A center that is simply made straight is best made with a shoulder that won't allow it to be pushed back in the chuck, and if used in a 3 jaw chuck, likely will need to be trued up before each use when it has been removed from the chuck. The best setup is to have a driving plate made to drive lathe dogs rather than a faceplate, and a center that is the proper length to allow the dog to engage the slots in the driving plate, and best that the center is soft enough to allow truing up with a tool bit, also the bushing and the center and the spindle nose should be marked so that the center is in its most concentric location when removed and re inserted.