多段法渗碳碳浓度分布的解析计算方法

Analytic method to calculate the carbon concentration in multi-stage carburizing

多段法渗碳的数学模型是线性偏微分方程。线性偏微分方程的一个重要性质是可迭加性。文章以球形工件多段法渗碳为例 ,建立起多段法渗碳的数学模型并运用迭加原理和分离变量法求得了球形工件多段法渗碳定解问题的解析解 ,即碳浓度分布函数。碳浓度分布函数可以更加深刻地描述多段法渗碳的物理本质。

The mathematical model of multi stage carburizing is a linear partial differential equation, and superposability is an important property of the linear partial differential equation.In this paper,the mathematical model of the sphere multi stage carburizing is introduced and its analytic solution is obtained based on the superposition principle of the linear partial differential equation and the method of separation of variables. With the carbon concentration function, the physical meaning of the multi stage carburizing can be described more incisively.