基于有限差分和有限元方法的镁合金轧制计算结果分析

Calculation results analysis of magnesium alloy rolling based on finite difference and finite element methods

通过有限元方法、有限差分方法、理论计算结合轧制实验,对比分析了AZ31镁合金板材各物理场的分布结果,以提高AZ31镁合金的计算精度。在轧制速度为246 mm·s^(-1)、温度为300~500℃和不同压下率条件下,采用有限差分法和有限元法对AZ31镁合金板材热轧过程进行数值模拟,运用有限差分程序和Abaqus有限元软件对轧制过程中的平均压力、等效应变以及轧制力进行了对比分析,同时测试了400℃不同压下率下的轧制力。结果表明:有限差分方法计算出的平均压力大于有限元方法的计算结果,压下率小于30%时,相对误差在20%以下,随压下率的增大,二者的计算结果差异逐渐增大,有限差分法计算的平均压力在中心点附近有明显的峰值。等效应变的有限元计算结果与实验结果的变化趋势基本一致,但实验结果存在明显的不对称性。轧制力的实验结果表明,与有限差分法相比,有限元法的轧制力计算结果与实验结果更接近,400℃各压下率下的相对误差均小于4%。

The distribution results of each physical field of AZ31 magnesium alloy sheet were compared and analyzed by finite element method(FEM),finite difference method(FDM),theoretical calculation and rolling experiment to improve the calculation accuracy of AZ31 magnesium alloy.Under the conditions of rolling speed of 246 mm·s^(-1),temperature of 300-500℃and different reduction ratios,the hot rolling process of AZ31 magnesium alloy sheet was simulated numerically by FDM and FEM.The average pressure,equivalent strain and rolling force in the rolling process were analyzed and compared using finite difference program and Abaqus finite element software.The rolling force with different reduction ratios at 400℃was measured.The results show that the average pressure calculated by FDM is larger than that calculated by FEM.When the reduction ratio is less than 30%,the relative error is less than 20%.With the increase of reduction ratio,the difference between the two calculation results gradually increases.The average pressure calculated by FDM has a distinct peak value near the central point.The variation trend of the equivalent strain calculated by FEM is basically consistent with that of experimental results,but there is obvious asymmetry in the experimental results.The experimental results of rolling force show that compared with FDM,the calculation results of rolling force by FEM are closer to the experimental results,and the relative errors with each reduction ratio at 400℃are less than 4%.