An analytic model for the low-pressure carburizing process

Low-pressure carburizing is a clean and efficient surface modification process that enables the creation of a high-strength surface layer. Low-pressure carburizing primarily employs the pulse process, which consists of a boost process and a diffusion process. The distribution of carbon content is calculated using Fick's law, which is now typically done using numerical methods. In this paper, the analytic solution for solving the second Fick's law with a periodic initial condition is derived using the Fourier series and Green's function. The analytic model consists of the analytic solutions for the boost process and diffusion process. The surface carbon transfer coefficient is related to the surface carbon content and the total carburized carbon mass, while the diffusion coefficient is beneficial for achieving a deeper carburizing depth. Withs an increase in the surface carbon content high point and the decrease of the difference between surface carbon content high point and low point, carburizing efficiency increases under a fixed carburizing target. The carbon content distribution is almost the same when the total carburized mass is the same for different carburizing strategy.