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I noticed that the screw-on of my water tap often loosens itself up after I rotate the tap left and right enough times. Every time I rotate the tap left, it loosens the screw a bit, then if I rotate the tap right, the screw does not tighten itself to the same amount.

This, repeated enough times, loosens the screw enough so that the tap would leak.

I thought it might be solved if the screw would have a wavy thread. So, for example, instead of gently sloping downwards by 1 mm every revolution, it would slope up 1 mm for the first half, and down 2 mm for the second half. This way, the screw would lock itself in a local "peak" in the thread, and not loosen itself no matter if I rotate the tap left or right.

Is there such a kind of screw? If so, what are they used for? If not, is it because they have some kind of mechanical weakness?

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This idea doesn't work, because screwing the parts together will tend to strip the threads before the parts are fully squeezed together.

Instead, engineers use different general methods to get the threads to lock and not unscrew themselves in the manner you experienced, as follows:

1) using screws or nuts with plastic inserts in them which interfere with the threads in the mating part. These are called nylock fasteners or lock nuts.

2) using threads whose diameter increases progressively along the length of the threaded portion, so as to generate progressively more interference as the parts are screwed together. these are called tapered or pipe threads.

3) inserting a lock washer between the parts with teeth that bite into the nut or screw head that discourage the parts from unthreading.

4) assembling the part with a glue applied to the threads that sets up and prevents the parts from being unscrewed. This glue is called thread locker.

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