一段式和二段式渗碳(氮)扩散方程的解析解及其物理意义

Analytical solution of diffusion equation of one-stage or two-stage carbonizing (nitriding) and its physical meaning

利用热量扩散方程在第三类边界条件下和一维、半空间内已有的积分求解公式,对工件预先未经渗碳和预先经过渗碳这两种初始条件,分别推导出一段式和二段式渗碳(氮)时扩散方程的解析解。通过对该解进行的数学分析和物理分析,可以更进一步地理解工件表面碳(氮)浓度的变化规律;并预测出在等温扩散条件下获得碳平台分布需要的最佳扩散时间。

Using integral formula of diffusion equation of heat quantity based on the third boundary condition and one-dimension-half-space,the analytical solution of diffusion equation of one-stage or two-phase carbonizing（nitriding）was derived,respectively,for two initial conditions,with or without pre-carbonizing.Through mathematical and physical analysis,the regular pattern of carbon（nitrogen）concentration in part surface can be further understood,and the optimum diffusion time needed for obtaining carbon terrace in isotherm diffusion condition can be forecasted.