A Dissertation on Locking screws

Any taper less than Seven (7) Degrees is considered a locking taper.

So the thread of a screw is a taper if you laid out the Pitch Diameter as a leg length on a 2 D drawing and the thread " Pitch" as the height of a triangle . 7 degrees (Tangent is .1228) has a taper height of roughly 1/8 the length of the leg of the laid out triangle

length of Leg equals 1 and height equals .1228 = Tangent of 7 degrees !

Since we want the to know what pitch will lock, we know that the long leg of the triangle was D x Pi, all we have to do is multiply the height by Pi to find the ratio of a locking screw . Therefore, .1228 times Pi = .385

So when the Thread "Pitch" is less than 38 % of the Thread Pitch "Diameter", the screw is locking.

As an Example on a 1" diameter screw, a 2 1/2 TPI would not lock, while a 3 TPI would. ( 2 1/2= .4% while 3 = .33%)

None of this applies to a milling machine leadscrew , nor is it intended to.

Vibration from cutting is like a hammer being taken to the part. Even Press fits can be moved with a hammer.

Rich