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Table of Content

    30 March 2002, Volume 23 Issue 1
    Paper
    Coupled Torsional-Axial Vibration of the Crankshaft for a High Speed Diesel Engine
    Shu Gequn,Lü Xingcai
    2002, 23(1):  1-5.  doi:10.3969/j.issn.1000-1093.2002.01.001
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    This paper studied the principle and method of calculation for the coupled torsional-axial vibra?tion of the crankshaft for a high speed vehicle diesel engine. The paper analysed the coupled vibration of ve?hicular diesel engine crankshaft, and proposed expressions for the amplitude of vibration. The paper con?structed a multi-mass model and matrix equation by combining equations for torsional vibration and coupled vibration, with an analysis of the method of calculation. With a newly designed testing set-up the axial and torsional vibration of the crankshaft at the free-end of an in-line 6 cylinder diesel engine was measured. Its results agree well with those from calculations. It verifies the analysis given for the coupled vibration of high speed diesel engines.
    A Study on the Monitoring of Wearing Conditions in Engines Based on Oil Analysis
    Ren Guoquan,Zheng Haiqi,Zhang Yingtang, Luan Junying
    2002, 23(1):  6-9.  doi:10.3969/j.issn.1000-1093.2002.01.002
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    Metallic particles are worn off because of the reciprocating functions in engines, the particles bear important information of tne equipment’s wearing condition. Oil spectrometric technology, probability theory and statistics are used to study the concentration and gradient limits of the chief metallic particles according to the data. The limits are classified as normal, warning and abnormal. In order to improve the accuracy of the technique, fuzzy synthesis judgement method is used to determine the condition of wear of an engine. Better effect in monitoring is achieved as seen in an example.
    Energy Analysis Method for the Gliding Trajectory of a Projectile
    Ding Songbin,Wang Zhongyuan
    2002, 23(1):  10-13.  doi:10.3969/j.issn.1000-1093.2002.01.003
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    A study on the trajectory properties of a gliding projectile was done according to the energy conservation law. The necessary conditions for gliding flight were deduced, and the method of calculation, approximate formula for estimating the gliding range were also proposed. At the same time, selection of the initial time of the gliding flight was discussed. The results are meaningful to the design for the gliding pro?jectile regarding the aerodynamics and the control system.
    An Engineering Calculation Model for the Depth of Penetration of a Projectile in Steel Fiber Reinforced Concrete Embedded with Steel Spheres
    Wang Mingyang, Liu Xiaobin, Qian Qihu
    2002, 23(1):  14-18.  doi:10.3969/j.issn.1000-1093.2002.01.004
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    The paper studied effects of oblique incidence of projectiles and the existence of steel spheres on the depth of penetration by introducing two parameters Al, A2 based on theory of cavity-expansion. Sim?ple and practical formulas were obtained for the depth of penetration of projectiles into steel fiber reinforced concrete embedded with steel spheres.
    Numerical Simulation of Multi-Phase Explosion
    Liu Qingming, Bai Chunhua, Zhang Qi,Liang Huimin
    2002, 23(1):  19-22.  doi:10.3969/j.issn.1000-1093.2002.01.005
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    Based on theory of multi-phase thermodynamics of gas, particle and droplet in mixture and turbulent combustion, fuel air explosive explosion was simulated. Histories of the explosion parameters of fuel air explosive were given and the mechanism of explosion was revealed.
    Experimental and Theoretical Study on the Performance of Laser Ignition of Energetic Materials
    Zhang Xiaobing, Yuan Yaxiong, Ren Ruhai
    2002, 23(1):  23-26.  doi:10.3969/j.issn.1000-1093.2002.01.006
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    Laser ignition performance of energetic materials, including black powder, pyrotechnic materi?als, propellants having different particle diameters, were studied. The ignition delay was measured and anal?yses were conducted. On the basis of above, a mathematical model of laser ignition was established and nu?merical simulation conducted.
    A Novel Method for Preparing HNIW with Concentrated Nitric Acid
    Zhao Xinqi,Ma Pengchang
    2002, 23(1):  27-29.  doi:10.3969/j.issn.1000-1093.2002.01.007
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    A novel method for preparing γ-HNIW by the nitration of tetraacetylhexaazaisowurtzitane with nitric acid of 90% ?98% concentration was studied, and the prepared product γ-HNIW is of high pu?rity and high yield. The nitration reactions proceed stepwise according to the structures of the isolated di-, tetra- and penta- nitrocage derivatives.
    A Study on the Expansion Mechanism of Ammonium Nitrate
    Lu Ming, Lu Chunxu, Liu Zuliang
    2002, 23(1):  30-34.  doi:10.3969/j.issn.1000-1093.2002.01.008
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    Expanded ammonium nitrate (EAN) is a kind of self-sensibilized and modified AN. EAN is made from the AN solution containing special surfactants under vacuum. In this paper, the process of ex?pansion of AN and the action of special surfactants are studied. The results show that the AN solution changes from an unsaturated state to a super saturated state under high vacuum and the action of special sur?factants, which causes the AJN to crystallize rapidly and the volume of the system to expand abruptly. In the course of vacuum drying, the central voids, pore channels and cracks are produced m EAN, which cause the EAN ’ s sensitivity of initiation to improve remarkably. The special surfactants may decrease the surface tension of AN solution, they also act as foaming agents and quicken the crystallization velocity of AN.
    A Study on the Moving Features of Explosive Reactive Armor by Numerical Simulation and Experiments
    1:Wu Cheng, Jiang Jianwei, Feng Shunsha,Ren Xiaoxue;2:Liu Beisuo
    2002, 23(1):  35-38.  doi:10.3969/j.issn.1000-1093.2002.01.009
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    Numerical simulation for the velocity histories and moving features of plates in a typical explo?sive reactive armor of practical size was carried out following the Autodyn-2D code. The experimental and simulation results show that the plate velocities at different times are precisely determinated. Particularities of the velocity histories allow the tandem shaped charge warhead to posses a shorter time delay and to defeat the main armor in a better attacking status. The experimental measurements have approved the demonstra?tions of the numerical simulations.
    A Study on the Diffraction of Television-Based Passive Bistatic Radar Ranging at Low Altitudes
    Guo Qiang, Tao Ran, Wang Yue, Zhou Siyong
    2002, 23(1):  39-44.  doi:10.3969/j.issn.1000-1093.2002.01.010
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    The paper compares the passive bistatic radar with the conventional monostatic and bistatic radar when detecting targets at low altitude in some given direction and considers the characteristic of televi?sion transmitter fully. In the light of the effect of ground diffraction on ranging of different radar, it is shown that the bistatic radar, using a television transmitter as the illuminator has a potential advantage over conventional radar in detecting targets Deyond the horizon at low altitude because of particular advantages in height gain and diffracting power. At the same time, an important role that the height gain and diffraction effect play in ranging, is extensively studied, putting forward an effective method of deciding optimal wave?length so as to make the ranging of radar maximal.
    Performance Analysis of an Overlapping Hybrid Spread Spectrum Communication System with Multi tone Jamming
    Yang Wenge,Wang Ynanqin
    2002, 23(1):  45-48.  doi:10.3969/j.issn.1000-1093.2002.01.011
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    This paper analysed and studied the performance of overlapping incoherent hybrid DS-SFH spread spectrum communication systems in the presence of multitone jamming, and educed the multitone jamming effect on the performance of an overlapping asynchronous hybrid DS-SFH spread spectrum com?munication systems. The paper analysed the substantial improvement in the performance of hybrid spread spectrum communication systems by using the forward error correction code.
    Two Improved Doppler Centroid Estimation Techniques in Imaging through Doppler Beam Sharpening
    Sun Hongbo, Gu Hong, Su Weimin,Liu Guosui
    2002, 23(1):  49-53.  doi:10.3969/j.issn.1000-1093.2002.01.012
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    Doppler centroid estimation is one of the most important steps in the DBS imaging of airborne pulse Doppler radars. Under the condition that marked inertial navigation units (INU) measurement errors do exist, two new Doppler centroid estimation techniques in frequency-domain and time-domain were pro?posed. The new algorithm obviates the effects of non-homogeneity in sight and fluctuations of echoes, and the precision of estimation is improved significantly. These algorithms are applied to some radar data, and results oi imaging proved their effectiveness.
    Experimental Study on the Adaptive Passive Tracking and Size Estimation of Ships
    1:LIU Xun,Zhang Wenjun,Yu Songyi;2:Xiang Jinglin
    2002, 23(1):  54-58.  doi:10.3969/j.issn.1000-1093.2002.01.013
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    Three specific parts of a ship are measured with acoustic intensity vectors. Under the condi?tion that the ship maneuvers, it can be tracked and its longitudinal size estimated with the self-adaption Kalman filter. Emulation results show the effectiveness of the method.
    Method of Weighted GPS+ GLONASS Single-Point Positioning
    Hu Guorong, Cui Weihong
    2002, 23(1):  59-63.  doi:10.3969/j.issn.1000-1093.2002.01.014
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    It is well-known that the precision of GPS observations is different from that of GLONASS. Therefore, the correct determination of the weights of observations is vital for a combined GPS/GLONASS positioning. In this paper, the method of weighted GPS + GLONASS single-point positioning based on pos- teriori-estimation was proposed, which is more reasonable than weighting on the basis of experience. The method can be extended to apply in relative positioning using pseudo-range or carrier phase observations.
    The Quality and Efficiency Analyzing Alterable Laser Thread Length Scanning SLS RP Processing
    Zhu Linquan,Cheng Jun
    2002, 23(1):  64-66.  doi:10.3969/j.issn.1000-1093.2002.01.015
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    This paper analysed the quality and efficiency of alterable laser thread length scanning in SLS RP processing as compared with the spot scanning processing. Analyses and compares the two constructions of their optical systems and the power densities of two focussing beams. Quality advantage of the alterable thread length scanning system is evident. Its efficiency is about two times higher than the spot scanning processing.
    Low Frequency Ultrasonic Multi-Mode Lamb-Like Wave Method for the Characterization of the Bonding Layer in Ultra-Thin Adhesive Composites
    :1:Zhang Rui Wan Mingxi Chen Xiao;2:Cao Wenwu
    2002, 23(1):  67-71.  doi:10.3969/j.issn.1000-1093.2002.01.016
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    A low-frequency ultrasonic Lamb-like wave method suitable for characterizing the thickness, density, shear and longitudinal wave velocities of the bonding layer of an ultra-thin adhesive composite was presented. The dispersion property of the low frequency Lamb wave propagating along the ultra-thin adhe?sive composite was derived, forming the basis of the characterization method. Sources of the evaluation er?ror for the parameters and sensitivity of the method for different parameters were analyzed. Using the ultra?sonic coupler and a pair of broadband longitudinal wave transducers with IMHz center frequency, one can successfully estimate the parameters of the ultra-thin bonding layer (having a thickness of I12μm) of alu?minum/ steel composite, employing the leaky guided wave frequency-domain analysis method.
    Detection and Recognition of Ship Noise Based on Higher-Order Cumulant
    Zhou Yue, Yang Jie, Hu Ying
    2002, 23(1):  72-78.  doi:10.3969/j.issn.1000-1093.2002.01.017
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    The gaussianity of water acoustic signal was studied by higher-order statistics. Some rules were found. They show that ship noise can be regarded as non-Gaussian signals. Calm sea noise late at night is Gaussian ana sea noise in the daytime must be deemed to be non-Gaussian. Based on these charac?ters, the method of detecting the non-Lraussian signal in a non-Gaussian background is put forward by using the higher-order cumulant T2,and ulteriorly making use of this method to solve the problem detecting the ship noise from the sea noise. In addition, based on the higher-order cumulant of the ship-noise, the char?acters of diagonal slices and non-diagonal slices are abortively studied and on second thoughts they are re?garded as character eigenvectors for classifying three types of the ship noise. By using the IMMNN classifi?er, fine results have been obtained.
    Finite Element Computational Method and Resultant Analysis of the Transverse Self-Oscillation Characteristics of a Slender Spinning Rocket
    1:Rong Jili;2:Li Ruiying
    2002, 23(1):  79-82.  doi:10.3969/j.issn.1000-1093.2002.01.018
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    The transverse self-oscillation characteristics of a spinning rocket in flight was studied. Rotor- dynamics is applied in the analysis. The dynamic equation of transverse vibration of spinning rockets was presented with the finite element method. Numerical method of the equation was also given. By this given equation and method a numerical program was developed. The precessing speeds, critical speeds, including the relevant deflection modes and angular modes of a slender spinning rocket or projectile can be computed by this program. Some numerical analysis of the precession speed, critical speed, as well as the deflection modes and angular modes is made for sample projectiles.
    A Study on Vessel Velocity in Evading Torpedo Attack When Taking Hydroacoustic Countermeasures
    Zhang Xinhua, Liu Decai, E Qun
    2002, 23(1):  83-85.  doi:10.3969/j.issn.1000-1093.2002.01.019
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    The noise energy radiated from a ship will change with the ship’s velocity. Based on the ener?gy change, the acquisition range of a passive homing torpedo will change also. The probability of passive homing torpedo to find a vessel running in the velocity of 18kn and 30kn is respectively estimated from the point view of energy detection based on sonar equation in this paper. Furthermore, effects of the evasion velocity on the survival probability of a vessel were studied by simulating the countermeasure process. Cal?culation results show that the range of acquisition of passive homing torpedo to a vessel running at its maxi?mum velocity will be higher than that running in usual velocity under the same conditions. The survival probability is higher in normal evasion velocity than in speeded velocity in some alarm areas.
    Utilization of the Theory of Optimal State Prediction in Amending Three-Point Guidance Trajectories
    Guan Weiqun, Zhang Jing
    2002, 23(1):  86-89.  doi:10.3969/j.issn.1000-1093.2002.01.020
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    The method of compensation for dynamic error in three-point guidance for transversely maneu?vering targets was studied. Beam rider guidance system was first analyzed, and control system improvement principles introduced. Then according to the theory of optimal state prediction in stochastic optimal estima?tion, the trajectory amendment scheme the leading position error method of the compensation for dy?namic error and the structural design scheme of the improved control system were proposed. The method is finally simulated with its ideal mathematics model. Results of simulation showed that the dynamic error in three-point guidance for transversely maneuvering targets can be effectively compensated with the trajectory amendment scheme.
    Lie Symmetries and Conserved Quantities of Nonholonomic Systems Having Variable Mass and Unilateral Constraints
    Liang Jinghui
    2002, 23(1):  90-93.  doi:10.3969/j.issn.1000-1093.2002.01.021
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    The paper establishes the determining and restriction equations of Lie symmetries for nonholo- nomic systems of variaole mass with unilateral constraints. It gives the structural equation and the con?served quantities, using the invariancy of ordinary differential equations under infinitesimal transforma?tions. The paper also studies the inverse problem of Lie symmetries. Applications of the results are given by an example.
    Analysis of Thin Plate by Elasto-Plastic Large Deflection Spline Finite Strip Method
    1:Han Zhiwu, Nie Yuqin;2:Liu Cai;3:Ren Luquan
    2002, 23(1):  94-97.  doi:10.3969/j.issn.1000-1093.2002.01.022
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    Based on the large deflection incremental theory in solid mechanics, the finite strip method in structural analysis was extended and an elasto-plastic large deflection spline finite strip method established, based on the Updated-Lagrangian method. A C-Ianguage software package FSMAP (Finite Strip Method Analysis Program) was developed in this paper, and was used to analyze the tnin plate. It was proved that the results agree well with those given in literatures. The method has the advantage of being stable in calcu?lation and flexible in the treatment of boundary conditions.
    A Study on the Characteristics of Vibration in Non-Linear Cutting Processes
    Wang Xibin, He Ming, Zhang Weimin
    2002, 23(1):  98-101.  doi:10.3969/j.issn.1000-1093.2002.01.023
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    Based on available research results this paper gave a discussion on experiments conducted upon medium carbon steel 45 and stainless steel, applying highly-sensitive vibratory accelerated sensors to detect the cutting process and catastrophic signal, carrying out basic research in the vibration of nonlinear cutting process and the picking-up of signals. The result shows that catastrophe of the process of metal cutting tends mostly to increase the component of low frequency of detected signal. Schemes RMS, FC,RVF, RMSF and KK can be used as target of detection and diagnosis of the phenomena of catastrophe.
    Chaotic Signals of Snips Based on the Singular System Analysis
    Li Yaan, Xu Demin, Zhang Xiaomin
    2002, 23(1):  102-105.  doi:10.3969/j.issn.1000-1093.2002.01.024
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    The state space reconstruction of chaotic signals having low S/N ratio was investigated by means of Singular System Analysis (SSA) . After the reconstruction of Lorenz signals with different S/N ratios and four types of ship noise signals, it is found that SSA has more advantages than the Method of De?lay (MOD) as an traditional method m chaos theory. By calculating the L2 norm of state trajectories, the singular spectrum of chaotic signal is quantitatively determined. It suggests a new method for the feature extraction in chaotic signatls.
    Short Papers
    Realization of Stochastic Passage Characteristics in a Future Airspace Window Firing System
    1:Hu Jinchun, Sun Zengqi;2: GUO Zhi
    2002, 23(1):  106-108.  doi:10.3969/j.issn.1000-1093.2002.01.025
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    Stochastic passage characteristics play an important role in ensuring Iiring efficiency. On ana?lyzing the relationship between the characteristics and target movement, the demand for it can be trans?formed to that of the limit of target movement estimation. It can be realized with the matured LMI technol?ogy by modeling and estimation of the movement.
    Finite Element Analysis of the Temperature Field in Bolometer Detectors
    Gu Wenyun, Pi Defu, Zhou Shiyuan
    2002, 23(1):  109-111.  doi:10.3969/j.issn.1000-1093.2002.01.026
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    The temperature distribution on an uncoolea infrared bolometer detector is computed using the finite element numerical method. The introduced model can simulate both the steady state and the transient temperature field of the top surface of the thermal sensitive layer on a bolometer detector. By computing chiefly the temperature field on the sensitive film oi the detector, the influence of different sizes of detector constructions upon some performance parameters is analyzed to optimize the design of a bolometer detector. Analysis of the simulation result attests that the thermal isolation structure is important in the design of a bolometer detector thus endorsing the present work. Compared with data in relevant literature, the pro?gram is validated correct and accurate.
    Comprehensive Reviews
    Determination of Fracture Toughness for Bimaterial Interfaces
    Xiang Yibin, Wu Shichun
    2002, 23(1):  112-115.  doi:10.3969/j.issn.1000-1093.2002.01.027
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    Based on interfacial fracture mechanics, the variational rule of the interfacial fracture tough?ness with respect to the mixture mode was presented in this paper . Using the interfacial fracture energy and mixture mode as the primary microstructural parameters, data reduction methods in testing the mode I fracture toughness of the material interface were studied. This provided necessary experimental means to e- valuate the fracture resistance of actual material interfaces.
    Experimental Techniques and Analysis
    YBCO Semiconductor Membrane Thermionic Radiation and Its Broad Spectrum Response Characteristics
    1:Li jianli, Sun Qiang, Liu Jinghe, Li Yanhong, Sun Jing, Zhang Liang;2:Li Guodong, Huang Zongtan, Huang Chengcai, Li Dan, Huang Jiangping
    2002, 23(1):  116-119.  doi:10.3969/j.issn.1000-1093.2002.01.028
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    This paper studied the thermal radiation and the broad spectrum response character of the Y1Ba2CU3O7-δδ (YBCO) semiconductor membrane upon a Si substrate. It has been found that the spectrum about this kind of semiconductor has a good response character not only in the infrared region, but also in the submillimeter or even millimeter range. This membrane is a kind of new material used after the appear?ance of infrared VO2 membranes.
    An Experimental Study on Concrete Cutting with the Premixed Abrasive Water Jet
    Yang Qingwen, Qu Yukun, Zhang Xuehua
    2002, 23(1):  120-122.  doi:10.3969/j.issn.1000-1093.2002.01.029
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    Experimental apparatus was established for the cutting of concrete with the premixed abrasive water jet in submerged and unsubmerged conditions. Parameters affecting the depth of cut, such as the driving pressure, stand off distance, traverse velocity of the jet and abrasive density were studied. The cut?ting property in unsubmerged condition is compared with that under submerged condition. It is found that the stand off distance of the jet has much influence on the depth of cut in submerged condition. With an in?crease in the stand off distance, the depth of cut in submerged condition decreases faster than that in unsub?merged condition. Ihe driving pressure, traverse velocity and. abrasive density have less variety in the two conditions for the depth of cut. A guidance is thus provided in the development of new underwater cutting technology.
    Research Notes
    Integrated Hit Probability of Tank Firing at Armored Targets in Live-Fire Circumstances
    Diao Lianwang, Peng Yalin, Liu Huanzhang
    2002, 23(1):  123-125.  doi:10.3969/j.issn.1000-1093.2002.01.030
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    The method presently used to compute nit probability of tanks firing at armored targets cannot fully satisfy the needs of research of combat simulations and firepower employment because of its limita?tions .Integrated hit probability is defined in this paper according to the distribution of firing direction an?gles from which a tank fires at armored targets. The paper discussed the computing method of integrated hit probability and an example was provided. It also analyzed the data of integrated hit probability and gave a concise computing formula using nonlinear regression. The result of integrated hit probability can be of value to the fields of firepower employment, combat simulation and tactical decision of commanders.
    Kinematic Analysis of an Ejecting Rescue Man-Parachute System
    1;Xue Xiaozhong, Mi Zhihao;2: Huang Changqiang,Du Haiwen
    2002, 23(1):  126-128.  doi:10.3969/j.issn.1000-1093.2002.01.031
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    This paper built up a kinematic mathematical model for a man-parachute system. The man- parachute system was analyzed and calculated. Security measures cluing ejecting rescue on high altitude plateau areas were pointed out.
    Experimental Study on Anti-Armor Bomblets
    Zhao Yuqing
    2002, 23(1):  129-131.  doi:10.3969/j.issn.1000-1093.2002.01.032
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    This paper introduced the present status of progress, main specification, and methods of test?ing of anti-armor bomblets carried by cargo shells in artilleries. Results of tests on the metal liner, its mate?rial, shape, angle, and processing as well as the explosive and partition board structure were described. Copper liner seems to be appropriate considering the performance price ratio. Cavity liner of 48°angle coun?tersink with a wall thickness of 0.8?I .Omm is recommended. Use of high density, high exploding-speed explosives, and enlarging the volume of charge column, seems to be beneficial to increasing the depth of penetration.
    Some Views on the Evaluation of Degrees of Coverage of Plastics-Bonded Explosive’s Molding Powder Using X-Ray Photoelectron Spectroscopy
    1:Song Huajie;2:Dong Haishan, Hao Ying
    2002, 23(1):  132-135.  doi:10.3969/j.issn.1000-1093.2002.01.033
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    In some present literatures the method frequently given to evaluate the degree of coverage of molding powder for plastic bonded explosives(PBXs) is through the X-ray photoelectronic spectroscopic in?tensities of the PBX samples. A simple theoretical analysis of the method and analyses of the experimental data on XPS for estimating the degrees of coverage of molding powders composed of TATB and different fluoropolymers were given in this paper. It has been discovered that there exist much theoretical limitations in the method, and that the degrees of coverage of the TATB / fluoropolymers molding powders obtained according to this method is often dubious.
    Theoretical Explosion Temperature of AIuminiferous RDX Obtained by Thermochemistry Calculation
    1:Zhang Hong;2:Wang Kaiming;3:Zhu Zhenghe
    2002, 23(1):  136-138.  doi:10.3969/j.issn.1000-1093.2002.01.034
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    Based on principles of thermochemistry and under conditions of given equilibrium components are calculated the highest temperatures attainaole when RDX and aluminiferous RDX are detonated. The relationship between the aluminium content and the detonation temperature is discussed ? I he optimal con?tent of aluminium for different application purposes is suggested.
    A Real-Iime Automatic Measuring System of Charge Temperature for Guns
    1:Zhou Yanhuang, Chen Jincao, Yu Yonggang;2:Huang Fengliang
    2002, 23(1):  139-141.  doi:10.3969/j.issn.1000-1093.2002.01.035
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    The charge temperature for gun charges changes with ambience temperature, the charge tem?perature field being in non-equilibrium. A real-time automatic measuring system of charge temperature for guns was designed based on indirect measurement. It can realize real-time automatic temperature monitor?ing, display and transmit for every kinds of charges in different places. Based on the significance and neces?sity of real-time precise measurement of charge temperature, the principle, basic structure, system hard?ware, software design and results of qualification for the function of a real-time automatic measuring system of charge temperature for guns were presented.
    Predicted Heating Distributions for Blunt Biconic at an Angle of Attack
    Pan Xiaoqiang, Li Hua, Ding Meng
    2002, 23(1):  142-144.  doi:10.3969/j.issn.1000-1093.2002.01.036
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    An effective method for calculating the heating rates on warheads of blunt biconic was devel?oped. The method is based on reference enthalpy theory and semi-empirical formulas. The boundary- layer edge conditions are determined by the CFD method solved by Euler equations of two dimensions. Results of the method are in good agreement with existing experimental results.