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This paper aims to enhance the speed of rigid overhead systems by investigating the impact of important parameters of the overhead system and pantograph on the interaction performance, specifically the contact force between the panhead of the pantograph and the contact wire of the overhead system. To accomplish this, this paper first builds a rigid overhead system model based on the finite element method. The pantograph–contact wire interaction simulation is achieved by including a three-stage lumped mass pantograph model. The Sobol sensitivity analysis method is utilised to determine the contribution of different parameters to the contact force standard deviation. Subsequently, an optimisation approach is used to minimise the contact standard deviation at various speeds by adopting five crucial parameters. The sensitivity analysis of 13 variables indicates that the span length, bending stiffness, and linear density of the conductor rail, and the masses of the pantograph head and upper frame are the most relevant variables for the contact force standard deviation. The quantification of each parameter’s contribution reveals that the increase in bending stiffness generally has a positive effect in reducing the contact force fluctuation, while the decreases in other variables are preferred. The optimisation analysis shows that the optimised contact force standard deviation decreases by 39.18%, 66.77%, and 61.02% at speeds of 90 km/h, 120 km/h, and 150 km/h, respectively, compared to the original values.

As a common disturbance to the railway pantograph-catenary system, the crosswind may deteriorate the current collection quality and threat operational safety. The main topic of this paper is to study the effect of crosswind on the interaction performance of pantograph-catenary considering the aerodynamic forces acting on both the pantograph and catenary. The pantograph-catenary system of the Chengdu-Chongqing passenger special railway is adopted as the analysis object. The absolute nodal coordinate formulation (ANCF) is employed to build the catenary model, of which the numerical accuracy is validated via the comparison with the field measurement data collected from an inspection vehicle operating at 378 km/h. A special spatial grid is defined for the pantograph-catenary system to generate the stochastic wind field based on the empirical spectrum. According to the quasi-steady theory, the wind load acting on the catenary is derived. Computational fluid dynamics (CFD) is employed to calculate the lift and drag forces acting on each component of the pantograph, which are used to derive the equivalent aerodynamic force that can be applied in the lumped-mass model. The simulation results indicate that the pantograph-catenary system of Chengdu-Chongqing passenger special railway has an acceptable performance with a crosswind speed of 20 m/s. But when the crosswind increases up to 30 m/s, some contact force statistics exceed the safety threshold with a turbulence intensity of more than 17%. Through the analysis of the operational safety, it is found that the contact wire always works within the safety range of the pantograph head with a crosswind speed of 30 m/s. But some safety issues can be seen from the maximum uplift of the pantograph head with a turbulence intensity of more than 21%.

When two electric multiple units are non-electrically connected together for improving the transport capacity in high-speed railways, double pantographs frequently operate simultaneously to decrease the current capacity on a single pantograph collector. In this case, the contact force between the trailing pantograph and the catenary severely fluctuates due to the wave propagation along the catenary triggered by the leading pantograph. Therefore, this paper proposes two estimator-based H ∞ control strategies for active double-pantograph to decrease the contact force fluctuation considering the actuator time delay. To obtain the pantograph states, a robust recursive state estimation method is presented, which can effectively deal with randomly missing measurements. In addition, to overcome parametric uncertainties and non-differentiable actuator time delay, two robust multi-objective H ∞ controllers involving linear matrix inequalities are introduced according to whether the time delay can be predetermined or not. The effectiveness and robustness of the control strategies are investigated through implementing a nonlinear double-pantograph-catenary system model. Simulation results show that, for both the leading pantograph and the trailing pantograph, the proposed control strategies can decrease the contact force fluctuation with high efficiency even though the actuator time delay exists.

The numerical tools can be used to facilitate the design of the railway pantograph-catenary system. The validation of the current numerical results is mostly performed at a speed slower than 350 km/h. This paper aims at the validation and analysis of the numerical results at a super-high-speed. The catenary model is constructed based on a nonlinear finite element approach employing the absolute nodal coordinate formulation. A multibody dynamics model is adopted to represent the pantograph. The measurement data are collected by an inspection vehicle equipped with an instrumented pantograph operating at 378 km/h in Chengdu-Chongqing high-speed line. Comparing the numerical simulation and the field test shows that the present pantograph-catenary model can provide reliable numerical results at 378 km/h. The numerical analysis of pantograph-catenary interaction at super-high-speed shows that the trailing pantograph performance does not comply with the assessment standard at 378 km/h. The adjustment of double-pantograph interval and messenger wire tension can effectively improve the trailing pantograph performance.

The numerical tools are widely used to facilitate the design of the railway catenary. Only radical results are obtained as the current assessment is generally performed without any practical errors. In this paper, the most common error, the contact line height variability, is appropriately included in evaluating the current collection quality. Based on the real-life contact line height data collected from a high-speed network, the heights of the key points in the contact line are extracted, of which the pointwise stochastics is represented by the PSD function. Random samples are generated by the inverse Fourier transform based on the Monte Carlo method. An advanced initialisation procedure is presented to properly include the contact line height variability in the initial configuration. A stochastic analysis with a high cut-off frequency is performed to evaluate a double pantographs-catenary system’s current collection quality. Unlike the deterministic result obtained by the perfect design data, the contact line height variability causes uncertainty. The present analysis method indicates some risks of safety accident and contact loss which the traditional simulation cannot capture with ideal design data or low cut-off frequency.

An analytical model is used to study the wave propagation property in the high-speed railway catenary system subjected to a moving pantograph. The contact and messenger wires are modelling by tensioned cables. The Fourier transform is exploited to find out the solution of the governing equation of the tensioned cable, whose vertical deflection is assumed as the superposition of two waves propagating to opposite sides. Through applying the boundary conditions of a real railway catenary system, the wave propagation model of the catenary system is constructed. The effect of the messenger/contact wire tensions on the wave reflection and transmission at the dropper point is analysed. On the basis of a complete model subjected to a moving load, the wave propagation behaviour in the contact wire is analysed. The results demonstrate that several groups of dominant wave frequencies can be observed from the forward and backward waves under the excitation of a constant moving load. Two significant wave components are introduced by a time-varying moving load due to the Doppler Effect. The effect of the matching between the dominant wave frequencies and the natural frequencies sensitive to the moving load on the contact quality is investigated in combination with a realistic FEM pantograph-catenary model. The results show that the resonance may occur when the dominant wave frequency is consistent to the natural frequency sensitive to the moving load, which can be used to reveal the effect of operation and structural parameters on the current collection quality of a pantograph-catenary system.

Galloping of an electrified railway overhead contact line (also known as catenary galloping) is a large-amplitude wind-induced vibration under extreme conditions that is extremely detrimental to the railway infrastructure. This paper attempts to conduct a numerical simulation of catenary galloping and analyse its galloping behaviour. Computational fluid dynamics is utilized to calculate the aerodynamic coefficients of the contact wire with different classes of wear. The mechanism of catenary galloping is revealed by the Den Hartog theory. To describe the non-linear behaviour of catenary galloping, a non-linear finite element method is employed to establish the catenary model, which properly considers the geometrical non-linearity of the contact/messenger wire and the non-smooth non-linearity of droppers. Considering the effect of fluid-induced vibration, the self-excited forces acting on the contact wire are derived. Through several numerical examples, the galloping responses of the catenary are analysed with different tension classes and stochastic wind. The results demonstrate that the extreme wear of the contact wire caused by the long-term passage of pantograph can change the aerodynamic coefficients of the cross-sections of the contact wire and cause the system’s instability under steady wind load. It is concluded that upgrading the catenary tension class can effectively suppress catenary galloping. The stochastic wind only has small effect on the catenary galloping. The stochastic wind only has small effect on the catenary galloping.

The increase of train speed leads to a violent vibration of the pantograph and overhead system. To evaluate the interaction performance of the pantograph and overhead system, a whole railway dynamics model including the track, vehicle, pantograph, and overhead system is established. The overhead system is represented by the finite element approach using the analytical formulas of nonlinear cable and truss elements. The vehicle is modeled by a multi-rigid-body system with a pantograph installed on its roof. A beam element with elastic foundations is used to model the track, which possesses harmonic and random irregularities. An iterative algorithm is implemented to solve the nonlinear behavior of the coupling model. The nonlinearities in the deformation of overhead system, the contact of the pantograph and contact line, and the contact of the vehicle-track are properly considered. Several numerical simulations are implemented to systematically investigate the influence of the vehicle-track vibration on the dynamic behavior of pantograph and overhead system. The results indicate that the vehicle-track vibration induced by the rail irregularities with large amplitude or certain wavelength can significantly aggravate the interaction performance of pantograph and overhead system.

This paper studies the evolvement of the wear irregularity of contact wire using wire thickness data measured yearly from a section of railway catenary. The power spectral density and time–frequency representation based on the wavelet transform are employed for data analysis, with an emphasis on local wear irregularities that are crucial for contact wire condition assessment. To investigate the cause of wear irregularity evolvement and the mutual influence with the pantograph–catenary dynamic interaction, simulations considering the influence of wear irregularity are carried out based on the finite element method. Analyses of the actual wear irregularities and the dynamic contact force under singular and complex wear irregularities are performed. Although the wear irregularity has limited impact on the pantograph–catenary interaction, it can induce the vibration of pantograph and contact wire that will lead to a notable increase of contact force standard deviation. The evolvement of wear irregularity is closely associated with the span length and dropper distribution of catenary structure and the running direction of pantograph. In addition, it is found feasible to detect the wear irregularity based on contact force, on condition that the sampling frequency is high enough to reflect the indicative frequencies.

Due to its long-span structure and large flexibility, an electrified railway catenary is very sensitive to environmental wind load, especially the time-varying stochastic wind, which may lead to a strong forced vibration of contact line and deteriorate the current collection quality of the pantograph–catenary system. In this paper, in order to study the wind-induced vibration behavior of railway catenary, a nonlinear finite element procedure is implemented to construct the model of catenary, which can properly describe the large nonlinear deformation and the nonsmooth nonlinearity of dropper. The spatial stochastic wind field is developed considering the fluctuating winds in along-wind, vertical-wind, and cross-wind directions. Using the empirical spectra suggested by Kaimal, Panofsky, and Tieleman, the fluctuating wind velocities in three directions are generated considering the temporal and spatial correlations. Based on fluid-induced vibration theory, the model of fluctuating forces acting on catenary are developed considering the spatial characteristics of catenary. The time- and frequency-domain analyses are conducted to study the wind-induced vibration behavior with different angles of wind deflection, different angles of attack, as well as different geometries of catenary. The effect of spatial wind load on contact force of pantograph–catenary system is also investigated.

Active control of pantograph could be performed to decrease the fluctuation in pantograph-catenary contact force (PCCF) in high-speed railway. However, it is difficult to obtain the states of the pantograph when state feedback control is implemented. And the measurements may randomly miss due to the severe operation condition of the pantograph-catenary system (PCS). To address this issue, a robust recursive state estimation method (RRSEM) is presented is this paper. First, a nonlinear model of double-pantograph-catenary system (DPCS) is established by means of the finite element method. Then, the RRSEM is introduced to estimate the pantograph states based on the dynamic model. The simulation results indicate that the proposed RRSEM is able to accurately estimate the states of the leading pantograph (LP) and the trailing pantograph (TP).

A multidisciplinary integrated design concept is firstly applied to synthesize optimum pantograph. Three disciplines are involved in the integrated design of the high-speed pantograph. They are the kinematics, the dynamics and the control. In this study, the objective function of the kinematics involves the curve of pan-head to guarantee the kinematics stability. Genetic algorithm is proposed to get the optimum design parameters of pantograph. Based on design parameters of high-speed pantograph, the lumped mass model is deduced. So, the dynamic contact force is obtained. When a high-seed train is running, the contact pressure of the pantograph-catenary is changed. So, the objective function of the active control is to minimize the contact pressure fluctuation by using optimal control. The integrated design pantograph not only satisfies the kinematics, the dynamics and the control constraints but also has synthesized optimum pantograph. The results lay a theoretical foundation to develop the new high-speed pantograph.

A high speed pantograph-catenary model considering the friction excitation and air damping is established in this paper. Through the numerical simulation, the contact force of pantograph-catenary system is evaluated and the influence of the friction coupling on the current collection is analyzed. Then the contact force of the model is calculated with different speeds of the static wind. The results show that the friction of the pantograph-catenary contact surfaces at a high speed leads to the additional vertical vibration, which may result in the contact loss and the deterioration of current collection of pantograph-catenary system. Therefore, it is necessary to take the friction coupling between surfaces into account in the high-speed pantograph-catenary dynamic simulation.