You must drill a good hole to successfully tap a good part. Period.
The drill must be sharp on both edges or it may drill eccentrically and drill an over-sized hole. Inspect the end of the drill with a 10x loupe, and check to see that both corners of the edges look the same. Try this on a new, larger drill first and you'll see what I mean.
A dull drill may generate a lot of heat as you drill, work-hardening some materials and making them more difficult to tap. Don't be cheap, always use a good, sharp drill.
Use of a good cutting fluid helps reduce friction, reducing some of the heat, and flushing chips out of the flutes of your drills and taps. Always choose a fluid suitable for the material you are drilling and tapping. Some fluids stain some materials. Check the containers for cautions.
Tap drill sizes are only suggested starting points. You will probably need to adjust the size of drill up or down a little depending on the depth of the hole, the material you are tapping, and your set-up. It is a good idea to first experiment a little with some scrap material of the same type and thickness.
Holes drilled with a hand held drill or drill handpiece will not be accurate. If your part is important, hold it in a vise or fixture and use a drill press.
Some materials push-away when drilled and tapped, others have a memory and shrink back. Titanium is notorious for that, it squeals like a pig when it is being machined with tools not properly relieved behind the cutting edges.
Always measure your drills with a micrometer before drilling a part, to be certain you have the correct size. Measure twice, cut once, just like they taught you in shop class in junior high school.
CAUTION: You should always work in a well-lit and well-ventilated area, and always wear your OSHA approved safety glasses when working with any cutting tools. You only get one set of eyes, take good care of them.
NEVER, ever, grab any cutting tool that is still in motion. If it is spinning, wait for it to stop. Cutting tools and the chips they make are sharp. They will cut.
NEVER place your finger between a part and the end of a drill. A drill can easily cut through soft flesh and bone. Why anyone would do this in the first place is beyond me, but in 40+ years of metalworking sales we've seen it happen.
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