Critical Speeds of Rotating Shafts with Single Loads Equations and Calculators

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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. 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.

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Load Configuration
Equation
Critical Speeds Rotating Shaft Variable Load location Calculator
Critical Speeds Rotating Shaft Load at Center Calculator 
Critical Speeds Rotating Shaft Fixed Ends Calculator
Critical Speeds Rotating Shaft Fixed Ends Central Load Applied Calculator
Critical Speeds Rotating Shaft One Fixed End Calculator
Critical Speeds Rotating Shaft Fixed End Cantilevered Calculator
Two Concentrated Loads General Equation *

Critical Speed Equation 8

Critical Speeds Rotating Shaft fixed Ends Two Loads Calculator
Critical Speeds Rotating Shaft Fixed Ends Two Identical Loads Calculator
Critical Speeds Rotating Shaft Fixed Ends Two Identical Loads Calculator
Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator
Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator
Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator

Where:

N1 = first critical speed, RPM
N2 = second critical speed, RPM
??1 = static deflection, (in, m) at W1 if shaft is horizontal
??2 = static deflection, (in, m) at W2 if shaft is horizontal
E = modulus of elasticity (young's modulus), (psi, N/m2)
d = diameter of shaft, (inches, m)
W1 = load applied to shaft, (lbs, Kg)
I = Area Moment of Inertia , (in4, m4)
l = distance between centers of bearings, (inches, m)
a = distance from bearings to load, (inches, m)
b = distance from bearings to load, (inches, m)

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