How can we model a railway suspension system?
Firstly, the vibrations caused in a train can either be because of the surface roughness of the track or the unevenness of the track. These vibrations, obviously, are originated at the wheel rail interface. Since the wheel is an almost rigid body, the vibrations produced at the interface are transmitted to the car body and in between these two there is the vehicle boogie which connects them. The amplitude and phase of the vibration at the wheel-rail interface is considerably different to the one transmitted to the the car body. Why? Its because the car body-boogie-wheelset system together is not rigid.(each of car body, boogie and wheelset are assumed to be rigid independently).
So, connecting these rigid bodies with a spring makes sense than connecting them with rigid rods. These springs are used to represent the actual suspension system. But, can we accurately represent the suspension system of a train with just a spring? No, we need a damper to account for the non-linear behavior of the vibration transmission.
The vibration originated at the wheel -rail contact dampens itself or, to be put precisely, gets dampened by the suspension system. Ideally speaking, springs are designed in such way that the car body doesn’t experience the effect of vibration, at the wheelset. So, to conclude, we can represent a railway suspension system with a spring and damper arranged in parallel. The resistance force provided by the damper and spring corresponds to the force applied on it. Here is a rough model of the railway suspension system.
