Regression model of the extraction force of an automatic rifle cartridge case

Reliable extraction of the cartridge case after firing is essential to the proper functioning of a gas-operated gun. This study presents a predictive model for the extraction force of a 7.62×39 mm steel cartridge case, based on the maximum chamber pressure and the contact friction coefficient (between the cartridge case and the chamber). A Central Composite Design (CCD) with two factors was used to generate the simulation data from finite element models developed in ANSYS. A reduced quadratic regression model was constructed and statistically validated, showing a high predictive capability (R2 = 0.969, adjusted R2 = 0.953). The model reveals that friction has a stronger influence on the extraction force than the maximum pressure, and that their interaction is non-linear. Experimental validation at the design centre, using a custom-built extraction test rig, yielded an average measured force of 39.10 N, closely matching the predicted value of 38.90 N (error = 0.51 %). The proposed model is a fast and reliable tool for the design and optimisation of ammunition and extractor mechanisms in small arms.