I am a retired tool and die maker and author of the book “Machinery’s Handbook Made Easy”. I have tapped thousands of holes and broken dozens of taps. Anyone who says they never broke a tap is either lying or they haven’t tapped very many holes. The main reasons for tap breakage is:
• They are started crooked. Taps do not follow the previously drilled hole.
• The hole is drilled too small
• The tap is dull
The members have given some good methods of getting out broken taps. The only thing I would add is when you are machining out a broken drill or tap with a carbide drill or end mill, it is very important to advance the tool in a controlled way. In a drill press or vertical mill, set the quill stop at the top of the hole and dial the quill stop down about a 32nd of a turn at a time, so that you are only machining a few thousandths at a time. This is impossible to do with a hand- held hole shooter.
You can avoid breaking taps by making sure you start the tap square to the hole and calculating your thread percentage. Most tap drill charts allow for about 75% of effective thread. This is fine for most general purpose applications, but there are times when you should be using 50% to 60% effective thread to avoid tap breakage. To do this we use a formula:
For inch threads:
Hole size = Major diameter of thread; minus (.01299 x % of thread desired ÷ #of threads per inch)
For example: 60% thread for a ¼ - 20 tap would be;
Hole size = ¼ (or .25) minus (.01299 X 60 ÷ 20)
Hole size = .211 or #4 drill. A number 4 drill is .209, but drills drill slightly oversize.
For metric threads:
Hole size = Major diameter of thread; minus (1.08253 x pitch x percent thread desired)
For example: 50% thread for a M6 x 1.0 tap would be:
Hole size = 6.0mm minus (1.08253 x 1.0 x .50)
Hole size = 5.46mm
Use 50% to 60% thread for small taps in stainless steels, tool steels, and tough materials. Use 100% thread for sheet metal and non-metals.
I have started to find cheap carbide bits in UK shops like Halfords, starting the pilot hole on the tap can be tricky.
A diamond burr (I use a spherical one) in a Dremel will get the surface of the exposed broken tap flat and put a dimple in the centre.