Table of Content

31 March 2022, Volume 43 Issue 3

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Contents

2022, 43(3):  0. 

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Paper

Polarization Characteristics of Laser Communication System in Atmospheric Channel

TAO Zonghui, LIU Weiqi, CHEN Yanan, NI Xiaolong, LOU Yan, LIU Xianzhu, JIANG Huilin

2022, 43(3):  481-488.  doi:10.12382/bgxb.2021.0817

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The intensity scintillation effects of different initial polarized laser beams transmitted in atmosphere are studied，while the expression of intensity scintillation of polarized laser beams is given. A new multi-parameter high-precision controllable laser light source was designed，and a simulation device was used for atmospheric turbulence simulation.The scintillation effects of laser beams with different initial polarization states in atmospheric turbulence were researched experimentally.The results show that the scintillation factor decreases with the increase in the polarizing angle when the polarizing angle is 45°≤ θ<90°. For 0°<θ≤45°，the scintillation factor decreases with the decrease in the polarizing angle.The scintillation factors of left- and right-hand circularly polarized laser beams vary with turbulence intensity in a similar way.Compared with linearly polarized laser beams，the intensity scintillation factors of left- and right-hand polarized laser beams under the same atmospheric turbulence are smaller than that of linearly polarized light at any polarizing angle. By optimizing the polarization state of the laser communication system，the influence of atmospheric turbulence on the laser communication system can be effectively suppressed，the intensity fluctuation of the receiver and the bit error rate of the laser communication system can be reduced，and the performance of the laser communication system can be effectively improved.

Motion Trajectory of Solid Particles in C1xb Solid Rocket Motor

GU Xingpeng， LI Junwei， QIAO Wensheng， WU Sheng， HAN Lei， WANG Qi， WANG Ningfei

2022, 43(3):  489-502.  doi:10.12382/bgxb.2021.0136

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The force of condensed-phase particles in C1xb solid rocket motor (SRM) is analyzed based on internal flow field of motor. The velocity and acceleration of particle at different moments are obtained，and a two-dimensional particle motion trajectory model is established. Based on this model，the spatial distribution rule of particles in SRM is obtained. On this basis，the effects of motor rotation，initial position of particle and particle size on the movement of condensed-phase particles are studied. Results show that the particles leaving the upstream and downstream surfaces of aluminized hydroxyl-terminated-polybutadiene propellant have a greater probability of colliding with inner wall. Larger size particles increase the probability of collision with inner wall during particle movement. Rotation has more influence on spatial distribution of particles in motor in comparison with axial overload.

Energy Release Characteristics of CL-20-based Composite Explosives in Confined Spaces

LIU Zheng, NIE Jianxin, XU Xing, ZHU Yingzhong, LIU Pan, GUO Xueyong, YAN Shi, ZHANG Tao

2022, 43(3):  503-512.  doi:10.12382/bgxb.2021.0163

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The quasi-static pressure generated by the implosion of explosive samples with R_e of 0.35-1.0 was tested experimentally to study the explosion energy release characteristics of CL-20-based composite explosives in confined spaces. Based on the ideal gas adiabatic model and aluminum particle gasification combustion equation, the explosion energy release processes of explosive samples with different R_e were calculated and analyzed. The result shows that the quasi-static pressure of the composite explosive increases first and then decreases with the increase in R_e, and the quasi-static pressure reaches the maximum with R_e of 0.83. The energy released from the composite explosive in 20 ms also shows a trend of increasing first and then decreasing with the increase in R_e. The quasi-static pressure generated by the explosion of explosives in confined space are mainly determined by the actual energy released by the explosive and the time scale of energy release within a certain period of time. AUTODYN is used to simulate the action process of explosion of explosive samples with different R_e in confined space, and the maximum relative deviation of the calculated value of quasi-static pressure from the experimental results is 4.7%.

Influence of Ablation Products of Aircraft Pyrolytic Carbonized Material on Plasma Flow Field

NIE Chunsheng， YANG Guang， NIE Liang， ZHOU Yu， ZHAO Liang

2022, 43(3):  513-523.  doi:10.12382/bgxb.2021.0161

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The heat-resistant material on the surface of high-speed aircraft will decompose and ablate at the high temperature generated by aerodynamic heating. After entering the flow field，the ablation products react with the high-temperature air in the flow field， thus affecting the component concentration and plasma distribution in the air flow field around the aircraft. Based on solving the thermochemical non-equilibrium Navier-Stokes equations，a three-dimensional plasma flow field calculation method coupling the ablated wall surface is established. The plasma flow field of RAMC-II is predicted and compared with the flight test data to verify the reliability of the proposed method. The influence of material ablation on plasma flow field of lifting body aircraft is analyzed. The results show that the electron density in the flow field on the head of the aircraft is the highest， the electron density in the body area is reduced by two or three orders of magnitude，and NO⁺ and N⁺ contribute most to the electron number density in the flow field. The ablation products injected into the flow field increase the separation distance of shock wave and the thickness of plasma layer. With the development of the flow downstream，the ablation rate of the aircraft body decreases， but the influence range of ablation products on the plasma flow field becomes larger， and the electron number density of the body flow field increases to a certain extent.With the increase in Mach number， the ablation rate of wall increases， and the influence of ablation products is more obvious. The peak electron density on stagnation line changes little， but the electron number density on symmetrical surface of body increases significantly. For the same kind of ablative materials with different components， the influences of ablated products of different materials entering into the flow field on the shock wave separation distance and the peak electron number density are different.

Pd(OH)₂/CeO₂ Catalyst for Hydrogenolytic Debenzylation Reaction of Hexabenzylhexaazaisowurtzitane and Tetraacetyl-dibenzyl-hexaazaisowurtzitane

BAO Lingxiang, YAN Zhiyuan, SONG Jianwei, WEI Gaixia, SUN Chenghui, PANG Siping

2022, 43(3):  524-532.  doi:10.12382/bgxb.2021.0126

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Palladium hydroxide catalysts play a key role in the preparation of hexanitrohexaazais- owurtzitane (CL-20).Eight kinds of Pd(OH)₂/CeO₂ catalysts，for which two kinds of CeO₂ are used as catalyst support，were prepared by deposition-precipitation method. The effects of the preparation temperature，immersion time，the kinds of alkali，pH and the structure of support on the catalytic performance of Pd(OH)₂/CeO₂ are investigated.Pd(OH)₂/CeO₂ catalysts exhibit excellent catalytic activity in the hydrogenolytic debenzylation reaction of both hexabenzylhexaazaisowurtzitane (HPIW) and tetraacetyl-dibenzyl-hexaazaisowurtzitane(TADBIW)，and the yields of products can reach 91% and 95%，respectively.When the amount of Pd used in catalyst is 0.10% (wt/wt) of HBIW substrate，the yield of TADBIW reachs 91%.When the amount of Pd is 0.28%（wt/wt）of TADBIW substrate，the yield of the product is as high as 87%.In this research，a small amount of Pd catalyst is used to efficiently catalyze the hydrogenolytic debenzylation reaction of HBIW and TADBIW，which broadens the way for low-cost preparation of CL-20.

Numerical Simulation of Ejecting a Missile From Missile Ejection System with Flexible Cylinder Based on Corpuscular Method

ZHAO Zhen， JIANG Yi， LIU Xiangxin， LI Yulong， YAN Song

2022, 43(3):  533-541.  doi:10.12382/bgxb.2021.0098

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The working mechanism of a flexible cylinder ejection system and its ejection mode are studied to further improve the controllability, concealment, repeatability and lightweight of cold launch equipment. Corpuscular method is used to calculate the gas jet inside the flexible cylinder, and simulate and calculate the fluid-structure interaction of the flexible cylinder combined with finite element method. The experimental results and the numerically simulated results of the flexible cylinder ejection system are compared to verify the correctness and reliability of the numerical calculation method. For a 16-ton missile, the multi-nozzle ejection and ejection medium of the flexible cylinder ejection system were explored by changing the calculation parameters. It is found that the missile overload has two peaks and is relatively smooth during the work of the flexible cylinder ejection system. The ejection kinetic energy of the missile is basically unchanged and the missile overload is optimized by adjusting the starting time of each nozzle. In the flexible cylinder ejection system using supercritical carbon dioxide, instead of high-pressure nitrogen or high-pressure air, as the ejection medium, the ejection kinetic energy obtained by the missile is reduced by about 41.1%, and the ejection time of the system is extended by about 17.1%.

Multi-sensor Cooperative Management for Ground Target Tracking under Road Constraints

ZHANG Yunpu， SHAN Ganlin

2022, 43(3):  542-555.  doi:10.12382/bgxb.2021.0122

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A multi-sensor cooperative management method is proposed to effectively track the ground target under road constraints and control the radiation loss of the sensor system. The sensor management process is described as a partially observable Markov decision process. A road-constrainted target tracking model and a sensor interception loss model are established, the calculation methods for tracking accuracy and interception loss are presented, and a correction method for target prediction state in Doppler blind zone is proposed. In order to solve the problem that a management scheme is difficultly got when the system state dimension is high, a Levy flight-salp swarm algorithm is designed to obtain a high-quality solution quickly. The simulated results show that the proposed algorithm has better global search capability, and can find high-quality solutions while shortening the optimization time compared with the classic optimization algorithms. The proposed management method can effectively solve the problem of ground target tracking, which not only guarantees the completion quality of the tracking task, but also improves the survivability of the sensor system.

Adaptive Control Based on RBF Neural Network for Electro-optical System

ZHANG Tongtong, JIANG Huhai, YUE Wei, SI Chen, YUAN Man

2022, 43(3):  556-564.  doi:10.12382/bgxb.2021.0117

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For improving the tracking accuracy，the servo control algorithm is optimized to enhance the control accuracy and rapidity of control system after hardware design and system integration. A tracking error model is proposed theoretically. According to the proposed model，the numerical computation is implemented. The result illustrates that the control algorithm plays an important role in controlling the tracking errors of electro-optical system. The radial basis function (RBF) algorithm is employed here to adaptively adjust the control system parameters for improving tracking accuracy and robustness. Both the theoretical analysis and hardware-in-the-loop simulation are practiced to verify the availability of the proposed method. It is proved that the proposed method can achieve less than 28 ms delay and lower than 4% attenuation within 3 Hz bandwidth.

Attitude and Trajectory Calculation of Ejection Seat within the Dynamic Period

JI Xiabin， ZHANG Tong， ZHANG Ruixin， XU Hang， WANG Pei， JIN Liying

2022, 43(3):  565-573.  doi:10.12382/bgxb.2021.0129

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Aiming at the problem that the third-generation ejection seats currently in service cannot autonomously obtain the ejection attitude and trajectory in tests. The research is based on the principle of self-enclosed inertial navigation, with the aid of the overload and angular velocity data collected during the tests, and through low-pass filtering and moving average processing, the quaternion method and the two-interval coning compensation algorithm were used to calculate the attitude and trajectory within the dynamic period after ejection, The posture and trajectory curves of the dynamic period from two 0-0 tests of the X1 ejection seat and two 450 km/h tests of the X2 ejection seat were obtained. Compared with the optical measurement results. The results show that: 1) The two-interval coning compensation method improved trivial effect on the quaternion method, there is no need to consider the influence of the error caused by the rotation of the non-fixed axis after the ejection. 2) For the both 0-0 tests, the main factor affecting the calculation accuracy of the eastern trajectory is the roll angle error. The main factors affecting the calculation accuracy of the northern trajectory are the yaw angle error and the pitch angle error. The main factor affecting the calculation accuracy of the sky trajectory is the pitch angle error. 3) For the both 450 km/h tests, the main factor affecting the calculation accuracy of the eastern and northern trajectory are the cumulative error, the cumulative error has a small effect on the calculation accuracy of the sky trajectory.According to analysis, the errors mainly come from the installation, alignment, data collection and processing process, and subsequent error correction research will be carried out.

On the Motion Characteristics of Cavity Wall in the High-speed Water Entry of Trans-media Vehicle

LI Yiguo， WANG Cong， WU Yuyan， CAO Wei， LU Jiaxing， HE Qiankun

2022, 43(3):  574-585.  doi:10.12382/bgxb.2021.0145

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The high-speed water entry of a trans-media vehicle involves unsteady multiphase flow，which has strong theoretical research significance and engineering application value. In order to obtain the motion characteristics of cavity wall in the high-speed water entry of the vehicle，an experimental study is carried out on the high-speed water entry of a rotating body model. The influences of different excitation effects on the evolution characteristics of the cavity are analyzed. The relationship between the extreme displacement of the cavity and the dual independent variables including attitude angle and cavitation number is extracted，for which surface fitting is performed. The experimental results show that both the splash ring above the free liquid surface and the relative displacement of cavity wall below the free liquid surface are approximately symmetrical during the vertical water entry. The splash ring on the upstream side is significantly larger than that on the downstream side during the non-vertical water entry. When the cavitation number is 0.008 5-0.008 8，the positive excitation dominated by energy transfer and cavitation leads to the extreme displacement of cavity wall on the upstream side，and the smaller the attitude angle is，the stronger the positive excitation effect is. Below the 3D depth position，the negative excitation effect of inhalation effect can be ignored relative to the positive excitation effect of cavitation effect. The extreme displacement on the downstream side is approximately symmetrical，and that on the upstream side is approximately linear on the fitted surface.

Numerical Simulation on Kinematic Characteristics of Trans-media Aircraft during Water-skipping

TIAN Beichen， LIU Taotao， WU Qin， HUANG Biao

2022, 43(3):  586-598.  doi:10.12382/bgxb.2021.0164

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Inspired by the phenomenon of hydroplaning in life，the flexible skipping motion mode is widely used for trans-media aircraft，which greatly improves the penetration ability of naval weapons. The kinematic characteristics of a trans-media aircraft with complex configuration are studied numerically，and the influence of water-entry parameter on the skipping process of trans-media aircraft over calm water surface is emphatically analyzed. The research results show that the skipping process of trans-media aircraft over water surface can be divided into stable skipping phase and hydroplaning phase，the movement trajectory of trans-media aircraft at the stable skipping phase fluctuates in a sinusoidal pattern，and it is subjected to a large slamming load at every water contact moment. When the water-entry velocity of trans-media aircraft is in the range of 10-55 m/s，the water-entry pitch angle range of the aircraft can increases first and then decreases in the skipping process over water surface with the increase in the entry velocity. When the entry velocity is 30 m/s，the effective range of the water-entry pitch angle of the aircraft is from -8° to 10°.The greater the water-entry velocity is，the greater the slamming load is，the more the number of stable skipping is and the farther the stable skipping distance of the aircraft is. When the pitch angle of water-entry is from 0° to -5°， the trans-media aircraft has the most stable skipping times over the water surface，the longest skipping distance，and the most stable skipping attitude.

Mathematical Model of Gas Bubble around the Outlet of Underwater Ejection Canister for Submarine-launched Missile

LIU Haotian， FU Debin， BI Fengyang， YANG Huawei， LU Bingju

2022, 43(3):  599-604.  doi:10.12382/bgxb.2021.0089

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The gas bubble around the outlet of underwater ejection canister for submarine-launched missile significantly affects the launching safety of missile. Based on the physical mechanisms of expansion-induced depressurization and contraction-induced pressurization of gas bubble，a mathematical model of gas bubble evolution is proposed to analyze the characteristics of bubble loading. The water flow fields are simulated by an incompressible potential flow model and solved by the direct boundary element method. The gas flow fields are calculated by an uniform pressure model. The gas bubble model is validated by comparing with experimental data and numerically simulated results. It is shown that the proposed model can be used to predict the load status of gas bubble for the early stage of missile leaving the launch canister.

Numerical Models for Calculating Ship Hydrodynamic Pressure Field in Restricted Waters with Significant Blocking Effect

DENG Hui， WANG Erli， YI Wenbin， WANG Kebin， ZHANG Zhihong

2022, 43(3):  605-616.  doi:10.12382/bgxb.2021.0106

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Pressure mine works on the signal from ship hydrodynamic pressure field，which is more dangerous in shallow and offshore waters and so on. For obtaining the signals from ship hydrodynamic pressure fields in different restricted waters，a CFD numerical model is proposed based on the viscous theory，and the hydrodynamic characteristics, such as sinkage，trim，wave making and resistance, are calculated and validated. And a finite difference numerical model is established based on the potential flow theory，and the ship hydrodynamic pressure fields calculated by the two numerical models are compared. It is found that the two numerical models are different，but their calculated results are consistent，and they are both suitable for restricted waters with significant blocking effect or mixed flow.The results show that the more obvious the blocking effect is，the higher the grid division quality is，with giving small time step and setting denser grids near the water bottom and shore boundaries. If the blocking effect is more obvious，the restricted water has more significant effect on the hydrodynamic pressure field，and its negative pressure peak changes greatly，which may lead to the unreasonable design of mine fuze parameters，and miss the best detonation time.

Numerical Simulation of Measuring Ship's Induced Magnetic Field by Geomagnetic Field Simulation Method

WANG Kaisong， ZHOU Guohua， LIU Yuelin， WANG Yufen， LIU Shengdao

2022, 43(3):  617-625.  doi:10.12382/bgxb.2021.0110

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Geomagnetic field simulation method has the advantages of fast measurement speed and convenient implementation, but the measurement accuracy of induced magnetic field is restricted by the uniformity of simulated geomagnetic field, so it is of great significance to study its influence law for popularizing and applying geomagnetic field simulation method. Based on the principle of geomagnetic field simulation method, with the help of COMSOL Multiphysics, an analytical example of an ellipsoidal shell is designed to verify the effectiveness of the simulation platform in analyzing geomagnetic field simulation method to measure induced magnetic field, and then a ship-type example is designed for numerical simulation. The variation law of the accuracy of measuring ship's induced magnetic field by geomagnetic field simulation method affected by the uniformity of simulated geomagnetic field and the influence of bridge structure on the measurement accuracy of induced magnetic field are quantitatively analyzed. The results show that the measurement accuracy of induced magnetic field is better than 90% when the uniformity of simulated geomagnetic field reaches 91%. If the uniformity continues to increase, the improvement effect of induced magnetic field measurement accuracy will slow down and the cost-effectiveness ratio of engineering will decrease. The influence of bridge structure on uniformity evaluation is 0.2%, and the influence degree of induced magnetic field measurement accuracy is 2.7%. When the overall uniformity is higher than 91%, its influence degree drops to 2.5%, so the influence of this structure on measuring induced magnetic field can be ignored. The research conclusion provides a basis for the further popularization and application of geomagnetic field simulation method in practical ship degaussing, and also provides a certain reference for optimization design of geomagnetic field simulation coils.

Active Disturbance Rejection Control of Dish-shaped Underwater Vehicle with Omnidirectional Control

ZHANG Wenqing， ZOU Jiayun， ZHANG Xiaochuan， HAN Mei， ZOU Sichen

2022, 43(3):  626-636.  doi:10.12382/bgxb.2021.0148

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The autonomous control of dish-shaped underwater vehicle under the condition of underactuation and multiple constraints is studied.A mechanical model of the underwater vehicle is established，and the underactuated control characteristics and the planar biaxial symmetrical structure of underwater vehicle are analyzed. An omnidirectional drive mechanism with four water jet thrusters is designed，and an omnidirectional control power output equation is given.An active disturbance rejection controller (ADRC) is designed，and a visual simulation platform of UAVs based on MATLAB+MFC is established. Through a large number of numerical experiments，the reliability and effectiveness of the controller are verified，and the smooth operation of the underwater vehicle in the dynamic process of three-dimensional space is realized.

An Algorithm for Underwater Target Localization of Multistatic Sonar System with Unknown Signal Propagation Speed

FAN Chao, WANG Ding, YANG Bin, YIN Jiexin

2022, 43(3):  637-652.  doi:10.12382/bgxb.2021.0134

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For the unknown propagation speed of acoustic signal under water，a closed-form localization algorithm based on error constraint equation is proposed to estimate the acoustic signal propagation speed and target location for underwater multistatic sonar system，in which the time difference of arrival is taken as an observable quantity.The proposed algorithm falls into two steps. In the first step，the nonlinear observation equations are transformed into the pseudo-linear equations by introducing auxiliary variables，and the initial estimation solutions of target location and signal propagation speed are obtained. In the second step，a new optimization model is obtained according to the equality constraint of estimated error of the initial estimation solutions，and the Lagrange multiplier method is used to solve the problem.Then the jointly estimated mean square error of the proposed algorithm is derived. It is theoretically proven that the estimated mean square error can reach the corresponding Cramér-Rao bound. Finally，the theoretical analysis of the estimated mean square error is verified by numerical simulation，and the comparison shows that the proposed algorithm is superior to the existing algorithms.

Axis Self-adaptive Design and Dimensional Synthesis of Knee Joint of Lower Limb Exoskeleton

MA Chunsheng, YIN Xiaoqin, MA Zhendong, MI Wenbo

2022, 43(3):  653-660.  doi:10.12382/bgxb.2021.0171

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A hybrid exoskeleton of knee joint and a motion planning algorithm based on Lie algebra are proposed to solve the problem of “parasitic force” between human and machine.The mapping between the driver and the human motion is established by using the kinematic model，the human motion is sensed，and the joint configuration space is constructed. A parameter selection method based on screw theory and particle swarm optimization algorithm is introduced to optimize the size of knee exoskeleton with the objective of workspace area and global transmission index.The simulated and experimental results show that the workspace of knee exoskeleton covers the motion range of knee joint，and the motion transfer efficiency of limb is greater than 0.7；and the exoskeleton can accurately adjust its own motion axis according to the human motion and eliminate the “parasitic force” between human and machine.

Influence of Extrusion Deposition 3D Printing Process Parameters on Propellant Size and Tensile Strength

ZHOU Menglei, NAN Fengqiang, HE Weidong, WANG Moru, DU Ping, WANG Binbin

2022, 43(3):  661-666.  doi:10.12382/bgxb.2021.0103

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For the problem that the propellant structure is difficult to meet the increasing demand of complex structure, a model of extrusion deposition 3D printing is established, and the process parameters in the extrusion deposition 3D printing are determined.The influences of 3D printing process parameters, such as needle inner diameter, printing speed and temperature, on propellant size and tensile strength were experimentally studied. The results show that, when the inner diameter of the needle is 0.7 mm, the printing speed is 3 mm/s, and the temperature is 35 ℃, the size of printed propellant sample is the best. When the inner diameter of the needle is 0.7 mm, the printing speed is 4 mm/s, and the floor temperature is 35 ℃, the tensile strength of printed propellant sample is the best.

A Novel 3-DOF Quasi-zero-stiffness Vibration Isolation Platform with Delta Mechanism and Its Characteristics

WENG Zeyu， LIU Shengli， WU Xiaoyu， YU Hanghang， WANG Wujiang， ZHU Fuhong

2022, 43(3):  667-675.  doi:10.12382/bgxb.2021.0144

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A novel Delta mechanism with three translational degrees of freedom in space is proposed to realize the spatial three-dimensional low-frequency vibration isolation.A parallel mechanism with negative stiffness is deduced from the Delta mechanism. Then a three-DOF parallel quasi-zero stiffness vibration isolation platform is constructed by connecting the parallel mechanism with a vertical spring with positive stiffness.The statics and dynamics models of the vibration isolation platform are established to analyze the stiffness characteristics and natural frequencies of the vibration isolation platform in different spatial coordinates.The result shows that the static characteristic of the vibration isolation platform is linear in the horizontal direction and is only related to the horizontal displacement. In the vertical direction，it has quasi-zero stiffness characteristic，which can obtain a lower natural frequency，and is only related to the vertical displacement. When the vibration isolation platform deviates from the equilibrium position，the zero-stiffness characteristic is no longer obvious. The vertical natural frequencies of the vibration isolation platform with the parallel mechanisms with and without negative stiffness were test. The test results show that the vibration isolation platform with the parallel mechanism with negative stiffness can greatly reduce the vertical natural frequency of the system.

Transmission Characteristics of Limited Angle Steel Belt Transmission System and Effect of Pre-tension Force on Output Characteristics

LU Qiang， GAO Zhifeng， ZHONG Xiaobin， DAI Jun， HUANG Qiu, HU Shaoyun

2022, 43(3):  676-685.  doi:10.12382/bgxb.2021.0080

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A mathematical model of the limited angle steel belt transmission system is established to analyze its transmission characteristics and the influence of pre-tension on its output characteristics，and the influencing factors of the limited angle steel belt creep rate and transmission ratio are studied. Based on the rigid-flexible coupling dynamics model and the mathematical model for calculating the pre-tension force of steel belt，the influence of pre-tension force on the output characteristics of the transmission system is studied through the multi-body dynamics simulation software and the physical prototype experiment.The results show that the thickness of steel belt，the rolling angle，the ratio of rolling angular velocity to steel belt transmission speed，the transverse displacement and the radius of friction wheel are the main factors affecting the creep rate and transmission ratio of steel belt. The larger the pre-tension force is，the smaller the deviation of output angle is，the higher the output precision is，and the more stable the transmission is. When the pre-tension force is 11 N，the overshoot is 40% and the output angle error is 6.4%. When the pre-tension force increases to 84 N，the overshoot decreases to 1%，the response time decreases to 20%，and the output angle error decreases to 1.4%.The mathematical model of creep rate，transmission ratio and pre-tension force can provide theoretical basis and effective reference for the research on limited angle steel belt transmission system.

Robust Optimization Design of Fixture Locating Scheme Based on Constrained Multi-objective Optimization Algorithm

LU Yuming, ZHANG Xiangfei, LI Ming, ZHAO Minqing

2022, 43(3):  686-693.  doi:10.12382/bgxb.2021.0064

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Designers usually design a robust fixture locating scheme according to their own experience or some specific optimization methods. The lack of the designer's experience and the different using conditions often result in the lack of universality of this design method. A constrained multi-objective optimization algorithm is proposed to design fixture locating scheme. The proposed algorithm include a feasible solution search phase based on steady-state evolution and a double population optimization phase. In the proposed algorithm, a grid constraint decomposition approach and a feasibility criterion-based approach are used to solve the constrained multi-objective optimization problems. The reliability of the proposed algorithm is verified by validating the test function and comparing with other algorithms. An optimization design of the fixture locating scheme was completed based on the kinematics model of fixture locating scheme. The results show that the design method has the better universality and practicability, which not only simplifies the design program of fixture locating scheme, but also reveales the relationship among the offset variances of workpiece in different directions.

Structural Optimization Design of Double-decker Ball Bearing Based on Response Surface Methodology

HU Jing， ZHAI Jiutong， ZHANG Xinming， LI Hailong， XUN Bo

2022, 43(3):  694-703.  doi:10.12382/bgxb.2021.0137

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Compared with traditional single-decker ball bearing，the double-decker ball bearing has higher maximum speed and longer service life. However，the use of double-decker ball bearing is constrained due to its large mass. To solve the problem，the structure of double-decker ball bearing is optimized. The equivalent stress，contact stress，and temperature rise of the bearing are obtained through finite element analysis. The local sensitivity of each design variable is analyzed based on the response surface method，and the parameters that are highly correlated with the objective function are determined.The multi-objective optimization design of double-decker ball bearing is carried out using the multi-objective genetic algorithm，in which the bearings' mass，fatigue life and temperature rise are takren as the optimization goals，and the ball diameter，number of balls and coefficient of groove curvature radius are taken as the design variables. The optimal internal geometric parameters of double-decker ball bearings were obtained. A test device was built according to the optimized results.The results show that the mass of the optimized double-decker ball bearing is reduced by 10.47%，the maximum contact and equivalent stresses are decreased by 9.11% and 6.45%，repectively，and the maximum temperature is increased by 1.9%.

Time Sequence Control Method for Series Power Supply

TAN Qiang， GAO Yinghui， CHEN Hongtao， KANG Xin， SUN Yaohong， YAN Ping

2022, 43(3):  704-711.  doi:10.12382/bgxb.2021.0112

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The pulse capacitor voltage for battery packs connected in series (BPCSs) power supply is a key metric in electromagnetic propulsion. In the repetitively charging mode, the capacity fades after the battery pack charging the pulse capacitor for many times, thus making the pulse capacitor voltage not reach the setting value of voltage in the specified time. Hence, the consistency of the electromagnetic propulsion cannot be guaranteed. A time sequence dynamic adjustment algorithm is proposed based on the theoretical model of BPCSs power supply. The time sequences are adjusted to improve the charging speed when the battery packs are connected into the circuit. The experimental results show that the charging time is shortened by 9.3%, the average current is increased by 10.2% and the average power is increased by 10.3% using the proposed method at the capacity-loss of 40 V, which makes the voltage of pulse capacitor reach the setting value in time in the repetitively charging mode.

Remaining Useful Life Prediction of Equipment under Random Degradation Stress

XU Xiaodong， TANG Shengjin， XIE Jian， YU Chuanqiang， WANG Fengfei， HAN Yangyang

2022, 43(3):  712-719.  doi:10.12382/bgxb.2021.0018

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The effective remaining useful life prediction plays a key role in improving the reliability and safety of equipment. The uncertain internal aging state and external working condition have great affect on the degradation rate and state-of-health of equipment. A novel method for predicting the remaining useful life of equipment under the random stress is proposed. The random degradation stress is introduced into the aging process of equipment，and a degradation model for equipment is established based on Wiener process. An off-line prior parameter estimation method based on expectation maximization algorithm and particle swarm optimization algorithm is proposed. The random parameter is updated online in Bayesian framework，and the probability distribution function of the remaining useful life prediction result is derived. The proposed method is verified by the experimental degradation data of lithium-ion batteries. The results show that the proposed method can be used to effectively improve the prediction accuracy of remaining useful life and reduce the uncertainty of prediction results in considering the influence of random stress on the degradation law of equipment.

Data Simulation of Maintenance Material Demand for Armored Equipment

ZHANG Lei, LI Shimin, KANG Shugui, WANG Tiening, GUO Mengchao

2022, 43(3):  720-728.  doi:10.12382/bgxb.2021.0113

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The predictive effect of the big-data-driven prediction model on the consumption demand of equipment maintenance materials with small sample size is not ideal. A data simulation expansion algorithm is proposed. The AP clustering algorithm is improved by taking the accumulated equipment consumption at different time stages as similarity measure, and the data at different time stages are clustered by iteration. Each relative equipment consumption in the report stage, in which the data are clustered as the same category, is considered as normally distributed data. The normal distribution characteristics of each component of a vector to be predicted are calculated, and a large number of random samples are generated by using mathematical software as the simulation training samples of the data-driven prediction model. The numerical results show that the simulation training samples generated by this method can effectively improve the predictive effect of the big-data-driven prediction model with few samples, and with the increase in the number of simulation sample data, the predicted results of different prediction models are stable near the same predicted value, which effectively improves the credibility of the predicted results of the data-driven model.