辊中心倾斜角度这一变量,改进辊系弹性变形简化模型,使辊系在非对称工况下也能满足弯矩平衡条件。在辊系变形数值计算方面,根据Timoshenko深梁理论建立挠曲平衡微分方程,采用有限差分法对四辊轧机辊系变形进行数学建模,计算辊系的角位移和挠曲变形。该有限差分模型采用递推方式进行挠曲计算,避开了影响函数法中的大量矩阵乘法运算,计算效率有较大提高。分别通过与影响函数法、有限元法对非对称工况的计算结果进行对比,验证基于有限差分法的快速辊系变形计算方法具有较快的计算速度和较高的精度。

Research on Rapid Online Calculation Methods of Roll Stack Deformation

Elastic deformation calculation of work roll and backup roll is a key part of shape setup model in strip rolling mill,its numerical efficiency and accuracy are the main factors that have restricted the application of online calculation.In the aspect of physical modeling,comparing with the conventional influence function method,the physical model of roll stack is improved by the introduction of central inclination angle of work roll,thus the balance of bending moment will be met even in an asymmetric work condition.In the aspect of numerical calculation,the equilibrium differential equations of deformation are established based on Timoshenko’s deep beam theory,and mathematic model of roll stack deformation is fully deduced by finite difference method,then the angular displacement and elastic deformation are calculated under asymmetric work condition.This numerical model employs recurrent formula instead of influence function method for deformation calculation,therefore,the computation complexity is largely reduced by a considerable reduction of matrix multiplication.High computational accuracy and efficiency of rapid roll stack deformation model based on finite difference method are validated respectively by contrasting with the influence function method and the finite element method in an asymmetric work condition.