Can I quote from a post on here a while ago when we were discussing a suspension problem & the need to drill out a bolt “Don’t break a drill, their really hard, even grotty ones.I broke a tap in part of a locomotive I was building & had to take the frames to another town to have the broken bit spark eroded, you can’t do that if you brake a drill in a mounting point. And there’s always tomorrow”.
Firstly how far is the tap in, the more thread in there the greater the likelihood of failure as the torque resistance increases with the square of the depth (I think that’s correct, it’s a loooong time since I had cause to remember things like that).
I hate to question your choice of tools but was it a tap from a well known manufacturer or an offering from the Far East.
There was no YouTube when I was building the loco & so no useful advice from that source but now I’d be looking on there for guidance. I recall pages of advice some credible others less so, a high percentage of these were contributions from America The Americans have been remarkably successful in most of there endeavours; going up seems to be a speciality, going down, we’ll I’ll have to make your own mind up.
Unless you have used a spiral fluted tap you might be able to knock some thin rod (a pop rivet mandrill ?) down the flutes & by gripping those work the tap out. Or you might just be getting more junk into the mix.
See if anyone in your area does spark erosion, they might have some portable kit.
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