模拟板带轧制三维变形的流面条元法

STREAM SURFACE STRIP ELEMENT METHOD FOR SIMULATION OF THE THREE-DIMENSIONAL DEFORMATIONS OF PLATE AND STRIP ROLLING

提出模拟板带轧制过程三维变形的一种新的数值方法——流面条元法。沿着金属的流动轨迹,将变形区划分为若干流面(曲面)条元,为方便分析和计算,又将其映射为平面条元。横向位移和高向位移的纵向分布被分别构造为四次曲线和二次曲线,其横向分布均用三次样条插值函数表示,高向分布均用二次曲线拟合。根据塑性力学流动理论,分析推导了变形区三维变形和应力的数学模型。与曾经提出的流线条元法相比,考虑了应力与变形沿高向的不均匀分布,实现了精确的三维分析和计算。仿真实例表明,该方法和模型符合实际,为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。

A new method-the stream surface strip element method (SSSEM) for simulating the three-dimensional deformations of plate and strip rolling process is put forward. The rolling deformation zone is divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements are mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal are respectively constructed to be a quartic curve and a quadratic curve, the lateral distributions of them are expressed as the third-power spline function, and the altitudinal distributions of them are fitted to be the quadratic curve. From the flow theory of plastic mechanics, the three-dimensional deformations and stresses of the deformation zone are analysed and formulated. Compared with the streamline strip element method (SSEM) that is put forward, the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction, and realizes the precise three-dimensional analysis and computation. The simulation examples indicate that the method and the model accord with facts, and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.