Chris at ClipSpring gives reference early on in his John Wilding Large Wheel Clock project to the late William Smith from the USA who perhaps did not originate but certainly popularised the use of a SuperGlue arbors in his series of clock making and tooling books.
Bill's books and videos are still available direct from the US and also from a UK outlet. Chris has expanded its use to fixture plates on the milling table to replace vacuum plates and magnetic equivalents. You will notice that in Chris's videos he still uses Bill's special concoction paste for metal polishing.
Bill suggests that standard single applicant SuperGlue goes off better at an air interface. (At the time of his authorship twin pack SuperGlue might not have been readily available). Bill postulates that having the grooves in the end face of the arbor increases the net length of air interface and therefore makes the bond stronger. Once stuck the finished wheel does take some removing and heat while recommended does have the effect of noxious fumes. I note the comment above that the grooves also perhaps allow 'squash distribution' of excess glue into the grooves to give a more flat/even fixing surface between the brass and the aluminium.
To answer the original question by TickTock and with apologies to the Grannies and their eggs : –
The arbor needs to be ideally the same diameter or ideally a bit less than the wheel OD being cut in order to allow the tooth cutter to pass through the brass and into the softer aluminium backing. The arbor's whole purpose is to provide support to the tooth cutting action.
The blank arbor should be mounted in the lathe chuck. (Once mounted it is not removed until the wheel is completely finished). After mounting the arbor, the grooves are cut into the end face. There is nothing magical about these but a 2-3mm gap (land) between grooves works OK and the depth can be similar. A rounded end cutter is a good profile to use cutting perpendicular to the arbor front surface. A hole is drilled into the centre of the arbor to be larger than the desired size of the finished hole in the wheel being cut.
Having cut both the grooves and the centre hole the arbor should be faced off. This removes any residual burrs that could 'push' the blank away from the surface and ensures that the face of the wheel blank will be axial to the lathe bed.
The arbor is slowly turned in the chuck and single pack SuperGlue is applied (not too excessively) onto the 'lands'. The chuck is stopped. The oversize wheel blank, having been degreased and having an undersized central hole is held in place by hand on the point of a centre in the tailstock and the tailstock is slid (not wound) to impact the blank onto the arbor face. The tailstock is locked in place and the handwheel wound quickly to apply pressure to the wheel blank against the face of the arbor and then the tailstock adjuster is locked in place. After 5 minutes the wheel will be fixed solidly. Some would recommend having the chuck slowly turning while this placement is done.
The blank is now turned to the specified OD for the wheel being cut. Cuts should not be aggressive as they will be applying a shearing force to the bond.
Once the wheel is cut to size the edge of the wheel is marked with a Sharpie pen or similar and then three adjacent teeth are cut back and forth until the marker inking disappears. This defines the depth of cut and the cutter now needs to be locked at this depth. The remaining teeth can now be cut and once all teeth are finished, the final action is to drill and ream the hole in the blank to size. This ensures concentricity of all processes in the wheel manufacture. (There is an immense feeling of relief when the final tooth is cut and it is the same size as the others … or alternately the neighbour's garden will receive an aluminum/brass addition for its Gnomes to play with).
Assuming success, the only problem now is getting the newly cut wheel off the arbor and heat or a solvent will be needed for this with due respect to any fumes.
The arbor can be stored for future use but will need an initial facing to clean off the prior use glue and grooves before repeating the process.
Hope that helps TickTock (and any others not yet elevated to Granny status).
Alan