Kawasaki blowing smoke intermittenly, burning oil

Actually the rings do rotate some, but shouldn't rotate that much

Rings rotate a lot.

Place a piston on a rod vise. Take photos of a piston with your rings installed. Run the engine for ten minutes at WOT, drop the throttle and again WOT during this time. Give it several RPM run-ups. Disassemble and shoot a pic of the piston back in the rod vise and you'll find the rings aren't in the very same orientation. Same for all piston engines. Air (fuel) cooled, liquid cooled are all rotating their piston rings.

Done this on race tracks time and time again. Make a 4 second pass, tear down, change any parts hurt on the pass. If pistons and rings are good, move the ring gap back to maximum orientation and reinstall.

Had people take their engines home from our machine shop, run them hot and bring them back in for us to check out. Tear down shows the rings out of the alignment I personally always use for all engines. Always place the ring gaps at maximum orientation. 90 degrees is minimum, 180 degrees is maximum and most efficient for compression and least amount of oil consumption.

Reasons for running them hot varied. Too lean, too much time either in the crank or distributor, lack of cooling liquids, etc. Engines can't help human's stupidity. lol

With horizontal engines, gravity will try to rotate all of the ring gaps to the top as the gap is lighter than the ring.
I have not pulled all that many engines down but in most that I have the rings were between 11 and 2 ( clock positions )

Update on this issue. I replaced the head gasket. I took it out and started mowing. Ran great for about 30 minutes then all the sudden a sputter of the engine and a puff of blue smoke. Continued to do this about every 45 seconds or so. It seemed to be worse if the engine was under more of a load, like running through a patch of thicker grass or going up a hill. It didn't seem to do this at all if the PTO wasn't engaged.

I'm prepared to replace the rings, but obviously that's not a quick or easy job so I just want to be sure there isn't something simple that I'm overlooking that I should check first.

A side note to this discussion, I can understand if the rings are worn and that was causing this issue, but if the rings continuously move A LOT then this wouldn't seem to be an issue of the rings being all aligned, if so, they would soon move to another position and self correct. Either the rings don't move nearly as much as was described earlier, or my problem would not be an issue of ring alignment, in fact, nobody's would. Why would ring gap placement be so important, as we all know it is, if the rings were continuously moving that much?

with out trying to get into a mechanics diploma course, it goes like this.
Your rings do not seal against the cylinder wall because of their spring.
They get forced into the wall by cylinder gasses going through the gap, getting under the ring and pushing it into the wall.
If there is 200 psi on top of the piston, there is also 200 psi under the ring pushing it onto the wall creating the seal.
When you first install the rings they need help during the initial break in period because neither them , nor the actual bore are 100% round.
If the ring gaps are all in a line a lot of the compressing gas will simply blow down the line of holes.
They take months teaching mechanics exactly how this works and why this works which I am not going to try here so you will either have to believe me or go to some of the better piston ring sites and read their theory pages.

I wasn't doubting you Bert, the other post had me confused about rings moving around "a lot". I should have stayed out of your ring gap placement discussion anyway.

This post was about determining what is causing the intermittent smoking on my mower. Now that I've ruled out the head gasket, I just want to make sure I haven't overlooked something simpler before I replace the rings.

bert is correct. On our Hemis, we use what is called Dyke's rings. They are made in an L shape. There is little to no tension on the cylinder walls until valves are closed and on the compression stroke. Then they seal up like a locked box. That is how we put 1471 huffers on top of the heads as well as huge wiffles. Without them, you're not going to make upward of 6000 horsepower. Even with that ring, we still get about 4 gallons of fuel past the rings and out of the exhaust during a perfectly clean pass.

I appreciate that but it doesn't help.me at all toward resolving the problem I posted about. I don't have a hemi on my mower so most of that makes no sense to me at all.

I would do a leak down test before I tear down any engine,,not sure if you have the tools though.

Good advice, thanks. I don't have the tools but I know where to go. Thanks