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
	Open: Critical Speeds Rotating Shaft Variable Load location Calculator
	Open: Critical Speeds Rotating Shaft Load at Center Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Central Load Applied Calculator
	Open: Critical Speeds Rotating Shaft One Fixed End Calculator
	Open: Critical Speeds Rotating Shaft Fixed End Cantilevered Calculator
Two Concentrated Loads General Equation *
	Open: Critical Speeds Rotating Shaft fixed Ends Two Loads Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Two Identical Loads Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Two Identical Loads Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator
	Open: Critical Speeds Rotating Shaft Fixed Ends Identical Load Distances Calculator

Where:

N1	= first critical speed, RPM
N2	= second critical speed, RPM
Δ1	= static deflection, (in, m) at W1 if shaft is horizontal
Δ2	= 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)

Related Resources:

• Critical Speeds of Rotating Shafts with Distributed Loads Equations
• Critical Speeds of Rotating Shafts Review