旋转稳定弹丸非线性角运动吸引域计算方法

doi:10.3969/j.issn.1000-1093.2021.06.009

兵工学报 ›› 2021, Vol. 42 ›› Issue (6): 1195-1203.doi: 10.3969/j.issn.1000-1093.2021.06.009

旋转稳定弹丸非线性角运动吸引域计算方法

杨志伟¹，王良明¹，钟扬威^1,2，王垚^1,3，张喜峰³

(1.南京理工大学能源与动力工程学院, 江苏南京 210094; 2.中国航天科工集团有限公司第九总体设计部, 湖北武汉 430040; 3.北方华安工业集团有限公司, 黑龙江齐齐哈尔 161046)

上线日期:2021-07-19
通讯作者: 王良明（1963—），男，教授，博士生导师 E-mail:lmwang802@163.com
作者简介:杨志伟（1990—），男，博士研究生。E-mail: patch1205b@163.com
基金资助:
武器装备预先研究项目(2020年)

Calculation Method for the Nonlinear Angular Motion Attraction Domain of Spin-stabilized Projectile

YANG Zhiwei¹， WANG Liangming¹， ZHONG Yangwei^1,2， WANG Yao^1,3， ZHANG Xifeng³

(1.School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China;2.The 9th Overall Design Department, China Aerospace Science and Industry Corporation, Wuhan 430040, Hubei, China;3.North Hua’an Industry Group Co., Ltd., Qiqihaer 161046, Heilongjiang, China)

Online:2021-07-19

摘要/Abstract

摘要： 为计算旋转稳定弹丸的非线性角运动吸引域，建立了包含几何非线性和气动非线性的弹丸角运动方程。通过分析角运动方程原点及其周围平衡点的性质，将原点分为非唯一稳定平衡点和唯一稳定平衡点两种情况。针对原点为非唯一稳定平衡点情况，根据对称性得到原点的吸引域；针对原点为唯一稳定平衡点情况，通过计算原点处次临界Hopf分岔极限环半径得到其吸引域。以某型155 mm榴弹为例进行仿真验证和分析计算，结果表明：所采用方法能够准确计算原点周围不稳定的极限环，且该极限环就是原点吸引域的边界；马格努斯力矩三次项系数是影响原点吸引域大小的主要因素；在超音速范围内，随弹丸初速增加，原点吸引域先减小、后增大；空气密度越大，原点吸引域越小；移动平台发射的旋转稳定弹丸运动失稳也是由吸引域的影响造成的。

关键词: 旋转稳定弹丸, 非线性角运动, 吸引域, 平衡点, 次临界Hopf分岔

Abstract: An angular motion equation, including geometric nonlinearity and aerodynamic nonlinearity, for spin-stabilized projectile is established to calculate the attraction domain of nonlinear angular motion of projectile. The properties of the origin and its surrounding equilibrium points are analyzed, and the origin in the attraction domain is divided into non-unique stable equilibrium point and unique stable equilibrium point. For the case where the origin is non-unique stable equilibrium point, the attraction domain of the origin is obtained according to the symmetry. And for the case where the origin is the unique stable equilibrium point, the attraction domain is obtained by calculating the limit cycle radius of the subcritical Hopf bifurcation at the origin. The analysis calculation and simulation verification of a 155 mm grenade as an example were made. The results show that the proposed calculation method can be used to accurately calculate the unstable limit cycle around the origin, and the limit cycle is the boundary of attraction domain of the origin. The cubic term coefficient of Magnus moment is the main factor affecting the size of origin attraction domain; in the supersonic range, the area of the origin attraction domain first decreases and then increases with the increase in the projectile’s initial velocity. The greater the air density is, the smaller the area of the origin attraction domain is. The instability of the spin-stabilized projectiles launched from the mobile platform is also caused by the attraction domain.

Key words: spin-stabilizedprojectile, nonlinearangularmotion, attractiondomain, equilibriumpoint, subcriticalHopfbifurcation

中图分类号:

TJ012.3⁺3

杨志伟，王良明，钟扬威，王垚，张喜峰. 旋转稳定弹丸非线性角运动吸引域计算方法[J]. 兵工学报, 2021, 42(6): 1195-1203.

YANG Zhiwei， WANG Liangming， ZHONG Yangwei， WANG Yao， ZHANG Xifeng. Calculation Method for the Nonlinear Angular Motion Attraction Domain of Spin-stabilized Projectile[J]. Acta Armamentarii, 2021, 42(6): 1195-1203.

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旋转稳定弹丸非线性角运动吸引域计算方法

Calculation Method for the Nonlinear Angular Motion Attraction Domain of Spin-stabilized Projectile

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