To eliminate the creak, it was necessary to make the left axle nut (which presses on a torque-transfer washer) very tight (33 lb ft?). Given how little material cross-section is in the axle at the left side where the electrical cable comes out, there may be danger of the axle snapping off. Is there a recommended tightening-torque for the axle nuts?
Closer inspection of the torque transfer washer shows (see picture) that it contacts the fork dropout slot on one side but not the other. Presumably, the use of motor braking causes the torque direction to switch, and the transfer washer rotates to contact at the other side. After many cycles of back-and-forth torque transfer, the axle nut gets loose, and a creak develops.
As others have discussed:
"Regen braking can slowly loosen the axle".
See also this and this thread. They suggest using thread locker (Loctite 242) and adding washers that allow rotation between the nut and torque arm (in this case torque washer).
No fit is perfect, and the axle will have some rotation with respect to the torque transfer device. But the axle shouldn't rotate with respect to the nut, or the nut will get loose. So there needs to be differential rotation between the nut and torque washer.
To favor desired rotation (axle and nut rotate together with respect to torque washer) over undesired rotation (axle rotates with respect to torque washer and nut), we want more friction between the nut and axle (thread locker) and less friction between the nut and torque washer (add lubricated plate washers).
8/31/2019 Update: 400 km ago, I added a smooth washer between the right axle nut and dropout, and also applied Loctite 243 to that thread. The left axle nut is tight but has no extra washer or Loctite. The axle creak, which was coming back every 100 km or so, has
5/13/2020 Update: 600 km after the 8/31/2019 update, I noticed that both left and right axle nuts were very loose. The loosening and creaking problem is unsolved. Now I am re-torquing the nuts every 150 km or so. A new motor controller might be easier on the axle and nuts.
Fall, 2022: After over 3000 km on the smooth new motor controller, the axle has stayed tight despite heavy regen-breaking. For the previous loosening, I blame the re-synchronization jerk of the original controller when engaging the throttle after coast. Despite its briefness, this always felt like the most violent part of the ride. It stands to reason that the repeated torque impulses (about one per km) gradually loosened the axle.
