Imported Animation Clips for Prefab Child Objects

Hello Everyone,

Short: I imported an .fbx object with some animation clips into unity and want to play them. My Problem is that they only work when I attach the animator controller to the parent object. Is there a way to attach the animation to the child objects?

Background: I want to do an AR animation of a woodcutting machine. At the end the wood is cut into 4 piece which should then levitate into the air. I haven't found a way of playing the animation simultaneously (4 times the animation of the wood pieces levitating) by using layers or blend tress, since they only add up to the animation and it ends always with 1 piece levitating 4 times as high into the air.
What works for me is when I duplicate the whole prefab and play the animation 4 times at the same time so to say. So it is 4 woodcutting machnies cutting a piece of wood each and levitating 1 different part into the air which looks like one piece is cut into 4 pices.
However i would like to only copy the wood 4 times and let it run on 1 machine 4 times instead of having 4 big machines to compute everytime. Unfortunately putting the animation clips (imported as .fbx) on the wood pieces does not work. It only works if I drag the animation controller on the machine (the machine is the parent and the wood the child object). What am I doing wrong?

Thanks for any help!