How do you make a close spiral or a spiral fold

The software refuse to sweep it in one piece and in segments refuse to unite them

Is this what you are trying to achieve?

Not exactly but it is definitely very cool. I was wondering if the thinning ending was also possible.

What I’m trying to achieve is a tightly wrapped spiral like the ones on the photos. I want to make rolls like those for some models and I really have no idea how.

With no gaps between the tube sections.

Here I enlarged the diameter before doing both sweeps and made the inner end a full spherical radius. Overlapping the sweep does work.