# Evaluation of Dynamics of a Freight Wagon Model with Viscous Damping
## 1 Introduction  
The suspension damping of freight wagons is achieved in the majority of bogie and two-axle wagon types by dry friction. This solution has been used practically since the early days of railway development and was also the basis for two-axle passenger coaches. Over time, viscous damping, provided by hydraulic dampers, became widely installed in passenger rolling stock, while dry-friction damping remained the domain of freight rolling stock and some special-purpose vehicles. It should be noted that dry friction is practically always present in the suspension and can be an additional, undesirable factor that affects the assumed damping characteristics. The additional damping force in the form of dry friction can be contributed to by, for example, the joints of the links, spring elements, and other interacting surfaces. Design solutions of friction dampers show differences between different types of wagons and bogies. In the oldest solutions of the single-axle running gear of the two-axle freight wagons with horn guides, the damping of vertical vibrations was mainly realized by dry friction developed on the contact surface of the leaf springs. Also contributing to the damping of vertical vibrations in this type of running system are the sliders, bolted to thevertical walls of the axleboxes, which interact with the sliding liners of the guides. However, contact between the sliding surfaces also occurs when the longitudinal play is exhausted due to longitudinal displacements of the wheelset. A more recent, UIC-standardized solution, the so-called UIC double-link suspension, uses parabolic or trapezoidal leaf springs attached via double links to the vehicle frame. As in the classical solution, vertical vibrations are mainly damped by dry friction between the leaf springs, while displacements in the longitudinal direction are damped by dry friction developed in the link pin-end bearings pairs and lateral displacements by friction in the link-end bearings [1]. The damping of lateral and longitudinal displacements only occurs when a certain threshold force is exceeded, since for small amplitude movements the joints experience pure rolling [2]. The UIC double-link suspension model is depicted in Figure 1.  
Vertical vibration damping by dry friction between leaf springs and other suspension elements (e.g., links and pins) is also used in two-axle freight wagon bogies--e.g., in DB 665 (standardized by UIC), presented in Figure 2, or Polish 1 XT. The leaf springs in these bogies are installed in primary suspension. For the Y25 bogie family, the implementation of the primary suspension damper has taken a more complex form--the friction damper force depends on the load on the external (tare) spring. The friction damper consists of a pusher pressed by a spring holder against a friction plate fixed on the outer side of the axlebox. The spring holder is the upper spring seat on one side of the axlebox and is connected to the bogie via a Lenoir link positioned at an angle. As a result of the inclined position, the link exerts an angle-directed force (acting along the link) on a pin located in the spring holder. In this pin, there is a vertical component of the force, balancing part of the vertical load of the bogie, and a longitudinal component, pressing the spring holder against the pusher. The longitudinal component is responsible for the pressure on the pusher and increases with the wagon load (progressive characteristic) [3]. The Y25 bogie model and its friction damper  
Figure 1: UIC double-link suspension of a single-axle running gear. (**a**) Running gear model; (**b**) Diagram of a double-link connecting parabolic springs to a vehicle frame. Figure 2: DB 665 bogie with parabolic springs. A three-piece bogie (Figure 4), used predominantly in USA, Russia, China, and Australia, as well as other countries, has only a secondary suspension (between a bogie and a vehicle body) with wedge friction dampers. This bogie exists in two variations: with constant or with variable damping force.