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The most vulnerable element of modern electric buses, which are dynamically charged, are pantographs. The article describes the main reasons for the wear and tear of pantographs. The calculation of the probability of failure-free operation of the pantograph systems is made.

Increasing the speed of a pantograph deteriorates its aerodynamic performance and aggravates the problem of flow-induced vibration, which is not conducive to the stability of the pantograph - catenary system (PCS). Currently, commercial high-speed trains operate at speeds exceeding 350 km/h, with line test speeds exceeding 450 km/h, making the impact of airflow on pantograph dynamics increasingly significant. Therefore, a simulation study on the bidirectional coupling between pantograph aerodynamics and structural dynamics is urgently needed. This study proposes a bidirectional coupling method for the pantograph based on overset grids. The user-defined functions (UDF) in Fluent enable real-time data exchange between aerodynamic forces and structural displacements. The flow field was modelled using the Shear Stress Transport k-ω turbulence model and Reynolds-averaged Navier - Stokes equations, and the dynamics is computed by Newmark-Beta solving the differential equations. It was found that the calculation method in this study was reliable and efficient. The motion of the pantograph assembly in the flow field will change the airflow mode, thus affecting the aerodynamic characteristics of the assembly, and the high-frequency and stochastic aerodynamic excitation will lead to an increase in vibration of the pantograph assembly, especially at the contact strip. For example, when the pantograph operated in the knuckle-upstream direction at 450 km/h, it exhibited poor PCS interaction, with a mean contact force of 50 N, a standard deviation of 36 N, and an overall offline rate of 7%. This study introduced a novel approach to pantograph fluid - structure coupling, offering valuable insights for predicting high-speed pantograph performance and evaluating PCS interactions.

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.

This paper is concerned with the application of the spectral tau and collocation methods to delay multi-order fractional differential equations with vanishing delay r x ( 0 < r < 1 ) . The fractional derivatives are described in the Caputo sense. The model solution is expanded in terms of Chebyshev polynomials. The convergence of the proposed approaches is investigated in the weighted L 2 -norm. Numerical examples are provided to highlight the convergence rate and the flexibility of this approach. Our results confirm that nonlocal numerical methods are best suited to discretize fractional differential equations as they naturally take the global behavior of the solution into account.

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.

We study sequential fractional pantograph q-differential equations. We establish the uniqueness of solutions via Banach’s contraction mapping principle. Further, we define and study the Ulam–Hyers stability and Ulam–Hyers–Rassias stability of solutions. We also discuss an illustrative example.

In the pantograph-catenary sliding electrical contact of an electrified railway, friction and conduction are coplanar, which determines that pantograph-catenary friction and current collection are interactive. In order to study the coupling relationship between friction and wear and current receiving quality, based on experimental data, the evaluation index system of friction and wear and current receiving quality is established. The coupling coordination model of friction and wear and current receiving quality is constructed by the entropy method and coupling coordination degree, and its comprehensive level, coupling correlation degree, and coordination degree are studied. The results show that they are in a state of high coupling interval aggregation, and the coordination value first decreases and then increases with the increase in current. According to the coupling and coordination characteristics under different conditions, it provides a basis for the selection of pantograph-catenary system operating conditions and the formulation of optimization strategies.

Accurate pantograph models are crucial to obtain reliable simulations of the pantograph-catenary dynamic interaction. Non-linearities can make it a challenge to find a model design that fits the dynamic behaviour of the real pantograph. In this work, we propose a novel pantograph model including a particular non-linear mechanism, whose dynamic behaviour significantly affects the pantograph response. This mechanism is composed of two rigid bars and an oblique pre-stressed spring with dry friction and exhibits a complex non-linear behaviour. The objective is to design a model capable of reproducing the behaviour of the real pantograph, which is represented by the dataset of dynamic measurements in the pantograph tests. From a proper parametric representation of the model, the optimisation of the parameters by a genetic algorithm has achieved a good agreement with the experimental data. The resulting optimised model behaves similarly to the real pantograph for a wide range of excitations that vary in type, amplitude and position. Since the higher number of simulations performed in the optimisation makes it necessary to use an efficient simulation tool, we propose an efficient strategy to integrate systems with Coulomb’s friction.

This paper presents a new computational technique for solving fractional pantograph differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use Müntz-Legendre wavelet and its operational matrix of fractional-order integration. First, the Müntz-Legendre wavelet is presented. Then a family of piecewise functions is proposed, based on which the fractional order integration of the Müntz-Legendre wavelets are easy to calculate. The proposed approach is used this operational matrix with the collocation points to reduce the under study problem to a system of algebraic equations. An estimation of the error is given in the sense of Sobolev norms. The efficiency and accuracy of the proposed method are illustrated by several numerical examples.

The emissions from traditional fossil heavy-duty trucks have become a conspicuous issue worldwide. The electrical road system (ERS) can offer a viable solution for achieving zero CO2 emissions and has high energy efficiency in long-distance road cargo transport. While many kinds of pantograph structures have been developed for the ERS, their corresponding pantograph-catenary dynamic characteristics under different road conditions have not been investigated. This work performs a numerical study on the dynamics of the pantograph-catenary interaction of an ERS considering different pantograph structures. First, a pantograph-catenary-truck-road model is proposed. The reduced catenary model and reduced-plate model transmission method are used to minimize model scale. Three different types of ERS pantograph structures are considered in the model. After validation, the pantograph-catenary dynamics under the influence of truck-road interactions with complex road roughness and different pantographs are studied and compared. The corresponding vibration transmission mechanism is further focused. The results show that the truck-road interaction has a significant effect on the pantograph-catenary interaction, but the pantograph with only one lower and upper arm can isolate the roll vibration motion transmission from the truck to the collector head, which has the best dynamic performance and is suggested for use in the ERS.