埋头弹高速冲击挤进入膛特性研究

doi:10.2382/bgxb.2022.0834

摘要/Abstract

摘要：

为研究埋头弹高速冲击挤进入膛过程的力学机理和运动规律，将某40 mm口径埋头弹火炮作为对象，分析建立其内弹道过程的数理模型，并通过实弹射击试验验证内弹道模型的准确性。考虑界面间的摩擦和接触特性，采用FEM-SPH耦合算法建立了高速冲击挤进模型，将内弹道数值解作为边界条件，通过数值计算得到弹带变形、弹丸运动、弹丸姿态和挤进阻力等变化规律。研究结果表明：所建立的弹道模型准确合理，弹丸的初始上膛速度为78.2 m/s；整个挤进过程分为减速挤进和加速挤进阶段，两阶段之间弹丸处于准静止状态，减速挤进过程中弹丸姿态发生周期性的变化，摆动角幅值不断下降，加速挤进过程，摆动角迅速增大，随着挤进完成摆动角呈现出减小的趋势，完成挤进用时2.65 ms，完成挤进时弹丸速度为73.92 m/s；挤进过程弹带表面温度接近材料熔点；动态挤进阻力呈现两次“上升-下降”过程，最大挤进阻力为95.288 kN，完全挤进时阻力降低并稳定到10 kN。

关键词: 埋头弹, 内弹道, 冲击挤进, FEM-SPH耦合算法, 弹丸姿态, 挤进阻力

Abstract:

To study the mechanical mechanism and motion law of the high speed impact engraving process of cased telescoped ammunition, the physical and mathematical interior ballistic models were analyzed and established with a 40mm caliber CTA gun as the research object, and the interior ballistic model was verified by live fire experiments. Considering the friction and contact characteristics between the interfaces, a high-speed impact engraving model was built by the FEM-SPH coupling algorithm, and the numerical solution of the interior ballistics was used as the boundary condition to obtain the change laws of the deformation of the rotating band, projectile motion, projectile attitude and engraving resistance by numerical calculations. The results showed that: the established ballistic model is accurate and reasonable; the initial velocity of the projectile at the bore was 78.2m/s; the entire engraving process can be divided into the decelerating and accelerating phases, and the projectile was in the quasi-static state between the two phases; during the decelerating engraving process, the projectile attitude changed periodically, and the amplitude of the oscillation angle decreased continuously; the oscillation angle increased rapidly during the accelerating engraving process; as the engraving was completed, the oscillation angle showed a decreasing trend; the engraving time was 2.65 ms and the projectile velocity was 73.92 m/s at the completion of engraving; the surface temperature of the rotating band during the engraving process was close to the melting point of the material; there were two "rise - fall" processes in the dynamic engraving resistance with the maximum engraving resistance of 95.288 kN, and the resistance decreased and stabilized at 10 kN at the moment of fully engraving.

Key words: cased telescoped ammunition, interior ballistic, impact engraving, FEM-SPH coupling algorithm, projectile attitude, engraving resistance

师军飞, 钱林方, 陈红彬, 付佳维. 埋头弹高速冲击挤进入膛特性研究[J]. 兵工学报, 2023, 44(3): 656-669.

SHI Junfei, QIAN Linfang, CHEN Hongbin, FU Jiawei. High-Speed Impact Engraving Characteristics of Cased Telescoped Ammunition[J]. Acta Armamentarii, 2023, 44(3): 656-669.

图/表 24

图1 埋头弹火炮内弹道物理模型

Fig. 1 Physical model of interior ballistics of the CTA gun

表1 埋头弹装药参数

Table 1 Charge parameters of CTA

参数	数值	参数	数值
ω_b/g	1.5	u_1b	4×10^-8
ω_z/g	375	u_1z	1.8×10^-8
ω_c/g	58	u_1c	2×10^-8
n_b	0.82	ρ_b/(kg•m^-3)	1 600
n_z	0.82	ρ_z/(kg•m^-3)	1 600
n_c	1	ρ_c/(kg•m^-3)	850
f_b/(kJ•kg^-1)	1 000 000	α_b/(m³•kg^-1)	0.001
f_z/(kJ•kg^-1)	1 150 000	α_z/(m³•kg^-1)	0.001
f_c/(kJ•kg^-1)	700 000	α_c/(m³•kg^-1)	0.000 825
V_0b/m³	6.9×10^-6	V₀/m³	7.5×10^-4
S₁/m²	1.36×10^-3	S₂/m²	1.27×10^-3
l_k/m	0.172	l_g/m	2.98
p_bs/MPa	2.5	p_bd/MPa	8
φ₁	1.005	φ₂	1.05
m/kg	1	θ	0.25

图2 内弹道数值求解程序图

Fig. 2 Diagram of the numerical solution procedures of interior ballistics

图3 平均膛压数值结果与实测值换算结果的对比

Fig. 3 Comparison of the numerical results of the average bore pressure with the conversion results of the measured values

图4 弹丸速度-时间、位移-时间曲线

Fig. 4 Velocity-time and displacement-time curves of the projectile

图5 弹丸姿态示意图

Fig. 5 Schematic diagram of projectile attitude

图6 挤进过程弹带的形貌和受力示意图

Fig. 6 Schematic diagram of the shape of and force on the rotating band during the engraving process

图7 高速冲击挤进入膛过程示意图

Fig. 7 Schematic diagram of the high-speed impact engraving process

图8 挤进系统有限元网格

Fig. 8 Finite element meshes of the engraving system

图9 SPH质点与Lagrange网格的耦合示意图

Fig. 9 Coupling diagram of SPH particles and Lagrange grids

图10 弹带的网格和SPH粒子

Fig. 10 Meshes and SPH particles of the rotating band

表2 弹带材料模型参数

Table 2 Material parameters of the rotating band

参数	数值	参数	数值
A/MPa	90	D₁	0.54
B/MPa	292	D₂	4.89
n	0.42	D₃	-3.03
C	0.01	D₄	0.014
m	1.68	D₅	1.12
T_r/K	294	T_m/K	1356

图11 SPH-FEM接触耦合算法

Fig. 11 SPH-FEM coupling contact algorithm

图12 弹带塑性变形过程

Fig. 12 Plastic deformation process of the rotating band

图13 试验和仿真得到的弹带形貌对比

Fig. 13 Comparison of the shape of the rotating band obtained from the test and simulation

图14 弹带典型部位SPH粒子

Fig. 14 SPH particles in typical parts of the rotating band

图15 弹带表面典型部位的温度

Fig. 15 Temperature of typical parts of the rotating band surface

图16 弹带表面典型部位的等效应力

Fig. 16 Equivalent stress of typical parts of the rotating band surface

图17 挤进速度-时间曲线

Fig. 17 Velocity-time curve of engraving

图18 挤进加速度-时间曲线

Fig. 18 Acceleration-time curve of engraving

图19 挤进过程中的能量变化规律

Fig. 19 Energy variation during the engraving process

图20 弹丸横向摆动角和纵向摆动角

Fig. 20 Lateral and longitudinal osllication angles of the projectile

图21 弹丸横向摆动角速度和纵向摆动角速度

Fig. 21 Angular velocity of transverse and longitudinal oscillation of the projectile

图22 动态挤进阻力变化规律

Fig. 22 Resistance variation law of dynamic engraving resistance

参考文献 30

[1]	钱林方, 侯保林, 徐亚栋. 火炮弹道学[M]. 北京: 北京理工大学出版社, 2016.
	QIAN L F, HOU B L, XU Y D. Gun ballistics[M]. Beijing: Beijing Institute of Technology Press, 2016. (in Chinese)
[2]	张浩, 周彦煌. 埋头弹火炮零维内弹道模型及计算[J]. 弹道学报, 2005, 17(2): 80-83.
	ZHANG H, ZHOU Y H. A 0-dimensonal interior ballistic model and calculation of cased telescoped ammunition gun[J]. Journal of Ballistics, 2005, 17(2): 80-83. (in Chinese)
[3]	钱环宇, 余永刚. 埋头弹随行装药内弹道性能的数值分析[J]. 弹道学报, 2018, 30(3): 35-39.
	QIAN H Y, YU Y G. Numerical analysis of interior ballistic performance of cased telescoped ammunition with traveling charge[J]. Journal of Ballistics, 2018, 30(3): 35-39. (in Chinese)
[4]	MONREAL-GONZÁLEZ G, OTÓN-MARTÍNEZ R A, VELASCO F J S, et al. One-dimensional modelling of internal ballistics[J]. Journal of Energetic Materials, 2017, 35(4): 397-420.
[5]	刘静, 余永刚, 严小林. 可燃药筒材料高压燃烧性能的测量与计算[J]. 弹道学报, 2017, 29(2): 54-57.
	LIU J, YU Y G, YAN X L. Measurement and calculation of combustion performance of combustible cartridge under high pressure[J]. Journal of Ballistics, 2017, 29(2): 54-57. (in Chinese)
[6]	郭俊廷, 余永刚. 半可燃药筒埋头弹内弹道性能数值模拟[J]. 弹道学报, 2021, 33(3): 52-56.
	GUO J T, YU Y G. Numerical simulation of interior ballistic performance of cased telescoped ammunition with semi-combustible cartridge[J]. Journal of Ballistics, 2021, 33(3): 52-56. (in Chinese)
[7]	张浩, 周彦煌. 埋头弹火炮挤进过程研究[J]. 弹道学报, 2006, 18(1):76 -79.
	ZHANG H, ZHOU Y H. Research on the engraving process of CTA[J]. Journal of Ballistics, 2006, 18(1): 76-79. (in Chinese)
[8]	SUDARSAN N V, SARSAR R B, DAS S K, et al. Prediction of shot start pressure for rifled gun system[J]. Defence Science Journal, 2018, 68(2): 144-149. doi: 10.14429/dsj.68.12247 URL
[9]	邹利波, 冯广斌, 侯保林, 等. 基于温度修正的弹丸挤进身管过程摩擦模型[J]. 兵工学报, 2021, 42(6): 1148-1156. doi: 10.3969/j.issn.1000-1093.2021.06.004
	ZOU L B, FENG G B, HOU B L, et al. Friction model of projectile engraving process based on temperature correction[J]. Acta Armamentarii, 2021, 42(6): 1148-1156. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.06.004
[10]	DING C J, LIU N, ZHANG X Y. A mesh generation method for worn gun barrel and its application in projectile-barrel interaction analysis[J]. Finite Elements in Analysis and Design, 2017, 124: 22-32. doi: 10.1016/j.finel.2016.10.003 URL
[11]	程申申, 陶如意, 王浩, 等. 弹丸不同结构尼龙弹带挤进过程的阻力特性[J]. 兵工学报, 2021, 42(9): 1847-1857.
	CHENG S S, TAO R Y, WANG H, et al. Dampling characteristics of projectile in engraving process of nylon sealing band[J]. Acta Armamentarii, 2021, 42(9): 1847-1857. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.09.005
[12]	郭俊行, 刘琦, 丁宏民, 等. 基于光滑粒子法的某大口径火炮不同膛线弹丸挤进过程研究[J]. 振动与冲击, 2021, 40(24): 75-81.
	GUO J X, LIU Q, DING H M, et al. A study on rotating band engraving process for large caliber gun projectile with different rifles[J]. Journal of Vibration and shock, 2021, 40(24): 75-81. (in Chinese)
[13]	SHEN C, ZHOU K D, LU Y, et al. Modeling and simulation of bullet-barrel interaction process for the damaged gun barrel[J]. Defence Technology, 2019, 15(6): 972-986. doi: 10.1016/j.dt.2019.07.009 URL
[14]	马明迪, 崔万善, 曾志银, 等. 基于有限元与光滑粒子耦合的弹丸挤进过程分析[J]. 振动与冲击, 2015, 34(6): 146-150.
	MA M D, CUI W S, ZENG Z Y, et al. Engraving process analysis of projectiles based on coupling of FEM and SPH[J]. Journal of Vibration and shock, 2015, 34(6): 146-150. (in Chinese)
[15]	李淼, 钱林方, 孙河洋. 某大口径火炮弹带热力耦合挤进动力学数值模拟研究[J]. 兵工学报, 2016, 37(10): 1803-1811. doi: 10.3969/j.issn.1000-1093.2016.10.006
	LI M, QIAN L F, SUN H Y. Research on coupled thermo-mechanical model during rotating band engraving process[J]. Acta Armamentarii, 2016, 37(10): 1803-1811. (in Chinese) doi: 10.3969/j.issn.1000-1093.2016.10.006
[16]	LI Z, GE J L, YANG G L, et al. Modeling and dynamic simulation on engraving process of rotating band into rifled barrel using three different numerical methods[J]. Journal of Vibro Engineering, 2016, 18(2): 768-780.
[17]	纪杨子燚, 钱建平. 定装式弹丸不同膛内自由行程下挤进过程的动态响应[J]. 弹道学报, 2018, 30(1): 56-60.
	JI Y Z Y, QIAN J P. Dynamic response of fixed cartridge case during engraving process under different in-bore free path[J]. Journal of Ballistics, 2018, 30(1): 56-60. (in Chinese)
[18]	HU C B, ZHANG X B. Influence of multiple structural parameters on interior ballistics based on orthogonal test methods[J]. Defence Technology, 2019, 15(5): 690-697. doi: 10.1016/j.dt.2019.06.014 URL
[19]	XIN T, YANG G L, XU F J, et al. Modeling, simulation and uncertain optimization of the gun engraving system[J]. Mathematics, 2021, 9(4): 1-25. doi: 10.3390/math9010001 URL
[20]	KEINÄNEN H, MOILANEN S, TERVOKOSKI J, et al. Influence of rotating band construction on gun tube loading—Part I: numerical approach[J]. Journal of Pressure Vessel Technology, 2012, 134(4): 041006. doi: 10.1115/1.4006354 URL
[21]	TOIVOLA J, MOILANEN S, TERVOKOSKI J, et al. Influence of rotating band construction on gun tube loading—part II: measurement and analysis[J]. Journal of Pressure Vessel Technology, 2012, 134(4): 041007. doi: 10.1115/1.4006355 URL
[22]	DING L, JIANG J W, MEN J B, et al. Numerical simulation of the fracture characteristics of copper EFP with different constitutive models[J]. Journal of Physics: Conference Series, 2021, 1813(1): 012012. doi: 10.1088/1742-6596/1813/1/012012
[23]	WU B, ZHENG J, TIAN Q T, et al. Friction and wear between rotating band and gun barrel during engraving process[J]. Wear, 2014, 318: 106-113. doi: 10.1016/j.wear.2014.06.020 URL
[24]	RITTER J J, BEYER R A. Primer output and initial projectile motion for 5. 56- and 7. 62-mm ammunition[R]. MD, US: Army Research Laboratory Technical Report, 2015, ARL-TR-7479.
[25]	刘东尧, 孙鹏, 张欣尉, 等. 两种中口径弹药弹带动态挤进阻力特性的实验研究[J]. 弹道学报, 2020, 32(3): 5-8.
	LIU D Y, SUN P, ZHANG X W, et al. Experimental study on engraving resistance properties of band of two medium caliber projectile[J]. Journal of Ballistics, 2020, 32(3): 5-8. (in Chinese)
[26]	许辉, 黄陈磊, 王希阔, 等. 枪弹动态挤进阻力理论与实验[J]. 兵工学报, 2022, 43(9):2263-2273. DOI: 10.12382/bgxb.2021.0875. doi: 10.12382/bgxb.2021.0875
	XU H, HUANG C L, WANG X K, et al. Theoretical and experimental research of the projectile dynamic engraving resistance[J]. Acta Armamentarii, 2022, 43 (9): 2263-2273. DOI: 10.12382/bgxb.2021.0875. (in Chinese) doi: 10.12382/bgxb.2021.0875
[27]	WU B, FANG L H, ZHENG J, et al. Stain hardening and strain-rate effect in friction between projectile and barrel during engraving process[J]. Tribology Letters, 2019, 67(39): 38-45. doi: 10.1007/s11249-019-1150-2
[28]	JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[C]// Proceedings of the 7th International Symposium on Ballistics. Hague, the Netherlands: IBC, 1983: 541-547.
[29]	周彦煌, 王升晨. 实用两相流内弹道学[M]. 北京: 兵器工业出版社, 1990.
	ZHOU Y H, WANG S C. Practical two-phase flow interior ballistics[M]. Beijing: Publishing House of Ordnance Industry, 1990. (in Chinese)
[30]	STIFFLER A K. Friction of plastic rotating bands[R]. MS, US: Mississippi State Engineering and Industial Researchstation, 1984.