Constraints only horizontal displacements between parts

[Sara.......]

Hi!
I have two parts one above the other. I need to define a constraint that allows only vertical movement and restraints horizontal displacements and rotations. I try with a kinematic coupling, but I have some warnings of numerical singularity under gravity loads. Also, when I perform a modal analysis I have that three factorizations in a row failed.
I think that I have a problem with the mass definition because in a dynamic implicit step, I have that the global mass matrix is singular. Without this constraint everything work, but I don't know how to proceed and fix these error.

Is there a better constraint I could use?

The constraint is between the violet and the yellow parts.
Thanks

 

[FEA way]

Connector will help if the parts are going to be separated. Otherwise, contact with rough friction property might be the way to go.