This is a heavy duty holesaw mandrel. The shank on this is 7/16 inch and requires a 1/2 inch drill chuck. My drill has a 3/8 inch chuck.
I had to make several dozen 3 inch holes in our soffets (also spelled 'soffit') for ventilation louvers. I ground the shank flats down freehand so the mandrel would fit my drill. It worked, but it wobbled terribly.
(The image is from Amazon.com.)
Step 1: Build it back up
I decided to restore my mandrel, but sized for my drill chuck and on center so it does not wobble. The first step was to build the shank up again by welding. A wire feed welder makes this much easier than with a stick welder. (I did not take photos while I was actually doing this project, so this is a recreated photo.)
Step 2: Replace the pilot bit temporarily
I needed a way to put the mandrel into a chuck so I could spin it on center. The pilot bit is 1/4 inch. I loosened the set screw that holds it in place and inserted a piece of 1/4 inch rod in its place.
Step 3: Chucked in the drill
I put the 1/4 inch rod into my drill chuck. The mandrel now spins in the drill on center without any wobble. Of course, you cannot use a holesaw on it like this.
Step 4: Grind until round and on center
I held the drill so the mandrel made light contact with a spinning grindstone. Hold it so contact with the grindstone does not cause the drill to bump, but the grindstone slowly and smoothly takes away high spots and the shank of the mandrel is round and on center. Experiment with the speed of the drill to find the speed at which you can hold the drill most smoothly. If there are low spots and voids fill them with a little additional welding and grind again until round and on center.