Replacing broken pivot.

[HSL]

Hello
I have a question about how to best remove an broken pivot from the arbor. It seems like the pivot is made of a hardened steel is pushed into a hole in the wheel arbor.
My plan is to use a split stake and remove the wheel and lantern pinion and then try to drill out the residues from the previous pivot and press in a new one.
I have a Lorch 6mm lathe and a EMCO UNIMAT 3 lathe to use in this operation but don't know which tool to use for the best result. I have been reading about people breaking of drills and so on in this operation. 
So now I wounder what would be the best way to proceed drilling out this pivot in your mind?
The wheel in question comes from a German HAU or in English HAC clock and runs the fly.
Here are some pictures of it..

 

 

[oldhippy]

How are you going to hold that in a lathe. The steel is quite soft so you should not have any trouble drilling it out. Smooth of the face, find the centre and tungsten drill with a drop of oil will go into that like butter.  

[clockboy]

This subject has been covered on many occasions on the forum including by myself recently see below: However I was attempting to replace a French pivot of 0.50mm & I suspect yours is not as difficult although the same technics are applied or just search youtube which also has this subject covered.

 

[nickelsilver]

You'll definitely want the end getting drilled supported. Maybe your Lorch has a drilling plate, if not Clockboy's thread has a YT link showing a simple setup to do it. Agree these clocks use softer steel that drills readily with normal drills.

[HSL]

Looked at the videos in Clockboys link and think the Lorch with a drilling plate seems to be the way to go,
I have ordered 0.5 mm HSS drills and will give it a go this weekend.
Tried out a collet for the arbor and it seems to fit with the no:20.