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    30 November 2024, Volume 45 Issue 11
    Electronic edition of this issue
    Electronic edition of this issue
    2024, 45(11):  0. 
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    Contents
    Contents
    2024, 45(11):  0. 
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    Development and Trend of Research on Fault Diagnosis Methods for Ammunition Loading System
    WANG Bin, XU Yadong, WANG Liangkuan
    2024, 45(11):  3765-3780.  doi:10.12382/bgxb.2024.0506
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    The ammunition loading system is the key system to realize the automation of artillery. The system has a high level of complexity due to the tight coupling among its mechanical, electrical and hydraulic subsystems. The harsh operating environment results in the increased failure rate and reduced reliability of ammunition loading system, which in turn affects the overall performance of the artillery. Given these influences on system functionality, the focused research into fault diagnosis methods is of particular importance. Therefore, this study focuses on the ammunition loading system, analyzes the characteristics of faults in the ammunition loading system, and summarizes the typical fault analysis methods for the system. The study also provides an overview of the research progress and existing problems in the fault diagnosis methods for ammunition loading system. In addition, the development and application of current fault diagnosis technologies provide effective approaches to improve the reliability of ammunition loading system. By understanding the research progress of multi-domain fault diagnosis methods, this paper discusses the future development trends of fault diagnosis technologies for the ammunition loading system, summarizes the individual factors influencing the research on fault diagnosis of ammunition loading system, and provides a research perspective for future exploration.

    Coupling Characteristics of Pressure Pulsation in the High-pressure Oil Circuit of Piston Pump-motor System
    WANG Hujiang, MAO Ming, LIN Yu, MAO Feihong, WANG Tao, TANG Shousheng, BAO Qianqian
    2024, 45(11):  3781-3791.  doi:10.12382/bgxb.2024.0405
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    There is inherent pressure pulsation in the high-pressure oil circuit of piston pump-motor system, which causes vibration and noise, and worsens the smoothness of power transmission, thus having serious effect on the reliability and life of the system. Previous studies have focused on the pressure pulsation in high-pressure piston pumps. However, there is a lack of research on the coupling characteristics of pressure pulsation in the high-pressure oil circuit of piston pump-motor system. To address the above problems, the coupling mechanism and characteristics of the pressure pulsation in the high-pressure oil circuit of piston pump-motor system are revealed, and a new method of decoupling the pressure pulsation in the high-pressure oil circuit of piston pump-motor system is proposed. The pump source excitation is found to be the primary source of pressure pulsation in the high-pressure oil circuit of piston pump-motor system by using the proposed decoupling method. For the coupled pump motor in the paper, the average contribution of pump source excitation to the pressure pulsation is as high as 72% when the pump is at full displacement, while the contribution of motor to the pressure pulsation is only 28%. The proposed method and the conclusions drawn deepen the understanding of the coupling characteristics of pressure pulsation in the high-pressure oil circuit of piston pump-motor system. This provides theoretical support for the further suppression and utilization of the pressure pulsation in the high-pressure oil circuit of piston pump-motor system.

    Characteristics of Muzzle Shock Wave Overpressure on the Surface of Vehicle-mounted Howitzer’s Crew Compartment
    WEI Shengcheng, QIAN Linfang, XU Yadong, YIN Qiang
    2024, 45(11):  3792-3805.  doi:10.12382/bgxb.2023.0687
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    The shock wave overpressure acting on the surface of crew compartment during artillery firing is a key boundary condition for studying the protective performance of vehicle-mounted howitzer’s crew compartment against muzzle shock wave. To explore the characteristics of muzzle shock wave overpressure on the surface of crew compartment, a systematic firing experiment plan is designed for a specific equipment. The experiments cover both the main and auxiliary firing sectors of vehicle-mounted howitzer, capturing the overpressure data of the shockwaves at different positions on the crew compartment under seven firing angle conditions. The attenuation patterns of shock wave overpressure on the crew compartment surface at various spatial locations relative to the muzzle and crew compartment were obtained through experiment. A computational model of muzzle blast flow field is established using the unsteady three-dimensional inviscid Euler equations. Simulation and numerical analysis are performed to evaluate the shock wave overpressure on the crew compartment surface under extreme conditions.The simulated results show good agreement with the experimental data in terms of the change trend of shock wave overpressure, with a peak overpressure error of less than 4% when the muzzle airflow velocity is properly considered. The research results indicate that the muzzle shock wave influenced by the ground and the structure of crew compartment, forms a secondary overpressure distribution with obvious peaks on the surface of vehicle-mounted howitzer’s crew compartment. Factors such as the orientation of muzzle brake vents and the raised structures on the crew compartment contribute to a more severe muzzle shock wave overpressure on the surface of crew compartment.

    Nonlinear Suspension Characteristic Control Methods for High-mobility Off-road Vehicles
    CHEN Yijie, ZHANG Yafeng, ZHENG Fengjie, XU Long, ZHENG Guanhui
    2024, 45(11):  3806-3819.  doi:10.12382/bgxb.2024.0767
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    To improve the mobility performance of off-road vehicles, this paper proposes a swing-cylinder hydro-pneumatic suspension system, which utilizes a high-pressure pneumatic principle and a back-pressure adjustable damping valve structure for the real-time adjustment of stiffness and damping characteristics. The vibration responses achieved by different stiffness control methods are comparatively analyzed using a single-wheel suspension model, and the fixed-point equations are derived for frequency-domain damping properties.A graded stiffness adjustment strategy and a frequency-domain hybrid damping control method are proposed. The effectiveness of the proposed method is verified through a single-wheel suspension dynamics model, and a high-mobility tracked vehicle dynamics model is established for the simulation analysis of a full-vehicle. The results show that the driving speed of off-road vehicle with the suspension employing the combined stiffness and damping control is increased by more than 25% compared with that of off-road vehicle with the traditional passive suspension under the actual road conditions of Kangzhuang, Yangbajing and Tuoli. These findings demonstrate the superior vibration suppression capabilities of the proposed control method, supporting the adaptive regulation of stiffness and damping characteristics of suspension system.

    Multi-objective Optimization of Filament Winding Constrained Structure of Electromagnetic Gun
    ZHAO Wei, HOU Baolin
    2024, 45(11):  3820-3832.  doi:10.12382/bgxb.2023.1144
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    Through the classical lamination theory and coordinate transformation, the material model is simplified, and the modeling of complex laminated composite is avoided. A multi-objective improved immune clonal cuckoo algorithm (MOIICCA) is proposed for the multi-objective optimization of fiber winding constrained structure of electromagnetic gun. The accuracy of MOIICCA algorithm is verified by 100 simulation calculations of ZDT1-ZDT3 test function, and the performance of MOIICCA algorithm is measured by inverted generational distance (IGD) evaluation index. By introducing the learning method of deep neural network and taking 646 groups of electromagnetic gun finite element calculation results as the training set, the deep neural network agent model which meets the engineering application requirements is trained to replace the finite element simulation, thus improving the computational efficiency of multi-objective optimization. Finally, MOIICCA algorithm is used to optimize the constrained structure of electromagnetic gun fiber winding, and the Pareto solution set is obtained. IGD results show that MOIICCA algorithm has higher computational accuracy and efficiency than the multiple objective particle swarm optimization algorithm and the non-dominated sorting genetic algorithm II, and has more advantages in solving the high-dimensional problems, and t. The test results also show that MOIICCA algorithm can get better Pareto set in a shorter time. The results of the first 10 sets of Pareto solutions show that the fiber layer 1 of the winding structure mainly improves the circumferential strength, and the fiber layer 2 mainly balances the circumferential strength and axial stiffness.

    Comprehensive Electromagnetic Protection Method of Radio Fuze for Electromagnetic Railgun
    WEN Ruihu, LI Ping, HUANG Zheng, WANG Haibin, LI Pengfei
    2024, 45(11):  3833-3840.  doi:10.12382/bgxb.2023.0944
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    The transient strong magnetic field environment in the bore during the launch of electromagnetic railgun can lead to the induced current in the radio fuze circuit, which affects the normal operation of fuze. Therefore, the shielding and protective measures need to be taken for the reliable operation of fuze. Based on Faraday’s law of electromagnetic induction, a comprehensive electromagnetic protection method is proposed for the radio fuze of electromagnetic railgun. A high permeability material shell is used for magnetic shielding to reduce the magnetic induction intensity of fuze circuit, and the rate of change in the magnetic induction intensity of fuze circuit is reduced by utilizing the eddy current effect of high conductivity material. The fuze circuit area is reduced by optimizing the circuit design, and the dot multiplication between the fuze circuit and the magnetic field is reduced through circuit board layout. The finite element model of radio fuze in the strong magnetic field environment of electromagnetic railgun is simulated and analyzed. The results show that the comprehensive electromagnetic protection method is effective. The research results can be used for reference in the design of radio fuze of electromagnetic railgun in the future.

    Design of a Neural Network Acceleration Autopilot for Spinning Projectile Based on Adaptive Disturbance Observer
    WANG Wei, YANG Jing, NAN Yuxiang, LI Junhui, WANG Yuchen
    2024, 45(11):  3841-3855.  doi:10.12382/bgxb.2023.1085
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    The spinning projectiles are influenced by various disturbances during flight, includingthe model uncertainties due to the drastic variations in aerodynamic parameters during cross-domain flight, as well as the external perturbations caused by external forces and moments. The research aims to address the robust control challenges of dual-channel spinning projectiles in high-dynamic flight environments. A pseudo-inverse feedback controller is designed based on the trajectory linearization control method, and an adaptive feedforward compensation controller is developed using radial basis function neural networks to accurately approximate the model uncertainties. Finally, an adaptive disturbance observer is designedby treating the neural network approximation errors and external disturbances as total disturbance based on the fixed-time stability theory, which is used to accurately estimate and compensate for total disturbance. The ultimate uniform boundness (UUB) of the closed-loop system is rigorously proven through Lyapunov theory. The effectiveness of the proposed methodology is illustrated through numerical simulations.

    Intelligent Penetration Policy for Hypersonic Cruise Missiles Based on Virtual Targets
    LI Jiashen, WANG Xiaofang, LIN Hai
    2024, 45(11):  3856-3867.  doi:10.12382/bgxb.2023.1048
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    An intelligent penetration policy using virtual targets and contextual Markov decision process (CMDP) for hypersonic cruise missiles is proposed to constrain the trajectory deviation and improve the generalization performance in different combat scenarios. The stationary virtual targets are chosen within a tubular envelope with the planned trajectory as axis, and the deep reinforcement learning algorithm is applied to decide their position relative to the axis. Then the proportional guidance law is used to guide the cruise missile to attack these virtual targets one by one with proportional guidance law, thus shaping a maneuvering trajectory meeting the requirements of penetration within the given envelope. The optimal penetration policy for a combat scenario is extended to the probability distribution of combat scenarios using CMDP to improve the generalization performance. The results demonstrate that the penetration policy constrains the trajectory deviation during penetraton and exhibits adaptability to variations of interceptor’s launch position and maneuvering capability.

    Cavity Forming Characteristics of Ballistic Soap Penetrated by Sub-millimeter Particles and Injury Threshold
    WANG Shaohong, FAN Ruijun, WANG Jinying, LI Haijie, PI Aiguo
    2024, 45(11):  3868-3878.  doi:10.12382/bgxb.2023.1017
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    Ballistic soap is widely used in the field of wound ballistics, as an equivalent target of biological target, to observe the damage characteristics of wound channels for assessing the potential damage of ammunition. However, there is still a lack of damage standards for sub-millimeter particle damage elements of low collateral damage munitions to the biological targets. The dimensional analysis method is used to determine the forming characteristics of penetrating cavity, and the actual wound trajectory of soap target is obtained through the particle driving test. The evolution law of penetrating cavity of sub-millimeter particles is analyzed by numerical simulation, and the critical damage conditions of sub-millimeter particles on the soap target equivalent target are established. The conical cavity produced by sub-millimeter particles penetrating the soap target is represented by inlet diameter and cavity depth. The results show that the cavities caused by sub-millimeter particles with different densitues, sizes and velocities are significantly different, and the cavity characteristics are related to specific kinetic energy. The volume of the cavity produced by penetrating the soap target increases with the increase in the the density, size and velocity of particle material. The larger the particle size is, the deeper the penetration into the soap target is, and the inlet diameter expand to 2.0-2.5 times of the particle size. According to the fragment killing criteria, the injury thresholds of sub-millimeter particles with different particle sizes to the soap target are determined. The energy density of particle penetration should exceed 0.83J/cm2 to cause damage to the soap target. The numerically simulated, test and theoretically analyzed results agree well with each other, and the the influence law of penetration effect is consistent. The results can provide theoretical reference for the structural design of low collateral damage warhead and the effect evaluation.

    Low Speed Impact Resistance of Gradient Encapsulated Circuit Board Structure
    ZHU Xiufang, ZHOU Hongyuan, ZHANG Hong, CHEN Xinmin
    2024, 45(11):  3879-3891.  doi:10.12382/bgxb.2023.0949
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    Encapsulating protection has been widely used in automobiles, ships and weapons. It can enhance the integrity of electronic equipment and improve the resistance to external shocks and vibrations. However, the traditional homogeneous resin encapsulating materials have insufficient toughness and poor impact resistance. In response to this issue, this paper designs the resin gradient encapsulated materials reinforced with carbon nanotube (CNT) and studies the impact resistance of gradient encapsulated circuit board structure. The enhancing effects of different CNT contents on resin matrix and the impact resistance of gradient encapsulated structures are analyzed through quasi-static tensile tests and dynamic drop hammer impact tests. The energy absorptions of different gradient layers are obtained and the damage and failure of internal circuit boards are evaluated through finite element simulation analysis. The research results show that the encapsulating material with 0.7wt % CNT exhibits a higher tensile strength, which is 16% higher than that of pure epoxy resin; The impact strength and critical failure energy of V-shaped encapsulated gradient plate are higher than those of other gradient types, and are increased by 40% and 15.8%, respectively, compared to the homogeneous plate. The buffering and energy absorption properties of the encapsulating materials have a positive impact on the protection of internal electronic components, with the gradient layer containing a higher CNT content exhibiting an increased energy absorption. The gradient encapsulation method proposed in this paper provides a reference for the protection design of electronic components under impact environment.

    Investigating the Shockwave Collision of Different Metals Driven by Two-point Lateral Symmetric Initiation
    REN Guowu, KANG Huaipu, ZHANG Shaolong, ZHANG Chongyu, CHEN Yongtao, TANG Tiegang
    2024, 45(11):  3892-3902.  doi:10.12382/bgxb.2023.0936
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    The initial interactions of oblique shockwaves in metal samples under symmetric detonation loading is studied for the analysis of its subsequent dynamic evolution and failure mechanisms. Prior experimental and numerical investigations primarily centered on the dynamic process at later stage and initial interactions of shockwaves within the metal are very scarce to be examined. The dynamic characteristics of metal lead(Pb), oxygen-free high-conductive copper (Cu-OFHC) and W-Ni-Fe alloy(W4Ni2Fe) impacted by two oblique shockwaves are investigated using the shockwave polar theory and numerical simulations. Based on the shockwave polar theory and the Hugoniot equation of state, the critical conditions of the transition from regular reflection to Mach reflection for the shockwave reflections of three metals above are obtained to predict their reflection characteristics in the numerical simulations. The numerical results show that Mach reflection occurs in all three metals, which is consistent with the theoretical predictions. Through the comparative analysis of transverse pressure profiles in the same region of the three metals, it is found that the Mach stem for Pb is much wider than those of Cu-OFHC and W4Ni2Fe, and the three-wave loading region formed by the incident shockwave, Mach stem and reflected shockwave in Pb is also larger than those in the latter two. The fundamental origin stems from the lower sound velocity for metal Pb. For the three metals, the ultimate width of Mach stem is estimated and the dynamic behavior in the collision zone is discussed based on the free-surface velocity profile and decison criteria. Finally, based on the pressure and free-surface velocity profile, a symmetric oblique shockwave collision dynamics model is established, laying the fundamental theory on elucidating the dynamic behavior of metal.

    A DDPG-based Trajectory Planning Method for Collision Avoidance of Morphing Spacecraft
    DING Tianyun, XIA Yi, MEI Zewei, SHAO Xingling, LIU Jun
    2024, 45(11):  3903-3914.  doi:10.12382/bgxb.2023.1182
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    To address the problem of the strong coupling between the guidance and morphing decision of morphing spacecraft, a morphing collision avoidance trajectory planning method of considering obstacle constraint based on deep deterministic policy gradient (DDPG) is proposed. A kinematic model of morphing aerospace craft is established according to morphing parameter. A longitudinal guidance law with a range error correction function and a lateral guidance law based on line-of-sight angle deviation are designed to realize the obstacle circumvention and ensure the terminal guidance accuracy. Then a Markov decision model is constructed to facilitate a continuous morphing. The angle of attack, Mach, and relative distance from the spacecraft to the obstacle are taken as the state space. The potential field penalty function considering collision and the smallest terminal guidance error reward function is considered in the design. The DDPG network is then trained to generate a map of decision instruction from the state space and obtain the optimal shape decision instruction. The simulated results show that, compared with configuration-fixed spacecraft, the guidance accuracy and lateral obstacle avoidance ability of morphing spacecraft are improved by optimizing the shape, and the requirement for the detection ability of air borne radar is reduced to save the detection cost.

    Finite Mass Inflation and Wake Recontact Phenomenon of Cross Parachutes
    HOU Xiayi, HU Jun, YU Yong
    2024, 45(11):  3915-3925.  doi:10.12382/bgxb.2023.0840
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    The finite mass inflation characteristics and wake recontact phenomenon of folded cross parachutes are investigated. The fluid-structure interaction numerical simulation is conducted using the arbitrary Lagrangian-Eulerian (ALE) method for the cross parachute-load system with mass ratio from 0.17 to 0.94 and Froude number from 6.8 to 383.9 during deceleration. The effects of the mass ratio and Froude number on the inflation process of cross parachute are studied. The peak deployment load and canopy collapse parameter are discussed. The phase diagrams for the three different inflation results of cross parachute, namely, normal inflation, reinflation after wake recontact, and complete failure after wake recontact, are plotted in relation to the mass ratio and Froude number. The three inflation processes of cross parachute are analyzed in detail. The deployment load, drag coefficient, and transient change in the projected diameter of canopy are studied, and the fluid-structure interaction mechanisms of different inflation processes are studied by taking into account the structural deformation of parachute, stress distribution and unsteady flow field. The results indicate hat the dimensionless peak deployment load and canopy collapse parameter increase with the increase in Froude number. During the finite mass inflation process of parachute, there is intense momentum exchange between the canopy and air around it, which may lead to high-speed wake flow interacting with the canopy to cause a significant collapse or even complete collapse of the cross parachute.

    Event-combined Visual-inertial Odometry Using Point and Line Features
    LIU Yumin, CAI Zhihao, SUN Jialing, ZHAO Jiang, WANG Yingxun
    2024, 45(11):  3926-3937.  doi:10.12382/bgxb.2023.1221
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    Visual-inertial odometry is a key technology for robots to achieve autonomous localization. As an asynchronous vision sensor, the event cameras have complementary to the traditional cameras. For the scene of low light condition, high dynamic range and high-speed motion, the output of event camera and the traditional image are fused.A real-time visual inertial odometry using point and line features is proposed combined with the inertial measurement unit (IMU). An algorithm for generating an event image from event stream is proposed, a point-line feature detection method combined with events is designed, anda back-end sliding window optimization algorithm is designed based on the idea of visual-inertial tight-coupling. The dataset test and UAV flight test are conducted. The test results on the dataset show that, compared with the visual-inertial odometry using point and line features only on the traditional image, the proposed odometry can reduce the positioning error by more than 22% on average in the scene of high-speed motion, and it can reducethe positioning error by more than 59% on average in the scene of low light condition and high dynamic range.

    Analysis of Electromagnetic Characteristics of an Integrated Electromagnetic Ejection and Arresting Gear
    ZHAO Tong, LI Desheng, YE Lezhi, JIA Yahui, WANG Bin, LI Zequn
    2024, 45(11):  3938-3948.  doi:10.12382/bgxb.2023.1120
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    In view of the inherent disadvantages of large footprint, complex structure and heavy weight of linear catapult device, this paper proposes an electromagnetic ejection and arresting gear with a single axis integrated steel cable drive. The gear consists of permanent magnet energy storage motor, eddy current clutch, eddy current brake and winding wheel. The structure and working principle of the gear are introduced. The electromagnetic theoretical models of eddy current clutches and eddy current brakes are developed based on the Ampere loop theorem. By comparing the results with 3-D finite element calculations, the electromagnetic characteristics of eddy current clutch and eddy current brake are analyzed. The correctness and effectiveness of the electromagnetic theoretical model are verified using a small-scale experimental prototype of the eddy current brake. Finally, a dynamic analysis of the electromagnetic ejection and arresting gear is conducted. The results indicate that the gear can accelerate a 30000kg aircraft from 0m/s to 70m/s within 2.1s. And it can also make a 72m/s aircraft stop in 2.6s, meeting the design requirements.

    Non-singular Sliding Mode Control of Non-minimum Phase Hypersonic Vehicles
    WEI Qiaoling, DU Yuxin, ZHOU Chao, WANG Fang
    2024, 45(11):  3949-3958.  doi:10.12382/bgxb.2023.1158
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    A sliding mode control strategy based on Byrnes-Isidori (B-I) standard is proposed to solve the tracking and controlling problems of non-minimum phase hypersonic vehicles under external disturbance. A new integral sliding mode surface and a novel composite reaching law are designed. The exponential and sign functions are combined in the reaching law to enhance the anti-vibration capability and rapid convergence performance of the hypersonic vehicle. A robust sliding mode controller is constructed to ensure the asymptotic stability of internal dynamics by using the sliding mode control method. And a non-singular terminal sliding mode controller is constructed to ensure the practical finite time stability of velocity tracking error and the bounded stability of external dynamics. Combining the robustness and fast convergence speed of the non-singular terminal sliding mode control, a terminal sliding mode disturbance observer is designed to solve the external disturbance in the velocity subsystem and altitude subsystem.The stability is proved by using the Lyapunov theory, proving the practical finite-time stability of the estimation error. The effectiveness of the control strategy based on the B-I standard is verified by simulation comparison.

    Kinematics and Dynamics Modeling of 1T2R Heavy-load Parallel Stabilized Platform with Analytical Solution
    QIANG Hongbin, DU Liangliang, KANG Shaopeng, LIU Kailei, ZHOU Ling, ZENG Shuisheng
    2024, 45(11):  3959-3969.  doi:10.12382/bgxb.2023.1168
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    In order to solve the parasitic motion of the heavy-load parallel stabilized platform of one translation and two rotations ship, which is not conducive to solving the analytical solution of kinematics and increases the difficulty of control system, a platform mechanism of 1T2R variant 3UPS-PUU-2SS parallel stabilized platform with analytical solution is proposed to remove the accompanying rotation around z-axis. By analyzing the motion characteristics of the spatially constrained branched chain, it is proved that the parallel platform does not rotate around z-axis. The spatial closed-loop vector equation method is used to establish the constraining equations and kinematic models, and then the analytical solutions of parasitic motion and inverse kinematics are obtained. The reachable workspace of the parallel platform is plotted by the fast polar coordinate search method, and the dexterity of the workspace is analyzed by the Jacobian matrix conditional number. A dynamic model of the parallel platform is established based on the virtual work principle, and the numerical solution is carried out by the 5-order polynomial interpolation method, and the theoretical curve of driving force is drawn, which is compared with the dynamic simulation curve of the finite element analysis software. The theoretical and simulated results show that the achievable workspace can meet the motion compensation requirements of a ship in the fourth-level sea state, its global dexterity is greater than 0.32, and the maximum error between the theoretical and simulated results of the dynamic model is within 1.42%, which verifies the accuracy of the dynamic model.

    A Post-failure Traffic Reconfiguration and Scheduling Optimization Method for Time-sensitive Networking
    LI Ji, GUO Yonghong, NIU Haitao, GUO Xin, HOU Zeng
    2024, 45(11):  3970-3982.  doi:10.12382/bgxb.2024.0141
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    In the existing studies on time-triggered (TT) traffic reconfiguration in time-sensitive networking (TSN), the redundancy status of the traffic is often overlooked, making it difficult to balance both TT traffic latency performance and the efficiency of reconfiguration scheme solutions in practical deployments. To address this issue, an optimization method for traffic reconfiguration and scheduling after failures is proposed. This method improves the solution efficiency of the reconfiguration scheme by introducing a fast reconfiguration algorithm and its corresponding enhancements at the expense of the latency performance of non-redundant traffic while ensuring solution success. Additionally, the proposed method flexibly adjusts the scheduling strategy of unaffected TT traffic, and incorporates a tabu search-based optimization algorithm with an associated objective function to enhance the overall TT traffic latency performance after reconfiguration. Experimental results demonstrate that the proposed method improves the solution efficiency by more than 75.03% compared to the commonly used incremental reconfiguration methods, and slightly improves TT traffic latency performance after multiple rounds of reconfiguration, showing a significant potential for practical application.

    Design and Optimization of Locust-hindfoot-inspired Embedded Missile Ejection Device
    CAI Yunlong, YANG Lina, QUAN Liang, YANG Baosheng, REN Ruoyu
    2024, 45(11):  3983-3997.  doi:10.12382/bgxb.2024.0180
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    Inspired by the biomechanical mechanism of locust jumping, an ejection device with joint torsion spring and double trapezoidal structure is designed, which has the ability to achieve large ejection stroke for low thrust demand and keeps the characteristics of initial bow angular velocity and angle during missile separation. The efficient mechanism layout parameters are optimized by the optimization methods based on parameterized models and Kriging surrogate models. The influence of arm flexibility effect on missile ejection separation parameters during launch is studied based on a rigid-flexible coupling dynamic model. The projectile-machine, separation process is investigated based on computational fluid dynamics. The research results indicate that the optimization method based on parameterized models and Kriging surrogate models can be used to quickly obtain the mechanism parameters that meet the design requirements. In the process of ejection, the flexible deformation of middle arm will lead to the difference between the actual separation parameters and the ideal design parameters. The flexible effect cannot be ignored in the detail optimization design, and the structural stiffness should be increased to reduce the design deviation. The given design example can meet the design criteria and the missile can be safely separated, proving the effectiveness of the new design in this paper.

    Converted State Equation Kalman Filter for Three-dimensional Target Tracking
    LIU Zengli, ZHANG Wen, CAO Qihong, ZHAO Xuanzhi, LIU Kang, ZENG Sai
    2024, 45(11):  3998-4010.  doi:10.12382/bgxb.2024.0182
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    The three-dimensional spherical coordinate measurements collected by the radar and sonar system are nonlinear with the Cartesian coordinate state of the moving target, which limits the tracking accuracy, and. it is more difficult to use the Doppler measurement with strong nonlinearityefficiently. Aiming at the above problems, a state vector composed of distance, pitch angle, azimuth angle and their derivatives is constructed to linearize the measurement equation,and the ordinary differential dynamics equation is discretized in a two-dimensional time-varying polar coordinate system composed of distance and pitch angle.Then the azimuth angle is introduced based on the projection relationship, and a typical three-dimensional constant velocity and constant acceleration motion model in the spherical coordinate system are established. Combined with the standard Kalman filter, the tracking is realized to avoid the nonlinear errorsunder the linear Gaussian framework. The effectiveness and performance advantagesof the proposed method in several three-dimensional tracking scenarios are verified through simulation.

    Research on the Vulnerability of Artillery Barrel under Shock Wave Loading
    QIAO Zhen, CHENG Wei, WANG Heng, ZHANG Tuan, ZHOU Li
    2024, 45(11):  4011-4019.  doi:10.12382/bgxb.2023.1034
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    In response to the lack of theoretical research methods and the incomplete construction of criterion models for the vulnerability of artillery barrels subjected to shock wave, a theoretical research method for the vulnerability of artillery barrels subjected to shock wave is proposed. A dynamic model of the artillery barrel subjected to shock wave is established based on the Euler-Bernoulli beam model and the rigid-plastic beam model. A physical damage criterion of the functional damage of the barrel is constructed according to the transition of elastic-plastic state and the degree of plastic deformation of the barrel. Based on the relationship between the natural vibration period of barrel, the positive pressure duration of shock wave and the damage criterion of shock wave, a coefficient for determining the damage criterion of shock wave is proposed, and a relationship formula for quantitatively determining the shock wave damage criterion is constructed. A mathematical model for the damage criterion of artillery barrel subjected to shock wave is established based on the similarity law of explosion. A damaging criterion for the barrel subjected to shock wave is obtained based on the proposd mathematical method. It shows that the function of the artillery barrel is damaged when CX≥16.44.

    Multi-scale Blind Image Restoration Algorithm Based on Salient Region Detection
    ZHAO Xiaoqiang, WANG Tao, SONG Zhaoyang, JIANG Hongmei
    2024, 45(11):  4020-4030.  doi:10.12382/bgxb.2023.0992
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    The blind image deblurring algorithm based on priority takes a long time for image deblurring,and has aunidealsalient edge structure extraction capablity. A multi-scale blind image restoration algorithm based on salient region detection is proposed.In order to restore more clear images, an image pyramid is constructed by using a rough-to-finemulti-scale iterative framework. In the aspect of image single scale, asalient region with strong edge structure is extracted first, and the l0 norm constraint is applied to it. Asalient mapping prior is proposed. Then the salient mapping prior and the maximum posteriori probability are introduced into the traditional image deblurring model to construct a point spread function estimation model, and the semi-quadratic splitting algorithm is usedto solve the non-convex problem of the model. When restoring the point spread function, the change of point spread function similarity is used to limit the transition iteration in each scale. Finally, the fuzzy image and the final estimated point spread function are deconvolved to obtain the restored image. The experimental results show that, compared with the existing mainstream deblurring algorithms, the proposed algorithm can effectively suppress the ringing and artifact phenomena in both synthetic and real data setsand get a good visual experience, the evaluation indexes are better than those of the comparison algorithm, and the image restoration time is greatly reduced.

    Research on Tracking Strategy of Roll-pitch Seeker
    YAO Jiazhi, SONG Yansong, SONG Jianlin, WANG Wei, AN Yan
    2024, 45(11):  4031-4038.  doi:10.12382/bgxb.2023.0977
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    In order to simplify the tracking process of roll-pitch seeker, a tracking scheme for roll-pitch structure is proposed and experimentally proven.The working principle and characteristics of roll-pitch seeker are analyzed, and a new method for tracking the targets based on aeliminating image rotation mechanism is proposed, which can be easily and effectively applied in engineering practice. Compared with traditional coordinate conversion methods, the accuracy of the proposed method is less affected by mechanical errors such as optical axis, and has higher fault tolerance, applicability, and real-time performance. It can also compensate for the disturbances in any direction through feedback from angular rate gyroscope data. In addition, based on the different installation methods of gyroscopes, the stability formula is obtained by deriving the stabized platform state of the seeker and the relative motion relationship between the seeker and the missile body, and the design of the control system is completed. Finally, rhe experimental verification is conducted through semi-physical simulation.The static tracking experimental results demonstrate the practicality of the proposed tracking method. The traditional coordinate conversion method and the proposed method are used for tracking in the dynamic tracking experiment. Dynamic experimental results show that the proposed method is still applicable in the presence of carrier disturbances. Compared with traditional coordinate conversion methods, the proposed method significantly improves tracking accuracy, reducing the RMSE values of x-axis and y-axis tracking errors by 79.10% and 90.04%, respectively.

    Experimental Study on Dynamic Response of Upper Structure of High-rise Building under Far-field Explosion Shock Wave Loading
    YIN Wenjun, CHENG Shuai, LIU Wenxiang, LIAO Zhen, MA Long, ZHAO Bin, ZHANG Dezhi
    2024, 45(11):  4039-4051.  doi:10.12382/bgxb.2023.0960
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    In order to study the dynamic response of the upper structure of high-rise building under the far-field explosion shock waveloading, 1∶30 scaled models of high-rise building are designed for the field explosion experiment. The shock wave pressure curves and the displacement parameters at different heights of the modelsare obtained through experiment, and the experimental loading state is judged by the numerical simulation method. The damage patterns of the models and the measured data are analyzed. The results show that the failure mode of high-rise building frame column is mainly subjected to shear failureand the frame beam is mainly subjected to bending failureunder the effect of far-field explosion shock wave. In addition, the interaction between different components has an important influence on the failure mode. When the angle between the explosion center and the building is less than or equal to 25°, the pressure parameters of shock wave are the same all over the surface.When the whole structure is still in the elastic deformation stage, the change curves of horizontal displacement in the early stage of each height position approximately coincide with each other, and the motion periodsare consistent.The peak values of the displacement are different in the later stage due to the different heights, which are linear with the heights. The deformation and damage of the building mainly depend on the specific impulse, and are little affected by the peak shock wave pressure.

    The Positioning Accuracy of Ammunition Coordination Considering the Uncertainty of Dynamic Loads
    ZHANG Yuntian, CHEN Longmiao, CHEN Guangsong, WANG Mingming
    2024, 45(11):  4052-4061.  doi:10.12382/bgxb.2024.0658
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    To analyze the impact of uncertain input parameters on the precision of coordination in the dynamic random process of ammunition coordination, the propagation of dynamic uncertainty in the process of ammunition coordination is studied based on the direct probability integral method (DPIM). A rigid-flexible coupling dynamic model of ammunition coordination mechanism is established, and the probability density integral equation of the coordination process is derived. The Karhunen-Loeve (K-L) expansion method is employed to reduce the dimensionality of dynamic random driving load, thus quantificatying the uncertainty in the positioning angle of ammunition coordination arm under dynamic uncertainty conditions based on DPIM. Comparisons with experimental results indicate that the simulation output of the ammunition coordination positioning aligns basically with the experimental test results, which validates the accuracy of the proposed model. Additionally, the probability density function obtained using the DPIM method shows a smaller error, which confirms the effectiveness of the new method. The coordination positioning results under the effects of dynamic random loads and uncertain parameters demonstrate that the K-L method effectively reduces the dimensionality of dynamic random loads in the coordination process, with positioning errors increasing as the coordination angle increases. The computational results provide strong support for the reliability design of automatic ammunition loading system.

    Wear Characteristics of Coordinated Ammunition Ramming Mechanism in Automatic Ammunition Loading System for Artillery
    TIAN Ye, CHEN Guangsong, LIU Taisu
    2024, 45(11):  4062-4070.  doi:10.12382/bgxb.2024.0634
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    The coordinated ammunition ramming mechanism in the automatic ammunition loading system is an important part to complete the ammunition transfer. Due to the long-term impact loads during firings, the countershaft holes of the coordinated ammunition ramming mechanism experience wear-induced clearance variations, affecting the accuracy of ammunition coordination. Studying the wear of the coordinated ammunition ramming mechanism is crucial for enhancing its reliability. To investigate the wear characteristics of the coordinated ammunition ramming mechanism, a mathematical model based on the modified Archard wear model is developed, and the wear coefficient is determined through experiments. A finite element simulation model for the mechanism’s dynamic response is established and validated using experimental data. The finite element simulation and the Arbitrary Lagrangian-Eulerian (ALE) adaptive grid technology are used to simulate the wear process, revealing the mechanism’s wear characteristics, such as the relationship between wear depth and cycle count, and the location of maximum wear. The results indicate that the initial wear is intense. After approximately 350 coordinated ammunition transfers, the wear transits from intense to steady, with the wear rate decreasing as the wear process continues. Wear at the contact edge of shaft hole is more pronounced than elsewhere throughout the wear process.

    Traumatic Ballistic Properties of SEBS Gel
    XU Haoran, WEN Yaoke, DONG Fangdong, QIN Bin, SHEN Luyu
    2024, 45(11):  4071-4080.  doi:10.12382/bgxb.2023.0818
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    The gel made of styrene-ethylene-butylene-styrene (SEBS) block copolymer and white oil has similar properties to ballistic gelatin. Compared with ballistic gelatin, it has good temperature stability, excellent transparency, and aging resistance. The mechanical properties are comprehensively measured to investigate the feasibility of using SEBS gel as a substitute for ballistic gelatin in trauma ballistic test. First, the quasi-static and dynamic mechanical properties of SEBS gels with four different mass fractions (15%, 20%, 25%, and 30%) are tested using a universal material testing machine and an improved Hopkinson pressure bar to study the impact of copolymer content on the mechanical properties of the gel. The mechanical properties of SEBS gel are compared with those of 10% and 20% ballistic gelatins to determine the mass fraction that is most similar to the mechanical properties of ballistic gelatin. Then, SEBS gels with three different mass fractions (15%, 20%, and 25%) are penetratedusing 5.8mm rifle bullets, and the moving postureof bullet and the temporal cavity evolution of a target are recorded by high-speed photography. The experimental results of SEBS gel are compared with those of the ballistic gelatin with 10% mass fraction. The test results show that the stress-strain curve of 10% ballistic gelatin is between those of 15% and 20% SEBS gels, and the stress-strain curve of 20% ballistic gelatin is between those of 20% and 25% SEBS gels under quasi-static compression. The mechanical properties of 20% and 30% SEBS gels are similar to those of 10% and 20% ballistic gelatins, respectively, at high strain rates. The maximum cavity diameter of 15% SEBS gel is closest to that of the 10% ballistic gelatin, but the cavity expansion and contraction rates of SEBS gel are higher than those of ballistic gelatin. This study provides data support for the replacement of ballistic gelatin with SEBS gel as a new soft tissue substitute.

    Numerical Simulation of Coating Spalling on Barrel Based on Phase-field Coupled Cohesive Force Model
    GAO Jian, ZOU Libo, YU Cungui
    2024, 45(11):  4081-4093.  doi:10.12382/bgxb.2024.0227
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    The coating on the inner chamber may peel off during the use of barrel, shortening the service life of barrel weapon. The mechanism behind this phenomenon is not yet clear. To study the phenomenon of coating peeling in the barrel of barrel weapons, A numerical simulation method for the phase-field model (PFM) coupling with the cohesive zone model (CZM) is proposed. Considering the superiority of continuous medium mechanical properties of PFM in crack propagation simulation and the universal applicability of CZM in multiphase material interface damage simulation. PFM is used to simulate the crack propagation behaviors inside the coating and substrate, while CZM is used to simulate the damage at the interface between the substrate and the coating. The finite element simulation is made for one crack and two cracks propagating at the interface to address the phenomenon of crack deflection, and the simulated results are compared with experimental data. The effects of different crack spacings on interface damage are studied,and the influence of phase-field characteristic length on crack propagation behavior is also discussed. The research results show that, when the crack extends to the interface between the substrate and the coating, it will turn to propagate to both sides along the interface, and eventually making the interface be failure; when multiple cracks propagate to the interface, the interface damage mainly occurs in the area between the multiple cracks, ultimately evolving into coating peeling. The crack spacing has an impact on the initial damage and the development rate of interface damage. The proposed numerical simulation method of the phase field coupled cohesive force model can serve as a computational method for studying the failure mechanism of barrel coatings.

    Mechanical Response of Body Armor during Rifle Bullet Penetration Based on Bond-based Peridynamic Method
    WANG Jilong, WEN Yaoke, LIU Dongxu, WANG Huicheng, SHEN Zhouyu, LUO Xiaohao
    2024, 45(11):  4094-4105.  doi:10.12382/bgxb.2024.0275
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    At present, there is still a lack of research on the mechanical response of body amor under the impact of bullets. In this paper, a bond-based peridynamic method combined with the traditional Lagrangian method is used to numerically simulate the process of a 5.56mm SS109 rifle bullet penetrating a NIJ level III SiC/ultra-high molecular weight polyethylene (UHMWPE) body amor. The accuracy of the numerical model is verified by comparing it with the penetration test results of body amor based on the three-dimensional digital image correlation method. The research results show that the velocity of bullet decreases from 810m/s to 157.57m/s after penetrating the body armor for 50μs, and the ceramic block contacting with the bullet severely fractures.The bond-based peridynamics method can effectively track the evolution of cracks when the bullet impacts the ceramic insert plate. The radial cracks generated by the impact of an SS109 bullet at 810m/s on the SiC ceramic insert plate are outwardly expanded basically within 10μs, and the severely damaged area is essentially shaped within 30μs. Ultimately, the radial cracks, hoop cracks, and delamination cracks parallel to the impact surface are formed under the complex action of pressure wave. The maximum back face signature (BFS) value of body armor is 18.41mm. Due to the orthotropic nature of UHMWPE laminate, the effective strain on the back side is distributed in an “L-shaped” pattern centered around the point of impact and the maximum effective strain occurs at about ±45° on the bulge boundary. The equivalent stress field presents a “diamond-shaped” distribution, and the stress concentration occurs at the four corners of the “diamond”.

    Effect of Inner Bore Structure of a Large-caliber Gun on the Inner Wall Loadings of Barrel during Engraving Process
    LI Yifan, FU Jiawei, YANG Diao, LI Yanze
    2024, 45(11):  4106-4118.  doi:10.12382/bgxb.2024.0646
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    During the engraving stage of projectile, the inner bore of gun barrel is in a harsh environment of high temperature, high pressure, rapid compression and friction. A severe wear at the beginning of rifling is caused by the large loadings on the inner wall of barrel during engraving process. The influences of different inner bore structures on the inner wall of barrel are studied using a large-caliber shallow rifling barrel as the object. The constitutive relationship of the rotating band material under high temperature and high strain rate is constructed through split Hopkinson pressure bar experiment, and the plastic deformation of rotating band, the engraving resistance, and the variation of loadings on the inner wall of barrel during the engraving process are analyzed using a finite element method. And the three-dimensional thermo-mechanical coupling engraving finite element models are established considering different bore structures such as rifling width, rifling cross-sectional shape, and forcing cone taper. The influences of different bore structures on inner wall loadings of barrel during the engraving process are calculated. The research results indicate that, for this type of gun, both the forcing cone structures and rifling structure have a significant impact on the loadings on the inner wall. Firstly, the increase in the forcing cone taper can lead to an increase in the engraving resistance and the loadings on the inner wall of barrel, and the ending time of engraving process and the peak times of the engraving resistance and the loadings on the inner wall of barrel are also advanced. Secondly, the peak loadings on the inner wall of barrel significantly increase with the width of land. But the top of the driving side can be changed to effectively reduce the loadings on the inner wall of barrel. The peak value of the loadings on the inner wall of barrel is decreased by 9.87% after rounding and 5.59% after chamfering. This study contributes to enriching the design methods of bore structures based on the lifespan of the barrel.

    Stress States of Anisotropic Material Gun Barrel by Firing the Projectiles with Different Jacket Materials
    GE Zhongyu, ZHOU Kedong, LU Ye, LIU Jinhao
    2024, 45(11):  4119-4132.  doi:10.12382/bgxb.2024.0676
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    The stress field and temperature field of barrel in the firing process of a small caliber rifle are studied. An accurate thermo-mechanical coupling finite element model of the projectile/barrel interaction during the motion of projectile in the barrel is established, in which the effect of temperature on the mechanical properties of barrel and jacket materials and the anisotropy of the mechanical properties of barrel steel are considered. The engraving motion patterns of steel and copper jacketed projectiles, and the change of stress state in the barrel are obtained by the numerical simulation. The simulated results show that the different materials of projectile jacket have great influence on the engraving process,the engraving resistance of steel jacketed projectile is greater than that of copper jacketed projectile, and the in-bore stress of steel jacketed projectile is also greater than that of copper jacketed projectile. The stress distributions at different axial positions of barrel are different, the maximum stress at the chamber throat is on the land driving side, and the maximum in-bore stress at the muzzle is on the groove. This work is conducive to the optimization of projectile/barrel matching.

    Rigid-flexible Coupling Dynamic Modeling and Characteristics Analysis of a Rotational Chain Magazine
    LIU Taisu, YIN Qiang, LI Yong, ZHANG Yuntian
    2024, 45(11):  4133-4144.  doi:10.12382/bgxb.2024.0698
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    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.

    Time Discrimination Method of Multi-transmitter and Multi-receiver Circumferential Laser Fuze
    ZHA Bingting, XU Guangbo, QIN Jianxin, ZHANG He
    2024, 45(11):  4145-4154.  doi:10.12382/bgxb.2023.0948
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    It is difficult to distinguish backscattering signal from target echo signal, which is an important factor affecting the detection accuracy of fuze. In addition, when the echo signal is saturated, the conventional time discrimination circuit fails. According to the characteristics of laser echo signal in smoke and dust environment, a full-waveform sampling time discrimination algorithm based on multi-transmitter and multi-receiver laser fuze is proposed to effectively extract the target echo signal and complete the selection of laser ranging timing end point. In order to suppress the noise interference and keep the main waveform characteristics of the original echo signal, the echo signal is preprocessed by filtering and threshold interception, the feature extraction method is adopted based on the preprocessed signal, and then the shape characteristics of the characteristic signal are replaced by those of the original echo signal. Three kinds of echo signals in laser detection are tested to verify the feasibility of the proposed algorithm. The experimental results show that the proposed algorithm can effectively identify three types of echo signals, and calculate the best echo return time for different echo signals, which effectively improves the accuracy of time discrimination.

    Appointed-time Prescribed Performance Control for Missile Cold Launch Response Based on Nonlinear Filters and Dynamic Surface
    YU Xiaochuan, YANG Xiaowei, LIANG Xianglong, ZHU Weilin, YAO Jianyong
    2024, 45(11):  4155-4174.  doi:10.12382/bgxb.2024.0773
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    Focusing on the unsupported random vertical launching process of a vehicular missile launching system, this paper proposes an idea of actively regulating the oscillation of launch canister and hence controlling the attitude of missile through the hydraulic actuator, which ensures the launching safety and the adaptability of vehicular missile launching system to the launching site. A 6-DOF dynamics model of the launching system is established, which takes into account the interactions among the launch canister, adapters and missile. The seventh-order state-space equation is derived by combining with the pressure dynamic equation of the hydraulic system. For avoiding the problem of “differential explosion” in a backstepping controller design of the seventh-order nonlinear system, the dynamic surface technique based on a smooth nonlinear filter is introduced to simplify the controller design. Meanwhile, in order to suppress the influence of hard-to-modelling factors on the launch dynamics, a time delay estimation control method is introduced for the estimation and attenuation of unmodeled errors and external disturbances. The fast convergence of missile tracking is achieved and the prescribed indicators of oscillation amplitude and angular velocity are met by using the appointed-time prescribed performance control method. The calculation results of mathematical model are compared with the results from the finite element model to verify the correctness of the proposed launch dynamics model. In addition, the launch dynamic response results under the influences of proportion-iIntegral-differential (PID) controller, dynamic surface controller, controller with dynamic surface and time delay estimation, and controller with the appointed-time prescribed performance are compared. The results show that the proposed controller can be used to constrain the angle of missile within 0.5° and the angular velocity within 1.5°/s when a missile comes out of the launch canister.

    Dynamics Modeling and Stability Control of Marching Tank Gun Control System
    WANG Bin, ZHANG Jianshu, DUAN Zhifeng, YUE Qixing, GANG Kuankuan, MIAO Yangyang
    2024, 45(11):  4175-4190.  doi:10.12382/bgxb.2024.0485
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    Taking the external disturbances caused by the uneven road surfaces of marching tank gun control system (TGCS) and the unbalanced moment of tank gun elevation motion during TGCS operationinto consideration,a two-axis coupled two-degrees-of-freedom (2-DOF) dynamics model of the marching TGCS is established using the second kind of Lagrange method. In terms of the actual force and motion state of TGCS,an electromechanical coupling dynamics model is established for the marching TGCS, which is equipped with permanent magnet synchronous motors (PMSM) in the azimuthal and elevational direction drive system and the gear reduction gearboxes and roller screws in the transmission mechanism. A stable tracking controller for marching tank with finite-time convergence characteristicsis designed to quickly reject the effects of internal and external disturbances of the marching TGCS on the stable tracking of target. This design is based on a nonsingular fast terminal sliding mode (NFTSM) control law and a linear extended state observer (LESO). The stability precision and arrival time of TGCS for marching tank are calculated based on the stable tracking process for targets. The computational results are then compared with those obtained by utilizing traditional control methods under various operating conditions. The findings demonstrate that the proposed tracking controller exhibits rapid response speed,strong robustness against disturbances,and high tracking accuracy,thereby validating the effectiveness of the controller design.