From the white paper “How to Size a Worm Gear Screw Jack” here’s a look at how critical speed helps determine the final design of a linear motion system.
Critical speed is the speed that excites the natural resonance frequency of the screw. The critical speed will vary with the diameter, unsupported length, end fixity and rpm of the screw. Since critical speed can also be affected by the shaft straightness and assembly alignment, it is recommended that the maximum speed be limited to 80 percent of the calculated critical speed. Due to the slow speeds at which jacks move, it is often not a large concern when choosing the size of a jack. However, critical speed should still be measured when making design considerations, especially when considering longer travel lift shafts.
Here is a simplified formula used for calculating critical speed for jacks:
N = Critical Speed (rpm)
d = Root Diameter of Screw (inch)
L = Length Between Bearing Supports (inch)
Cs = End Fixity Factor
0.36 for mounting condition A
1.00 for mounting condition B
1.47 for mounting condition C
2.23 for mounting condition D