The plastic piece that helped secure the cat tree broke due to years of use.  This model includes a bit more plastic than the original, however I felt it added to the structural integrity since the original broke.  

I have uploaded two versions of the model, one with and one without ridges.  I find the ridges help with the fit, however mine fits in a cardboard tube.  

There is a space for a nut to be embedded in the model.  You will need to add a pause in your slicer to take advantage of this.  

I printed with 80% cubic infill, but that is probably overkill.  Do what works best for you, though I would recommend at least 50%.  

This was printed using PLA.