Equivalent Bar Conceptions for Computer Analysis of Pantographic Foldable Structures

An equivalent bar conception is firstly developed for the computer analysis of pantographic foldable structures. The uniplet of two three node beam elements is assumed as a six bar assembly with respect to least norm least square solution for the elastic strain energy equality. The equilibrium equation is developed for the equivalent models, and the internal forces formulated sequently for backup calculation. This procedure is proved practical for some engineering, and some interesting concepts proposed. Finally, three numerical tests are presented.

Numerical Study on Reduction in Aerodynamic Drag and Noise of High-Speed Pantograph

Reducing the aerodynamic drag and noise levels of high-speed pantographs is important for promoting environmentally friendly,energy efficient and rapid advances in train technology.Using computational fluid dynamics theory and the K-FWH acoustic equation,a numerical simulation is conducted to investigate the aerodynamic characteristics of high-speed pantographs.A component optimization method is proposed as a possible solution to the problemof aerodynamic drag and noise in high-speed pantographs.The results of the study indicate that the panhead,base and insulator are the main contributors to aerodynamic drag and noise in high-speed pantographs.Therefore,a gradual optimization process is implemented to improve the most significant components that cause aerodynamic drag and noise.By optimizing the cross-sectional shape of the strips and insulators,the drag and noise caused by airflow separation and vortex shedding can be reduced.The aerodynamic drag of insulator with circular cross section and strips with rectangular cross section is the largest.Ellipsifying insulators and optimizing the chamfer angle and height of the windward surface of the strips can improve the aerodynamic performance of the pantograph.In addition,the streamlined fairing attached to the base can eliminate the complex flow and shield the radiated noise.In contrast to the original pantograph design,the improved pantograph shows a 21.1%reduction in aerodynamic drag and a 1.65 dBA reduction in aerodynamic noise.

Modelling dynamic pantograph loads with combined numerical analysis

Appropriate interaction between pantograph and catenary is imperative for smooth operation of electric trains.Changing heights of overhead lines to accommodate level crossings,overbridges,and tunnels pose significant challenges in maintaining consistent current collection performance as the pantograph aerodynamic profile,and thus aerodynamic load changes significantly with operational height.This research aims to analyse the global flow characteristics and aerodynamic forces acting on individual components of an HSX pantograph operating in different configurations and orientations,such that the results can be combined with multibody simulations to obtain accurate dynamic insight into contact forces.Specifically,computational fluid dynamics simulations are used to investigate the pantograph component loads in a representative setting,such as that of the recessed cavity on a Class 800 train.From an aerodynamic perspective,this study indicates that the total drag force acting on non-fixed components of the pantograph is larger for the knuckle-leading orientation rather than the knuckle-trailing,although the difference between the two is found to reduce with increasing pantograph extension.Combining the aerodynamic loads acting on individual components with multibody tools allows for realistic dynamic insight into the pantograph behaviour.The results obtained show how considering aerodynamic forces enhance the realism of the models,leading to behaviour of the pantograph-catenary contact forces closely matching that seen in experimental tests.

Aerodynamic Analysis and Optimization of Pantograph Streamline Fairing for High-Speed Trains

A pantograph serves as a vital device for the collection of electricity in trains.However,its aerodynamic resistance can limit the train’s running speed.As installing fairings around the pantograph is known to effectively reduce the resistance,in this study,different fairing lengths are considered and the related aerodynamic performances of pantograph are assessed.In particular,this is accomplished through numerical simulations based on the k-ωShear Stress Transport(SST)two-equation turbulence model.The results indicate that the fairing diminishes the direct impact of high-speed airflow on the pantograph,thereby reducing its aerodynamic resistance.However,it also induces interferences in the flow field around the train,leading to variations in the aerodynamic resistance and lift of train components.It is shown that a maximum reduction of 56.52%in pantograph aerodynamic resistance and a peak decrease of 3.38%in total train aerodynamic resistance can be achieved.

Experimental and Numerical Investigation on the Aerodynamic Characteristics of High-Speed Pantographs with Supporting Beam Wind Deflectors

Aiming to mitigate the aerodynamic lift force imbalance between pantograph strips,which exacerbates wear and affects the current collection performance of the pantograph-catenary system,a study has been conducted to support the beam deflector optimization using a combination of experimental measurements and computational fluid dynamics(CFD)simulations.The results demonstrate that the size,position,and installation orientation of the wind deflectors significantly influence the amount of force compensation.They also indicate that the front strip deflectors should be installed downwards and the rear strip deflectors upwards,thereby forming a“π”shape.Moreover,the lift force compensation provided by the wind deflectors increases with the size of the deflector.Alternative wind compensation strategies,such as control circuits,are also discussed,putting emphasis on the pros and cons of various pantograph types and wind compensation approaches.

非线性随机Pantograph微分方程及其θ-方法的均方渐近稳定性

本文主要研究了非线性随机Pantograph微分方程,讨论了其零解的均方渐近稳定性并给出了零解均方渐近稳定的充分条件.在本文的第三部分,我们将随机θ-方法应用于这类问题,获得了数值解均方渐近稳定条件.

一类比例延迟系统的散逸性

讨论了一类比例延迟系统的散逸性,并证明了变步长Euler方法应用于该系统后仍然保留其散逸性。

单支方法关于多延迟Pantograph方程的稳定性分析

本文主要讨论了单支方法关于多延迟pantograph方程解的存在唯一性及渐近稳定性 ,同时将非线性多延迟系统数值解的有关结论推广到多延迟pantograph方程 ,证明了单支方法对于ODEs的A(α) 稳定等价于单支方法关于多延迟pantograph方程NGPk(α) 稳定 .

The Geometry of Felix Escrig. Simplified ModellingTechniques for Modular Deployable Structures ofExpandable Frames

This paper catalogues the morphology of modular deployable structures of expandable frames developed by the late Felix Escrig at the University of Seville, Spain. The research describes the geometric logic behind these structures, proposes simplified graphic methods for their design, and outlines their characteristics according to their level of geometric precision, structural stability and deployability. Finally, the paper establishes tools and guidelines for their future development.

Runge-Kutta方法关于无穷延迟系统的稳定性分析

主要针对无穷延迟Pantograph方程构造了Runge-Kutta数值方法,并讨论了此方法在一定的条件下是p-稳定的和弱p-稳定的.

Optimization of high-speed railway pantographs for improving pantograph-catenary contact

A crucial system for the operation of high-speed trains is the pantograph catenary interface as it is the sole responsible to deliver electrical power to the train. Being the catenary a stationary system with a long lifespan it is also less likely to be redesigned and upgraded than the pantographs that fit the train vehicles. This letter proposes an optimization procedure for the improvement of the contact quality between the pantograph and the catenary solely based on the redesign of the pantograph head suspension characteristics. A pantograph model is defined and validated against experimental dynamic characteristics of existing pantographs. An optimization strategy based on the use of a global optimization method, to find the vicinity of the optimal solution, followed by the use of a deterministic optimization algorithm, to fine tune the optimal solution, is applied here. The spring stiffness, damping characteristics and bow mass are the design variables used for the pantograph optimization. The objective of the optimal problem is the minimization of the standard deviation of the contact force history, which is the most important quantity to define the contact quality. The pantograph head suspension characteristics are allowed to vary within technological realistic limits. It is found that current high-speed railway pantographs have a limited potential for mechanical improvements, not exceeding 10% 15% on the decrease of the standard deviation of the contact force. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301306]

Numerical investigation of influence of pantograph parameters and train length on aerodynamic drag of high-speed train

This study investigates the influence of different pantograph parameters and train length on the aerodynamic drag of high-speed train by the delayed detached eddy simulation(DDES) method. The train geometry considered is the high-speed train with pantographs, and the different versions have 3, 5, 8, 10, 12, 16 and 17 cars. The numerical results are verified by the wind tunnel test with 3.6% difference. The influences of the number of cars and the position, quantity and configuration of pantographs on flow field around high-speed train and wake vortices are analyzed. The aerodynamic drag of middle cars gradually decreases along the flow direction. The aerodynamic drag of pantographs decreases with its backward shift, and that of the first pantograph decreases significantly. As the number of pantographs increases, its effect on the aerodynamic drag decrease of rear cars is more significant. The engineering application equation for the aerodynamic drag of high-speed train with pantographs is proposed. For the 10-car and 17-car train, the differences of total aerodynamic drag between the equation and the simulation results are 1.2% and 0.4%, respectively. The equation generalized in this study could well guide the design phase of high-speed train.

Pantograph and catenary system with double pantographs for high-speed trains at 350 km/h or higher

The paper is aimed at developing an optimized design of the pantograph and catenary system with double pantographs at a speed of 350 km/h for the Wuhan-Guangzhou high-speed railway. First, the pantograph and catenary system for the Beijing-Tianjin high-speed railway was analyzed to verify whether its design objective could be fulfilled. It shows that the system is not able to satisfy the requirement of a sustainable running speed of 350 km/h. Then a new scheme for the pantograph and catenary system is proposed through optimization and renovation of the structure and parameters of the pantograph and catenary system, including the suspension type of the catenary, tension of the contact wire, and space between two pantographs. Finally, the dynamic performance of the new system was verified by simulation and line testing. The results show that the new scheme of the pantograph and catenary system for the Wuhan- Guangzhou high-speed railway is acceptable, in which the steady contact between the rear pantograph and the catenary at the space of 200 m can be maintained to ensure the current-collection quality. A current collection with double pantographs at a speed of 350 km/h or higher can be achieved.

Numerical Study on Aerodynamic Performance of High-Speed Pantograph with Double Strips

Pantograph is a critical component of the high-speed train.It collects power through contact with catenary,which significantly affects the running safety of the train.Pantograph with double collector strips is one common type.The aerodynamic performance of the collector strips may affect the current collection of the pantograph.In this study,the aerodynamic performance of the pantograph with double strips is investigated.The numerical results are consistent with the experimental ones.The error in the aerodynamic drag force of the pantograph between numerical and experimental results is less than 5%.Three different conditions of the strips are studied,including the front strip,the rear strip,and the double strips.Results show that the presence of the front strip will affect the lift force of the rear strip,and reduce the resistance of the rear strip under the opening condition.Meanwhile,the rear strip has few effects on the front strip under the opening operation condition.The law of the resistance for the interaction between two strips under the closing condition is similar to the opening one.

Influence of pantograph fixing position on aerodynamic characteristics of high-speed trains

To study the influence of the pantograph fixing position on aerodynamic characteristics of high-speed trains, the aerodynamic models of high-speed trains with eight cars were established based on the theory of com- putational fluid dynamics, and eight cases with pantographs fixed on different positions and in different operational orientations were considered. The pantographs were fixed on the front or the rear end of the first middle car or fixed on the front or the rear end of the last middle car. The external flow fields of the high-speed trains were numeri- cally simulated using the software STAR-CCM＋. The results show that the pantograph fixing position has little effect on the aerodynamic drag force of the head car and has a large effect on the aerodynamic drag force of the tail car. The influences of the pantograph fixing position on the aerodynamic lift forces of the head car, tail car and pan- tographs are obvious. Among the eight cases, considering the total aerodynamic drag force of the train and the aerodynamic lift force of the lifted pantograph, when the pantographs are fixed on the rear end of the last middle car and the lifted pantograph is in the knuckle-upstream ori- entation, the aerodynamic performance of the high-speed train is the best.

Pantograph-catenary electrical contact system of high-speed railways:recent progress,challenges,and outlooks

As the unique power entrance,the pantograph-catenary electrical contact system maintains the efficiency and reliability of power transmission for the high-speed train.Along with the fast development of high-speed railways all over the world,some commercialized lines are built for covering the remote places under harsh environment,especially in China;these environmental elements including wind,sand,rain,thunder,ice and snow need to be considered during the design of the pantograph-catenary system.The pantograph-catenary system includes the pantograph,the contact wire and the interface—pantograph slide.As the key component,this pantograph slide plays a critical role in reliable power transmission under dynamic condition.The fundamental material characteristics of the pantograph slide and contact wire such as electrical conductivity,impact resistance,wear resistance,etc.,directly determine the sliding electrical contact performance of the pantograph-catenary system;meanwhile,different detection methods of the pantograph-catenary system are crucial for the reliability of service and maintenance.In addition,the challenges brought from extreme operational conditions are discussed,taking the Sichuan-Tibet Railway currently under construction as a special example with the high-altitude climate.The outlook for developing the ultra-high-speed train equipped with the novel pantograph-catenary system which can address the harsher operational environment is also involved.This paper has provided a comprehensive review of the high-speed railway pantograph-catenary systems,including its progress,challenges,outlooks in the history and future.

Fatigue life evaluation on key components of high-speed railway catenary system

The fatigue load spectrum and operation life evaluation of key components in the catenary system under the high speed train running condition were investigated.Firstly,based on the catenary model and pantograph model,the couple dynamic equations of pantograph–catenary were built with the Lagrange’s method;then the dynamic contact force was obtained by the Newmark method at the train speeds of 250,280 and 300 km/h,respectively.Secondly,the finite element model(FEM)of one anchor section’s catenary was built to analyze its transient response under the contact force as train running;then the loading time history of messenger wire base,steady arm,registration tube,oblique cantilever,and straight cantilever were extracted.Finally,the key components’fatigue spectrum was carried out by the rain-flow counting method,and operation life was estimated in consideration of such coefficients,such as stress concentration,shape and dimension,surface treatment.The results show that the fatigue life of the catenary system reduces with the increasing of train speed;specifically,the evaluated fatigue life of the steady arm is shorter than other components.

Numerical Simulation of the Aeroacoustic Performance of the DSA380 High-Speed Pantograph Under the Influence of a Crosswind

The object of research of this paper is the DSA380 high-speed pantograph.The near-field unsteady flow around the pantograph was investigated using large eddy simulation(LES)while the far-field aerodynamic noise was analysed in the frame of the Ffowcs Williams-Hawkings(FW-H)acoustic analogy.According to the results,the contact strip,base frame and knuckle are the main aerodynamic noise sources,with vortex shedding,flow separation and recombination around the pantograph being related key physical factors.The aerodynamic noise radiates outwards in the form of spherical waves when the distance of the noise receiving point is farther than 8 m.The sound pressure level(SPL)grows approximately as the 6th power of pantograph operating speed.The aerodynamic noise energy is mainly concentrated in the region of 400-1000 Hz,and the frequency band is wider with crosswind than without crosswind.The peak frequency displays a linear relationships with the operating speed and crosswind velocity,respectively.The aerodynamic and aeroacoustic generation from the knuckle-downstream orientation of the pantograph is superior to those of the knuckle-upstream orientation model.This finding may be used for the optimal design of future pantograph configurations in the presence of crosswind.

Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph

Aiming at the problem that aerodynamic uplift forces of the pantograph running in the knuckle-downstream and knuckle-upstream conditions are inconsistent,and their magnitudes do not satisfy the corresponding standard, the aerodynamic uplift forces of pantographs with baffles are numerically investigated, and an optimization method to determine the baffle angle is proposed. First, the error between the aerodynamic resistances of the pantograph obtained by numerical simulation and wind tunnel test is less than 5%, which indicates the accuracy of the numerical simulation method. Second, the original pantograph and pantographs equipped with three different baffles are numerically simulated to obtain the aerodynamic forces and moments of the pantograph components.Three different angles for the baffles are-17°, 0° and 17°.Then the multibody simulation is used to calculate the aerodynamic uplift force of the pantograph, and the optimal range for the baffle angle is determined. Results show that the lift force of the baffle increases with the increment of the angle in the knuckle-downstream condition, whereas the lift force of the baffle decreases with the increment of the angle in the knuckle-upstream condition. According to the results of the aerodynamic uplift force, the optimal angle of the baffle is determined to be 4.75° when the running speed is 350 km/h, and pantograph–catenary contact forces are 128.89 N and 129.15 N under the knuckledownstream and knuckle-upstream operating conditions,respectively, which are almost equal and both meet the requirements of the standard EN50367:2012.

On aerodynamic noises radiated by the pantograph system of high-speed trains

Pantograph system of high-speed trains become significant source of aerodynamic noise when travelling speed exceeds 300 km/h. In this paper, a hybrid method of non-linear acoustic solver （NLAS） and Ffowcs Williams-Hawkings （FW-H） acoustic analogy is used to predict the aerodynamic noise of pantograph system in this speed range. When the simulation method is validated by a benchmark problem of flows around a cylinder of finite span, we calculate the near flow field and far acoustic field surrounding the pantograph system. And then, the frequency spectra and acoustic attenuation with distance are analyzed, showing that the pantograph system noise is a typical broadband one with most acoustic power restricted in the medium-high frequency range from 200 Hz to 5 kHz. The aerodynamic noise of pantograph systems radiates outwards in the form of spherical waves in the far field. Analysis of the overall sound pressure level （OASPL） at different speeds exhibits that the acoustic power grows approximately as the 4th power of train speed. The comparison of noise reduction effects for four types of pantograph covers demonstrates that only case 1 can lessen the total noise by about 3 dB as baffles on both sides can shield sound wave in the spanwise direction. The covers produce additional aerodynamic noise themselves in the other three cases and lead to the rise of OASPLs.