### Critical Speeds of Rotating Shafts with Single Loads Equations and Calculators

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            Two Concentrated Loads General Equation *             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)

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