Carburizing process is an unsteady process, which conforms to Fick’s second law:
Where: t is the carburizing time, s; C is carbon content, kg / m3; Xi is the distance of carbon atoms in the diffusion direction, m; D is the diffusion coefficient, m2 / s, which is generally a function of temperature and carbon content:
Where: t is the temperature, ℃; D0.4 is the diffusion constant when the carbon mass fraction is 0.4%, taking d0.4 = 25.5 mm2 / S; B is the constant of the relationship between diffusion coefficient and carbon concentration, taking B = 0.8; Q is the activation energy of carbon atom diffusion, q = 141 kJ / mol; R is the gas constant.
The diffusion boundary conditions of carbon atoms are:
Where: CE and CS are the actual carbon content in the carburizing reaction furnace and the carbon content on the surface of the gear shaft respectively; β Is the carbon atom transfer coefficient, which can be expressed as:
Where: β 0 is a constant, take β 0 = 0． 003 47 mm / s; E is the activation energy, taking e = 34 kJ / mol.