If you are of my generation you probably played with TinkerToys. They were wood dowels that were split on the ends so they could be inserted into round wood connectors. If you were like me you would have connected them in a straight horizontal line to see how long you could make it before it would fail. What was happening is that with each connector, the structure would get a little less rigid. And as the load on the free end kept increasing each connection would give a little bit and the straight line would begin to droop.
The same thing is occurring with your milling tool systems. You have multiple connections that are not 100% rigid. Cutter to collet to toolholder to spindle to headstock.
The spindle bearings do not have 100% preload or they wouldn’t rotate. The connection of the toolholder shank in the spindle taper is not a 100% perfect mating or you could never get the toolholder out. The cutter shank has a minus tolerance that allows its insertion into a plus tolerance toolholder or collet bore. Most systems collapse around the shank, but there is still some micro-slippage. Each connection’s “play” contributes to flexibility we measure at the tool point.
FYI – TinkerToys are still produced 105 years after their introduction in my home state of Pennsylvania by K’NEX.
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