Rigid-flexible Coupling Dynamic Modeling and Characteristics Analysis of a Rotational Chain Magazine

doi:10.12382/bgxb.2024.0698

Abstract

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

CLC Number:

TJ301

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.

Figures/Tables 24

Fig.1 Composition of magazine structure

Fig.2 Main topological relationships of magazine structure

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

Fig.3 Direction of deformation deflection and angular displacement

Fig.4 Schematic diagram of rigid-flexible coupling

Fig.5 Experimental device of magazine

Fig.6 Comparison of simulated and experimental results of magazine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

References 26

[1]	钱林方, 徐亚栋, 陈龙淼. 车载炮射击理论和方法[M]. 北京: 科学出版社, 2022.
	QIAN L F, XU Y D, CHEN L M. Shooting theory and methods of vehicle mounted cannon[M]. Beijing: Science Press, 2022. (in Chinese)
[2]	侯保林, 樵军谋, 刘琮敏. 火炮自动装填[M]. 北京: 兵器工业出版社, 2010.
	HOU B L, QIAO J M, LIU C M. Automatic loader of artillery[M]. Beijing: Publishing House of Ordnance Industry, 2010. (in Chinese)
[3]	赵伟, 侯保林, 闫少军, 等. 链式回转弹仓区间不确定性动力学模型[J]. 兵工学报, 2024, 45(6): 1991-2002. doi: 10.12382/bgxb.2023.0379
	ZHAO W, HOU B L, YAN S J, et al. A dynamic model of interval uncertainty of rotational chain shell magazine[J]. Acta Armamentarii, 2024, 45(6):1991-2002. (in Chinese) doi: 10.12382/bgxb.2023.0379
[4]	文浩, 侯保林, 林瑜斌, 等. 曲线链式回转弹仓动力学模型不确定参数辨识[J]. 兵工学报, 2024, 45(5): 1460-1471. doi: 10.12382/bgxb.2022.1196
	WEN H, HOU B L, LIN Y B, et al. Dynamic model uncertain parameter identification for a curved chain rotary shell magazine[J]. Acta Armamentarii, 2024, 45(5): 1460-1471. (in Chinese) doi: 10.12382/bgxb.2022.1196
[5]	马超超, 许金, 贾正荣, 等. 计及配合间隙的电磁发射重载链传动机构优化设计方法[J/OL]. 海军工程大学学报: 1-7 [2024-01-07]. http://kns.cnki.net/kcms/detail/42.1106.E.20231107.1417.010.html.
	MA C C, XU J, JIA Z R, et al. Optimization design method of heavy-duty chain transmission mechanism used for electromagnetic launch considering fit clearance[J/OL]. Journal of Naval University of Engineering, 1-7 [2024-01-07]. (in Chinese)
[6]	陈冬, 钱林方, 陈志群, 等. 基于改进拟连续算法的回转弹仓位置控制[J]. 兵工学报, 2024, 45(5): 1436-1448. doi: 10.12382/bgxb.2023.0064
	CHEN D, QIAN L F, CHEN Z Q, et al. An improved quasi-continuous algorithm for rotational shell magazine position control[J]. Acta Armamentarii, 2024, 45(5): 1436-1448. (in Chinese) doi: 10.12382/bgxb.2023.0064
[7]	鲍丹, 卫俞凯, 金鑫, 等. 考虑输出约束和输入饱和的弹仓自适应控制[J]. 兵工学报, 2024, 45(3): 789-797. doi: 10.12382/bgxb.2022.0896
	BAO D, WEI Y K, JIN X, et al. Adaptive control of magazines considering output constraints and input saturation[J]. Acta Armamentarii, 2024, 45(3): 789-797. (in Chinese) doi: 10.12382/bgxb.2022.0896
[8]	郝驰宇, 冯广斌, 闫鹏程, 等. 基于MFBD的输弹机刚柔耦合动力学建模及仿真分析[J]. 振动与冲击, 2016, 35(15):161-167.
	HAO C Y, FENG G B, YAN P C, et al. Rigid-flexible coupled dynamic modeling and simulation for a ramming mechanism based on MFBD[J]. Journal of Vibration and Shock, 2016, 35(15):161-167. (in Chinese)
[9]	闫鹏程, 郝驰宇, 孙华刚, 等. 基于RecurDyn的开式链传动输弹机动力学联合仿真研究[J]. 火炮发射与控制学报, 2015, 36(2):31-35.
	YAN P C, HAO C Y, SUN H G, et al. Study on dynamical cosimulation of open chain Drive ramming mechanism based on recurDyn[J]. Journal of Gun Launch & Control, 2015, 36(2):31-35. (in Chinese)
[10]	陆栋栋. 重型单向齿形推弹链的设计研究[D]. 南京: 南京理工大学, 2016.
	LU D D. Study on the design of heavy single tooth push-pull chain[D]. Nanjing: Nanjing University of Science and Technology, 2016. (in Chinese)
[11]	李伟, 马吉胜, 狄长春, 等. 考虑参数随机性的供输弹系统动力学及动作可靠性仿真研究[J]. 兵工学报, 2012, 33(6):747-752.
	LI W, MA J S, DI C C, et al. Simulation research on dynamics of ramming system and action reliability considering the randomness of the parameters[J]. Acta Armamentarii, 2012, 33(6): 747-752. (in Chinese)
[12]	LI Y, QIAN L F, CHEN G S, et al. Multiple clearance robustness optimization of a chain ramming machine based on a data-driven model[J]. Nonlinear Dynamics, 2023, 111(15): 13807-13828.
[13]	WEI K, CHEN L M, ZOU Q. Model-driven full system dynamics estimation of PMSM-driven chain shell magazine[J]. Defence Technology, 2024, 39:147-156.
[14]	张雷雨, 李剑锋, 杨洋. 装甲车辆用立式弹药舱的设计与动力学分析[J]. 兵工学报 2017, 38(5): 843-851. doi: 10.3969/j.issn.1000-1093.2017.05.002
	ZHANG L Y, LI J F, YANG Y. Design and dynamics analysis of vertical ammunition cabin for armored vehicle[J]. Acta Armamentarii, 2017, 38(5): 843-851. (in Chinese)
[15]	王光建, 姜铁牛. 弹链系统间隙铰多体动力学模型仿真与试验[J]. 机械工程学报, 2008, 44(5): 238-241.
	WANG G J, JIANG T N. Simulation and experiment of multi-body system dynamic model with clearance joint for ammunition belt system[J]. Chinese Journal of Mechanical Engineering, 2008, 44(5):238-241. (in Chinese)
[16]	刘太素, 钱林方, 陈光宋, 等. 某输弹机开式链传动建模及动力学特性分析[J]. 兵工学报, 2018, 39(11): 2109-2117. doi: 10.3969/j.issn.1000-1093.2018.11.004
	LIU T S, QIAN L F, CHEN G S, et al. Dynamics modeling and analysis of open chain drive transmission for a ramming mechanism[J]. Acta Armamentarii, 2018, 39(11): 2109-2117. (in Chinese)
[17]	魏继卿, 许耀峰, 刘小蒙, 等. 自动弹仓回转选弹动力学仿真及优化[J]. 火炮发射与控制学报 2015, 36(2): 36-39.
	WEI J Q, XU Y F, LIU X M, et al. Dynamics simulation and optimization of automatic magazine’s turning-round shell-selecting device[J]. Journal of Gun Launch & Control, 2015, 36(2): 36-39. (in Chinese)
[18]	胡胜海, 郭彬, 邓坤秀, 等. 含非线性接触碰撞的大口径舰炮弹链柔性铰多体模型[J]. 哈尔滨工程大学学报, 2011, 32(9): 1217-1222.
	HU S H, GUO B, DENG K X, et al. A multibody model with flexible joints and the nonlinear contact-impact of an ammunition chain of a large caliber naval gun[J]. Journal of Harbin Engineering University, 2011, 32(9): 1217-1222. (in Chinese)
[19]	CHEN G S, CHEN L M, TANG J S. An edge center based strain-smoothing element with discrete shear gap for the analysis of Reissner-Mindlin shell[J]. Thin-Walled Structures, 2022, 175: 109140.
[20]	TANG J S, QIAN L F, CHEN L M, et al. Flexible multibody dynamic analysis of shells with an edge center-based strain smoothing MITC method[J]. Nonlinear Dynamics, 2023, 111: 3253-3277.
[21]	TANG J S, QIAN L F, MA J, et al. Knowledge-dominated and data-driven rigid-flexible coupling dynamics for rotating flexible structure[J]. Knowledge-Based Systems, 2024, 296: 111853.
[22]	MA J, CHEN G S, JI L, et al. A general methodology to establish the contact force model for complex contacting surfaces[J]. Mechanical Systems and Signal Processing, 2020, 140: 106678.
[23]	LIU T S, NIU Y Y, CHEN G S. A general methodology for simulation model validation and model updating of the coordination mechanism with uncertainty[J]. Journal of Mechanical Science and Technology, 2023, 37(12): 6271-6286.
[24]	FLORES P. Dynamic analysis of mechanical systems with imperfect kinematic joints[D]. Braga, Portugal: University of Minho, 2004.
[25]	MA J, WANG J, PENG J, et al. Data-driven modeling for complex contacting phenomena via improved neural networks considering link switches[J]. Mechanism and Machine Theory, 2024, 191:105521.
[26]	陈光宋. 弹炮耦合系统动力学及关键参数识别研究[D]. 南京: 南京理工大学, 2016.
	CHEN G S. The study on the dynamic of the projectile-barrel coupled system and the corresponding key parameters[D]. Nanjing: Nanjing University of Science and Technology, 2016. (in Chinese)