... I also have an old Craftsman (I think) with the same issue. It's a nice change to open something up and find what was shown on a youtube video!
Oh boy, just when I thought fixing my old 16 gal. Craftsman ( cir. 1980) shop vac was going to be quick and just like shown on YouTube!
Well, I did find an illustrated parts list on ereplacementparts so there is that. Parts are NA, no problem 'cause I was able to find the bearings (NTN 608 LB) several places.
I was able to get it apart with a bit of effort - mostly fighting rusty fasteners holding the lid and inner lid assemblies together. They had to be separated to remove the motor frame assembly, to get the armature assembly out, to get the lower bearing off the armature shaft, ...
I'll have the bearings on Tuesday 12/7/22. $18.50 shipped from Grainger, including tax. And yes, it cost more to ship than the 2 bearings cost.
More than once I thought to just stop and buy another shop vac for use in the basement, but other than the terrible noise, it did a fine job.
Here are some pics. to show what this model 113.178200 looks like.
1st shows the upper bearing with cooling fan on the armature.
2nd shows the fan that creates the vacuum attached to the lower armature. The inner lid has been removed.
3rd shows the fan removed from the armature shaft, revealing a plastic 'spacer'. The 4 motor frame assembly screws are now accessible.
4th shows the lower bearing and 'rubber' cushion that mounts with the bearing when assembled.