Thanks for that. It did occur to me that the bearing forces on opposite sides of the gantry wouldn't necessarily be equal, but I wasn't sure ... so I neglected it

That makes it, for worst case, m*g/4 + F/x*(Z+z). That makes it 340N and -63N for my router which is still well within the ratings.

I'll try working out the equations for if you've got 8 bearings and 4 rails next. That's a bit more difficult though.

Another thing I've neglected is the cutting force parallel to Y (and Z if you're drilling). The former isn't going to be that great, and I think the drilling force is only significant if it's more than the weight of the gantry ...though for Z there is a moment on the bearings assuming the drill isn't centered between them.

Can anyone point me to how to work out cutting force when drilling?