用四元数建立引信球转子定点转动的数学模型  

Mathematical Model of Fuze Ball Rotor Rotation Around Fixed Point with Quaternion

作　　者：陈会光[1] 王雨时[1] 闻泉[1] 

机构地区：[1]南京理工大学机械工程学院,江苏南京210094

出　　处：《兵工学报》2009年第6期688-694,共7页Acta Armamentarii

摘　　要：球转子机构是一种典型的引信隔爆机构,优化设计之后还可实现延期解除保险功能。应用欧拉运动学方程组建立的引信球转子转正运动数学模型,数值求解在球转子接近转正时存在着奇异性,为克服这一问题,应用四元数理论,在分析质心、形心与弹丸旋转轴均不重合时的球转子动力学基础上,建立了描述球转子在其腔室内定点转正运动的新的数学模型。这是一组非退化的线性微分方程组,没有奇异点,有助于得出不失真的球转子运动数值解,从而深入研究球转子的动态平衡角现象。The ball rotor device is a typical fuze primary explosive safety device, and can realize arming delay with optimized design. In order to conquer the fantasticality of the numerical results from the mathematical model established with the Euler kinematics equations for fuze ball rotor rotation when the rotor is nearly in alignment, on the basis of dynamics of the rotor whose mass center doesn＇t coin- cide with its geometric center and has an offset from spin axis of projectile, the new mathematical model of the rotor rotation around fixed point was established with quaternion method. This is nondegenerate linearity differential equations, without fantastic dot, of help to obtaining the distortionless numerical results of the rotor motion and consequently researching on the dynamic balance angle of the rotor deeply.

关 键 词：机械学 引信 球转子机构 延期解除保险 动力学分析 四元数 数学模型 

分 类 号：TJ430.1[兵器科学与技术—火炮、自动武器与弹药工程]