梁弯曲振动的键合空间表示及其在炮口扰动分析中的应用

doi:10.12382/bgxb.2022.0175

摘要/Abstract

摘要：

为模拟梁类复杂系统的动力学行为,基于键合空间理论建立Timoshenko梁弯曲振动的动力学模型和固有频率特性分析方法。定义梁单元势、流、动量和位变空间向量,推导以动量空间向量和位变空间向量及其1阶导数表示的梁单元状态方程;通过直接求解特征值问题获得梁弯曲振动的固有频率和相应振型,所提方法与解析法计算的前6阶固有频率最大相对误差为 0.7960%,MAC不小于0.9972,说明梁弯曲振动键合空间模型是正确的。在此基础上,将所建梁弯曲振动键合空间模型嵌入某火炮自动机系统发射动力学模型中,开展了炮口扰动分析,仿真与连发射击试验测试结果相符,说明所建炮口扰动分析模型是正确的,为弹炮耦合发射系统动力学分析提供了新方法。

关键词: Timoshenko梁, 弯曲振动, 固有频率, 炮口扰动, 键合空间法

Abstract:

In order to accurately simulate the dynamic behavior of complex beam system, a dynamic model for the Timoshenko beam is established based on the bond space theory, and the method to analyze the natural frequency is presented. The space vectors of effort, flow, momentum, and displacement for the beam unit are defined, and the state equations expressed in momentum space vectors, displacement space vectors, and their first derivatives are derived. Then, the natural frequencies and corresponding mode shapes of the bending beam are obtained by directly solving the eigenvalue problem. The natural frequencies of the free beam, calculated using the proposed bond space approach, match well with the analytical method. On this basis, the proposed model for the bending beam is used to extend the traditional launching system of the automatic gun. The calculated muzzle disturbance aligns well with the firing experiment, indicating that the proposed method is valid. This study provides a new method for the dynamic analysis of projectile-barrel coupling systems.

Key words: Timoshenko beam, bending vibration, natural frequency, muzzle disturbance, bond space method

林圣业, 王茂森, 谢杨杨, 李勇, 戴劲松. 梁弯曲振动的键合空间表示及其在炮口扰动分析中的应用[J]. 兵工学报, 2023, 44(6): 1775-1783.

LIN Shengye, WANG Maosen, XIE Yangyang, LI Yong, DAI Jinsong. Bond Space Expression of Bending Vibration in Timoshenko Beam and Its Application in Muzzle Disturbance Analysis[J]. Acta Armamentarii, 2023, 44(6): 1775-1783.

图/表 20

图1 梁弯曲振动的键合空间拓扑结构图

Fig.1 Bond space model for the beam unit

表1 自由梁前6阶固有频率

Table 1 First six natural frequencies of the free beam

序号	固有频率/Hz		相对误差/%	MAC
序号	键合空间法	解析法	相对误差/%	MAC
1	184.31	184.34	0.0163	1.0000
2	510.61	508.15	0.4841	1.0000
3	1001.93	996.19	0.5762	0.9999
4	1657.51	1646.76	0.6528	0.9995
5	2478.01	2459.97	0.7333	0.9987
6	3463.18	3435.83	0.7960	0.9972

图2 1阶固有振型

Fig.2 First-order natural mode of vibration

图3 2阶固有振型

Fig.3 Second-order natural mode of vibration

图4 3阶固有振型

Fig.4 Third-order natural mode of vibration

图5 4阶固有振型

Fig.5 Fourth-order natural mode of vibration

图6 5阶固有振型

Fig.6 Fifth-order natural mode of vibration

图7 6阶固有振型

Fig.7 Sixth-order natural mode of vibration

图8 某火炮自动机物理模型

Fig.8 Physical model of the automatic gun

图9 某火炮自动机键合空间模型

Fig.9 Bond space model of the automatic gun

表2 各结点下标的含义

Table 2 Description of the subscripts

下标	含义
1	炮箱
2~N	炮管
N+1	弹丸
i	身管上与缓冲装置联结点
j	身管上与弹带接触点
k	身管上与弹丸定心部接触点
1r	炮箱后导轨接触点
1f	炮箱前导轨接触点
jr	弹带接触点
kf	前定心部接触点

图10 炮口扰动测试原理

Fig.10 Test principle for measuring the muzzle disturbance

图11 测试实景图

Fig.11 Setup for measuring muzzle disturbance

表3 某火炮自动机主要参数

Table 3 Parameters of the automatic gun

参数	数值
口径/m	0.03
炮箱质量/kg	45
炮管长度/m	1.2
炮管材料密度/(kg·m^-3)	7800
炮管材料弹性模量/GPa	204
炮管材料泊松比	0.28
射速/(发·min^-1)	600
弹丸不平衡量/(g·mm)	50
连发数	10

图12 膛底压力-时间曲线

Fig.12 Breech pressure

图13 弹丸行程-时间曲线

Fig.13 Displacement of the projectile with time

图14 弹丸速度-时间曲线

Fig.14 Velocity of the projectile with time

图15 弹带与炮管接触力

Fig.15 Contact force between the band and the barrel

图16 弹丸前定心部与炮管接触力

Fig.16 Contact force between the front bourrelet of the projectile and the barrel

图17 仿真与试验结果对比

Fig.17 Comparison between simulated and experimental results

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