My front hub axle has already frozen when riding extreme downhill.
Looking at the hub, it looks like the right hand cone has self-tightened. Can you explain why this happens, and how to fix it?
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There is supposed to be a locknut on the axle, as well as the cone. When adjusting the bearings it's important to get the locknut quite tight against the cone, so that the pair cannot rotate on the threaded axle.
As you've found, if the cone can rotate then it will, from the rotation of the wheel. The left side will get looser (but will be somewhat limited from getting real loose by the axle-fixing nut or skewer) while the right side will get tighter (with nothing to prevent it from getting very tight). If both move together the axle will "migrate" right over time. If the left side is prevented from moving (either due to the fixing nut or a properly set locknut) then the bearing will get tighter and tighter.
To tighten the locknut properly you generally need a thin "cone wrench" of the appropriate size, to fit the narrow flats of the cone so it doesn't turn as the locknut is tightened.
It is a little tricky doing this, as, when you tighten the locknut, the bearing adjustment is inevitably changed slightly. So you have to slightly misadjust the bearing, then tighten the locknut and hope that the bearing is then properly adjusted.