When an old tip is removed from a Hakko soldering iron, the insert sleeve that is press fit inside the tip may remain on the heating element because it had become loose over time as the tip wore out. When you try to put a new tip onto a heating element that has the insert sleeve from the old tip still on it, you will likely think that the hole of your new tip is too small and the new tip will not fit on top of the heating element.
You can tell if the old sleeve insert is on the heating element by looking at the color of the heating element itself. The heating element is made of a ceramic material and in a new condition is white. Over time there can be some discoloration but overall, you should still be able to see the off-white ceramic material of the heating element. If the insert sleeve is on the heating element, there will be an obvious metallic appearance to the heating element.
With the iron unplugged from the station and cool to the touch, simply pull the insert sleeve off the heating element using your fingers. You may need to twist the insert sleeve slightly to help it come off the heating element.
IMPORTANT: Be sure never to bend the heating element or strike it with or against any object as the ceramic can be broken.
After the old insert sleeve has been removed, your new tips will fit perfectly.
In rare occasions the insert is wedged onto the heating element and can not be removed by hand. In this case you will need to heat the insert by powering on the iron. After 10-15 seconds the heat will cause the insert to slightly expand allowing you to remove the insert with pliers. Be very careful as you try to remove the insert. The ceramic can be easily broken if you do not pull the insert straight off. The parts will (obviously) be very hot. Turn the iron off immediately after removing the insert. After the iron has cooled replace with the new tip, enclosure and nut.