旋转尾翼弹箭极限圆锥运动稳定判据

doi:10.3969/j.issn.1000-1093.2019.07.001

兵工学报 ›› 2019, Vol. 40 ›› Issue (7): 1329-1338.doi: 10.3969/j.issn.1000-1093.2019.07.001

旋转尾翼弹箭极限圆锥运动稳定判据

陈亮¹，刘荣忠²，郭锐²，席滔滔¹，李培林¹，朱桂利¹，杨永亮², 邢柏阳², 高科²

(1.中国航天科技集团有限公司第七研究院第七设计部，四川成都 610100; 2.南京理工大学机械工程学院, 江苏南京 210094)

收稿日期:2018-10-10 修回日期:2018-10-10 上线日期:2019-09-03
通讯作者: 刘荣忠（1955—），男，教授，博士生导师 E-mail:liurongz116@163.com
作者简介:陈亮（1990—），男，博士研究生。E-mail:studentcl@163.com
基金资助:
国家自然科学基金项目（11372136）；中央高校基本科研业务费专项项目(30916011306)

Stability Criteria for Limiting Conical Motion of Rotary Fin-stablized Projectiles

CHEN Liang¹, LIU Rongzhong², GUO Rui², XI Taotao¹, LI Peilin¹, ZHU Guili¹, YANG Yongliang², XING Boyang², GAO Ke²

(1.The Seventh Design Department, the Seventh Research Institute, China Aerospace Science and Technology Corporation, Chengdu 610100， Sichuan, China;2.School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China)

Received:2018-10-10 Revised:2018-10-10 Online:2019-09-03

摘要/Abstract

摘要： 为获得旋转尾翼弹箭极限圆锥运动稳定判据，针对现有理论方法的不足，提出了改进理论模型。该模型通过对弹箭在准圆运动状态下的振幅平面方程进行泰勒展开，从而充分考虑幅值变化对振幅平面方程中根号项取值的影响；在此基础上，根据不同参数取值情况，对其非零奇点的存在性和稳定性进行分析，导出了弹箭在非线性静力矩和非线性马格努斯力矩作用下形成稳定极限圆锥运动的解析判据，并给出两条仅与攻角方程初始参数相关的综合判据条件J₁>0和J₂>0；以某型旋转尾翼弹箭气动及结构特征参数为例，对所得理论判据进行了验证。研究结果表明，给出的稳定极限圆锥运动形成判据，与现有理论结果相比，更为全面且明确，利用所得判据条件，可方便准确地对弹箭极限圆锥运动特性进行分析判断。

关键词: 极限圆锥运动, 非线性运动, 马格努斯力矩, 运动稳定性, 泰勒展开

Abstract: A modified theoretical model is developed to analyze the limiting conical motion characteristics of rotary fin-stablized projectiles. The amplitude plane equation of projectiles in the state of quasi-circular motion is expanded as Taylor series, by which the value change of the square-root term in the amplitude plane equation is fully considered. The existence and stability of the nonzero singular points for the amplitude plane equation are analyzed comprehensively according to the different parameter values. The analytic criteria are presented, which present the necessary conditions for the formation of stable conical motion under the action of nonlinear static moment and nonlinear Magnus moment. Furthermore, two condition expressions denoted as J₁>0 and J₂>0, which just relate to the initial parameters of the angle-of-attack equation, are claimed as the comprehensive criterions in this paper and are used for the primary analysis of conical motion stability. Finally, a rotary fin-stablized projectile with known aerodynamic and structural parameters is taken as an example to verify the theoretical critera. The results indicate that the stability criteria for the limiting Conical Motion of rotary fin-stablized projectiles proposed in this paper are more comprehensive and explicit than those of the current theory. Based on the proposed criteria, the characteristics of limiting conical motion can be analyzed and estimated conveniently and effectively. Key

Key words: limitingconicalmotion, nonlinearmotion, Magnusmoment, motionstability, Taylorexpansion

中图分类号:

TJ012.3⁺3

陈亮，刘荣忠，郭锐，席滔滔，李培林，朱桂利，杨永亮, 邢柏阳, 高科. 旋转尾翼弹箭极限圆锥运动稳定判据[J]. 兵工学报, 2019, 40(7): 1329-1338.

CHEN Liang, LIU Rongzhong, GUO Rui, XI Taotao, LI Peilin, ZHU Guili, YANG Yongliang, XING Boyang, GAO Ke. Stability Criteria for Limiting Conical Motion of Rotary Fin-stablized Projectiles[J]. Acta Armamentarii, 2019, 40(7): 1329-1338.

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第40卷
第7期2019 年7月兵工学报ACTA
ARMAMENTARIIVol.40No.7Jul.2019

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[3]	钟扬威，王良明，傅健，常思江. 弹箭非线性角运动稳定性Hopf分岔分析[J]. 兵工学报, 2015, 36(7): 1195-1202.
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旋转尾翼弹箭极限圆锥运动稳定判据

Stability Criteria for Limiting Conical Motion of Rotary Fin-stablized Projectiles

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