Using subdivision surface cuts up my object? Let me just preface by saying that I'm very new to blender and I'm sorry if I don't use the correct terminology. I hope that I'm making sense with how I'm describing my issue.

So I have no idea why but whenever I use the subdivision surface modifier it cuts up parts of my object? I have no idea why and would like to know how I can fix this since I really need to use it for round parts of the object that need it. I did already use the edge split modifier and that helped a lot but now I would like to use the subdivision surface modifier. I already have tried doing smoothing on it but didn't give me the kind of help that the subdivision surface does for it. I did also try to separate the object and that did work, however, I need my object to be only one (sorry, I don't know how to explain this?) and splitting it up caused me a lot of trouble to fix it. Or, if there is another way to smooth my round top and bottom (besides bevel) then I would be so appreciative.

Here are some photos (Top is when the modifier is applied, bottom is in edit mode and the top sides are what I'm trying to smooth out):
Without seeing your blend file I can only make an assumption, but it appears as if you have a double-vertex edge on your cylinders. I can create a similar look by creating a circle, deleting half, duplicating it, rotating the duplicated half 180 degrees, joining them, extruding the shape, and then applying a subsurf.



Try going into edit mode, change to vertex mode (press 1), select all vertices by pressing A, right clicking and selecting Merge Vertices -> By Distance.



See if that resolves your cylinder issue.





Edit:

The issue is that you have an extra edge loop which has been folded over. You can either merge those vertices at both the top and bottom of each cylinder, or recreate the geometry with a better plan.