SURFACE FINISH!
This is about surface finish, not thread strength or tap breakage or any of the other things everyone is bringing up. The original question was about surface finish!
Why, you ask! I don't know. But that is what he asked about. The effect on the surface finish that using a smaller tap drill would have.
So I will talk about surface finish and leave all the other details to others. First, it seems like Rons was asking about taps that cut the threads and not formed thread taps. His example of a 5/16" tap drill for a 3/8" thread and that is for a cut thread tap, not a formed thread tap. So we are talking about cutting the metal to make the threads, not pushing it out of the way.
IMHO, the surface finish of a thread that was cut by a tap is dependent on, in order of importance: the tap itself (cut, ground, it's finish, etc.), the cutting fluid used, and then, dead last, the size of the tap drill.
Why do I say that?
It should be somewhat obvious that a tap can not impart a better finish than the finish that it has. The same parts of a tap will trace across the corresponding parts of the thread being cut. So a small notch or hill on the cutting edge of a tap will be reproduced, in reverse in the thread. OK, different teeth of the tap will pass the same point on the thread, but still their effect will be a combination of their defects. So perhaps a bit better, but still generally the same level of finish. It is well known that ground taps make better threads than cut taps. This is an example of this idea. So I say that the primary factor on surface finish is going to be the tap itself.
Then cutting fluid comes in second. Cutting tools can have many problems generated between them and the metal being cut. Soft metals can build up on the cutting edge and deepen the cut. Hard chips can get dragged along and can cut the remaining metal themselves. And probably more that I don't even don't know about. A good cutting fluid for tapping will not be one that primarily cools the tap and metal being cut. Sure, it does that, but the cutting is slow so the amount of heat generated is minimal. No, the primary effect of the cutting fluid is to LUBRICATE. Many, dare I say most taps do not have any radial clearance. That means that the fully formed threads of the tap will be rubbing on the fully formed threads of the hole 100%. And that creates drag or friction. Friction can easily harm a surface that may have been cut cleanly by the tap's cutting edges. So by lubricating that interface between the outside of the tap and the inside of the hole, we not only decrease the amount of torque that is needed, but we also decrease the damage that can occur just behind that cutting edge.
That brings me to the tap drill size. Just how does that have any impact on the surface finish of the thread. Well, it may have a lot OR it may have very little. If a standard, multiple flute tap of the "taper, plug, bottom" type is used, then the chips will accumulate in the flutes. And, depending on the hole depth, they can become packed there very hard and rub against the thread being cut. This can damage the surface finish even if the tap itself does not. But now we come to the MANNER in which that tap IS USED. A careful and un-rushed machinist can frequently back the tap OUT of the hole and clean those accumulated chips out of the flutes BEFORE they can damage the surface finish. Or, a rushed machinist can just push that tap in as fast as possible without breaking it but allowing the chips to pack in solid and then rubbing against the thread being cut and damaging the surface finish.
So it is not so much the tap or the size of the tap drill, but the manner in which it is used that determines how much the surface is damaged by those chips. Of course, using a larger tap drill will mean that fewer chips are made so it will take longer for them to pack in the flutes. And using a smaller tap drill will mean more chips will be made so the flutes will fill up faster. But, the tap drill is not the primary mechanism for surface damage in this case. As I see it, that primary mechanism is the manner of use of the tap. The machinist's technique, if you will. Oh, and the lubrication qualities of the tapping fluid can also have a great effect on this.
And I do realize that all of the above is highly dependent on many other factors. Things like the material being tapped, the quality of the tap, the technique, and many others. I just tried to list the three primary things that I see and in the order in which I think they should be ranked. YMMV!
So, there you go: a surface finish discussion, as requested.
