旋转导弹喷气阻尼效应建模与分析

旋转导弹在主动段不仅受到气动力和气动力矩的作用,还受到质量特性变化和喷气的影响。为研究旋转导弹在主动段的运动特性,对其喷气阻尼效应进行了建模与分析。首先,将旋转导弹看作连续质点系,根据变质量力学的基本原理,建立了同时考虑气动力矩、喷气阻尼效应和变质量特性的旋转导弹动力学方程;然后,分别对喷气阻尼效应和非线性变质量特性作用下导弹自旋转速和锥形运动的特性进行了理论分析,推导了喷气阻尼效应和气动力矩共同作用下旋转速度的表达式,并分析了锥形运动的稳定性,得到了稳定的充要条件;最后,利用数值仿真对理论分析的结果进行了验证.理论分析和仿真结果表明:喷气阻尼效应和变质量特性会影响导弹的自旋转速和锥形运动特性;若要保持导弹转速不变,应使药柱半径略小于发动机喷口截面半径,而喷气阻尼效应增大了锥形运动的阻尼,有利于保持锥形运动的稳定;质量特性的非线性变化能使锥形运动更快收敛;喷气阻尼效应和变质量特性对旋转导弹运动特性的影响不可忽略,在设计和分析中应加以考虑.

Modeling and analysis of jet damping effect for spinning missiles

In the powered phase, spinning missiles are affected by not only aerodynamic forces and moments, but also variable mass characteristics and jet. In order to investigate the dynamic characteristics of spinning missiles in the powered phase, the jet damping effect was modeled and analyzed. Firstly, spinning missiles were modeled as continuous particle systems. The dynamics equations of spinning missiles considering aerodynamic moments, jet damping effect, and variable mass characteristic were established. Then, the characteristics of the spin speed and coning motion under the jet damping effect and nonlinear variable mass characteristics were theoretically analyzed respectively. Moreover, based on the sufficient and necessary condition for stability of coning motion, the expressions of spin speed, quasi-attack-angle and quasi-sideslip-angle were derived under the combined influence of jet damping effect and aerodynamic moments. Finally, the results of theoretical analysis were verified by numerical simulations. The theoretical analysis and numerical simulation results show that the variable mass characteristics and jet damping effect affect the missile''s spin speed and coning motion. To keep spin speed constant, the radius of grain should be slightly smaller than that of the engine nozzle. The jet damping effect increases the damping of coning motion, which is advantageous to coning motion stability. Nonlinear variations of mass characteristics can make cone motions converge faster. The variable mass characteristics and jet damping effect cannot be ignored in design and analysis.