Modeling of Pantograph-Catenary dynamic stability

Transcription

1 Technical Journal of Engineering and Applied Sciences Available online at TJEAS Journal / ISSN TJEAS Modeling of Pantograph-Catenary dynamic stability Saman Farhangdoust 1, Mohammad Farahbakhsh 2, Majid Shahravi 3 1. M.Sc candidate in Railway Engineering Department, Iran University of Science and Technology, Tehran, Iran 2. M.ScCandidate, Civil Engineering Department, Islamic Azad University, Mashhad Branch Mashhad, Iran 3. Assistant Professor, Railway Engineering Department, Iran University of Science and Technology, Tehran, Iran Corresponding author: Saman Farhangdoust ABSTRACT: The purpose of this paper is to describe the possibilities of investigating the effects of external variables on the stability of dynamic systems dynamics modeled by differential equation systems with periodic stability coefficients. The method used to analyze the influence of external harmonic forces on the stability of the longitudinal line parangalography - the contact wire of the electric locomotive. System parameters are two concentrated loads, bending rigidity, tensile horizontal viscous damping in mass per unit of yarn length, second coefficients of damping in the rigidity of system elements and constant speed specified in the template. With these parameters we study the stability of the system. In this study we analyze an overview based on background studies of pantograph systems. Keywords: modeling, dynamic system, Pantograph-Catenary system, control, stability INTRODUCTION To analyze the stability of the movement of the pantograph couple - contact wire, we consider a mathematical model consisting of two degrees of freedom dynamic model and dimensional model continuously. The mathematical model is reduced to a system of linear differential equations with periodic coefficients, which is studied with the methods of the theory of parametric stability. This analysis is performed by choosing from two main parameters of the model parameters and locates the limits of stable and unstable solutions in terms of these two parameters. In this paper, we study some aspects concerning the stability of our movement following physical and mathematical model. The dynamical model for a Pantograph-Catenary system adopted by us, consists of a vehicle (A) in uniform motion with velocity v, where the vehicle is used to compress with a force constant F, the oscillating system over the pantograph on the (Figure 1).

2 Figure 1. Dynamical Assembly of Pantograph-Catenary system (Teichelmann, 2005) Due to the fact that the railways must adequately capture the electrical power, the strength of Pantograph- Catenary contact should be kept as uniform as possible, avoiding the loss of Contact. The development of a mathematical model to evaluate the mechanical behavior of the system can be useful in order to get optimum mounting in the company known as Pantograph-Catenary. In recent years, several books have been published in the scientific literature on the study of pantograph Pantograph-Catenary dynamic interaction: in (Park, 2000) a study based on coupled systems of partial differential equations algebraic and differential equations are presented (Kim, 1999) presents a simplified method to evaluate the performance of the pantograph, in (Cho, 2008) a procedure based on modal analysis methods and penalty is introduced in (Poetsch, 1997) a method using a multi-body model and co-simulation is proposed, and finally, (Migdalovici, 2003)this hybrid procedure using theoretical and experimental modal analysis. A large part of the studies are based on models where the pantograph interacts with a single Contact wire along a series of spans of the same characteristics, but this is not considered completely true, because the overhead is installed in series 10 or 15 bays, which are not necessarily equal, and wherein the duration of the last of a series and the first bay of the following series are overlap. Overlap in space, the pantograph can interact with multiple contacts of that at the same time, also has a special configuration of the son in order to obtain a smooth transition between sets of spans. Moreover, in an actual set, each bay can have different characteristics terms of geometry, the number of drops, etc., so that the identification and generation of the other elements of the system of differential equations presents a particular difficulty. In this paper, a software tool that allows realistic simulations where several pantographs can interact with the son of contact of two catenaries with overlapping ranges, and wherein each bay may different characteristics is presented. A study of the dynamic pantograph from the real model, using independent coordinates and symbolic expressions is also developed. (Poetsch, 1997-Migdalovici, 2003) 1487

3 Figure 2. Connections between two dimensions of pantographs-catenaries (Kim, 1999) The pantograph essentially consists of a housing with a pedal foot and a mass of the head with a damping in a suspension that can rotate in the foreground plane in the transverse plane of movement with a vertical displacement in the common four degrees of freedom. Some models believe that the intermediate mass with a vertical movement in one degree of freedom represents five degrees of freedom. In the two-dimensional front rotation model, transversal and rotation are not considered to be equivalent to the assumption that the head mass is divided into two point masses located on intermediate mass articulated chassis. For dynamic simulation, because it is difficult to model the frame, this element is often simplified and counts as one mass point with vertical movement, which results in a known pattern of mass, and parameter values are generally provided by the pantograph planner. Figure 3. Pantograph main structure (Migdalovici, 2003) The dynamic analysis of catenaries has been a popular topic in engineering, because theses catenaries are widely used in various applications, e.g., contact wire in high speed rail way, suspension bridge, tethered satellites systems and so on. Recently, many studies about catenaries are focused on the contact wire system used in high speed railway, because the dynamic characteristic of catenaries are important parameters for high speed train such as KTX, Eurostar, Shinkansen and so on. In other words, tensioned Pantograph-Catenary properties such as presag in a static state determine the dynamic behavior and stability between the contact wire and the pantograph. Much research has been reported about the two-dimensional linear models of catenaries in high-speed rail way. Some examples of these studies can be found in Refs. (Kim, 2001 Cho,2008), in which the vibrations and stability, which may be incurred due to the interaction between the catenaries and the pantograph, were analyzed 1488

4 by the finite element method. In these studies, design parameters such as contact wire tension, stiffness variation and dropper slackness were studied. It was reported that dropper stiffness variation is an important factor for dynamic behavior of Pantograph-Catenary systems. Based on an extensible linear beam model, Kim and Choi (Kim, 1999) studied the wave propagation speed and the mode characteristic according to the tension, flexible rigidity and bending effect in linear Pantograph-Catenary model. Comparing to two-dimensional linear catenaries, only a few studies for non-linear catenaries or threedimensional linear models have been undertaken because the non-linear or three-dimensional models require more complicated formulation and analyses than two-dimensional linear models. The approaches to investigate the dynamics and stability of three-dimensional non-linear catenaries may be classified into two types: the threedimensional linear Pantograph-Catenary system and the two-dimensional non-linear Pantograph-Catenary systems. The two-dimensional non-linear Pantograph-Catenary theory has the assumption that the centerline ofa beam is not stretched and the nonlinearity of droppers is allowed. On the other hand, in the three-dimensional linear Pantograph-Catenary theory, catenaries can possess extension in the axial direction but the non-linearity of droppers cannot. Teichelmann, et.al (Teichelmann, 2005) studied the efficiency algorithm for calculation about the the static deflection of a non-linear complex structure. They assumed that the contact wire is beam and the droppers are bar elements. Yang and Ttsay (Yang, 2007) analyzed the non-linear elements about two dimensional models for high speed rail way, of which elements have three nodes. The slackness of the dropper is an important phenomenon, because the wave propagation and the wave reflection in the Pantograph-Catenary influenced by the slackness. The contact force between Pantograph-Catenary and pantograph are determined by wave propagation and reflection. Finally, the dynamic responses of the system are also investigated when applying a load to the contact line. For confirmation of the wave propagation and the reflection, we model the applied load as the point mass. Then, we calculate the contact force between the Pantograph-Catenary and the point mass when the velocity of the point mass is zero, and compared the theoretical wave speed with the simulation result by observing the variation of the contact force. Static analysis was carried out with respect to the droplet permeability, when the climbing force was used on the Pantograph-Catenary contact line. Since the dropper has the only elongation extension, the stiffness of the droplet does not contribute to the common stiffness matrix when the applied force relates to the dropper. This nonlinear phenomenon in the droplet affects the response of the waves. Therefore, this effect affects the contact characteristic between the Pantograph-Catenary in the pantograph. Figure 4 compares the variation of rigidity between the linear and the consideration of the slope of nonlinear models. In Figure 4, the line represents the rigidity of the linear model without taking into account the permeability, while the dotted line represents the rigidity of the nonlinear model. As shown in Figure 2, the stiffness difference is observed along the ranges by comparing the solid with the dashed line. This difference occurs because of permeability. In this study, these formulations carry out a dynamic analysis involving wave analysis in the Pantograph-Catenary system. (a) (b) Figure 4.Contact forces between the moving mass and the tensioned beam: (a) when the velocity is 0 m/s and (b) when the velocity is 50 m/s (Park, Yang, 2007) Figure 4 represents the contact forces between the moving mass in the tension carrier. Figure 4 (a) shows the contact silos when the mass rate is zero, when the holding time of the pantograph pantograph system in a 1489

5 strong climb is 50 N applied to the beam. As shown in this figure, the contact force is changed due to the expansion of waves in the sections. The wavelengths influenced by various factors, such as moment of inertia, surface, tension and density of the tensile beam. Among these factors, voltage is the most important parameter determining the speed of wave in this beam model. The theoretical speed of this model is calculated as 120 m / s, and the contact force changes with a time of 0.83 s. Since the wavelength is 100 m between 0.83 s, the wave speed as calculated numerically as 120 m / s. As shown in Figure 5 (b), the first change in the contact force occurs at 0.58 seconds. If it means that the distance traveled in the waves is 71 m, and the moving mass fights with a reflecting wave of 0.58 seconds. Since the distance between the waves is 71 m between 0.58 s, the wavelength is 122 m / s. Therefore, we can see that the developed model in the FEM formulation is reasonable. In figure 5, the contact forces between the moving mass in the pantograph-underground vehicle in Figure 5. In Figure 5 (a), the contact power is calculated when the velocity of the particulate mass is 50 m / s in the 50 N force used for the ticket system. Figure 5 (b) is a contact silos when the velocity of the moving mass is 100 m / s. In these two figures we can notice that the contact force changes rapidly. These rapidly varied variations cause the variable droplet rigidity, a permanent hand in geometric constraints. Figure 5. Dynamical Contact forces between the moving mass and the Pantograph-Catenary of Fig. 6: (a) when the moving mass velocity is 50 m/s and (b) when the moving mass velocity is 100 m/s. (Park, Yang, 2007) CONCLUSIONS AND DISCUSSION In this study, it is dynamically analyzed in the static behavior of the Pantograph-Catenary system for highspeed rail using finite elements. Static deviations are calculated according to the weight and voltage used for contact and wire wires. For the static and dynamic analysis, the lightness of the capillary, which has a geometric non-linear effect, is also taken into account. In addition, the dynamic responses of the system studied when the moving mass is applied to the load on Pantograph-Catenary. For the verification of the propagation wave propagation, the forces of the contacts between the moving mass in the tension carrier are calculated. In addition, the contact forces between the moving mass in the pantograph-catenary are calculated when the velocity of the moving mass is 50 m / s at 100 m / s. From the results of the simulations, we confirm that the developed FEM model in time integration is reasonable. REFERENCES Cho YH Numerical simulation of the dynamic responses of railway overhead contact lines to a moving pantograph, considering a nonlinear dropper, Journal of Sound and Vibration, Vol.315, 433~454. CHUNG YI, GENIN J Stability of a vehicle on a multispan simply supported guideway, Trans. of ASME, 100, Kim JS, Choi BD A study on Dynamic Characteristics of a Catenary System, KSNVE, Vol. 9, No. 2, 317~323. Kim JS, Park SH Dynamic Simulation of KTX Catenary System for Changing Design Parameters, KSNVE, Vol. 11, No. 2, 346~353 Kim WM, Kim JT, Kim JS, Lee JW A numerical study on dynamic characteristics of a catenary, KSME International Journal, Vol. 17, 860~869 MIGDALOVICI M, BARAN D About the stability of motion for two sprung superposed masses in contact with a wire, Proceedings ICSV10, , 1490

6 Park SH, Kim JS, Cho YH, Choi KY Vibrational characteristics of KTX catenary System for Changing design Parameters, Spring Conference of The Korean Society for Railway, Vol. 1, No. 1, 265~272. POETSCH G, all Pantograph/ Catenary Dynamics and Control, Vehicle System Dynamics, 28, , Teichelmann G, Schaub M, Simeon B Modelling and simulation of railway cable systems", ZAMM-Zeitschrift fur AngewandteMathematik und Mechanik, Vol. 85, 864~877 Yang YB, Ttsay JY Geometric nonlinear analysis of cable structures with a two-node cable element by generalized displacement control method, International Journal of Structural Stability and Dynamics, Vol. 7, 571~