I had a Grizzly G0602 prior to my current lathe a few years back. Parting was always a huge pain in the butt! It is a very hard thing to get ahold of if you've never done it before. Heck, I knew a guy who used to work on a massive lathe and parted all the time, but when he bought his own small hobby lathe, you'd have thought he'd never parted before. The key is rigidity, no doubt. And also lots and lots of fluid if you can manage it. I never had much luck with the High speed steel parting blades to be honest. If you can swing the $50 I would HIGHLY suggest picking up one of theses guys:
http://www.grizzly.com/products/Parting-Tool-with-Carbide-Insert/T10012. You don't need that exact one, but that style will make you life much easier, I promise! Also, I wouldn't buy the inserts from Grizzly, theirs aren't coated, I would suggest finding some on Ebay, they are a GTN 2.4 sized insert. It's also cheaper to go that route.
With that in hand just make sure you are right one center, and that you are perfectly perpendicular with the work. I use a little flower watering pump sprayer filled with water soluble cutting fluid and keep the blade flooded for the entire cut. Like this:
http://www.amazon.com/Pressurized-P...=1397026087&sr=8-9&keywords=pump+spray+bottle. You could use a squirt gun for all it matters though, just as long as you can get something between the cut and your blade. I usually run my auto feed and have my speed around 600. But you could (should?) take it slower until you get the feeds down right. IF you are going to use auto-feed, make sure and start slowwww, you can always speed it up, but once you jam your bit by feeding too quick and it catches and blows up in your face, you may rethink your hobbies, then go change your shorts.
I part off Stainless and aluminum all the time, but whenever I try to part 1018, It's always a chore, It has a tendency to catch more than any other material I find. Perhaps your problem is that your trying to part 1018, I always bandsaw my part and then clean it up in the lathe, I try to stay away from parting it. Others might have some better advice for it though.
Anyway, I managed to blow up 2 or 3 HSS parting blades when I first got my G0602, all of which scared the poo out of me. So be careful (Safety Glasses) and don't get too frustrated! The biggest help for me was ordering the above parting tool and using lots of cutting fluid.
Good Luck!