I've had this problem a few times in the past and reported here:
https://www.rotax-owner.com/en/912-914-technical-questions/6353-912-loses-500-rpm-during-climb
https://www.rotax-owner.com/en/912-914-technical-questions/6931-912-loses-500-rpm-during-climb-part-2
I did a ground test of the engine (it's in a Phoenix U15 LSA) to make a video recording of the exhaust pipe with a flow diverter tip installed. When the RPM was raised to 4800, a strong vibration shook the plane, and RPM dropped about 300 rpm. I reduced the throttle with the knob, and when I reached about 4400 rpm, the vibration ended, the rpm increased a bit, and I was able to go back to full power, and then lower the RPM, all without the strong vibration. This has happened before: twice shortly after takeoff, and 3 times on the ground (including this time), but it's been spread over almost two years and 142 engine hours. The engine has 580 hours TT.
The attached chart shows the two Rotax EGTs (EGT1 and EGT2 - left rear and right rear cylinders), and the two externally mounted EGTs I added (EGT3 and EGT4 - right front and left front cylinders), along with the RPM. Note that the externally mounted probes are strapped to the outside of the exhaust pipes and don't react nearly as quickly as the internally mounted EGTs.
The video recording of the exhaust pipe showed two quick puffs of smoke (video of one puff attached) at about 3:41 and 3:50 on the chart, which are near the end of the rough running period. [can't get the video to load, so I've attached a frame from the video showing the puff]
What the heck is going on? Some of my ideas...
My Rotax mechanic replaced all the rubber lines and overhauled the carburetors in April, as required by Rotax at the 5 year mark, but that substantial work doesn't seem to have affected my RPM loss problem. So, maybe things that weren't worked on are causing it, like the ignition system, feathering propeller, sticking valve, or?
The vibration feels like something is unbalanced. If the two position prop (feathered or cruise) is partially feathering, I think that would only slow the engine without causing vibration; if one prop blade is shifting position, maybe that would do it, but I can't think of how that is possible - maybe a hub inspection is worthwhile. Could a misfiring cylinder cause it, or a sticking exhaust valve?
I can provide more charts showing additional parameters - let me know what you need.
