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  • Volume 52,Issue 2,2025 Table of Contents
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    • Convergence Analysis on Polarization Parameter Estimator of Battery Equivalent Circuit Models

      2025, 52(2):1-9.

      Abstract (124) HTML (3) PDF 9.38 M (33) Comment (0) Favorites

      Abstract:To investigate the error convergence characteristics of power battery polarization parameter estimation under different operating conditions, the stability and convergence of the estimators are rigorously analyzed in this paper by using Lyapunov’s second method. The state equations of polarized parameter estimation errors are firstly derived based on the equivalent circuit model and the forgetting factor recursive least squares (FFRLS). Subsequently, the state equation is analyzed using Lyapunov’s second method to obtain the necessary condition for the asymptotic convergence of the estimator, i.e., continuously varying current input. A graphical method is proposed for analyzing the dynamic convergence properties of the error and justifying this necessary condition. Finally, the theoretical analysis process and results are validated using data generated from an experimentally calibrated battery model. The results show that the estimator can gradually converge to the vicinity of the true value under continuously varying current inputs, and the drastically varying positive and negative alternating conditions have better convergence properties.

    • Robust Optimization for Powertrain Mounting System Based on Vehicle Model

      2025, 52(2):10-19.

      Abstract (103) HTML (1) PDF 3.44 M (15) Comment (0) Favorites

      Abstract:Aiming to handle the complex situation that the parameters of the powertrain mounting system (PMS) of battery electric vehicles are both uncertain and correlated, the robust design optimization of PMS based on the vehicle model with 13 degree of freedom (DOF) is investigated. Firstly, based on Monte Carlo sampling and the correlation transformation method, the UTI-Monte Carlo (UMC) method for the uncertainty and correlation analysis of PMS inherent characteristic responses was proposed, where the probabilistic parameters were correlated. Then, an efficient method named the UTI-arbitrary polynomial chaos expansion (UAPCE) method was derived for the uncertainty and correlation analysis of PMS responses by combining the correlation transformation method and arbitrary polynomial chaos expansion. Next, based on the UAPCE method and correlation coefficient weighting method, a robust design optimization method of PMS was developed by considering the uncertainty and correlation of responses. Finally, a numerical example was used to verify the effectiveness of the proposed method. The analysis and optimization results based on the PMS model with 6 DOF and those based on the vehicle model with 13 DOF were compared. The results show that the calculated results using the vehicle model with 13 DOF can better reflect the vibration performance of PMS under the vehicle environment. Using the UMC as a reference method, the UAPCE method has good computational accuracy and efficiency in conducting the uncertainty and correlation analysis of PMS responses. The proposed robust design optimization method can configure the PMS parameters reasonably and improve the robustness of the system.

    • Development of Vehicle Thermal Management Performance Based on Digital Wind Tunnel

      2025, 52(2):20-27.

      Abstract (106) HTML (1) PDF 34.28 M (18) Comment (0) Favorites

      Abstract:To comply with China Ⅵ emission standards and Stage Ⅳ fuel consumption regulations, a high-power engine was installed in a commercial vehicle, and it is necessary to optimize the cooling system and enhance its heat dissipation capacity. This paper utilizes the lattice Boltzmann method (LBM) to establish a digital wind tunnel for thermal environment simulations, accurately predicting the vehicle’s heat balance and thermal protection performance, with a coolant temperature prediction error of less than 1 ℃ after comparison between the modelling and experimental data. Based on this, using the coolant temperature of the radiator and the intercooler outlet air temperature as optimization targets, the interactive effects among the condenser, intercooler, radiator, and fan intrusion were analyzed, leading to an optimized design. A simulation process suitable for virtual calibration of engine cooling systems is proposed. The results show that fan intrusion and intercooler height significantly affect the radiator’s heat dissipation performance. After iterative optimization, the air mass flow rate of the radiator and intercooler are increased by 5.01% and 7.87%, respectively, and the surface temperature distribution of the cooling module becomes more uniform, significantly improving the heat dissipation efficiency of the engine compartment.

    • Calculation and Experimental Research of Maximum Contact Heat Flux Density

      2025, 52(2):28-33.

      Abstract (103) HTML (2) PDF 3.04 M (15) Comment (0) Favorites

      Abstract:In unsteady state heat transfer processes, existing theories still cannot effectively solve the problem of initial heat flux density values. This article proposes the concept of maximum contact heat flux density and the contact heat flux density constant. Based on this, a calculation formula for the maximum contact heat flux density is proposed, which determines that the maximum contact heat flux density is proportional to the initial temperature difference between the two objects, and the proportionality coefficient in the formula is the contact heat flux density constant. Additionally, based on the experimental principle of approximating instantaneous heat flux with an extremely short average heat flux density, a heat flux testing platform is established to conduct temperature rise tests on metal sheets. The maximum contact heat flux density and contact heat flux density constant are calculated. Based on experimental research, the contact heat flux density constant is 1 022.51 W/(m2·K) for stainless steel 304 metal sheets with a thickness of 0.5~5.0 mm and a temperature rise of 100 K.

    • Numerical Simulation and Process Parameter Optimization for Online Aerosol Spray Quenching of 7003 Aluminum Alloy Profiles

      2025, 52(2):34-45.

      Abstract (90) HTML (2) PDF 23.83 M (9) Comment (0) Favorites

      Abstract:To investigate the influence of process parameters on the online aerosol spray quenching of 7003 aluminum alloy profiles, a simulation model for online aerosol spray quenching of 7003 extruded aluminum alloy profiles was established in this study. The variations of the temperature and stress fields during the aerosol spray quenching process of 7003 aluminum alloy profiles were studied, and the reliability of the aerosol spray quenching simulation model for the profiles was verified by quenching experiments. The response surface optimization method was used to investigate the influence of profile running speed, longitudinal nozzle spacing, and air water ratio of circumferential air mist cooling nozzle on the online quenching time and maximum equivalent stress during the quenching process of the profile. The optimal production process parameters for online aerosol spray quenching of the profile are obtained. The research results show that the optimal process parameters are a profile running speed of 30 mm/s, a longitudinal nozzle spacing of 155 mm, and an air water ratio of 1.32. Compared with the pre-optimized parameters, the online aerosol sprap quenching time of the profile is reduced by 33.1%, the maximum equivalent stress during the quenching process is reduced by 21.2%, and the maximum residual stress is reduced by 62.9%. The efficiency and quenching quality of the profile online aerosol quenching are significantly improved.

    • Research on In-plane Low-velocity Impact Performance of Automobile Orthogonal Trapezoidal Honeycomb Aluminum

      2025, 52(2):46-54.

      Abstract (86) HTML (5) PDF 19.78 M (15) Comment (0) Favorites

      Abstract:In this paper, an orthogonal trapezoidal honeycomb aluminum material is prepared, which is intended to be used as an energy-absorbing device for vehicles instead of traditional energy-absorbing box, and the impact mechanics and energy-absorbing properties of the material at low speed are studied. Firstly, a structure of orthogonal trapezoidal honeycomb aluminum was fabricated using an adhesive bonding method. Experimental methods were then employed to study the in-plane compression process of the material, obtaining stress and energy absorption characteristics of the material. Secondly, the deformation and stress of the material were analyzed by theoretical analysis method, and the energy absorption of the material was compared with the test results. Finally, the loading process of the material was simulated by means of simulation. Combined with the optimization design method, the optimal energy absorption parameters of the material were obtained as a plate thickness of 0.50 mm and an upper side length of 3.0 mm. At this time, the specific energy absorption of the orthogonal trapezoidal honeycomb aluminum material can reach 28.8 kJ/kg, which is better than the traditional energy absorption box structure. It characterizes the feasibility of orthogonal trapezoidal honeycomb aluminum replacing traditional energy absorption materials.

    • Kinematic Parameter Identification Based on Improved Fourier Series Trajectory

      2025, 52(2):55-63.

      Abstract (60) HTML (0) PDF 18.50 M (12) Comment (0) Favorites

      Abstract:Aiming at the problems of low welding efficiency, poor accuracy and unstable operation of welding robots in high-end manufacturing field, a method of kinematics parameter identification of welding robots based on improved Fourier series trajectory was proposed. Firstly, a kinematic model of the welding robot was established based on the MDH (modified denavit-hartenberg) criterion, and an error model of the welding robot was established based on differential kinematics. Secondly, the optimal improved Fourier series trajectory was found through pattern search algorithm, and 50 pose points with the smallest number of conditions were selected as the experimental pose set. Finally, a RLS-DEH (recursive least squares and differential evolution hybrid) algorithm was proposed, which can effectively improve the accuracy of parameter identification. The above method was validated using KUKA’s welding robot as the experimental object. The experimental results showed that after, substituting the optimal pose set obtained using the improved Fourier series trajectory method into the error model and identifying it using the RLS-DEH algorithm, the average absolute position error of the welding robot was reduced from 1 mm to within 0.05 mm, which improved the accuracy by 95% compared with the previous calibration, proving the efficiency and practicality of the proposed method.

    • Study of LiDAR SLAM Method Based on Column Features and Random Finite Sets

      2025, 52(2):64-75.

      Abstract (44) HTML (1) PDF 17.67 M (11) Comment (0) Favorites

      Abstract:Traditional data association-based simultaneous localization and mapping (SLAM) methods are prone to causing mismatches between observations and targets, leading to a decrease in pose estimation accuracy. This paper proposes a 3D LiDAR SLAM method for cluttered environments by combining column feature extraction method and random finite set theory based on sequential Monte Carlo implementation. Firstly, stable column features are extracted from segmented point clouds using the M-estimator sample consensus algorithm to obtain static surviving features and new features within a single frame of point cloud data. Subsequently, two types of features are introduced into the RB-PHD-SLAM (Rao-Blackwellized-probability hypothesis density-simultaneous localization and mapping) framework, and the sequential Monte Carlo method is employed to achieve inter-frame propagation of the vehicle’s trajectory probability density and the map posterior. This enables simultaneous estimation of environmental features and vehicle poses. Evaluation results based on both simulation dataset and KITTI dataset show that, compared with the classical FastSLAM algorithm, the proposed method improves the vehicle positioning accuracy by 44.99%, and reduces the average estimation error of feature location and feature number by 49.24% and 56.22%, respectively. These results indicate that the proposed method significantly improves the accuracy and robustness of SLAM, and helps to ensure safe operation of intelligent vehicles.

    • Improved RANSAC Point Cloud Plane Fitting Algorithm Based on DBSCAN

      2025, 52(2):76-87.

      Abstract (44) HTML (0) PDF 38.00 M (15) Comment (0) Favorites

      Abstract:To address the problem of poor point cloud plane fitting effect and easy misidentification of the random sample consensus (RANSAC) algorithm for noisy point cloud data, improvements to the algorithm are necessary. The proposed algorithm employs density-based spatial clustering of applications with noise (DBSCAN) to modify the selection strategy of the initial point set in the RANSAC algorithm and uses principal component analysis (PCA) to compute the normal vectors of each point in the point cloud. Two constraint conditions, the distance from the point to the plane and the angle between the normal vectors of the point and the plane, are simultaneously used as the criteria for determining the points within the RANSAC algorithm model. The point cloud simulation data with no noise and 300 and 500 noisy points are used for testing. The fitting results of the proposed algorithm are all approximate to the theoretical values, and the standard deviations of the inner point distance are 1.007×10-8, 0.003 and 0.007, respectively, better than those of RANSAC algorithm. Using actual workpiece point cloud data for testing in two operating scenarios, the proposed algorithm improves the fitting ratio of in-plane points by 24.7% and 24.6% compared to the traditional RANSAC algorithm, respectively. The completeness and accuracy of plane extraction are also superior to those of the RANSAC algorithm. Simulation and case analysis validate the effectiveness of the proposed algorithm.

    • Modelling and Experimental Study on Thermal-mechanical Coupling of Fine-pitch Gear Intermittent Hobbing

      2025, 52(2):88-97.

      Abstract (41) HTML (0) PDF 26.54 M (14) Comment (0) Favorites

      Abstract:In the fine-pitch gear manufacturing process, significant thermal deformation is prone to occur during the gear hobbing, which in turn affects its dimensional accuracy and operational performance. Based on the principle of spreading processing and the mechanism of metal destruction, a thermal-mechanical coupling model is proposed for the intermittent hobbing of fine-pitch gears. Steel fine-pitch gear specimens are prepared using various hobbing speeds. By comparing the measured profile deviations with the simulated plastic strain values, the accuracy of the proposed model is verified. The influence of modulus, cutting speed, and heat transfer condition on cutting stress, temperature, and thermal deformation is studied. The results show that the cutting stress is negatively correlated with the gear modulus and positively correlated with the cutting speed. The tooth surface defect density, temperature, and thermal deformation are positively correlated with the cutting speed. To reduce heat deformation and improve tooth accuracy and surface quality, the rotational speed of the hob and its diameter should be decreased. Additionally, convective heat transfer in the cutting zone should be enhanced.

    • Research on Intelligent Diagnosis of Rolling Bearings Based on Parallel Input Model of GADF and CWT

      2025, 52(2):98-108.

      Abstract (40) HTML (0) PDF 54.43 M (12) Comment (0) Favorites

      Abstract:Due to random uncertainty factors, such as the change in operating conditions of rolling bearings and noise interference, it is easy to lead to incomplete network feature extraction and the inability to capture local singular information of fault mutations. A parallel two-dimensional depthwise separable residual neural network (P2D-DSResNet) is proposed in this paper to address the aforementioned issues. By using Gramian angular difference field (GADF) and continuous wavelet transform (CWT), one-dimensional vibration signals can be transformed into two-dimensional time frequency images while preserving the complete time-frequency domain information. The P2D-DSResNet uses depthwise separable convolution instead of ordinary convolution in residual modules, which enhances feature learning ability and improves the model’s feature extraction capability for better fault diagnosis in high noise and varying operating conditions. The bearing data obtained from a fault simulation testbed are used for experimentation and analysis. A comparative analysis with other convolutional neural network methods demonstrates that the optimized algorithm model has good generalization ability and high fault recognition accuracy.

    • Reliability Assessment of Meta-action Unit Integrating Lifetime Information and Multi-performance Degradation Information

      2025, 52(2):109-121.

      Abstract (44) HTML (0) PDF 22.84 M (16) Comment (0) Favorites

      Abstract:To address the challenges of machine tool reliability modeling and the lack of reliability data, a reliability assessment method integrating lifetime information with multi-performance degradation information is proposed, starting from the basic motion units. Using the function-motion-action (FMA) decomposition method, the machine tool is broken down into its smallest motion units, i.e., the meta-action units. The reliability level of the machine tool is ensured by accurately assessing the reliability of the key elemental action units. A non-linear Wiener process model under random effects is developed to capture individual variations, shared characteristics, and non-linearity in degradation processes. To address limited degradation data, a reliability model incorporating failure life information is established using Bayesian methods. Finally, considering correlations among multiple performance degradation failures, a comprehensive reliability assessment model is formulated using the Copula function, with parameter estimation achieved via the MCMC-Gibbs sampling algorithm. Focusing on the worm gear rotation meta-action unit of a specific computerized numerical control gear hobbing machine, case studies and comparative analysis highlight the method’s feasibility and superiority.

    • System Reliability Analysis Method Based on Parametric Probability Box Model

      2025, 52(2):122-132.

      Abstract (41) HTML (0) PDF 9.95 M (13) Comment (0) Favorites

      Abstract:An efficient system reliability analysis method with a parametric probability box (p-box) model is proposed to solve the problem that the mixture of aleatory and epistemic uncertainty exists in mechanical systems. Firstly, the minimum reliability index of the single failure mode is obtained based on the sequential iteration decoupling method. Then, aiming at the multiple failure modes problem under the mixture of aleatory and epistemic uncertainty, the system reliability analysis model is established based on the parametric p-box uncertainty. Considering the correlation among the failure modes, the correlation coefficient matrix between each failure mode is calculated by the linear correlation degree analysis method. Finally, a reliability calculation method for both series and parallel systems is proposed, which has high reliability calculation efficiency and can meet the practical engineering requirements compared with the traditional double-loop Monte Carlo sampling method.

    • Braking Torque Enhancement Method of Star Sealing for Permanent Magnet Synchronous Traction Machines in Elevator System

      2025, 52(2):133-139.

      Abstract (40) HTML (0) PDF 8.49 M (12) Comment (0) Favorites

      Abstract:The braking torque of an elevator with contactor star sealing or conventional electronic star sealing is decreased at medium and high speeds, to ensure safe and effective braking when the elevator loses control in the medium and high speeds scenario, an electronic star sealing method based on optimal resistance is proposed in this paper, where the braking torque can be enhanced by the original drive system without any additional devices. The braking characteristic varies with different stator resistance when the conventional contactor star sealing is employed. By analyzing the relationship between phase voltage and current with a fixed PWM (pulse-width modulation) duty during electronic star sealing, the relationship between virtual resistance and PWM duty is disclosed. Then, it dynamically changes the PWM duty based on the current amplitude, DC-link voltage and rotational speed, thereby changing the equivalent resistance of the permanent magnet synchronous traction machine, and ensuring that it is equal to the optimal resistance for the maximum braking torque, so as to enhance the braking torque. Finally, the feasibility and correctness of the proposed method were verified through experiments, and the braking torque at medium and high speeds is increased significantly compared with the conventional electronic star sealing.

    • High-precision Pipelined-successive Approximation Register Hybrid Analog-to-digital Converter Design

      2025, 52(2):140-150.

      Abstract (42) HTML (0) PDF 16.35 M (13) Comment (0) Favorites

      Abstract:To meet the requirements of the readout circuit of the photodiode array in the digital X-ray system for an analog-to-digital converter (ADC) with superior average performance, a high-precision pipelined-successive approximation register analog-to-digital converter is designed. It features a gain-enhanced amplifier structure with a pre-amplification stage to realize the high efficiency amplifier. The use of the least significant bit (LSB) averaging noise-resistant method simplifies the structure of the second-stage comparator, effectively reducing overall system power consumption. The self-adjusted comparator clock is also realized using a feedback loop based on a delay-locked loop (DLL), enhancing asynchronous timing robustness. The ADC circuit design, layout, and post-simulation verification were completed using the 0.18 μm EPI BCD process. Under 5.0 V supply voltage and 5 MS/s sampling rate conditions, the ADC achieves an ENOB of 15.61 bits, an SNDR of 95.73 dB, and an SFDR of 110.72 dB.

    • Active Damping Predictive Dead-beat Average Model Control for LCL Grid-tied Inverter

      2025, 52(2):151-163.

      Abstract (44) HTML (1) PDF 20.10 M (12) Comment (0) Favorites

      Abstract:To address the inherent resonance issue of LCL grid-connected inverters, the optimized current control method and active damping method are proposed. To minimize the influence of digital system delays on current control and active damping, the deadbeat average model and compound delay elimination method are proposed. Because the control model is the basis of current control and time-delay compensation, a deadbeat average model for inverter-side current feedback control is established by introducing an oversampling method and incorporating signal processing method. This approach transforms the conventional single-sample instantaneous control into multi-sample average control, which improves the accuracy of the control model. Based on the established model, a predictive dead-beat average model (PDBAM) control method is proposed through the introduction of predictive control combined with the double-updated PWM method, which provides accurate delay compensation and improves the stability and robustness of the system. Based on PDBAM control, the average capacitor-voltage feedforward method is proposed, which eliminates the influence of digital delay on active damping and further strengthens the robustness of the system under weak grid conditions. The experimental results prove the effectiveness of the proposed method in this paper.

    • High Order Sliding Mode Control of Three-phase Staggered Parallel Bidirectional DC-DC Converter Based on Flat Theory

      2025, 52(2):164-175.

      Abstract (39) HTML (0) PDF 7.69 M (16) Comment (0) Favorites

      Abstract:This paper addresses the issue of bus voltage fluctuations caused by uncertain factors, such as power fluctuations in distributed photovoltaic systems and frequent switching of loads in direct current (DC) microgrids. The study focuses on a three-phase interleaved parallel bidirectional DC-DC converter in the energy storage unit of the microgrid and proposes a differential flatness-based and improved super-twisting sliding mode dual closed-loop composite control strategy based on a cascade finite-time extended state observer (CFT-ESO). Firstly, a mathematical model of the three-phase interleaved parallel bidirectional DC-DC converter is established. The DC system is transformed into a differentially flat system based on the theory of differential flatness. The estimation accuracy of the system’s total disturbance is improved by combining a two-level finite-time extended state observer with fast convergence. Secondly, a dual closed-loop control system is employed, with inner-loop differential flatness control and outer-loop improved super-twisting sliding mode control. This control strategy not only enhances the dynamic response of the system but also suppresses chattering using a higher-order sliding mode control algorithm, while addressing the non-minimum phase problem in the boost mode of the converter. Next, the stability of the control system is proven using Lyapunov theory. Finally, the control strategy is validated through simulations using MATLAB/Simulink software and an experimental platform. The results demonstrate that the proposed control approach effectively mitigates disturbances and improves the transient performance of the system.

    • Event-triggered Predictive Control for Linear Systems Based on Variable Horizon Strategy

      2025, 52(2):176-185.

      Abstract (39) HTML (0) PDF 1.63 M (14) Comment (0) Favorites

      Abstract:In this paper, an event-triggered model predictive control scheme based on a variable horizon strategy is proposed for constrained continuous linear time-invariant systems with additive disturbances. Firstly, an event-triggered mechanism without Zeno behavior is designed based on the deviation between the optimal state trajectory and the actual state trajectory to reduce the frequency of solving optimization problem. Next, in order to reduce the computational complexity of solving optimization problem when the actual state approaches the terminal set, a more efficient adaptive prediction horizon update mechanism in the form of exponential shrinkage is designed. Then, based on the dual-mode control strategy, an adaptive event-triggered model predictive control algorithm is proposed, and sufficient conditions are provided to ensure the feasibility of the algorithm and the stability of the closed-loop system. Finally, the effectiveness of the proposed algorithm is verified based on a mass-spring-damper system, and the results show that the proposed scheme can effectively reduce system resource consumption and computational complexity for solving optimization problem without losing control performance.

    • Analysis on Anti-galloping Effect of Catenary Positive Feeder Aerodynamic Damping Sheet in Strong Wind Area

      2025, 52(2):186-198.

      Abstract (38) HTML (0) PDF 34.81 M (15) Comment (0) Favorites

      Abstract:To suppress great galloping under the influence of the wind-break wall wake for the catenary positive feeder of the Lanzhou-Urumqi high-speed railway in the strong wind area, based on the aerodynamic theory, the geometric model of the catenary positive feeder after installing the aerodynamic damping sheet is established. The fluid-solid two-way coupling solution of the galloping response of the positive feeder is realized by combining the user-defined program (UDF) and the dynamic mesh technology. The results show that the galloping amplitude of the positive feeder is the smallest when the installation angle of the fixed aerodynamic damping sheet is 140°. The suspended aerodynamic damping sheet is suspended vertically downward and has a galloping suppression effect after installation. When the length of the damping sheet structure of different suspension modes is 0.75D, the galloping amplitude of the positive feeder reaches the minimum, and the aerodynamic damping sheet has the best galloping suppression effect. The aerodynamic damping sheet also has a certain weight effect to offset part of the vertical wind load, which is more suitable for the operating environment of the high wind section of the catenary of Lanzhou-Urumqi high-speed railway, and it is recommended to use the metal material aerodynamic damping sheet. After installing the aerodynamic damping sheet, the channel of the air flow through the wire is limited, resulting in pressure difference and further leading to slowing down the air flow rate, enhancing the aerodynamic resistance, consuming the energy brought by the vibration of the wire, and reducing the amplitude and frequency of the vibration.

    • Flashover Characteristics and Simulation Analysis of Bird Droppings on 110 kV Insulated Coated Drainage Line

      2025, 52(2):199-208.

      Abstract (39) HTML (0) PDF 34.22 M (21) Comment (0) Favorites

      Abstract:To reduce the probability of such flashover accidents caused by bird droppings, a new type of insulated coated drainage line was developed. This line utilized high-performance silicone rubber insulating materials to fully coat the steel-cored aluminum strand, and an umbrella skirt was installed on the surface of the drainage line. Simulation analysis was conducted to examine the influence of the silicone rubber insulation layer and bird droppings on the spatial electric field distribution of the drainage line. The flashover characteristics of insulated coated drainage lines against bird droppings were studied by simulation test. The simulation results show that with the increase of the thickness of the insulating layer, the surface electric field intensity decreases gradually. As the thickness of the semiconductor layer increases, the electric field intensity on the surface of the drainage line decreases. The test results show that the insulation layer coated by bare wire can significantly improve the insulation performance of the drainage line, and the silicone rubber insulation coating is obviously better than the buckled silicone rubber insulation sheath. Every 1 mm increase in the thickness of the silicone rubber insulation layer results in breakdown voltage increases of about 10.7 kV, and the semiconductor layer can further improve the insulation performance. The umbrella skirt can effectively prevent the spread of the arc on the surface of the insulated coated drainage line.

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