willaim The brass sleeve is the correct one for the motor it is known as a press fit but do NOT hit with a hammer without FIRST supporting the other end of the motor SHAFT ONLY you WILL destroy the motor and the same thing for the brass outside diameter like you said it is also tapered to mount the chuck it is a press fit actually it is called a friction fit the bigger chucks use it as well its called a Jacobs taper or a Morse taper but no need to hit with a hammer just make sure it is clean and the inside of the chuck is clean and it will hold -just push it one with a bit of pressure. It seems that a lot of people who bought this set up do not understand how to put it together and think that it is faulty but it is how it goes together I have read that some have applied heat to the brass sleeve and pushed it on the motor shaft that way- because the brass will expand just a bit to fit the motor shaft with light pressure. I hope this helps someone.

willaim I was told by a You Tube guy who bought this item and I am a viewer of his channle said it was a 10 mm spindle