Critical or Whirling Speed given Stiffness of Shaft Calculator

✖Stiffness of Shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.ⓘ Stiffness of Shaft [S_s]			+10% -10%
✖Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.ⓘ Mass of Rotor [m]			+10% -10%

✖Critical or whirling speed is the speed at which unwanted vibration happens when a vessel is rotating.ⓘ Critical or Whirling Speed given Stiffness of Shaft [ω_c]

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Critical or Whirling Speed given Stiffness of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor)
ω_c = sqrt(S_s/m)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Critical or Whirling Speed - Critical or whirling speed is the speed at which unwanted vibration happens when a vessel is rotating.
Stiffness of Shaft - (Measured in Newton per Meter) - Stiffness of Shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.
Mass of Rotor - (Measured in Kilogram) - Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Shaft: 2.3 Newton per Meter --> 2.3 Newton per Meter No Conversion Required
Mass of Rotor: 0.0005 Kilogram --> 0.0005 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_c = sqrt(S_s/m) --> sqrt(2.3/0.0005)

Evaluating ... ...

ω_c = 67.8232998312527

STEP 3: Convert Result to Output's Unit

67.8232998312527 --> No Conversion Required

FINAL ANSWER

67.8232998312527 ≈ 67.8233 <-- Critical or Whirling Speed

(Calculation completed in 00.015 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Critical or Whirling Speed of Shaft Calculators

Static Deflection of Shaft

LaTeX Go Static Deflection of Shaft = (Mass of Rotor*Acceleration Due to Gravity)/Stiffness of Shaft

Critical or Whirling Speed given Static Deflection

LaTeX Go Critical or Whirling Speed = sqrt(Acceleration Due to Gravity/Static Deflection of Shaft)

Critical or Whirling Speed given Stiffness of Shaft

LaTeX Go Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor)

Critical or Whirling Speed in R.P.S

LaTeX Go Critical or Whirling Speed = 0.4985/sqrt(Static Deflection of Shaft)

Critical or Whirling Speed given Stiffness of Shaft Formula

LaTeX Go

Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor)
ω_c = sqrt(S_s/m)

What is meant by critical speed of a shaft which are the factors affecting it?

In solid mechanics, in the field of rotor-dynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. The factor which affects the critical speed of a shaft is diameter of the disc, span of the shaft, and eccentricity.

How to Calculate Critical or Whirling Speed given Stiffness of Shaft?

Critical or Whirling Speed given Stiffness of Shaft calculator uses Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor) to calculate the Critical or Whirling Speed, Critical or Whirling Speed given Stiffness of Shaft formula is defined as a measure of the rotational speed at which a shaft begins to vibrate violently, which can lead to its failure, and is dependent on the stiffness of the shaft and the mass of the rotating element. Critical or Whirling Speed is denoted by ω_c symbol.

How to calculate Critical or Whirling Speed given Stiffness of Shaft using this online calculator? To use this online calculator for Critical or Whirling Speed given Stiffness of Shaft, enter Stiffness of Shaft (S_s) & Mass of Rotor (m) and hit the calculate button. Here is how the Critical or Whirling Speed given Stiffness of Shaft calculation can be explained with given input values -> 67.8233 = sqrt(2.3/0.0005).

FAQ

What is Critical or Whirling Speed given Stiffness of Shaft?

Critical or Whirling Speed given Stiffness of Shaft formula is defined as a measure of the rotational speed at which a shaft begins to vibrate violently, which can lead to its failure, and is dependent on the stiffness of the shaft and the mass of the rotating element and is represented as ω_c = sqrt(S_s/m) or Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor). Stiffness of Shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit & Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.

How to calculate Critical or Whirling Speed given Stiffness of Shaft?

Critical or Whirling Speed given Stiffness of Shaft formula is defined as a measure of the rotational speed at which a shaft begins to vibrate violently, which can lead to its failure, and is dependent on the stiffness of the shaft and the mass of the rotating element is calculated using Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor). To calculate Critical or Whirling Speed given Stiffness of Shaft, you need Stiffness of Shaft (S_s) & Mass of Rotor (m). With our tool, you need to enter the respective value for Stiffness of Shaft & Mass of Rotor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Critical or Whirling Speed?

In this formula, Critical or Whirling Speed uses Stiffness of Shaft & Mass of Rotor. We can use 2 other way(s) to calculate the same, which is/are as follows -

Critical or Whirling Speed = 0.4985/sqrt(Static Deflection of Shaft)
Critical or Whirling Speed = sqrt(Acceleration Due to Gravity/Static Deflection of Shaft)

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