Well, with the old 2 blade version, I did get some chatter when coring some osage orange. It is a particularly hard wood. They did beef up the platform considerably from that first version. To me one of the draw backs to this system is that it can do this with some woods. It is not as sturdy or strong maybe as the Oneway system, which is rock solid all the way out to the end of the biggest blade they have, and that is because of the support finger under the cutting blade. The McNaughton also likes to chatter, and more so on harder woods than softer ones.
One cause can be height issues. Most coring systems say that you should have the cutting edge at center height. I prefer mine slightly above center height, like 1/8 inch or so for Oneway and Woodcut, though I use the McNaughton 99% of the time. With the McNaughton, I keep it over 1/4 inch high. You do not want to be cutting below center!!!!!! These are scrapers, and on the inside of a bowl when using scrapers, you want to be at or slightly above center. The McNaughton has a lot of 'flex' in the system, so if you start at center height, then by the time you get to the center, you can be considerably below center. The Woodcut has a little bit of flex in it, much less than the McNaughton. The Oneway has no flex in it.
Do make sure your cutter is sharp. I prefer a coarse diamond card, like 220 grit, and will go across the bevel rather than up and down. This leaves a better burr. Walnut, for reasons I don't really understand, seems to be hard on all cutting edges, so you may need to resharpen more often with it than other woods. Probably every bowl.
Hope this helps some.
robo hippy