摘要为了研究转速-攻角闭锁现象发生的机理和规律，推导了弹箭运动的动力学模型，进 而建立了转速-攻角闭锁的数学模型，利用劳斯判据，给出了解析形式的转速-攻角闭锁 运动的稳定性条件。以某导弹为例通过数值仿真，成功预示了闭锁现象的发生；求出了 不同参数条件下，闭锁稳态参数的解析解，通过数值仿真验证了解析解具有较好的精度； 研究了闭锁运动的规律，发现闭锁稳态转速的方向不仅和初始条件有关还和不同参数条 件下稳态解的情况有关；对于存在两个反向的稳态转速的情况，找出了全初始攻角方向 角下都不会发生稳态反转的初始转速-初始攻角区域。将解析形式的稳定性条件作为约 束，利用稳态解析解给出了稳态转速的优化设计模型，进行求解得到了较好的优化结果。81013

毕业论文关键词 转速-攻角闭锁 解析解 稳定性 优化设计模型

Title Analysis of Spin-Yaw Lock-In for a Rotationally Symmetric Missile

Abstract In order to study the mechanism and law of spin-yaw lock-in, the equations of motion were derived and thus, the mathematic model of spin-yaw lock-in motion was demonstrated。 The analytic stability condition of lock-in was given by Routh criterion，which can be used as an constraint in the later optimal design for lock-in spin．Taking a missile for an example, the paper shows that the lock-in of the coning motion and the rolling motion can occur by numerical integration of the equations of motion。 The analytical solutions for spin rate, amplitude, and phase angle for the steady-state equilibrium motion were found under different conditions。 The solutions were evaluated valid by comparison with numerical integration。 Moreover, the paper shows that the occurrence of positive or negative lock-in spin is determined not only by initial conditions but the solutions for equilibrium motion, because there can be only one lock-in spin under some conditions。 For the conditions with two opposite lock-in spin, calculations have identified regions of an initial spin rate-amplitude plane that determine only one spin can occur over all initial phase angle。 Finally, we attempted an optimal design model for lock-in spin is presented as an application of the spin-yaw lock-in model to the design of projectiles or missiles。

Keywords  spin-yaw lock-in  analytical solutions  stability  optimal design

本科毕业设计说明书 第 I  页

目 次

1  绪论 1

1。1  研究背景 1

1。2  研究现状 2

1。3  本文的研究内容 6

2  弹箭动力学模型 7

2。1  坐标系及变量定义 7

2。2  空气动力和力矩 8

2。2。1  气动力 8

2。2。2  气动力矩 9

2。2。3  非线性诱导力矩 12

2。3  质心运动及绕心运动方程 13

2。4  阻力方程和转速方程 15

2。5  复攻角运动方程 16

3  转速-攻角闭锁的数学模型