Lifting Force on a quill

I am working on a device to take the slop out out most mill-drill quills. I need to know what the formula would be for the force that the different cutters exhibit in lifting the quill from the desired position. It seems counterintuitive that a right hand end mill would be pulling downwards due to the helix angle of the flutes yet the end mill tend to lift upward as it cutting across the slot. I can imperically try different different counterforces but I like to engineer it based on calculations. Any idea?
Dan Mauch
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