弹丸刚体外弹道及其引信力学环境数值解算稳定性  

The stability research of numerical solution for rigid body exterior ballistics and fuze mechanical environment in exterior ballistics

作　　者：回建豪 王雨时[1] 闻泉[1] 彭启蒙 HUI Jianhao;WANG Yushi;WEN Quan;PENG Qimeng(School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学机械工程学院,南京210094

出　　处：《兵器装备工程学报》2024年第11期42-50,共9页Journal of Ordnance Equipment Engineering

摘　　要：针对弹丸刚体外弹道常微分方程组及引信惯性零部件轴向过载求解稳定性问题,借助计算机,以不同数值计算方法和不同积分时间步长对弹丸刚体外弹道常微分方程组及引信惯性零部件轴向过载求解,得到刚体外弹道常微分方程组的数值解,即刚体外弹道含质心运动和绕质心运动的诸元,在此基础上又得到了引信惯性零部件轴向过载的数值解。通过大量仿真发现:应用龙格-库塔法、阿当姆斯预报-校正法和吉尔法解算刚体外弹道常微分方程组,当积分时间步长取为0.05 s时,质心运动诸元解算结果均收敛;在积分时间步长取10^(-4) s时,绕心运动诸元解算结果也均收敛。而在解算引信惯性零部件轴向过载突变峰值时,发现若使峰值稳定,这3种方法均需调整积分时间步长小于或等于10^(-5) s。而求解引信惯性零部件轴向过载,只有吉尔法未失真。Aiming at the stability problem of solving the system of ordinary differential equations of the outer ballistic path of the projectile rigid body and the axial overload of the inertial parts of the fuze,with the help of the computer,we solve the system of ordinary differential equations of the ballistic path of the projectile rigid body and the axial overload of the inertial parts of the fuze with different numerical computation methods and different integration time steps,and then we get the numerical solution for the system of ordinary differential equations of the ballistic path of the projectile rigid body,i.e.,the plurals of the ballistic path of the projectile rigid body with the motion of the center of mass and the motion of the plurals around the center of mass.Numerical solutions for axial overloading of fuzed inertial components are obtained on this basis.By extensive simulation,it has been found that when using Runge-Kutta method,Adams method,and Gear method to solve the system of ordinary differential equations for rigid exterior ballistics,the elements of center of mass motion converge when the integration time step is set to 0.05 seconds;the element of motion around the center converge when the integration time step is set to 10^(-4) s.When calculating the peak value of the axial overload sudden change of the inertial component of fuze,it was found that if the peak value is converged,all three methods need to adjust the integration time step to be less than or equal to 10^(-5) seconds,but in this condition only the Gear method keep correct.

关 键 词：数值解算 外弹道解算 引信轴向过载 积分时间步长 吉尔法 

分 类 号：TJ012.3[兵器科学与技术—兵器发射理论与技术] TJ430.1