form tool for a pulley groove, chatter from the first touch

Ground a form tool the full width of a 1/2 inch pulley groove. It chatters on contact and the groove looks like a file. The 13 inch should be able to do this. I think the tool is the problem and not the whole lathe, but I would like to be wrong in a useful direction.

A form tool that wide is a crowbar. Cut the groove with a parting blade in steps, or a narrower form and move over. Relief on a wide form has to be real or the heel chatters instantly. Your lathe is not the accused.