OK, now I've got it. This can happen on any drilling or milling machine.
You simply need a more rigid setup. Use a shorter drill bit, or a center
drill, just to get things going. I once bought about 5 6" long center
drills. I use those when I'm going to drill with a bigger drill, like
a 1/2" drill bit. Those are longer, and so I need more headroom above
the table. I can still get down to the workpiece if I use a long center
drill. Once you have the hole started, then use a skinny drill bit to
go through. If the material is at all tough then pay strict attention
to your speeds. 75 surface feet per minute is pretty good for HSS drills
cutting steel. Take 300 and divide it by the diameter in inches to get
a rough RPM. For instance, a 1" drill you'd run at 300 rpm. Or a 1/8"
drill you'd run at 2400 rpm. Point is, don't run a small drill bit
slowly. Bad things happen. I bought a whole box of 1/8" drills, top quality,
best I could buy, because I so often drill my first hole with that size.
Once you've got a through hole, on your little drill press I would step
up slowly to your desired size, because that will minimize the forces
deflecting your table.

A long skinny bit will almost always skitter on a new surface. You can
sometimes get away with a short skinny bit i.e. a screw machine drill.
Or you can center punch your holes and follow up your accurate centerpunch
with a big whopping centerpunch you drive in with a 2 pound hammer. I know
a good machinist who does that and his drills don't wander because his
centerpunches catch the bit.

Grant

Chris wrote:

Grant wrote:

Do you mean that if you chuck up a drill bit, power off, grab the

outside
of the chuck and wiggle that there is tangible side play in one or
more
directions? That would be terrible if so. Or do you mean that if you
put
a workpiece on the table, chuck up a drill bit, start the motor, and
as
you lower the drill bit into the workpiece as it touches it "skitters"
around a little? These are two very different issues and I'm still not
clear on which you've got going on.

Once more into the breach...

1) power off, bit in, quill retracted: no noticeable side to side
play. a very little bit of rotational play (as described in your
article on spline wear).
2) power on, bit in, quill extended until bit contacts work: bit moves
off target (centre punch or mark)slightly, then digs in and starts
cutting.

Thanks for your patience.

Chris