变扩散系数离子渗氮模型的建立与验证

A new model of ion-nitriding based on variant diffusion coefficient

在离子渗氮过程中 ,扩散系数D是随氮质量分数而变化的 .结合这一情况 ,利用Crank -Nicolson差分方程 ,并假定工件的硬度值与其含氮量是成正比关系 ,建立基于变扩散系数的离子渗氮的新模型 ,并利用Matlab工具对其进行计算机模拟及实验验证 .结果表明 ,2 0CrMnTi渗氮 8和 10h后 ,实测的横截面显微硬度曲线与通过本模型计算而得的硬度曲线较好地相符 ;本模型成功地模拟了离子渗氮过程的氮质量分数变化 .同时 ,随着时间的延长 ,迭代法对误差进一步放大 .本模型只需通过简单易行的硬度测量 ,即可对离子渗氮过程的氮质量分数分布进行定量地预测 ,获得较为满意的结果 ,对指导生产具有很大的意义 .

In ion-nitriding process, diffusion coefficient D is a function of nitrogen concentration. assuming the hardness is in proportion to nitrogen concentration, a new model is proposed using Crank-Nicolson differential equation to describe the ion-nitriding process with variant diffusion coefficient D. The model is also simulated on computer using Matlab and validated by experiments. The result shows that after 8 h and 10 h ion-nitriding on 20CrMnTi, the measured hardness curve on the cross section is in good agreement with the computer-simulated result well, which indicates that this new model successfully simulates the change of the nitrogen concentration during ion-nitriding. Meanwhile, the error developed by iterative calculating accumulates with prolonged time . only the hardness measurement on cross section is needed to predict the nitrogen concentration on the cross section during ion-nitriding,