力学学报

PROGRESS AND PROSPECT OF AERODYNAMIC EXPERIMENTAL RESEARCH ON LINEAR CASCADE

Zhang Qingdian, Ma Hongwei, Yang Yi, Xiao Anqi

The aerodynamic experiment on linear cascade, which can provide numerous and systematic experimental results, is traditionally the main methods to verify the elementary aerodynamic performance of compressor and turbine. In recent years, the overseas and domestic researchers have carried out a large number of flow measurement experiments to reveal the internal flow mechanism and then explore methods to decrease flow loss of linear cascade flow field. In this paper, the overseas and domestic aerodynamic experiment research progress for linear cascade, especially for supersonic and transonic linear cascade has been reviewed and discussed from the viewpoints of experimental equipment, measurement technologies and experimental research content. Firstly, the development of linear cascade equipment and the methods for improving flow quality are reviewed, which can increase the inlet flow uniformity and outlet flow periodicity of the test section. Meanwhile, various aerodynamic experimental measurement technologies for linear cascade are discussed in detail, including measurements for blade surface pressure field, blade surface temperature field, flow velocity field and flow visualization. The existing problems and improvement methods for current measurement technologies are analyzed, respectively. Furthermore, mainly based on the decrease of flow loss, several key scientific problems and research progress for the aerodynamic experiment of linear cascade are discussed herein, including the interaction between shock wave and turbulence boundary layer in transonic cascade, tip leakage clearance flow research, baseline profile modification, multi-scale secondary flow vortex structures, unsteady flow characteristics, the cascade flow field research in vibration environment, and so on. Finally, based on the previous research, the prospects of the direction and the trends of linear cascade aerodynamic experimental research are discussed briefly, which may provide reference for future related studies. By understanding the phenomenon and mechanism of complex flow in cascade, it provides technical support for further improving the aerodynamic performance of compressor and turbine.

2022, 54(7): 1755-1777. doi: 10.6052/0459-1879-21-684

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SPECIAL ISSUE PREFACE: RESEARCH OF NONLINEAR VEHICLE SYSTEM DYNAMICS BASED ON DATA DRIVE

Wang Kaiyun, Li Shaohua

2022, 54(7): 1778-1779. doi: 10.6052/0459-1879-22-294

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REVIEW OF HEALTH MONITORING AND FAULT DIAGNOSIS OF AXLE-BOX BEARING OF HIGH-SPEED TRAIN

Gu Xiaohui, Yang Shaopu, Liu Wenpeng, Liu Zechao

With the flourishing development of high-speed train in China, research on the fault prognostics and health management has been paid more and more attention during its service and maintenance. Axle-box bearing is a key rotating component of the bogie in high-speed trains. Under the complex wheel-rail interaction, it is prone to cause in-service failures due to fatigue, overload, etc., which seriously affect the operational efficiency and safety of the train. However, the existing diagnosis methods cannot meet the dynamic and systematic requirements of modern high-speed train. It is necessary to develop more effective health monitoring and diagnosis techniques. In this paper, the state-of-art condition monitoring and fault detection systems and methods for axle-box bearing in maintenance, wayside and on-board are firstly introduced. Then, a review is presented including theoretical modeling and dynamic analysis of the coupled system of axle-box bearing and high-speed train, fault diagnosis of axle-box bearing based on signal processing and machine learning technologies from both positive and negative perspectives of dynamics. At last, the crucial points for further exploring methods and technologies in prognostics and health management of the axle-box bearing are summarized.

2022, 54(7): 1780-1796. doi: 10.6052/0459-1879-22-007

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POLYGONAL WEAR IDENTIFICATION OF WHEELS BASED ON OPTIMIZED MULTIPLE KERNEL EXTREME LEARNING MACHINE

Xie Bo, Chen Shiqian, Xu Mingkun, Yang Yunfan, Wang Kaiyun

Polygonal wheel is a common wear phenomenon in railway vehicles. With the increase in operating mileage, the degree of wheel wear increases significantly, which seriously affects the ride comfort and operation safety of the trains. It is of great significance to develop the polygonal wheel dynamic detection method with the help of monitoring big data. In this study, a polygonal wheel quantitative identification model is established based on the vertical acceleration signals of the axle box. Firstly, the main orders of the polygonal wheels contained in the acceleration signals of the axle box are identified through order analysis, and the acceleration amplitude corresponding to the main order is obtained at the same time. On this basis, the characteristic matrix of polygonal wheel wear amplitude identification is constructed by the acceleration amplitude of the main order and the entropy characteristic of the acceleration signal. Then the genetic mutation particle swarm optimized multiple kernel extreme learning machine (GMPSO-MKELM) identification model is established. Through the mapping between the characteristic matrix and the wear amplitude of the polygonal wheel, the wear amplitude identification is realized. The results of the simulation and field test show that the proposed model can effectively extract the main order of polygonal wheels from axle box acceleration. The identification accuracy of the proposed model is better than that of the comparison models in wear amplitude, and it has high detection efficiency. The proposed model can achieve accurate identification with a root mean square error of 0.0010 (simulation) and 0.0134 (field test). The proposed polygonal wheel identification model can provide a theoretical basis for the detection and intelligent maintenance of railway vehicle wheels.

2022, 54(7): 1797-1806. doi: 10.6052/0459-1879-22-083

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ANALYTICAL SOLUTION OF THE HUNTING MOTION OF A WHEELSET NONLINEAR DYNAMICAL SYSTEM

Shi Hemu, Zeng Xiaohui, Wu Han

Numerical methods are usually used to analyze the amplitude of limit cycle and nonlinear critical speed of railway vehicle system, which is inconvenient to study the rule of variation with vehicle system parameters. The wheelset system retains several critical elements that affect the dynamic performance of the railway vehicle system, such as the geometric nonlinear constraints of the wheel-rail, the wheel-rail contact creep relationship, and the suspension system, which can reflect the essential characteristics of the hunting motion of the railway vehicle system. The wheelset system has fewer degrees of freedom and parameters, which can be analyzed by the analytical method. In this paper, the nonlinear dynamics equations are nondimensionalized by choosing appropriate characteristic parameters, and the two-degree-of-freedom nonlinear differential equations with small parameters are obtained. The method of multiple scales is used to solve the equations analytically. The analytical expressions of the amplitude of the limit cycle of the wheelset system are given and its stability is judged. The analytical expressions of the bifurcation speed of the wheelset system are given, and then the analytical expressions of the nonlinear critical speed of the wheelset system are obtained. After the analytical solutions are verified by the numerical results, the influence of wheelset system parameters is analyzed by using the analytical solutions. The traditional calculation methods of bifurcation diagram (such as speed reduction method, path-following method, etc.) require a large number of numerical integration calculations on the differential equations to solve the nonlinear critical speed of the system. However, the analytical expressions obtained in this paper can directly give the nonlinear critical speed and amplitude of the limit cycle of the wheelset system, which is convenient for studying the rule of variation of the dynamic performance of the wheelset system with parameters and for quick comparison and screening of schemes, and provide a reference for the optimization design of bogie structure.

2022, 54(7): 1807-1819. doi: 10.6052/0459-1879-22-003

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SERVICE LIFE EVALUATION OF TRACTION MOTOR BEARINGS IN COMPLICATED VIBRATION ENVIRONMENT OF A LOCOMOTIVE

Liu Yuqing, Chen Zaigang, Ge Xin, Wang Kaiyun

Traction motor is the power source of the railway locomotive, therefore, the stability and reliability of the locomotive transmission system are directly affected by the service lives of its key components (e.g., the support bearings, etc). For the heavy haul locomotive, the traditional evaluation methods are mainly based on the fixed load conditions, therefore, it is difficult to accurately evaluate the service lives of motor bearings under complex external excitations such as track random irregularities. Based on the vehicle-track coupling dynamics, a locomotive-track coupled dynamics model with traction power transmission system considering the specific structures of the traction motor and rolling bearing is established. In addition, the effect of the impact wheel-rail interaction and gear engagement is considered in this study. Besides, the service lives of traction motor bearings in the complex vibration environment of a locomotive are assessed based on the linear damage accumulation criterion and ISO 281 standard. Results indicate that the vertical wheel-rail interactive force, gear meshing force, the centrifugal force of rotor, and unbalanced magnetic pull increase obviously under the external excitation induced by the track random irregularity. In the complex vibration environment of the locomotive, the interactions between the roller and race in motor bearings are intensified, and the corresponding fatigue lives of the driving end and non-driving end motor bearings are shortened. Furthermore, with the continuous deterioration of the line state and the improvement of the locomotive running speed, the predicted life mileages of the motor bearings decrease in the increasingly harsh service environment. Because of the large external dynamic loads, the service life of the driving end bearing is shorter than that of the non-driving end one. This evaluation method proposed in this study can provide a theoretical guidance for the design, selection, and service life prediction of motor bearings used in the locomotive.

2022, 54(7): 1820-1829. doi: 10.6052/0459-1879-21-545

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REMAINING LIFE ASSESSMENT OF HOOK TAIL FRAME IN RAILWAY HEAVY-HAUL WAGON BASED ON REAL LOADING SPECTRUM

Qin Tianyu, Ren Xinyan, Hu Feifei, Liu Yujie, Ao Ni, Kan Qianhua, Wu Shengchuan, Kang Guozheng

With the increase in the operation scale and frequency of China heavy-haul railroad wagons, the failure fracture problem of hook tail frame is becoming more and more serious. In this work, domestic 16/17 type hook tail frame (forged E-grade steel) was used as a research object, the basic mechanical properties and fracture performances of forged E-grade steel were firstly obtained by systematic material tests; secondly, a finite element model of the hook tail frame with initial crack defects was established; finally, the remaining life prediction of the damaged hook frame was calculated by using the NASGRO equation based on the measured loading spectrum. The results show that when the crack shape ratio of 0.8, 0.5, 0.3, the calculated remaining life of the hook tail frame gradually decreases, and the calculated remaining life of the fatigue crack propagation from 2 mm to 20 mm is 360000 km, 320000 km and 260000 km, respectively, all of which are less than one depot maintenance period; the remaining life ratios of the three profile ratios are small after crack expansion to 12 mm, which are only 4.7%, 4.0%, and 2.2% of the total remaining serviceable mileage. Therefore, it is reasonable to take 12 mm as the damage tolerance of the hook tail frame for stopping crack. To investigate the effect of near threshold area on crack propagation life, reducing the initial crack size to 0.5 mm with a shape ratio of 0.5, when the crack is near the crack propagation threshold area, the calculated remaining service mileage increases to 1.56 million km, which is 4.9 times of the initial crack of 2 mm, including three maintenance periods. These results can provide a basic reference for the optimization and strategy of the inspection interval of the hook tail frame widely used for railway heavy-haul railroad wagons.

2022, 54(7): 1830-1838. doi: 10.6052/0459-1879-21-687

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CHARACTERISTICS ANALYSIS ON BEARING ROTOR SYSTEM OF HIGH-SPEED TRAIN UNDER VARIABLE SPEED CONDITIONS

Wang Baosen, Liu Yongqiang, Zhang Bin

The development of high-speed trains has made the safety problem of its key components—bearings increasingly prominent. Existing bearing models are all established under uniform speed conditions and cannot describe the motion state of the system under variable speed conditions. To solve this problem, a dynamic model of the axle box bearing rotor system of a high-speed train under variable speed conditions is established. The model uses angle iteration to calculate the total angle that the rolling elements have rotated in an uneven time, and then determines the spatial position of the rolling elements at any time. Comparison experiments and simulations were carried out under constant speed and variable speed conditions, and they have a good agreement, which verifies the effectiveness of the model. The influence of outer ring fault, inner ring fault, and rolling element fault on the system stability are qualitatively analyzed by the axis trajectory, and the reliability of the analysis results is verified by experiments. The two-dimensional moment invariants are used as a characteristic indicator to quantitatively analyze the influence of three types of faults on system stability. The analysis results show that under uniform speed conditions, the effects of different types of faults on train stability are small. Under variable speed conditions, the outer ring fault has the greatest impact when the angular acceleration is slight, and the rolling element fault has the greatest impact when the angular acceleration is large, but the degree of impact gradually decreases with the size of the fault. Similarly, two-dimensional moment invariants are used to analyze the stability critical state of the rotor system and determine the maximum fault size corresponding to the critical state under different speed conditions and different fault types. The results show that that with the increase of the speed of the bearing inner ring, the maximum size corresponding to different fault types will decrease, and the fault size of the rolling element is mostly the smallest, indicating that the rolling element fault has the greatest impact on the stability of the system.

2022, 54(7): 1839-1852. doi: 10.6052/0459-1879-22-067

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DYNAMIC JOINT ESTIMATION OF VEHICLE SIDESLIP ANGLE AND ROAD ADHESION COEFFICIENT BASED ON DRBF-EKF ALGORITHM

Li Shaohua, Wang Guiyang, Yang Zekun, Wang Xuewei

The vehicle center of mass slip angle and the road adhesion coefficient are the key parameters required to realize the intelligence of the vehicle chassis. The vehicle's center of mass slip angle is crucial for improving vehicle safety and handling, and the tire-road adhesion coefficient determines the peak tire force, which in turn determines the vehicle's dynamic stability boundary. In this paper, a dynamic joint estimation method of vehicle mass side slip angle and road adhesion coefficient based on inertial measurement unit (IMU) and built-in speed/angle sensor (WSS) of in-wheel motor is proposed for four-wheel independent drive electric vehicles. The vehicle dynamics analysis of the four-wheel independent drive electric vehicle is carried out, and the vehicle center of mass side slip angle estimator is obtained by combining the Dugoff tire calculation model; the PCA multivariate analysis method is used to reduce the dimension of the high-dimensional data in machine learning, and the principal component characteristic parameters are extracted to establish the road adhesion coefficient estimator. The double radial basis neural network and the extended Kalman filter (double radial basis function and extended Kalman filter, DRBF-EKF) method with an adaptively adjustable network structure are used, the RBF neural network structure is improved by the K-means algorithm, and the extended Kalman filter is used for noise filtering to improve estimation accuracy. Therefore, dynamic joint estimation of vehicle center of mass slip angle and road adhesion coefficient is realized. Simulation and real-vehicle experiments show that the designed DRBF-EKF dynamic joint estimator has better real-time performance and estimation accuracy than the extended Kalman filter algorithm, which can adapt to the changes in road adhesion characteristics and vehicle speed during vehicle driving. Compared with the DRBF method, the estimation accuracy is significantly improved; and the optimal number of neurons in the hidden layer that can meet the estimation accuracy and real-time requirements at the same time is analyzed.

2022, 54(7): 1853-1865. doi: 10.6052/0459-1879-21-551

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VEHICLE TRACTION FORCE CONTROL BASED ON THE ROAD ADHESION COEFFICIENT ESTIMATION BY FFUKF

Wang Hongbo, Wang Chunyang, Gao Han, Xu Shihan

Traction control system (TCS) based on road adhesion coefficient estimation is designed for the rear drive tractor. Firstly , to track the time-varying nonlinear system in the classical Kalman filter, a fuzzy control theory and an attenuated memory filter are introduced into untraced Kalman filter, and the fuzzy forgetting factor unscented Kalman filter (FFUKF) is proposed to estimate road adhesion coefficient, so as to improve the tracking performance of the algorithm. Traction control includes torque control and braking control. Then, for the TCS torque control, the road adhesion coefficient and the vehicle acceleration when the slip rate of the driving wheel is near the target slip rate are used to calculate the target base torque, respectively. According to the vehicle state and chattering parameters, the extension set is divided into the classical domain, extension domain and non-domain with the extension control theory, and the dynamic weight coefficient is obtained by the correlation function of extension set. The base torque is designed by extension fusion of the target base torques calculated by the above methods. Next, the error between the actual slip rate and the target slip rate is used as the input, and the target feedback torque is obtained by using the fuzzy self-tuning PI controller. In terms of braking control, the PI pressure control and adhesion difference pressure are designed on two typical road surfaces, respectively. Finally, the test results show that the proposed FFUKF algorithm can track the tire-road friction coefficient more quickly, and the proposed TCS control strategy can effectively restrain the excessive slip of the driving wheels to control the slip rate of drive wheel in the best range, so that improving vehicle dynamic performance significantly.

2022, 54(7): 1866-1879. doi: 10.6052/0459-1879-22-211

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RESEARCH ON TRAILING ARM SUSPENSION SYSTEM OF FULL X-BY-WIRE CONTROL CHASSIS BASED ON DATA DRIVE

Yao Qi, Li Quantong, Du Qiuyue, Chen Song, Wang Xiangyu, Zhan Weiliang, Yin Siwei

The car is driven under extreme road conditions such as off-road, and there is a certain range of adjustment requirements for the body height. When the traditional suspension scheme is technically integrated with the full-wire chassis, there are mechanism motion interference, excessive wheel camber during the chassis lifting process, and wheel generation. Lateral displacement and other phenomena can easily lead to excessive tire wear, resulting in unstable driving. The key to solving the above problems is to convert the influence of vehicle height changes on the lateral parameters of tires into longitudinal rolling of the wheels, thereby achieving stable and long-travel vehicle height adjustment. . In this study, a seven-degree-of-freedom dynamic model of the whole vehicle is established, and the mechanical analysis of the suspension system guiding mechanism is carried out, and the two are collected as the input information of the system research; the relevant characteristic parameters of the elastic elements and shock absorbers are carried out through the sine wave vibration table. Acquire, carry out the kinematics simulation test of the integrated electric wheel based on the data drive, including the mechanical performance analysis of the key hinge position of the suspension system and the kinematic characteristics study of the overall structure of the electric wheel, so as to define the key performance indicators of the system, and combine the theory Research and simulation tests are carried out to determine the scheme of the double trailing arm active suspension system. The simulation results and the real vehicle verification show that the wheel camber problem can be effectively solved in the process of adjusting the height of the large stroke with the full-wire control platform equipped with the system scheme of this study. , the integrated electric wheel has good independent operation ability, and this research is of great significance to improve the vehicle's passability under extreme road conditions.

2022, 54(7): 1880-1895. doi: 10.6052/0459-1879-21-624

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NEURAL NETWORK LATERAL DYNAMICS MODELING AND CONTROL BASED ON ED-LSTM FOR INTELLIGENT VEHICLE

Fang Peijun, Cai Yingfeng, Chen Long, Sun Xiaoqiang, Wang Hai

Simplification and assumptions are usually made in the process of vehicle dynamics modeling, resulting in the model can not accurately reflect the actual dynamic characteristics of the vehicle under some working conditions, which affects the control accuracy and even safety. In view of this, this paper proposes a data-driven nonlinear modeling and control method, establishes a new neural network multi-step prediction model of vehicle lateral dynamics, and realizes the tracking control of reference trajectory of intelligent vehicle. Firstly, based on the analysis of vehicle single-track model and considering tire nonlinearity and longitudinal load transfer, a neural network lateral dynamics model is designed based on encoder decoder structure. Among them, the serial arrangement is used to expand the differential equation to describe the incomplete dynamic information, and the hidden layer neurons learn the highly nonlinear and strong coupling characteristics of the vehicle, so as to improve the global calculation accuracy of the model. Use the constructed data set for model training and testing, the results show that, compared with the physical model, the proposed model has higher modeling accuracy under different road adhesion coefficients, and has the ability to implicitly predict road friction conditions. Secondly, using the proposed model to design trajectory tracking control algorithm, according to the vehicle steady-state steering assumption, the required front wheel steering angle and steady-state sideslip angle are calculated, and the steady-state sideslip angle is incorporated into the steering feedback based on path error to realize the reference trajectory tracking control. Finally, comparative analysis of tests under different working conditions is carried out with Simulink/CarSim co-simulation and HiL experiments to evaluate the proposed control algorithm based on neural network model. The results show that the model can realize the accurate tracking control effect of intelligent vehicle at high speed, and has good lateral stability.

2022, 54(7): 1896-1908. doi: 10.6052/0459-1879-21-667

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AN AXISYMMETRIC IMMERSED BOUNDARY METHOD BASED ON 2D MESH

Cai Zhenggang, Pan Junhua, Ni Mingjiu

Immersed boundary methods is a common numerical simulation method to deal with moving boundary problems in particle two-phase flows. When the dimensionless parameters of studied physical problems meet certain requirements, its corresponding flow structure becomes axisymmetric. Hence, an axisymmetric immersed boundary method based on a 2D mesh and cylindrical coordinates is proposed in the present paper. A finite volume method is used as the spatial discretization in the present algorithm. And the governing equation is closed by a sharp stepped interface, which is used to replace the real solid immersed boundary. In order to improve the efficiency of computation, an adaptive mesh refinement technology is used to improve the mesh resolution near the immersed boundary. The using of cylindrical coordinates will produce a redundant source item from the viscous term in the momentum equation. The additional source term will be handled by using an implicit scheme. Moreover, in the direct numerical simulation of a sphere approaching a wall with a constant velocity, the pressure of the fluid in the gap dramatically changes because of the small gap. So, in order to accurately analyze the flow field, the required grid resolution is very high in the gap. Multiple projection-step calculations are carried out in one time step for maintaining the stability of the simulation. In the movement of a sphere free impacting a wall, a lubrication force model will be introduced to simulate the movement of the sphere near the wall even with a low grid resolution. Finally, simulation results on the flow past a fixed sphere, the flow past a circular disk, the stokes flow by a sphere approaching a wall and the flow caused by the sphere-wall collision prove that the present axisymmetric IBM algorithm is applicable and accurate for dealing with stationary and moving boundary problems in an axisymmetric flow.

2022, 54(7): 1909-1920. doi: 10.6052/0459-1879-22-110

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INFLUENCE OF DIVING DEPTH ON MOTION RESPONSE AND LOAD CHARACTERISTICS OF SUBMERGED BODY UNDER ACTION OF INTERNAL SOLITARY WAVE

Wang Chao, Du Wei, Du Peng, Li Zhuoyue, Zhao Sen, Hu Haibao, Chen Xiaopeng, Huang Xiao

Internal solitary waves frequently occur in ocean pycnocline. Because of its high crest, deep trough and huge energy, the seawater flow above and below the pycnocline will show a shear state and cause a sudden strong current. When hovering underwater, the submersible is likely to encounter internal solitary waves. Due to the flow field characteristics of internal solitary waves, the motion response and hydrodynamic load changes of the suspended submersible placed above and below the pycnocline are different, and even the phenomenon of falling deep will occur. This work aims to explore the influence of the submerged depth on the wave-body coupling based on mKdV theory and the CFD method. The velocity inlet boundary is used for wave generation. The overset grid and fluid-structure coupling methods are adopted to simulate the submerged body with multi-degree-of-freedoms. The motion response and hydrodynamic load of suspended submerged bodies at different depths are analyzed. The results show that under the action of internal solitary waves, the submerged body above and in the pycnocline move along the forward direction of the wave, sink at first and then rises, and the submerged body below the pycnocline will continue to sink against the current; The smaller the vertical distance between the submerged body and the wave surface, the more significant the influence on its surge, heave and velocity. However, the submerged body located in the pycnocline moves along the waveform at the interface, and its motion response and load changes are slightly affected; The directions of the horizontal force on the submerged body above and below the pycnocline are opposite. The peak value of the horizontal force is less than the peak value of the vertical force, and the submersible below the pycnocline always experiences a head-down moment, which eventually leads to falling deep.

2022, 54(7): 1921-1933. doi: 10.6052/0459-1879-21-649

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STUDY ON REBOUND BEHAVIOUR AND MAXIMUM SPREADING OF SHEAR-THINNING FLUID DROPLET IMPACTING ON A HYDROPHOBIC SURFACE

Zheng Nuo, Liu Hailong

Controlling the non-Newtonian fluid droplet impact process is of profound importance not only in academic interesting but also in the practice applications. However, the existing research about droplet impacting on solid surface mainly focuses on the Newtonian fluid, and the mechanism of non-Newtonian properties on droplet impact dynamics remains to be explored. In this study, the maximum spreading and rebound behaviour of shear-thinning fluids (xanthan gum aqueous solution with mass fraction ≤ 0.03%) droplets impacting on hydrophobic surface have been investigated experimentally. The morphological changes of droplets impact onto hydrophobic surface were captured by means of high-speed imaging technology, the spreading and recoiling process were studied. The experimental results show that under the same We, xanthan gum concentration showed little effect on the maximum spreading of droplets. However, the droplets differed greatly with different concentration in the recoiling stage, and with the increase of xanthan gum concentration three kinds of rebound behaviours, namely partial rebound, full rebound and deposition, were exhibited. The theoretical value of critical dimensionless recoiling height ξ_c for droplet rebound on the hydrophobic surface was obtained by using the energy conservation law, and the maximum dimensionless recoiling height ξ_max of droplets was found to be consistent with the scalar law ξ_max ~ αWe, with the slope decreasing with increasing xanthan gum concentration. Based on the effective Reynolds number Re_eff, an effective viscosity μ_eff expression was proposed, and the maximum dimensionless diameter β_max prediction model of shear-thinning fluid droplets was established. The predicted value of β_max obtained by the model achieved good agreement with the experimental measured value over a wide range of We.

2022, 54(7): 1934-1942. doi: 10.6052/0459-1879-22-135

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p-DSMC METHOD OF RADIATION EFFECT OF RAREFIED GAS ATOMIC WITH EXTREMELY SUPERSONIC

Yang Quanshun, Fang Ming, Li Langquan, Su Siyao, Yang Yanguang

The high temperature behind the extremely supersonic flow shock layer leads to the excitation of internal energy mode and accompanied by thermal radiation. The high temperature makes the air molecules completely dissociated, and the contribution of atomic components to radiation will reach more than 80%. Based on the optimized atomic radiation model and using the photon tracing direct simulation Monte Carlo (DSMC) method, the wall radiation heating of hypersonic two-dimensional cylinder at different Mach numbers in the rarefied flow region is studied. The wall pressure and heating with or without excited radiation effect and the translational, vibrational and rotational temperatures along the stagnation line are obtained. Without considering the excitation radiation effect, the wall pressure and heating obtained are in good agreement with the previous simulation results and the error is less than 5%. Especially at the stagnation point, the error is less than 1%. The translation, vibration and rotation temperatures obtained are also in good agreement with the literature results. Under the same flow conditions, considering the radiation effect, it is found that when the flow velocity is lower than 10 km/s, the radiative heating is not obvious. While the flow velocity is greater than 10 km/s, the proportion of radiative heating to convective heating will exceed 30% in the stagnation point. After considering the radiation effect, the maximum values of translational, rotational and vibrational temperatures in the non-equilibrium region have little effect. In addition, another important conclusion is that the concentration of atoms in the flow field is an important factor affecting the magnitude of the radiative heat flow on the wall.

2022, 54(7): 1943-1951. doi: 10.6052/0459-1879-22-046

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FINITE VOLUME MODEL OF WATER COLUMN SEPARATION AND REJOINING WATER HAMMER IN VISCOELASTIC PIPES

Wang Ning, Zhou Ling, Li Yunjie, Pan Tianwen

Finite volume method with second-order Godunov-type scheme was developed to simulate the water column separation and rejoining phenomenon in viscoelastic water pipes. Based on the traditional elastic pipe model, the viscoelastic effect was considered in the process of numerical simulation. The viscoelasticity term and unsteady friction term were introduced into the governing equation of hydraulic transient flow, and the finite volume method with second-order Godunov scheme was used to solve the problem of numerical discretization and calculation. The pressure adjustment coefficient was considered to calculate the influence of free gas on the calculation unit, meanwhile the slope limiter MINMOD function was introduced for the sake of avoiding the spurious oscillations of numerical simulation results. The ghost cell method was used to construct the boundary and realize the unified computation of computing area at the same time. The calculation results of the model established in this paper were compared with those of the existing model and the experimental results, and the sensitivity analysis of the influencing parameters was also carried out. The results show that the proposed model can accurately simulate the transient pressures fluctuation and changes in the cases of both pure water hammer and water column separation and rejoining water hammer, which were basically identical with the experimental data. Compared with the traditional MOC method, when the Courant number C_r is less than 1, the results of finite volume method's second-order Godunov scheme are more accurate and stable. In the process of pressure attenuation, viscoelastic effect plays a dominant role compared with pipeline friction. Compared with the mathematical model which only considers the elasticity of the pipe, the accuracy of simulation results can be significantly improved by considering the viscoelastic effect of the pipe, especially the relative error of the peak value of the pressure wave is significantly reduced.

2022, 54(7): 1952-1960. doi: 10.6052/0459-1879-22-069

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SPECTRAL ELEMENT METHOD FOR NONLINEAR THERMOMECHANICAL COUPLING PROBLEMS WITH HIGH TEMPERATURE GRADIENT AND THERMAL CONTACT RESISTANCE

Shi Xin, Zhao Jianning, Yang Miaomiao, Zhang Jialei, Liu Donghuan

The spectral element method for nonlinear thermomechanical coupling problems with high temperature gradient and thermal contact resistance is proposed here, and temperature-dependent thermal conductivity, elasticity modulus, Poisson’s ratio and thermal expansion coefficient, as well as the interface stress related thermal contact resistance are considered. The interpolation function of spectral element method is based on the unevenly spaced Lobatto points or Chebyshev points of the second kind. The spectral element method keeps both the high accuracy of spectral method and the flexibility of finite element method. Numerical results show that, the present spectral element method could solve the nonlinear thermomechanical coupling problems with high temperature gradient and thermal contact resistance with high accuracy and efficiency. Not only the convergency rate is larger than traditional finite element method, but also employ less degree of freedom and computational time to obtain results with higher accuracy, and has broad application potential in practical engineering thermomechanical coupling problems.

2022, 54(7): 1960-1970. doi: 10.6052/0459-1879-22-062

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EXPERIMENTAL STUDY ON THE EFFECT OF LOADING RATE AND GEOMETRIC SIZE ON THE FRACTURE BEHAVIOR OF CHINESE A508-III STEEL

Cui Guangshun, Bao Chen, Li Yilei, Sun Jianhua, Du Kaikai

The ductile-brittle transition of pressure vessel steels caused by the change of loading rate and geometric constraint is a key issue that needs to be solved in the field of nuclear energy safety. In order to accurately analyze the dynamic fracture behavior of Chinese A508-III steel, the fracture toughness tests of Chinese A508-III steel under different loading rate and geometric size were carried out by using INSTRON VHS high-speed material testing machine to investigate the effect of loading rate and geometric size on the dynamic fracture toughness of Chinese A508-III steel. The results show that the Chinese A508-III steel has good impact toughness. With the increase of loading rate, the total impact absorbed energy of the specimen basically remains constant, the absorbed energy of crack initiation increases, while the absorbed energy of crack propagation decreases. The J-Δa resistance curve and the conditional initiation toughness J_Q decrease with the increase of geometric constraint, but increase with increasing loading rate. When loading rate reaches a critical value, the conditional initiation toughness J_Q basically keeps constant and the fracture mode of the specimen changes from ductile fracture to ductile-brittle-ductile mixed fracture. The maximum J-integral value J_max is more suitable to describe the fracture toughness evolution of Chinese A508-III steel when brittle fracture occurs due to the occurrence of mixed fracture mode. With the decrease of out-of-plane geometric constraints, J_max increases linearly with the increase of Δa_m. The higher the in-plane geometric constraint of the specimen has, the greater the slope of the linear relation between J_max and Δa_m presents. As the geometric constraint of the specimen increases, the ductile-brittle transition loading rate of the material increases, but the value of J_max decreases. Changing the geometric constraint can only change the fracture mode of the material within a finite loading rate range, and when the loading rate exceeds a certain threshold value, the loading rate becomes the main factor affecting the fracture mode of the material.

2022, 54(7): 1970-1981. doi: 10.6052/0459-1879-21-613

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ELASTOPLASTIC ANALYSIS OF SURROUNDING ROCK OF DEEP ROADWAY BASED ON ROCK CREEP AND D-P CRITERION

Jing Wei, Chen Hongen, Yang Renshu, Jing Laiwang, Xue Weipei, Wang Fuqi

In order to deeply analyze the influence mechanism of rock creep and intermediate principal stress on the stability and zoning deformation characteristics of surrounding rock in deep high stress soft rock roadway, by analyzing the deformation characteristics of surrounding rock of deep roadway under long-term load, the four zones deformation mechanism of surrounding rock of deep roadway based on the creep characteristics of surrounding rock is revealed, the effects of intermediate principal stress, the rock mass expansion and the post peak strain softening characteristics are considered according to Druck-Prager criterion and correlation flow rule, and the elastic-plastic analytical solutions of stress, deformation and radius of four deformation zones of surrounding rock in deep high stress soft rock roadway are derived. Combined with the specific engineering example, through the comparative analysis of field monitoring data and calculation results obtained by using different mechanical models, the scientificity and feasibility of this theory are demonstrated, and reveals the influence law of different strength criteria and surrounding rock parameters on the zoning shape of surrounding rock in deep roadway. The results show that ignoring the creep characteristics of surrounding rock in deep high stress soft roadway will lead to the value of initial cohesion greater than the actual value, resulting in the theoretical bearing capacity of surrounding rock in deep high stress soft roadway greater than the actual bearing capacity. Increasing the intermediate principal stress coefficient in the range of [0, 0.7] can effectively control the expansion of plastic zone and broken zone of surrounding rock. When the initial cohesion and internal friction angle of surrounding rock decrease, the influence of intermediate principal stress coefficient on plastic zone, broken zone and roadway deformation of surrounding rock increases significantly. The research results can provide theoretical reference for underground engineering support design and surrounding rock stability evaluation.

2022, 54(7): 1982-1993. doi: 10.6052/0459-1879-21-619

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BRITTLE PLASTIC PERTURBATION SOLUTIONS OF PLASTIC ZONE RADIUS FOR CIRCULAR TUNNELS UNDER NON-HYDROSTATIC PRESSURES BASED ON THE UNIFIED STRENGTH THEORY

Zhang Changguang, Li Zonghui, Guan Ganghui, Sun Song

Based on the unified strength theory and the elastic-brittle-plastic model to comprehensively account for the intermediate principal stress effect and brittle softening of surrounding rock strength, an analytical solution of plastic zone radius for a circular tunnel under non-hydrostatic pressures was presented by using the perturbation method. Application ranges of the proposed perturbation solution were then discussed. It was validated against reported results from the complex variable function method, the perturbation method, numerical simulations, and the constant assumption of total loads. Finally, the influence of each factor on plastic tunnel shape and size was analyzed. It is found herein that the proposed perturbation solution of plastic zone radius for circular tunnels is a series of analytical ones considering different extents of the intermediate principal stress effect, and reduces to that of the elastic-perfectly plastic model. It should be applied to a plastic zone boundary with the biaxial symmetric elliptical-like completely surrounding tunnel perimeter, and the correctness and rationality of the perturbation solution is demonstrated by comparing with four methods available in the literature. Therefore, it has extensive theoretical significance and engineering application value. The perturbation parameter can significantly affect the size and long/short axis variation of tunnel elliptical-like plastic zone. The plastic zone range decreases obviously with both the increase of the intermediate principal stress effect and the post-peak strength parameters of surrounding rocks. The perturbation solution of Mohr-Coulomb strength criterion is shown to be conservative due to not take the intermediate principal stress effect into consideration, and the elastic-brittle-plastic model is more appropriate for tunnel plasticity analysis than the elastic perfectly-plastic model.

2022, 54(7): 1994-2007. doi: 10.6052/0459-1879-22-025

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DYNAMIC RESPONSES OF GRADED NON-HOMOGENEOUS UNSATURATED SOILS UNDER A STRIP LOAD

Shi Liwei, Ma Qiang, Shu Jinhui

Based on the three-phase porous media mixed theory, a graded non-homogeneous unsaturated foundation model is established and the dynamic response of graded non-homogeneous unsaturated soils subjected to a strip load is addressed. The general solutions of dynamic response for unsaturated foundation in frequency domain are derived by using the Fourier transform and Helmholtz vector decomposition. Then the calculation formula of displacement, stress, and pore pressure of graded non-homogeneous unsaturated soil is derived by combining with the reverberation-ray matrix method (RRMM), boundary conditions and general solutions of dynamic response for unsaturated foundation in frequency domain. Assuming that the continuous variation of physical and mechanical properties of unsaturated soils along the thickness-coordinate by exponential law distribution, the numerical solutions of displacement, stress, and pore pressure then obtained by using numerical inverse Fourier transformation, and the influence of soil heterogeneity on the dynamic response of unsaturated soil is discussed. The results show that the non-homogeneous of unsaturated soil has a considerable effect on the dynamic response of unsaturated soil, which significantly changes the vibration modes of vertical displacement, normal stress and pore pressure in the depth direction. The vibration frequency of pore air pressure in the depth direction increases with the increase of gradient factor, and the peak wave is constantly near the surface. The vertical displacement decreases with the increase of gradient factor, but the normal stress and pore water pressure first increase and then decrease with the increase of gradient factor, and the higher nonhomogeneity of soil is, the greater amplitude of normal stress and pore water pressure is.

2022, 54(7): 2008-2018. doi: 10.6052/0459-1879-21-612

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DIGITAL DESIGN AND MODEL VERIFICATION OF MIURA ORIGAMI METAMATERIAL STRUCTURES

Chen Yao, Ye Wangjie, Shi Jiayao, Feng Jian

Origami-inspired structures have bright engineering applications in many fields, such as aerospace engineering, flexible electronics, automobile, ships, and building structures. Miura origami metamaterial structures can be constructed by expanding the classic Miura origami patterns along three directions. Such structures possess the characteristics of high porosity, self-locking, flat folding, negative Poisson's ratio and programmable morphology. In order to better apply these metamaterials into energy-absorbing structures and deployable structures, this study introduces Matlab and Grasshopper to further improve the digital design method of Miura-ori metamaterial structures. Notably, digital modeling technology and 3D printing technology have been adopted to achieve unified modeling for zero-thickness origami models and non-zero-thickness three-dimensional origami models. Furthermore, a series of physical models are constructed for verification. Then, the advantages and disadvantages of using 3D printing technology to make origami metamaterial structural models have been discussed. On the basis of geometric parameters, analytical expressions for the crease length, relative density, and folding ratio of a Miura-ori metamaterial have been established. Abaqus/Explicit was used to analyze and verify the quasi-static compression process of these origami structures, and the influence law of relative density on the energy absorption index was revealed. The results show that the digital design method of metamaterial structure is efficient and accurate, which is convenient for structural selection and further optimization analysis. The obtained results from 3D printed models are in good agreements with the theoretical values. When panel configuration, thickness and crease length remain unchanged, the Miura origami metamaterial structure with a relatively lower density tends to exhibit better energy absorption efficiency.

2022, 54(7): 2019-2029. doi: 10.6052/0459-1879-22-080

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CHAOS RESEARCH OF COUPLED SD OSCILLATOR UNDER GAUSSIAN COLORED NOISE AND HARMONIC EXCITATION

Zhou Biliu, Jin Yanfei

As a typical oscillator with negative stiffness, coupled SD oscillator is widely used in engineering. At the same time, Gaussian colored noise exists widely in the external environment and may induce complex nonlinear dynamic behaviors, so its stochastic dynamic is a hot topic and difficult problem in nonlinear dynamics research. In this paper, the chaotic dynamics of bistable coupled SD oscillator under Gaussian colored noise and harmonic excitation are studied. The analytical expression of the homoclinic orbit of the coupled SD oscillator can not be given directly because its stiffness term is a transcendental function, which makes it difficult to analyze the chaos threshold. Firstly, the piecewise linearization approximation is used to fit the stiffness term of the oscillator, and stochastic Melnikov method for non-smooth system under Gaussian colored noise and harmonic excitation is developed. Based on random Melnikov process, then the chaos thresholds of the oscillator under weak noise and strong noise are obtained by the mean square criterion and the phase space flux function theory respectively, and the effect of noise intensity on chaotic dynamics is discussed. The results show that the chaotic region increases with the increase of noise intensity, that is, the increase of noise intensity is more likely to induce the coupled SD oscillator to produce chaos. When the damping is fixed, the chaos threshold decreases with the increase of noise intensity in the case of weak noise. However, the effect of noise intensity on chaos threshold is opposite for the case of strong noise. Finally, numerical results show that it is effective to study the chaos of coupled SD oscillator under Gaussian colored noise and harmonic excitation by the method in this paper. The results of this paper provide some theoretical guidance for the study of chaotic dynamics of stochastic non-smooth systems.

2022, 54(7): 2030-2040. doi: 10.6052/0459-1879-22-123

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FREE VIBRATION OF A BINARY COMPOSITE PLATE: A SEMI-ANALYTICAL APPROACH

Xue Jian, Niu Muqing, Zhang Wenyong, Chen Liqun

Binary composite plate is one of the common elements in metamaterial plate structure. A semi-analytical model of the free vibration of the structure is proposed for the binary composite plate composed of a matrix and an embedded body with different material parameters, and its vibration characteristics are studied. The plate is decomposed into two sub-regions based on the domain decomposition method and the distribution of binary materials. The non-smoothness of the local displacement and strain caused by the sudden change of stiffness in the composite plate is described by adding a local trial function to the mode shape function. Based on the essential boundary conditions of the binary composite plate and the condition of compatibility for the displacement at the joint of the two sub-regions, a new mode shape function is constructed. Based on the classical thin plate theory, the Ritz method with special trial functions is used to calculate the natural frequencies and modes of the binary material plate under different geometric configurations. The influence of the size and location of the embedded body on the vibration characteristics of the structure is investigated. The accuracy of this method is verified by the convergence analysis and the finite element simulation results. The results show that the classical global trial function will lead to inaccurate results when analyzing the modes with vibration localization, while the additional local trial function can significantly improve the convergence speed of the Ritz method and the accuracy of the results; the effect of the embedded body position on the low-order natural frequencies is not obvious, but it can significantly change the distribution of the low-order mode shape nodal lines and the region where vibration localization occurs.

2022, 54(7): 2041-2049. doi: 10.6052/0459-1879-22-160

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STRONG WEAK COUPLING FORM ELEMENT DIFFERENTIAL METHOD FOR SOLVING SOLID MECHANICS PROBLEMS

Hu Kai, Gao Xiaowei, Xu Bingbing

Element differential method (EDM) is a new strong-form finite element method. Compared with the weak form numerical methods, the method discretizes the governing equations directly and does not need any numerical integration. Therefore, the method has a relatively simple form, and it has high efficiency in calculating the coefficient matrix. But as a strong form method, more nodes or higher-order elements are needed to achieve a satisfactory calculation accuracy in the element differential method. At the same time, for some models containing singular points which occur on multi-material interfaces, abrupt changes in the boundary conditions, and especially at crack tips, accurate calculation results can not be obtained by the conventional element differential method. In order to overcome this weakness, a coupled method combining the element differential method and finite element method (FEM) is proposed in this paper. The main idea of the coupled method is that the finite element method is used around the singular points in the geometric model and the element differential method is selected at other parts. The strong weak coupling form not only retains the advantages of the element differential method but also ensures the accuracy of solving singular problems. At the same time, when dealing with large scale problems, the finite element method is selected for key components and the element differentiation method is used for other components. This treatment can not only obtain more accurate results but also can greatly improve the overall calculation efficiency for large scale 3D problem. In this paper, two typical examples are given, one is a two-dimensional problem with notch, and the other is a complex three-dimensional engine problem. Through the calculation and analysis of these two problems, the correctness, accuracy and efficiency of the proposed coupling method in solving two-dimensional singular problem and three-dimensional large-scale problem are proved.

2022, 54(7): 2050-2058. doi: 10.6052/0459-1879-22-087

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VULNERABILITY ANALYSIS OF NPP EQUIPMENT BASED ON NEURAL NETWORK

Liu Hongquan, Chen Shaolin, Sun Xiaoying, Wu Shaoheng

The vulnerability analysis is a vital part of the seismic probabilistic risk assessment of nuclear power plants. However, due to the complexity of nuclear power structures and the larger calculation scale, the vulnerability analysis of NPP equipment is very time consuming when considering soil-structure interaction (SSI). In order to develop an efficient vulnerability analysis method, this paper adopts a partition calculation method applied to NPP SSI analysis, and establishes an artificial neural network (ANN) using limited SSI analysis results to substitute the FEM process. Based on the regression method with log-normal assumption and Monte Carlo method to analyze the equipment vulnerability. The ANN numerical simulation includes the following contents. (1) Establish the best ANN model through cross-validation to substitute the FEM process, and the most relevant ground motion parameters are selected as the ANN input based on the semi-partial correlation coefficient. (2) Quantification and investigation of the ANN prediction uncertainty. It includes the aleatory uncertainty caused by the simplification of the seismic inputs and the epistemic uncertainty from the limited size of the training data. (3) Computation of fragility curves with Monte Carlo method and the regression method with log-normal assumption based on the prediction data of ANN model. This paper explores the impact on fragility curves induced by different seismic intensity measures and uncertainty of soil material. Meanwhile, the results verify the basic rationality of the lognormal assumption and provide a possible direction for the vulnerability analysis of NPP equipment.

2022, 54(7): 2059-2070. doi: 10.6052/0459-1879-21-466

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