基于流函数法的铝合金板材异步轧制应变计算数学模型

作为一种剧烈塑性变形技术,异步轧制是提高铝合金板材变形均匀性的重要方式。但由于异步轧制中存在多变量、强耦合、非线性等特点,其厚度方向变形机制难以精准解析。为深入研究异步轧制厚度方向变形情况,建立了一种板材异步轧制沿厚度方向应变计算模型。根据轧制过程的运动学特点,变形区被分为刚性-塑性-刚性区。在此基础上对变形区边界条件进行了修正,并采用流函数法建立近真实的运动学容许速度场。根据最小能原理和线性化积分手段建立了轧制功率消耗模型,解决了计算过程中的多参量非线性耦合问题,实现了变形区边界模型的快速计算。结合速度分量与应变速率分量,最终建立了异步轧制轧后应变计算模型。为了验证理论模型的准确性进行了数值模拟与异步轧制试验。与试验结果进行对比,计算结果最大误差为13.44%,最小误差为1.33%,整体计算耗时缩减到1 s以下。模型的建立可为异步轧制板材质量调控与预测提供重要理论参考。

Mathematical model for asymmetrical rolling strain of aluminum alloy plate based on the stream function method

Asymmetrical rolling is an important way to improve the deformation quality of aluminum alloy sheet as a severe plastic deformation technology. The deformation mechanism in thickness direction is difficult to be analyzed due to the characteristics of multivariable, strong coupling and nonlinearity in asymmetrical rolling of plate. In order to deeply study the deformation in the thickness direction of asymmetrical rolling, a strain calculation model along the thickness direction after asymmetrical rolling is established. The deformation zone is divided into rigid plastic rigid zone according to the kinematic characteristics of rolling process. On this basis, the boundary conditions of the deformation zone are modified, and the stream function method is used to establish the near-real velocity field. According to the minimum energy principle and linearized integration method, the rolling power consumption model is established, the multi-field and multi-parameter nonlinear coupling problem in the calculation process is solved, and the rapid calculation of the boundary model of the deformation zone is realized. Finally, the strain calculation model of asymmetrical rolling is established by combining the velocity components and strain rate components. In order to verify the asymmetrical of the theoretical model, numerical simulation and asynchronous rolling experiments were carried out. Compared with the experimental results, the maximum relative error of the calculation results is 13.44%, and the minimum relative error is 1.33%. The overall calculation time is reduced to less than 1 second. The establishment of this calculation model can provide an important theoretical reference for the quality control and prediction of asymmetrical rolling.