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Critical Speeds of Rotating Shafts with Single Loads Equations

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Critical Speeds of Rotating Shafts or Mass Review

Critical Speeds of Rotating Shafts with Single Loads: When calculating critical speeds, the weight or mass of the rotating cylinder or shaft is assumed to be zero or add 1/2 to 2/3 of the rotating shaft to the load mass. These formulas assume steel shafts having a modulus of elasticity E = 29,000,000. Keep in mind that a shaft with more than one load or distributed loads may have an infinite number of critical speeds. Typically, the first critical speed is most important for your design.

Load Configuration
Equation
Bearings
Bearings Supported
 
Bearings Supported
Bearings Fixed
Bearings Fixed

One Bearing Fixed,
O one Bearing Supported
One Bearing Fixed
One Free End

 

N = critical speed, RPM
d = diameter of shaft, in inches
W = load applied to shaft, in pounds
l = distance between centers of bearings, in inches
a = distance from bearings to load
b = distance from bearings to load

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