非线性力矩作用下气动偏心弹丸强迫圆锥运动稳定性条件  

Forced Conical Motion Stability Conditions for Pneumatic Eccentric Projectile under the Action of Nonlinear Moment

作　　者：舒敬荣 李红星 李宏玲[1] SHU Jing-rong;LI Hong-xing;LI Hong-ling(College of Electronic and Communication Engineering, Anhui Xinhua University, Hefei 230031, Anhui, China)

机构地区：[1]安徽新华学院电子通信工程学院,安徽合肥230031

出　　处：《兵工学报》2018年第5期875-882,共8页Acta Armamentarii

基　　金：国家自然科学基金项目(11272356);中国博士后科学基金项目(2012M521842)

摘　　要：为了指导无伞末敏弹等气动非对称弹丸的结构设计和气动设计,建立了气动偏心弹丸在三次方非线性静力矩和二次方非线性赤道阻尼力矩作用下的攻角方程,运用平均法求解了方程的近似解析解及其线性变分方程。在此基础上,根据Hurwitz判别准则,得到了气动偏心弹丸做强迫圆锥运动的渐近稳定条件,分析了该条件的物理意义,并应用数值计算算例对该条件进行了验证。结果表明,当自转角速度和气动偏心角满足一定的约束条件时,三次方非线性静力矩和二次方非线性赤道阻尼力矩作用下的弹丸可以实现固定攻角的稳定强迫圆锥运动。An angle of attack equation of pneumatic eccentric projectile under the action of cubic nonlin- ear static moment and quadratic nonlinear equatorial damping moment is established for the structure de- sign and aerodynamic design of pneumatic asymmetric projectiles, such as non-parachute terminal sensi- tive projectile, and the approximate analytical solution of the equation and linear variational equation are solved by using average method. On this basis, the asymptotic stability conditions of forced conical mo- tion for pneumatic eccentric projectile is obtained according to Hurwitz criterion, and the physical mean- ing of the conditions is analyzed. The numerical calculation example is used to verify the conditions. Re- sult shows that the projectile under the action of cubic nonlinear static moment and quadratic nonlinear e- quatorial damping moment can achieve steady forced conical motion at fixed angle of attack when spin ve- locity and pneumatic eccentric angle satisfy certain constraint conditions.

关 键 词：无伞末敏弹 气动偏心 非线性空气动力 圆锥运动 运动稳定性 

分 类 号：TJ012.33[兵器科学与技术—兵器发射理论与技术]