I use a very sharp drill bit; get one with a split point if you can.
Center the drill bit in the very small dimple in the center of the rivet. You do this more by feel than by sight. I never use a centerpunch or awl.
This next part is the key:
Give the drill chuck about 1/8 to 1/4 turn by hand. This will start curling up a nice chip and seats the bit, although you can't see it. Then start drilling slowly. You can steer the bit a little by using side force if it starts to wander.
Stop drilling when you're through the head, don't go all the way through the stem. If the head doesn't pop off, you can push it off with a putty knife, or even a piece of hard plastic, just be careful not to scratch the AlClad.
Works for me. I drilled at least 500 rivets this way without an accident.
center punch with an automatic center punch
drill with a small bit until you find the size that is the same as the rivet.
YOu can use that bit for all the rest of the rivets.
You may need numbered drill bits instead of english sizes.
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If the rivets are original they are number 4's or 4/32ths or 1/8". For #4 rivets use a 135 degree split tip #30 drill bit. High speed is best, at least a 2400 RPM drill motor works best. If you are more comfortable, center punch the rivet, then start drilling down the center. the head should pop off on the drill bit. Remove the head from the drill bit tip with pliers (if it did not come off the drill bit by its self)and drill out the shank. Same procedure if the rivets are #5's or 5/32" only use a #21 drill bit. If the rivets are #6 or 6/32 or 3/16th's use a #10 drill bit. If you are not sure what size they are, start with the #30 bit and step up to a #21 if the head does not drill off with with the #30. You should not have to go to the #10 but who knows. After you have drilled off a few it becomes much easier. Good Luck