I need to turn a cylindrical section down in the middle of a round bar. The major diameter is 1.25", and the minor diamter is ~5/8". I have left-hand & right hand turning tools, but I'm wondering what's the most efficient way to get a smooth section in the middle, with a square shoulder on each end. The cut's are deep enough that if I start with one, I'll have a tapered shoulder on the end opposite the square part to remove. I'm thinking it would be best to cut the square shoulder on the out-board end first, i.e. cut in & head towards the headstock, to minimize the cutting forces at the longest reach from the chuck.
Is there a trick to doing this neatly? I'm looking to get a nice polish on the whole thing when I'm done, and I'm concerned about "blending" the cuts from the two different tools in the middle of the reduced section.
Thanks!
Doug White