If you find yourself in the position I did to day you might save yourself a few scratches in your head and some gray hairs by following this guide.
I suddenly found myself standing with a broken bolt in my TAF upper left flipper assembly. It had simply sheered off (maybe due too the bracket had not been screwed tight enough) and the head was lying in the cab.
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BEFORE YO DO ANYTHING: Unplug the power!
First remove the bracket and coil. While removing, it might be a good idea to clean and inspect the coil sleeve
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Then punch a small mark in the remains of the screw.
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Make sure that the punched mark is in the center. This is VERY important.
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Drill deep into the remains of the screw. Make sure that you choose a drill bit that is way smaller in diameter than the screw (other wise you risk hurting the threads of the 'nut'). It will also be wise to arrange some kind of 'collector' of the metal flaking that will occur when drilling. You would not want that floating around in your pin when you connect the power again..... I used my vacuum cleaner.
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When the hole is drilled use a 'screw extractor' of a proportional size, put it in the newly drilled hole and rotate counter clockwise while applying a mild pressure. 'Screw extractors' are commonly found in most hardware stores for very little money.
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If all goes according to plan the 'screw extractor' will start gripping the inside of the drilled screw and slowly unscrew the broken bit.
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You have now solved the issue and saved the threads of the original nut/plate. Get a replacement screw and bolt all back together.
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I hope this helps you if you ever get in to this kind of trouble....
Cheers
/Micael