链式回转弹仓刚柔耦合动力学建模及特性分析

doi:10.12382/bgxb.2024.0698

摘要/Abstract

摘要：

考虑到装填系统轨道输送链具有链节大、负载大、速度大的特殊性,提出一种基于相对坐标法和板单元离散方式的刚柔耦合动力学建模方法。利用邻接体的相对运动关系推导出运动学方程及体坐标与铰坐标的转化关系,建立广义坐标为独立铰坐标的动力学方程。利用有限元方法,基于板单元理论将链节和弹筒离散化,以链节为例建立单个链节的刚柔耦合动力学方程,随后通过刚-柔运动约束形式,利用增广方程形式,建立轨道输送链系统的刚柔耦合动力学方程。基于此方法,建立某弹仓(闭式轨道输送链)轨道输送链和弹筒的刚柔耦合动力学方程,并在不同工况下将基于板单元离散的数值仿真与实验结果进行对比。基于建立的刚柔耦合动力学模型,分析弹仓传动构件支撑刚度、轨道间隙等因素对弹仓系统的影响。研究结果表明:数值仿真结果与实验结果的趋势基本一致;支撑刚度对系统动态响应的影响程度取决于动力系统的结构形式和受力形式;轨道间隙的变化对系统的动态特性具有较大的影响,在工程应用中需要合理控制间隙;上下轨道错位对弹仓动态特性影响较大,需要合理控制加工装配精度。

关键词: 火炮, 弹仓, 中厚板理论, 刚柔耦合, 动力学, 间隙, 轨道错位

Abstract:

Considering the unique characteristics of the autoloader’s rail conveyor chain, such as large chain links, heavy load and high speed, a rigid-flexible coupljng dynamic modeling method based on the relative coordinate method and the plate element discretization method is proposed. The relative motion relationships of adjacent bodies are used to derive the kinematic equations and the transformation relationship between body coordinates and hinge coordinates, thereby establishing the dynamic equations with independent hinge coordinates as generalized coordinates. The finite element method is used to discretize the chain links and cartridge cases based on plate element theory. Taking the chain link as an example, the rigid-flexible coupling dynamic equations for a single chain link are established. Subsequently, the rigid-flexible coupling dynamic equations for the rail conveyor chain system are developed by applying the rigid-flexible motion constraints in the form of augmented equations. Based on this method, the rigid-flexible coupling dynamic equations of the rail conveyor chain and cartridge cases for a certain magazine are established. The numerical simulation based on plate element discretization is then compared with experimental results under different working conditions. The effects of factors such as the support stiffness of transmission components and rail clearance on the magazine system, are analyzed by using the proposed rigid-flexible coupling dynamic model. The research results indicate that the numerically simulated results are generally consistent with the experimental results. The influence of support stiffness on the system’s dynamic response depends on the structural form and force application of the power system. The change in rail clearance has a significant effect on the system’s dynamic characteristics, thus necessitating the reasonable control of clearance in engineering applications. The misalignment of the upper and lower rails has a considerable effect on the dynamic characteristics of the magazine, requiring the reasonable control of machining and assembly accuracy.

Key words: gun, magazine, mid-thickness plate theory, rigid-flexible coupling, dynamics, clearance, rail misalignment

中图分类号:

TJ301

刘太素, 尹强, 李勇, 张云添. 链式回转弹仓刚柔耦合动力学建模及特性分析[J]. 兵工学报, 2024, 45(11): 4133-4144.

LIU Taisu, YIN Qiang, LI Yong, ZHANG Yuntian. Rigid-flexible Coupling Dynamic Modeling and Characteristics Analysis of a Rotational Chain Magazine[J]. Acta Armamentarii, 2024, 45(11): 4133-4144.

图/表 24

图1 弹仓结构组成

Fig.1 Composition of magazine structure

图2 弹仓主要结构拓扑关系

Fig.2 Main topological relationships of magazine structure

表1 构件的质量、惯量参数

Table 1 Mass and inertia parameters of components

构件名称	质量/kg	惯量/(kg·m²)
构件名称	质量/kg	I_xx	I_yy	I_zz
链轮	16.629	2.00	2.00	1.82×10^-2
链节	0.152	1.93×10^-4	2.01×10^-4	9.73×10^-6
弹筒	8.58	0.791	0.807	3.11×10^-2
滚轮	5.35×10^-2	5.20×10^-6	5.20×10^-6	8.31×10^-6
弹丸	45.1	2.48	2.48	0.168

图3 变形挠度和转角的方向

Fig.3 Direction of deformation deflection and angular displacement

图4 刚柔耦合示意图

Fig.4 Schematic diagram of rigid-flexible coupling

图5 某弹仓实验台架

Fig.5 Experimental device of magazine

图6 某弹仓仿真和实验结果对比

Fig.6 Comparison of simulated and experimental results of magazine

表2 不同柔性单元类型计算结果与实验的误差

Table 2 Errors between calculated and experimental results for different types of flexible units

空载、半载与满载	板单元计算结果与实验的误差	实体单元计算结果与实验的误差
空载	0.8925	0.9038
半载	0.9362	0.9393
满载	0.9647	0.9676

表3 弹仓输入参数

Table 3 Nominal values of magazine input parameters

输入参数	名义值	输入参数	名义值
滚轮半径/mm	15	链轮轴轴承支撑刚度/(N·m^-1)	5×10⁹
链节长度/mm	30	滚轮-轨道间隙/mm	0.3
弹筒-弹丸间隙/mm	0.5	链轮槽半径/mm	15.5
滚轮与链轮的摩擦系数	0.3	弹性模量/MPa	2.1×10⁵
滚轮与轨道的摩擦系数	0.3	泊松比	0.3
上轨道纵向初始位置/mm	0	下轨道纵向初始位置/mm	0
上轨道横向初始位置/mm	0	下轨道横向初始位置/mm	0

图7 弹筒和链节刚性和柔性时弹丸质心加速度对比

Fig.7 Comparison of the accelerations of the mass center of projectile for the rigid and flexible barrels and chains

图8 支撑刚度对弹仓驱动链轮角位移的影响

Fig.8 The influence of support stiffness on the angular displacement of magazine drive sprocket

图9 支撑刚度对弹仓驱动链轮横向位移的影响

Fig.9 The influence of support stiffness on the lateral displacement of magazine drive sprocket

图10 支撑刚度对弹仓驱动链轮横向速度的影响

Fig.10 The influence of support stiffness on the lateral velocity of magazine drive sprocket

图11 支撑刚度对弹仓驱动链轮纵向位移的影响

Fig.11 The influence of support stiffness on the longitudinal displacement of magazine drive sprocket

图12 支撑刚度对弹仓驱动链轮纵向速度的影响

Fig.12 The influence of support stiffness on the longitudinal velocity of magazine drive sprocket

表4 支撑刚度对链轮运动的影响结果

Table 4 The influence of support stiffness on the sprocket motion

刚度/ (N·m^-1)	链轮角位移 (2.5s)/rad	链轮横向位移 (2.07s)/m	链轮横向速度 (2.043s)/(m·s^-1)
5×10⁶	3.9886	-2.64×10^-5	0.0184
5×10⁹	3.9837	-7.33×10^-5	1.87×10^-5
5×10¹⁰	3.9824	-7.34×10^-5	2.7×10^-6

图13 轨道间隙对弹筒1位移的影响

Fig.13 The influence of rail clearance on the displacement of magazine barrel 1

图14 轨道间隙对弹筒1横向位移的影响

Fig.14 The influence of rail clearance on the lateral displacement of magazine barrel 1

图15 轨道间隙对弹筒1横向速度的影响

Fig.15 The influence of railclearance on the lateral velocity of magazine barrel 1

图16 轨道间隙对弹筒1转动角位移的影响

Fig.16 The influence of rail clearance on the angular displacement of magazine barrel 1

图17 轨道间隙对弹筒1转动角速度的影响

Fig.17 The influence of rail clearance on the angular velocity of magazine barrel 1

表5 轨道间隙对弹筒运动的影响结果

Table 5 The influence of rail clearance on the magazine barrel motion

间隙/ mm	弹筒1 位移 (3.0s)/ m	弹筒1 横向位移 (3.0s)/ m	弹筒1 横向速度 (2.0s)/ m	弹筒1转动角位移 (3.0s)/ m	弹筒1转动角速度 (3.0s)/ m
0.1	0.3029	-0.04672	0.03141	-0.40068	0.02719
0.3	0.3109	-0.04563	0.04223	-0.46204	-0.02007
0.5	0.3123	-0.04515	0.04711	-0.45678	0.01377
0.8	0.3124	-0.04435	0.03350	-0.46381	-0.00474
1.0	0.3125	-0.04379	0.03930	-0.45623	0.01454
1.5	0.3126	-0.04316	0.04355	-0.45127	0.02767

图18 轨道错位对链轮角位移的影响

Fig.18 The effect of rail misalignment on the angular displacement of sprocket

表6 轨道错位对链轮角位移到位的数值结果

Table 6 The effect ofrail misalignment on the angular displacement in place of the sprocket

影响因素	到位角位移/rad
参考值	3.91195
上轨道纵向远离链轮	3.89348
上轨道纵向靠近链轮	3.77134
下轨道纵向远离链轮	3.92077
下轨道纵向靠近链轮	3.87183
轴向偏转	3.69871
横向偏转	3.91233
横向错位	3.9314
纵向偏转	3.9236

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