This is from machinedesign.com
All theoretical analyses of self-locking worm gears deal with static conditions. In such an analysis, the load on the worm gear can�t drive the worm if the coefficient of friction between worm gear and worm is larger than the tangent of the worm�s lead angle. In other words, the friction angle must be larger than the lead angle to prevent backdriving.
Within the last 3 years, our failure analysis engineers investigated two accidents involving worm gears where the user was injured. In each case, a designer selected a worm gear speed reducer from a catalog and incorporated it into a lift device intended to raise and lower people. In both cases, the designer was under the impression that the load (person plus platform) could not self-lower. They both relied on self-locking worm gears to hold the cargo in a desired position and genuinely believed that no brake was necessary to supplement the worm gear in such a critical application.
So it is a matter of friction. There is your answer!
