Frances
The hollow mandrel is cut to length and left inside the pulley when the job is finished. Its turned true to whatever size centre hole you have made in the blanks and bored to fit the shaft that the pulley will go on. When each blank is fitted to mandrel its turned to finished size before putting the groove(s) in. This gives the truest possible running pulley as everything is done in one set up. If you are doing a free running countershaft you get the same accuracy by making the pulley on the shaft itself.
I bolted my slices together with hex socket cap screws. 6 tapped holes in the centre slice. Three tapped and three clearance holes in the end ones. Clearance holes for the cap screws, tapped holes to attach a collar carrying a pair of grub screws at 90° to each other to lock the pulley onto the shaft. If using a hollow mandrel sdrill through after fitting and extend the tapped holes so the screws go right through. With thin slices I'd probably make and fit the collar to the mandrel or shaft you are making it all on first then fix the first blank to that for extra stability. Might be just as easy to make the smallest pulley wider so the "collar" becomes merely a plain extension for the fixing screws. Still need a separate collar at the big end tho.
As ever there are lots of ways of tweaking the concept to suit your job and facilities. I only started out this way because the first step pulley I had to make was a big one, 6" OD I think, and I didn't want to waste a lot of material turning from solid. Especially as I had some plate in stock to make the blanks but would have needed to buy a big lump of bar to go from solid. Having done one and got my eye in I stuck with the method I knew. Overall somewhat more work than chomping direct from solid but its a lot of a small steps and if it goes wrong its easier to recover without scrapping the whole job. With a big one its possible to make the largest step as a ring and use the piece cut out of the middle for the smallest step.
Clive.