MATHEMATICAL MODELING OF THE SHOT PROCESS TAKING INTO ACCOUNT THE BARREL BULGE OF A FIREARM AS A MEANS OF INFLUENCING THE EFFICIENCY OF PERFORMANCE OF SERVICE AND COMBAT MISSIONS OF SECURITY FORCES

The role and place of operational control of armament parameters in ensuring the given efficiency of performance of service and combat tasks by security forces are noted. The barrel bulge diagnosing method based on the analysis of experimentally received ballistic elements of a shot is considered. To implement this method, you need to have reference curves for ballistic elements of shot – the pressure of the powder gases and the velocity of the projectile – which correspond to different degrees of manifestation of the barrel bulge. Reference curves can be obtained by simulating the firing process numerically. Simulation of the firing process by numerical method, taking into account the bulge, requires considering the loss of powder gases due to their breakthrough between the walls of the barrel and the projectile. Methods for accounting the loss of some of the powder gases in variable cross-section of the barrel were not developed at this time. Thus, improving the shot model taking into account the loss of powder gases due to bulge is an urgent task. The purpose of this work is to develop the mathematical description of the barrel bulge and obtain the mathematical basis for its accounting in the shot model. The mathematical description of the bulge by means of polynomial and trigonometric functions is given. The fundamentals of the bulge accounting in the shot model are considered. In particular, when modeling the firing process, the effect of the breakthrough of powder gases should be taken into account by introducing into the difference model of the shot a special factor ‒ the coefficient of loss of mass of powder gases. The curves for the pressure of powder gases and the velocity of the projectile for various samples of firearms are obtained by numerical modeling. The presence of the bulge can be well identified by the appearance of graphs of pressure and velocity for different degrees of this defect. The results of the work prove the possibility of barrel bulge detection by the curve analysis; moreover the location and the degree of manifestation of this defect can be determined.