I designed this sandpaper holder a while ago, and after a year of intensive usage, it deserves to be shared among the 3D community. It is a robust model, designed for the different density of sandpapers. You may orient the sandpaper portrait or landscape (see attached pictures). I have tested many designs, but this one with a threaded bolt and a nut befits me best. Once the sandpaper is wrapped around the base, the nut needs to be tightened lightly. To unscrew it push the holder down and unscrew the nut. A drop of oil to the bottom of the nut also does the trick.

Any resemblance to Star Trek Shuttlecraft is purely coincidental.

There are two models: 50mm x 70mm and 60mm x 100mm designed in Fusion 360. If you are interested in different dimensions, you may change LENGHT and WIDTH parameters in fusion360 (see attached parameters) or scale up the STL model. Here are Fusion 360 public links to both models
50x70: https://a360.co/2K54Mfy
60x100: https://a360.co/2KkeREO

• UPDATE July 2018
  I tried to print (the Base) with 10% infill and 0.9mm wall thickness to speed up a print but both my attempts failed. The bolt hasn't had enough structural integrity to withstand my abuse. Therefore I slightly change the design of the base. Now the threaded bolt has the 3mm hole in the centre. This way the centre's wall adds some additional strength to the model.