I’m aware this is an age old question but as far as I can tell it’s still an issue so…
Blender 2.78
If I leave scales on 1, the model looks fine until I animate it. After that the usual issues appear.
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The solution I use:
FBX export Scale to 0.01 in Blender.
Scale skeletal mesh (or skeletal mesh component) to 100 in UE.
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Not on import but directly on the skeletal mesh component - this scaling affects animations too.
For some reason import scaling didn’t go well for me (didn’t do a thing) but it might have been my luck.
Unanimated, animated, works so far. And is very simple to do so.
(Formatting is still weird here - double enter for a simple line break…)