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Table of Content

    30 September 2019, Volume 40 Issue 9
    Contents
    Contents
    2019, 40(9):  0. 
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    Paper
    Design of a Small-caliber Fuze Magnetorheological Grease Safety and Arming Device and Its Delay Time Characteristic
    ZHENG Jiajia, KAN Junwu, HU Ming , ZHANG Guang, WANG Jiong
    2019, 40(9):  1761-1769.  doi:10.3969/j.issn.1000-1093.2019.09.001
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    A novel small-caliber safety and arming (S&A) device is proposed to improve the fuze performance of modern small caliber projectile within a limited space, for which the “locking” and “unlocking” properties of magnetorheological (MR) grease with/without the presence of magnetic field are used. Based on the principle of MR grease flow through an abrupt contraction-expansion under squeezed pressure, the delay time for arming the firing section was obtained. The delay time mathematical model of reflecting the factors, such as structure size and fluid elasto-viscosity characteristics, is further derived by analyzing the fluid dynamic and magnetic fields. Simulated and experimental results show that the modified local damping coefficient favors to reduce the maximum model error to 6.7%. A delay time range of 9-84 ms was successfully achieved by adjusting the physical parameters, including orifice diameter, spinning rate and particle concentration, etc. Owning to a wide temperature operation range and reliable working mechanism, the proposed MR grease S&A device is expected to have extensive application prospects in small and medium caliber fuze systems. Key
    Asymmetric Deviation Characteristics of Hydro-mechanical Transmission Full Power Shift Timing
    YANG Shujun, BAO Yong, ZHANG Man, ZHANG Lu, ZHANG Yinjun, TIAN Lin
    2019, 40(9):  1770-1780.  doi:10.3969/j.issn.1000-1093.2019.09.002
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    In order to reduce the speed fluctuation and the wear of brakes, the asymmetric deviation characteristics of hydro-mechanical transmission (HMT) full power shift timing suitable for engineering applications are studied based on the full power shift method. A two-range arithmetic HMT is taken as the research object. The prior stable stage models of full power shift are established based on the full power shift method, including the hydraulic transmission model and brakes torque model during two brakes overlapping. The influences of advance and lag of shift timing on brake sliding process and prior stable stage are studied by theoretical analysis and experimental study. In the full power shift, the speed of fixed displacement hydraulic component can be lower than the ideal speed during the power shift from H range to HM range, and the negative deviation of ideal shift speed should be set. During the power shifting from HM range to H range, the speed of fixed displacement hydraulic component can be higher than the ideal speed, and the positive deviation of ideal shift speed should be set. The results reveal the influence of shift timing on the performance of prior stable stage. Key
    The Impact of Flow Pulsation of Axial Piston Pump on Gun Pitching Accuracy of a Multiple Rocket Launcher
    YUE Jiawei, DAI Bo, WU Xu, YANG Lin
    2019, 40(9):  1781-1786.  doi:10.3969/j.issn.1000-1093.2019.09.003
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    A simulation model of slanting axial piston pump is established by using AMESim software. The proposed model is used to study the influence of flow pulsation of an axial piston pump on the pitching accuracy of electro-hydraulic proportional system for a multiple rocket launcher. The effect laws of the slanting angle of piston pump and the rotating speed of input shaft on the flow pulsation are studied, and a typical working condition is identified. A new concept of flow pulsation volume is defined and used in the new mathematic model proposed in this work. The quantitative relationship of the fire angle and the gun pitching accuracy was obtained and analyzed by using MATLAB software. The results show that the period of flow pulsation remains unchanged with the increase in the slanting angle of piston pump, while its amplitude becomes larger. When the rotating speed of input shaft increases, the period of flow pulsation of piston pump decreases and its amplitude increases. The pitching accuracy caused by flow pulsation becomes smaller with the increase in the fire angle. The pitching accuracy caused by flow pulsation on the multiple rocket launcher meets the requirement for the pitching accuracy of servo system, and the theore-tical model can be taken as a reference for the design of hydraulic elevating mechanism.Key
    Analysis of Material Flow around Projectile Nose by Elbow-streamline Model during Long-rod Projectile Penetrating into Steel Target
    CHEN Haihua, ZHANG Xianfeng, LIU Chuang, DING Li, WANG Jipeng, DU Ning
    2019, 40(9):  1787-1796.  doi:10.3969/j.issn.1000-1093.2019.09.004
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    In order to study the two-dimensional rheological behavior of a long-rod projectile penetrating into steel target, a two-dimensional elbow-streamline penetration model was developed based on long-rod projectile hydrodynamic penetration model, mass conservation during penetration and elbow model. The impact velocity, reference point angle and reference point radius are considered in the proposed model. The material flow around the nose of tungsten long-rod projectile penetrating into a steel target was analyzed based on the proposed model and compared with the test results. The results show that the material flow around the tungsten long-rod projectile nose is non-uniformly distributed, and the flow velocity on the outer side is less than that on the inner side. The pressure on the long-rod projectile nose material is distributed gradiently. The proposed model is used to describe the material flow of long-rod projectile nose during penetration, and explain the process of transition from fluid to solid in the projectile nose at the final stage of penetration. It reveals the relation between the change of ballistics channel and the penetration state transition of projectile. Key
    Structural Response of Projectile in Reverse Ballistic Non-normal Penetrating Experiment
    LIU Jiancheng, ZHANG Leilei, XU Kun, PI Aiguo, SHI Wenqing, HUANG Fenglei
    2019, 40(9):  1797-1803.  doi:10.3969/j.issn.1000-1093.2019.09.005
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    To research the transient structural response of high-speed projectile, the reverse ballistic experiments of projectile abnormally penetrating into the 2024 Al target were carried out based on 152 mm gas gun launching system, and a digital image correlation method was used to measure the real-time response of projectile in the experiment. The responses of projectile at the penetration conditions of oblique angle, attrack angle, and both oblique and attack angles were compared to obtain the response rules of projectile at different impact conditions. The research results show that the effect of 3° attack angle penetration on the bending response of projectile body is more obvious than that of 10° oblique angle penetration, and the penetration effect at 5° attack angle is more obvious than that at 15° oblique angle penetration on it. The analysis of penetration condition at 5° attack angle and 15° oblique angle shows that the axial elastic strain 1/4 of the projectile nose is 4.6%, and there is only elastic deformation in the projectile tail.Key
    Fragments Loading Properties of Warship Bulkhead from Moving Fragmentations Kill Warhead
    LI Mao, HOU Hailiang, LI Dian, CHEN Pengyu, LI Yongqing, ZHU Xi
    2019, 40(9):  1804-1818.  doi:10.3969/j.issn.1000-1093.2019.09.006
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    On the basis of empirical formulas about mechanics of explosion and several reasonable assumptions, a space coordinates system of moving fragmentations kill warhead and target bulkhead was built, and a simple and practical mathematical model was deduced. The mathematical model is programmed with MATLAB program language in order to further understand the effect of initial warhead kinestates, including warhead position, attitude angle, planar motion, and rotational motion, on fragment loading acting on bulkhead, in which the target impact position, total mass of impacting fragments and expected value of impact velocity on each divided bulkhead surface are estimated. The calculated results show that the initial position, attitude angle and planar motion of warhead have major effects on the loading properties, while the rotational motion of warhead has an unremarkable effect on the fragment loading, and the root cause of aforementioned effect rules is the difference of fragments kinetic characteristics. Key
    Research on Looking-forward Altimetry Strategy for Missile-borne Monopulse Detector
    CHENG Cheng, GAO Min, ZHOU Xiaodong, KE Zhifei, HUI Jianghai
    2019, 40(9):  1819-1828.  doi:10.3969/j.issn.1000-1093.2019.09.007
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    The height of missile needs to be acquired in real time to perform the preset combat missions for the new generation optional burst height proximity fuze. A forward-looking altimetry strategy for missile-borne monopulse detector is proposed, which achieves high precision and fast terrain elevation calculation on the missile-borne platform with high real-time requirements. An altimetry model of missile-borne detector is established, and the altimetry algorithm of missile-borne monopulse detector is deduced from the theory of monopulse ranging. The altimetry algorithm is verified by simulation and field test. The experimental results show that the monopulse altimetry system can meet the precision requirement of the new optional burst height proximity fuze for burst height. The average error of simulation altimetry is 7.8%, the altimetry error of suspension flight test is less than 2.5 m, and the overall response time can meet the needs of the missile-borne platform. Key
    Penetration and Damage Effects of Reactive Material Jet against Concrete Target
    SU Chenghai, WANG Haifu, XIE Jianwen, GE Chao, ZHENG Yuanfeng
    2019, 40(9):  1829-1835.  doi:10.3969/j.issn.1000-1093.2019.09.008
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    The penetration and damage effects of reactive material jet on concrete target are studied through experiment and simulation. The typical damage pattern of concrete target subjected to reactive jet was obtained, and the influences of formulation and stand-off distance on damage effect were studied. The experimental results show that the reactive jet produces a large conical crater and a crack zone in concrete target. The reactive liner with more gaseous products induce more violent damage on the concrete target. The produced crater diameter is over 10 times of the shaped charge diameter at a stand-off distance of 1.0D. Based on the AUTODYN-3D platform, the reactive jet against concrete target is numerically simulated to reveal the influence mechanism of the stand-off distance on the damage effect. With the increase in stand-off distance, the amount of reactive material penetrating into the crater trajectory decreases, and the penetration depth increases firstly and then decreases. The kinetic penetration time and the reaction delay time of reactive materials match well at the stand-off distance of 1.0D. Key
    Modeling and Dynamic Analysis of a Rocket Towed Net System
    HAN Feng, ZHOU Qiao, CHEN Fang
    2019, 40(9):  1836-1848.  doi:10.3969/j.issn.1000-1093.2019.09.009
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    The complex dynamical behaviors of rocket-towed net system are analyzed for system design. A three-dimensional model consisting of a rigid rocket model and a lumped mass net model is built based on the aerodynamics theory. The rocket towed net system model is solved by the fourth-order Runge-Kutta method in simulation. The proposed lumped mass model is compared with a rigid multibody model, and the flight dynamics characteristics of rocket towed net system are studied by analyzing the center of mass trajectory, velocity, and pitch angle of rocket in the experimental results. The flying test of an experimental system prototype was conducted. Simulated and experimental results show that the desployed distance accuracy of rocket towed net system is about 90% of the system length. Key
    A Finite-time Cooperative Guidance Method Considering Cooperative Detection Efficiency
    ZHANG Shuai, GUO Yang, WANG Shicheng, WANG Shaobo
    2019, 40(9):  1849-1859.  doi:10.3969/j.issn.1000-1093.2019.09.010
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    For the multiple missiles intercepting a maneuvering target cooperatively, a cooperative guidance method considering a cooperative detection geometry configuration is designed based on the finite-time control theory. For the first-order dynamics of the missiles, a cooperative interception model with detection geometry configuration is established according to the relative motion equations of particles and the principle of cooperative detection. The sufficient conditions for the finite time boundedness of system state and the finite time stability of system input and output are given based on the differential inequality theory. And on this basis, a finite time cooperative guidance method is designed. The proposed method uses the measurement matrix to characterize the dynamic quality of system state and output, and can ensure that the state and output of guidance system are bounded and stable within a finite time interval. The simulated results show that the proposed guidance method can ensure that the LOS separation angle converges to the preset angle, the LOS angular rate converges to zero, and the acceleration does not exceed the maximum physical limit when a target is maneuvering. Compared with proportional navigation and optimal guidance law, the proposed method has the advantages in cooperative detection and guidance. Key
    An Improved Optimal Alignment Method of Strapdown Inertial Navigation System Based on Reverse Navigation Algorithm
    ZHU Bing, XU Jiangning, WU Miao, LI Jingshu, HE Hongyang, LI Feng
    2019, 40(9):  1860-1870.  doi:10.3969/j.issn.1000-1093.2019.09.011
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    Rapidity and precision are the important indicators for in-motion initial alignment of strapdown inertial navigation system (SINS). The optimized alignment method (OAM) can not be used to get enough observation information in a short time, which may degrade the alignment performance. An improved in-motion coarse alignment (IMCA) method based on the reverse navigation algorithm is proposed. In the IMCA method, the stored gyroscope and accelerometer data are reused and the integration procedure is extended using the reverse navigation algorithm. The extended integration procedure is used to construct new observation vector to achieve the improvement of alignment accuracy. The OAM in the body frame (b-frame) is derived, and then the influence of quantity of observation information on the precision of attitude determination is analyzed. The in-motion alignment experiments were carried out by using OAM and IMCA method based on the measured data of vehicle test, respectively. The experimental results demonstrate that the IMCA method can achieve higher alignment accuracy at the same conditions compered with OAM. The IMCA method can be effectively applied to the b-frame in-motion alignment. Key
    Research on the Dynamic Response of Thin-walled Square Tube under Repeated Blast Loads
    ZHOU You, JI Chong, WANG Leiyuan, SONG Shiqian, MA Huayuan
    2019, 40(9):  1871-1880.  doi:10.3969/j.issn.1000-1093.2019.09.012
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    As a typical engineering component, thin-walled square tube is widely used in construction, ocean and aerospace fields. Its structure may be subjected to the repeated blast loads. It is of practical significance to the research on dynamic response of thin-walled square tube under repeated blast loads. Experimental and numerical investigations were carried out on the dynamic response of thin-walled steel square tubes subjected to single and repeated blasting loads. The impact experiments of thin-walled square tube with 4 mm in wall thickness and 100 mm in cross-section width were made in the explosion field. Based on the full restart function of LS-DYNA and Euler-Lagrange coupling method, the dynamic responses of square tubes subjected to single or repeated blast loads laterally are numerically simulated, and the damage effects under different explosion numbers are described.A numerical method is proposed to reflect the material damage after blast load by damage factor. The results show that the deformation of square tubes subjected to repeated blast loads causes a damage accumulation. Under the same blast load, the deformed square tube has bigger effective strain increment than that of undamaged square tube. In the area around the mid-point, the sides and the plastic hinge position of square tube, the effective strain increment of the former is 2.47-3.88 times of the latter, which may cause the square tube to be damaged more seriously. The two sides of square tube are the weak areas, so it is easy to produce large plastic strain due to stress concentration, and a special protection is needed. Key
    LPI Radar Signal Recognition with Convolution Feature and Discrimination Dictionary Learning
    GUO Pengcheng, WU Liyang
    2019, 40(9):  1881-1889.  doi:10.3969/j.issn.1000-1093.2019.09.013
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    The selection of artificial features, low signal-to-noise ratio and small number of samples lead to low recognition rate for low probability of intercepting radar signal. A recognition algorithm with convolution feature and discrimination dictionary learning is proposed. The proposed algorithm is based on the time-frequency image representing a signal modulation type, and a two-dimensional signal is obtained by time-frequency transformation, which is input into LeNet-5. The network is retrained through MNIST data set. The network parameters of 2-6 layers are transferred to a new LeNet-5, and the data from the 6th convolution layer is extracted as convolutional feature. Finally, recognition is ended up by discrimination dictionary learning. Simulated results show that the network goes faster in convergence and optimization through pre-training, and can effectively extract the convolution feature of each kind of signal. Higher recognition rate is obtained through discrimination dictionary learning in the condition of low SNR and small samples compared with other algorithms. Key
    Adaptive Robust Picture Fuzzy Clustering Algorithm Based on Total Bregman Divergence
    WU Chengmao, SUN Jiamei
    2019, 40(9):  1890-1901.  doi:10.3969/j.issn.1000-1093.2019.09.014
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    As picture fuzzy clustering algorithm is not suitable for segmentation of image with noise or inhomogeneous intensity, an adaptive robust picture fuzzy clustering segmentation algorithm based on total Bregman divergence is proposed. An improved total Bregman divergence is constructed by combination of existing total Bregman divergence and neighborhood information of image pixel, which is suitable for image segmentation. It was introduced into the picture fuzzy c-means clustering optimization model, and a robust total Bregman divergence-based picture fuzzy clustering algorithm, in which the pixel spatial neighborhood information was embedded, was obtained. The difference between the gray values of current clustering pixel and its neighborhood pixel is used as the regularization factor of the robust picture fuzzy clustering model based total Bregman divergence, and thus the robust clustering segmentation method would be capable of suppressing the noise adaptively. The results show that the segmentation quality and anti-noise robustness of the proposed segmentation algorithm are improved more significantly than those of the existing picture fuzzy clustering and other robust fuzzy clustering algorithms. Key
    Experimental Research on Drag Reduction Characteristics of Underwater Vehicle during Pitching
    SONG Wuchao, WANG Cong, WEI Yingjie, XU Hao, LU Jiaxing
    2019, 40(9):  1902-1910.  doi:10.3969/j.issn.1000-1093.2019.09.015
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    The microbubble drag reduction of underwater vehicle is researched using a self-designed driving device, a high speed camera and a six-component force balance for studying the characteristics of microbubble flow and microbubble drag reduction during the pitching movement of underwater vehicle. The results show that the discrete microbubbles are uniformly distributed on the surface of the underwater vehicle at low air injection rate. During the pitching movement of an underwater vehicle, the axial force coefficient, lateral force coefficient, drag coefficient and lift coefficient are all sinusoidal, and the change period is basically synchronized with the period of the angle of attack. The drag coefficient of vehicle at various air injection rates increases approximately linearly with the increase in the angle of attack, and the drag reduction rate decreases linearly with the increase in the angle of attack. Key
    Preparation of Poly(p-phenylene Benzobisoxazole) by High Temperature Thermal Treatment of Isopropoxy FunctionalizedAromatic Polyamides
    CHEN Fenggui, GAO Yimeng, GUI Jiaxin, L Liping
    2019, 40(9):  1911-1917.  doi:10.3969/j.issn.1000-1093.2019.09.016
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    4,6-diamino-1,3-dihydroxy-benzene (DAR) used as monomer for the synthesis of high-performance poly (p-phenylene benzobisoxazole) (PBO) is easily oxidized and difficultly synthesized by traditional method, and the polymerization process is complicated and the spinning operation is also difficult. A novel method was developed to synthesize PBO by high temperature thermal treatment of isopropoxy functionalized aromatic polyamide, which was prepared by polycondensation of 4,6-diisopropoxy-1,3-diamine-benzene and terephthalic chloride. And the obtained PBO exhibits excellent thermal degradation temperature up to 562 ℃. The proposed method is used to avoid DAR by replacement of the more stable monomer as 4,6-diisopropoxy-1,3-diamine-benzene, greatly simplify the polymerization process for the improved solubility of monomer and polymer, and easily spin the obtained PBO precursor into nanofibers. Key
    Evolution Model of Equipment Support Network Considering Interdependent Relationship
    ZHANG Qiang, SONG Tailiang, CAO Junhai, YAN Xu, XING Biao
    2019, 40(9):  1918-1927.  doi:10.3969/j.issn.1000-1093.2019.09.017
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    With the continuous evolution of equipment support system of systems from traditional hierarchical tree structure to complex network structure, the original research methods and evolution laws can not solve the multi-network evolution problems encountered well. Based on the interdependence among different sub-network nodes, the theory of interdependent network is applied to the evolutionary analysis of equipment support network. The network characteristics of equipment support system of systems are analyzed, and the measures of network robustness are defined based on the maximal connected subgraph and network support efficiency. In the network evolution model, the evolution rules and steps of the model are determined according to the equipment support mechanism, the network interdependency proportional parameter F, which represents the proportion of maintenance, storage and supply nodes with interaction, and the interdependence redundancy parameter K, which represents the average number between some maintenance node and its neighbors in storage and supply network, are defined, and their effects on network robustness are analyzed through simulation. The simulated results of evolution model show that the robustness and overall support efficiency of interdependent network can be improved by controlling the parameters K and F. Key
    Support Capability Evaluation Method for Early-warning Counter-attack System of Systems Based on Evidential Reasoning
    SUN Zhipeng, CHEN Guiming, GAO Weigang
    2019, 40(9):  1928-1934.  doi:10.3969/j.issn.1000-1093.2019.09.018
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    For the evaluation of support capability of early-warning counter-attack combat system, the DoDAF method is used to establish an evaluation index system, and a support capability evaluation model is presented based on the belief rule base. The proposed model was used to evaluate the support capability of a unit, and the evaluated results were analyzed. The research results show that the support capability evaluation method based on the belief rule base can be used to effectively deal with the information uncertainty problem faced by the system support capability evaluation, and the improvement in different index levels has different effects on the degree of improvement in the system support capability. The weaknesses of the early-warning counter-attack system support capability can be accurately identified through the evaluation and analysis of the early-warning and counter-attack system support capability. Key
    Multibody Dynamics Modeling of Powered Parafoil System Using Equations with Quasi-coordinates
    ZHANG Qingbin, GAO Feng, GUO Rui, FENG Zhiwei, GE Jianquan
    2019, 40(9):  1935-1942.  doi:10.3969/j.issn.1000-1093.2019.09.019
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    An eighteen-degrees-of-freedom model of powered parafoil system was developed using hybrid Lagrange's equations of motion in terms of general quasi-coordinates, which is used to simulate the relative motion and connection of a payload with respect to a parafoil. Considering the feature of stable flight phase, the parafoil system is taken as three major parts, including canopy, payload and cord, and the aerodynamic forces on the canopy controlled by brake deflection are expressed in the form of polynomial equations, while the apparent mass and inertia effects are also regarded as external forces. In deriving the equations of motion by the Lagrange approach, the angular and translational velocities of each body are taken as general quasi-coordinates. An illustrative example is used to analyze the gliding and turning flight of the parafoil system, the relative motion simulations of single and multibody dynamic models are investigated for the different cases of design rigging length,change in deflection,and wind gust compared to the 6 DOF system. Results show that the proposed model can reflect the relative motion of parafoil system,and the oscillatory response is preferred to be reduced by use of payload connection. Key
    Analysis of Frictional Power Loss Characteristics of Cylindrical Roller Bearing for Air-conditioning Vane Compressor
    DENG Sier, HU Yusheng, SUN Yufei, XU Jia, NIU Rongjun, CUI Yongcun
    2019, 40(9):  1943-1952.  doi:10.3969/j.issn.1000-1093.2019.09.020
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    In order to reduce the frictional power loss of air-conditioning vane compressor, based on the dynamics theory of rolling bearing, a frictional power loss model of cylindrical roller bearing for air-conditioning vane compressor is established considering the periodic load factor. The influences of working condition and structural parameters on the frictional power loss characteristics of cylindrical roller bearing were analyzed. The results show that a larger bearing radial clearance is beneficial to reduce the frictional power loss under the certain conditions. The frictional power loss can be minimized by using reasonable cage guiding clearance and cage pocket clearance. The frictional power loss of bearing increases with the increase in the number of rollers. The number of rollers can be reduced to decrease the frictional power loss of bearing within the loading capacity of bearing. The frictional power loss of the improved vane compressor is 39% less than that of the conventional ones. Key
    Research Notes
    Analysis of Tank Driving Simulation Training Results Based on Support Vector Machine
    DENG Qing, XUE Qing, LUO Jia
    2019, 40(9):  1953-1960.  doi:10.3969/j.issn.1000-1093.2019.09.021
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    Training by tank driving simulator is an important way of improving equipment skill. A method of training effect analysis of tank driving simulator based on support vector machine (SVM) is proposed for the problems resulted from ignoring the collection and analysis of training data and the increase in training quality. In order to solve the issue of choosing SVM parameters,an adaptive particle swarm optimization (APSO) algorithm is adopted to determine the SVM parameters. Dynamic weight parameters are designed and the related inertance is entrusted for realizing the self-adaption of particle. The multi-location inquiry mechanism and the information from extreme point are used to keep the balance dot diversity of different particles.The SVM parameters can be automatically optimized by iterating and optimizing the object function. After the SVM based on particle swarm algorithm is used for the training effect analysis of tank driving simulator, the adverse effect of multidimensional factors on training score can be overcome. The experimental results show that SVM can be feasible and effective in the training effect analysis of tank driving simulator. Key
    Simulation of Tractive Performance of Off-road Tire on Gravel Road by Combined Finite Element-discrete ElementMethod and Experimental Validation
    XU Weipan, ZENG Haiyang, JIANG Chao, KOU Xizheng, ZANG Mengyan
    2019, 40(9):  1961-1968.  doi:10.3969/j.issn.1000-1093.2019.09.022
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    The research on the interaction between off-road tires and soft ground is of great significance to improve the travel performance of off-road vehicle on soft ground. The interaction between tire and soft ground can not be described by the finite element method or the discrete element method effectively. A FEM-DEM model in which the off-road tire is modeled by the finite elements and the gravel road is modeled by the discrete elements was established based on the indoor single wheel soil bin test. The proposed model can be used to accurately describe the complex mechanical properties of off-road tire and the granular features of gravel road. The tractive performance of off-road tire on gravel road at different slip rates is simulated by using the combined finite element-discrete element method in LS-DYNA. The tractive performance parameters of off-road tire, such as tire tractive force and rim sinkage, at different slip rates were obtained and investigated. The numerically simulated results are basically corresponded with the experimental results, which verifies the validity of the combined finite element and discrete element method in studying the interaction between tire and soft ground. Key