The contact force between pantograph and catenary is the most important parameter that should be considered and monitored. Contact force fluctuation is the opposite of contact quality. The more standard deviation in contact force you have, the less contact quality you have. The reason for contact force variation is either non-uniform vertical elasticity of catenary or wave reflection from boundaries. this couple of reasons are presented in the following movie.

The reasons for contact force oscillation in pantograph and catenary

Vertical elasticity of contact point means the vertical deflection of contact point due to unique reference load. The increasing number of droppers, Adding stitch wire and using compound catenary help the catenary to have more uniform vertical elasticity.

The contact wire boundaries are located at the beginning and end of the mechanical section. following movie shows that the wave reflection from boundaries, devide a mechanical section of catenary to three parts, reflection Free Area, the encounter with backward reflection and encounter with both reflections.

Three different zones according to wave reflection in the mechanical section of catenary

The graph of this video shows that the last spans become more important in high-speed trains. Simulation can prove this claim. for example, the contact force variation in the reference pantograph and catenary model of IEC 50318 is shown in the following figure.

contact force variation pantograph and catenary, the higher standard deviation in last spans

The last spans of the mechanical section in a catenary, play the role of a bottleneck in increasing the operation speed. It means to increase operation speed in a catenary, the improvement should be started from the last spans.

There are still some open questions:

1- How should the catenary be designed to reduce the wave reflection from boundaries and improve the contact quality (this article has some hints).

2- Is it possible to design any appropriate anti wave reflection damper for catenary? How much improvement can these dampers creat for the contact quality?

In continue, some part of studies and simulations which have been done by PANTOhealth team, are presented.

the considered problem for finding the optimum damped boundary condition

As an example, the above figure is considered for finding optimum dampers in the boundary. the following function is supposed to be minimised.

The considered function to be minimised

As soon as the optimum values for stiffness and damping are calculated, the following initial condition is considered to study the performance of the optimum damped boundary condition.

The initial condition to see the performance of optimum boundary condition

Tho following videos show the reflected wave from the boundaries with and without damped boundary.
non-damped boundary reflection
damped boundary wave reflection

In real catenary, it is difficult to mount the contact wire to fixpoint via a spring and damper. Therefore, the vibration absorber or tuned mass damper (TMD) are offered for this case (the following figure).

The result of using such dampers in catenary is shown in the following figure.

the effect of the damped boundary in catenary

It is important to mention that the improvement in contact quality is achieved in the bottleneck of the catenary.

The PANTOhealth team is open to having any cooperation to find out the answer to these questions.