Numerical simulation and process parameter optimization of gas nitriding in 4Cr5MoVSi splines

Gas nitriding is widely used to improve the surface durability and service stability of steel spline components; however, parameter selection for complex spline geometries remains largely experience-dependent. In this work, a three-dimensional engineering diffusion model was developed for an actual 4Cr5MoVSi spline geometry to predict nitrogen concentration and effective case depth. Nitrogen transport was described using an effective Fickian formulation with calibrated surface concentration and diffusion coefficient. Three representative gas-nitriding tests were used for parameter calibration and an experimental agreement check. The calculated case depths were 0.127, 0.183, and 0.201 mm, respectively, showing the same increasing tendency and comparable magnitude as the metallographically observed layers. Following parameter calibration and the experimental agreement check, the model was used to examine the effects of nitriding temperature, holding time, and ammonia dissociation rate. Temperature and ammonia dissociation rate showed non-monotonic effects, whereas holding time increased the case depth, but the incremental increase gradually diminished. A Box–Behnken response surface model was established, with a coefficient of determination R 2 of 0.9986 and an adjusted R 2 of 0.9967. Within the selected process window, the model-based favorable condition was approximately 580 °C, 14 h, and 70% ammonia dissociation rate, giving a predicted case depth of about 0.257 mm.