Product Expertise: Lumped Mass Model

Introduction:

The transfer of electric current from the overhead catenary Line (OCL) to the train is operated through the sliding contact created between the contact wire (CW) and Pantograph collector strips. During the operation of the train, a proper contact pressure has to be ensured between the pantograph and the OCL, to ensure the regular flow of electric current through the sliding contact.

Dynamic interaction between the pantograph and the OCL causes a dynamic fluctuation of the contact force with respect to its mean value. To ensure proper operation of the pantograph-catenary couple, the fluctuation of the contact force shall not be too large compared with the mean contact force, a requirement typically expressed by the following condition:

where Fm and σF are the mean value and standard deviation of the contact force.

The pantograph-catenary interaction is a critical issue for electrified railway systems, because it has important implications on the maximum service speed at which the electric rolling stock can be operated, and it sets some limits on the dynamic behavior of a railway vehicle as well as on the reliability, availability, and maintainability of the system.

Numerical Simulation of Pantograph-Catenary Interaction:

Numerical tools for the modeling and simulation of pantographs and the overhead equipment have evolved substantially, enabling the accurate and detailed simulation of the operation of pantograph-catenary coupling.

A mathematical model of pantograph-catenary interaction is obtained from three main ingredients: a mathematical model of the OCL, a model of the pantograph as a multibody (MB) vibrating system, and a mathematical description of the contact between the pantograph head and the catenary.

Wabtec Transit, as a Pantograph manufacturer takes ownership of the mathematical model of the Pantograph to support the car builder or infrastructure developer (OCL). Wabtec has rich experience the Wabtec has rich proficiency in the domain of dynamics, numerical solution, field trails, and current collection tests.

Pantograph Model:

The pantograph is designed as an articulated frame (typically a four-bar linkage) driven by a force applied to the lower member by an air bellow so that the desired pre-load (contact force in static condition) is applied to the OCL. The purpose of the articulated frame is to follow the OCL dynamical uplift in response to the force exchanged at the contact points. In addition, the pantograph head is fitted with a suspension.

The Pantograph mass model consists of multiple masses connected by springs and viscous dashpots. The three-mass model is shown in fig. 1 (a).

By performing the laboratory tests, it is possible to represent the dynamic behavior of the LX Pantograph by the lumped mass model. Our study is limited to performing the frequency response function (FRF) of the pantograph and determining the stiffness of the pan head suspension and air spring. Through FEM calculations, the second level (m2k2) stiffness parameters are calculated.

A dynamic response was captured from 80 N force between 0.1 to 20 Hz. This shows the Pantograph operates with very low frequency. The frequency response graph is plotted as below.

Fig:2 Frequency response vs displacement

With the above study, the masses are adjusted to filter respectively large displacements at low frequencies and small displacements at high frequencies especially to reduce dynamic interaction with catenary. Furthermore, studies can be undertaken to check the dynamic interaction with the catenary with the above inputs.


Source: Wabtec