I chucked my EZ-Outs in the back field
Not sure what you pitched but what you pictured are still screw or thread extractors.
I don't know if "EZ Out" or "Easy Out" was patented, a registered trademark, a brand name, or specific design, but generally was a generic shop term we used for any type or brand of screw extractor, like Xerox was generic for copy. Maybe someone can add an additional citation to this.
I have two types, the expensive ones off the Snap-On truck which are best for broken bolts or studs and work extremely well. They are hex headed and require the hole to be drilled the precise size which is marked on each separate extractor.
The fits all set which is tapered and driven or tapped in with a hammer work well for brass and iron pipe fittings. I refer to those as plumbers extractors.
You must be aware screw extractors have their limits and will seldom turn out portions of thread that broke off from terminal corrosion. (Cub head bolt)
They are also very ineffective if the hole is not or cannot be drilled perfectly straight and of sufficient depth in the exact center and size specified.
The rule of thumb which I follow is if a pair of Vise Grips clamped on tightly would have turned it without slipping before it broke and, I can drill a clean hole, an extractor will take it out the rest of the way.
The thread extractor is not the answer every time, but I assure you, I have extracted just as many broken fasteners or fittings than I have had to drill out, and later rethread the hole. I have also broken them by asking too much from them, something you must avoid at all cost.
If the broken fastener is within extraction parameters, the thread extractor is a time saving device which every mechanic I know goes to first before drilling big and having to tap new threads. If it works, it works, you save time which is money if you work on a flat rate scale of pay.
I have had greater success removing broken brass fittings with the cheaper tapered long nose extractors because for every quarter turn of the tap handle, another hammer tap ensures the cutting edge remains well purchased into the brass material. This type of extractor is not made to remove material but cut and hold similar to a lock washer.
As previously mentioned, plenty of penetrating oil should be used. When you have enough torque on it, it hasn't budged, and you feel it may snap, it probably will. Retreat and drill it out with a LH bit if you have a set.
When you use these little time savers often enough, you get a feel of what they'll take and what they'll break so you can choose your method of removal correctly.
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