快速三维塑性变形在线计算方法研究

Research on Rapid Online Calculation Method of Three-dimensional Plastic Deformation

带钢三维塑性变形计算是板带轧机板形设定模型的关键,其计算速度、精度及稳定性是当前制约轧制变形在线计算的重要因素。基于现有三维差分变形模型的理论局限性,结合增量理论和流体动力摩擦理论,考虑应力与应变之间的关系处理、带钢单元剪应力的作用及带钢与工作辊接触面上纵向与横向摩擦系数的不一致性等,构造了差分模型的基本方程,利用渐近分析原理对基本方程中的应力、应变及变形速率等参数进行归一化处理,建立了基于有限体积法的带钢三维塑性变形模型,并且通过稳定双共轭梯度算法实现快速稳定求解,得到热轧精轧机组各机架轧制压力的横向分布。通过与用ANSYS建立的有限元模型对比,结果表明计算结果可靠且稳定性好,计算时间由3.5 h缩短为31 ms,验证了快速三维塑性变形计算方法在线应用的可行性。

Three-dimensional plastic deformation calculation of strip is a key part of the shape setup model in strip rolling mill. The numerical efficiency, accuracy and stability of the calculation model are the main factors that have restricted the application of online calculation. Based on the theoretical limitations of existing models of three-dimensional difference deformation, combined with the incremental theory and hydrodynamic friction theory, considering the relationship between stress and strain, the effect of unit shear stress on the deformation zone and the difference of lateral and longitudinal friction coefficient at the interface between the working roll and strip, basic equations of the difference model are constructed. According to the asymptotic calculation principle, relevant parameters in the basic equations such as stress, strain, deformation rate, etc. are normalized. And then the three-dimensional plastic deformation model of strip is established by using the finite volume method, which can be used to calculate lateral rolling force distribution of each stand in hot strip mills rapidly by BICGSTAB algorithm. The feasibility of online application of the rapid three-dimensional plastic deformation model is validated by contrasting with the finite element model established by ANSYS software, which reflects that the result of calculation is reliable and stable and the computation time is shortened to 31 ms from 3.5 h.