I am using an Elite Directo 2019 turbo trainer. After every ride I have some pieces around my bike. How can I solve this problem? And where to search the issues? thank you for the answer. I am using a carbon framed bike.
So after Googling your model of trainer, it appears the dust is likely coming from the resistance mechanism. With the wheel off the only bicycle components I could see generating it (and depositing it in that area) would be the chain or cassette, which seems unlikely. There are a couple of reasons I could think of for the dust. One could be dust that was left over from manufacturing in the trainer, vacuuming or air washing the unit could help determine if this is the case. A second could be dust created by metal parts on the unit which are possibly breaking in and would theoretically lessen after a few rides (I'd check with the company's customer service on this front).
Personally, I'd clean the unit (with a vacuum and/or air compressor) to remove the pixie dust and if it is still appearing after two or three hours of riding I'd contact the manufacturer. It's normal to expect some break in period for mechanical products, and an issue like this goes away after a brief period of time and the unit continues to function, it should be fine. If not (it doesn't go away or doesn't continue to function) then the manufacture should replace it or provide a refund.