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)

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)

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)

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 .

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)

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)

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)

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 http://doi.org/10.14429/dsj.68.12247 https://publications.drdo.gov.in/ojs/index.php/dsj/article/view/12247 https://publications.drdo.gov.in/ojs/index.php/dsj/article/view/12247 Determination of short start pressure (SSP) for gun system has always been of paramount interest for gun designers. In this paper, a generalised model has been developed for theoretical prediction of SSP for rifled gun system using dimensional analysis approach. For this, parameters affecting the SSP of the gun like rifling dimensions, driving band dimensions, material properties of driving band, projectile mass and diameter are taken into consideration. For a particular case of large caliber rifled gun system, the model is established using linear relations among dimensionless groups of parameters. The model has been validated by data available from the open literature.

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 http://doi.org/10.3969/j.issn.1000-1093.2021.06.004 弹丸挤进身管过程中，弹带与身管之间的摩擦特性不仅对内弹道特性产生影响，而且影响对身管寿命的预测。在弹丸挤进过程中，弹带与身管之间的摩擦具有高速高接触压力特性。基于弹丸挤进过程中的弹带变形机理，提出一种新的描述弹带与身管之间摩擦特性的摩擦模型，该模型考虑了接触压力、滑移速度以及连发射击时温度升高导致弹带表层熔化的影响；建立热力耦合的弹炮匹配有限元模型，分析弹丸挤进过程弹带应力及温度变化，并与文献［24-25］提出的摩擦模型进行对比验证，研究弹丸挤进过程中的弹丸速度和弹带表层温度变化规律。结果表明：新的摩擦模型能够准确描述弹丸挤进过程中弹带与身管之间的摩擦特性。

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 http://doi.org/10.3969/j.issn.1000-1093.2021.06.004 During the extrusion of projectile into a barrel，the friction between the cartridge belt and the barrel not only affects the internal ballistic characteristics，but also affects the prediction of barrel life. The friction between the rotating band and the barrel has the characteristics of high speed and high contact pressure during the engraving process of projectile. A friction model for describing the friction characteristics of rotating band and barrel is proposed based on the deformation mechanism of rotating band during engraving process of projectile. In the proposed model，the contact pressure，sliding speed and the effect of elevated temperature on the surface melting of rotating band during burst of fire are considered. A coupled thermo-mechanical finite element model for projectile matching is established to analyze the changes in the stress of rotating band and the temperature during engraving process. The proposed model is compared with the models in Refs.［24-25］. The velocity of projectile after engraving and the surface temperature change of rotating band are analyzed in detail.The result shows that the proposed friction model can accurately describe the frictional characteristics of barrel and rotating band during engraving process.

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 http://doi.org/10.1016/j.finel.2016.10.003 https://linkinghub.elsevier.com/retrieve/pii/S0168874X16304085 https://linkinghub.elsevier.com/retrieve/pii/S0168874X16304085

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 http://doi.org/10.3969/j.issn.1000-1093.2021.09.005 A finite element model of the sealing band is established to research the mechanical properties of nylon sealing band of projectile launching from a large-caliber artillery during engraving process and analyze the influences of the the sealing bands with different structures on the engraving process. The pressure field is governed by an internal ballistic program，and the nonlinear mechanical behaviors are predicted based on the engineering software Abaqus. The pressure field and the structures through moving boundaries are coupled by using a user subroutine interface VUAMP in Abaqus. The different bottom radii and the nylon band structures with different widths and grooves were simulated and calculated. The simulated results show the mechanical properties and deformation evolution of band during the engraving process. The calculated results show that the larger the radius of projectile base is, the smaller the deformation space of band is and the greater the engraving resistance is. The sealing performance of band is improved with the increase in its width, but the resistance is also increased gradually. The sealing band groove can effectively change a single section of deformation into a multi-section of deformation, and the change of groove depth has a greater influence on the engraving resistance than the change of groove width.

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)

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 http://doi.org/10.1016/j.dt.2019.07.009 https://linkinghub.elsevier.com/retrieve/pii/S2214914719302326 https://linkinghub.elsevier.com/retrieve/pii/S2214914719302326

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)

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 http://doi.org/10.3969/j.issn.1000-1093.2016.10.006 为研究弹带挤进过程机理以及弹丸在挤进过程的运动规律，对大口径火炮挤进过程进行了仿真分析。考虑了火药气体在带锥度药室及坡膛内的分布，得到挤进时期的内弹道学方程，将该方程的解作为力边界条件，同时引入考虑温度的摩擦力模型来模拟身管与弹带间的摩擦，采用显式方法建立大口径火炮弹带挤进过程热力耦合仿真模型；分别对经典内弹道挤进过程和绝热挤进进行计算，验证了耦合计算的必要性；同时考虑不同弹炮间隙、卡膛速度以及初始摆角对挤进过程的影响，得到挤进过程中挤进阻力、弹丸速度、火药气体压力、弹丸摆角的变化规律。计算结果表明，弹炮间隙对挤进阻力和挤进速度有着重要的影响，而弹丸卡膛前摆角对弹丸挤进过程中的摆角有着重要的影响。

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 http://doi.org/10.3969/j.issn.1000-1093.2016.10.006 To investigate the mechanism of engraving process and the rule of initial motion of projectile during lauching process, the engraving process of rotating band of large-caliber howitzer is simulated. The gas pressure distribution of propellant in the tapered chamber is taken into consideration to get the interior ballistic equation during engraving process, and the solution of the equation is taken as the boundary condition of coupled thermo-mechanical analysis of engraving process. Meanwhile, the friction between the rotating band and the barrel is modeled using modified Coulomb model in which the temperature at the interface is taken into consideration. Uncoupled internal ballistic engraving process and adiabatic engraving process are calculated to verify the necessity of the coupled analysis. The resistance, projectile velocity, propellant gas pressure and projectile attitude are got by considering the changes in clearance between projectile and barrel, initial velocity and initial projectile attitude. The calculated results show that the clearance between projectile and barrel plays an important role in determining the resistance and projectile velocity, and the initial projectile attitude has a great effect on the projectile attitude in the process of engraving.

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 .

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)

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 http://doi.org/10.1016/j.dt.2019.06.014 https://linkinghub.elsevier.com/retrieve/pii/S2214914719301813 https://linkinghub.elsevier.com/retrieve/pii/S2214914719301813

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 http://doi.org/10.3390/math9010001 https://www.mdpi.com/2227-7390/9/1/1 https://www.mdpi.com/2227-7390/9/1/1 Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function cos(x) and irregular piecewise function as an example. In the reconstruction of cos(x) and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are 1.20 × 10−4, 2.52 × 10−3, 2.76 × 10−5, 1.68 × 10−2 and 4.02 × 10−3, 4.94 × 10−4, 1.11 × 10−3, 9.27 × 10−3, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies C2 and G2 continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

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 http://doi.org/10.1115/1.4006354 https://asmedigitalcollection.asme.org/pressurevesseltech/article/doi/10.1115/1.4006354/455951/Influence-of-Rotating-Band-Construction-on-Gun https://asmedigitalcollection.asme.org/pressurevesseltech/article/doi/10.1115/1.4006354/455951/Influence-of-Rotating-Band-Construction-on-Gun The effects of changes in geometries and material properties of rotating band and long range artillery projectile shell body on gun tube stress are presented. The results are based on numerical calculations (finite element analysis, FEA). Numerical explicit dynamic analyses were performed assuming elastic–plastic material behavior and nonlinear kinematics. Mechanical loading of shell body was controlled by pressure–time relationship based on the simulation of internal ballistic cycle. One degree slice of projectile and forcing cone section of gun tube was modeled as simplified smooth bore 3D analysis model. The results were in agreement with the measured results in firing trials and also with the results presented in open literature. Although simplified computations were used, the influences of the structural modifications of the rotating band and the shell body were shown.

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 http://doi.org/10.1115/1.4006355 https://asmedigitalcollection.asme.org/pressurevesseltech/article/doi/10.1115/1.4006355/455917/Influence-of-Rotating-Band-Construction-on-Gun https://asmedigitalcollection.asme.org/pressurevesseltech/article/doi/10.1115/1.4006355/455917/Influence-of-Rotating-Band-Construction-on-Gun The soft deformable metallic rotating band of large caliber projectiles prevents the gas leakage between the gun tube wall and the shell body by the band pressure on contact surfaces during the launch cycle of the gun. High rotating band pressures can lead to problems concerning gun tube wear, fatigue, and strength. The effects of changes in construction of rotating band and long range artillery projectile shell body on gun tube loading are studied experimentally. A practical analysis method for tube inner wall pressure computation from outer wall strain measurements is presented. The method is based on assuming stepped pressure load affecting on tube inner wall surface, when the projectile passes the measurement point. Although the analysis method was simplified, it was found to give useful and reliable results for comparative verification of different shell and band structures and their influences on gun tube loading. The structural design of the shell body and the rotating band were shown to be the most important aspects to cause the extreme loadings on the gun tube.

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 http://doi.org/10.1088/1742-6596/1813/1/012012 With three different constitutive model, LS-DYNA hydro code is applied to simulate the forming and fracture characteristics of Copper EFP. By comparison of numerical results of different models, the appropriate constitutive model to simulate the complete and fracture EFPs can be obtained. By comparison of experimental and numerical results, it can be concluded that Steinberg-Guinan constitutive model gives the best result to predict the complete EFP’s forming shape with minimum error, while Johnson-Cook constitutive model with failure model and h-adaptive algorithm is the most suitable method to predict the fracture of EFP in axial direction. The research results are important and significant in the deign of shaped charge, which could provide a guideline to predict the fracture of EFP in numerical simulation.

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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)

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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 https://dx.doi.org/10.12382/bgxb.2021.0875 . (in Chinese) DOI: 10.12382/bgxb.2021.0875 http://doi.org/10.12382/bgxb.2021.0875

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