Natural Circular Frequency 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_shaft]			+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%

✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency of Shaft [ω_n]

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Formula

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Natural Circular Frequency of Shaft

Formula

`"ω"_{"n"} = sqrt("S"_{"shaft"}/"m")`

Example

`"21.44761rad/s"=sqrt("2.3N/m"/"5g")`

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Download Critical or Whirling Speed of Shaft Formulas PDF

Natural Circular Frequency of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor)
ω_n = sqrt(S_shaft/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

Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
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: 5 Gram --> 0.005 Kilogram (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = sqrt(S_shaft/m) --> sqrt(2.3/0.005)

Evaluating ... ...

ω_n = 21.4476105895272

STEP 3: Convert Result to Output's Unit

21.4476105895272 Radian per Second --> No Conversion Required

FINAL ANSWER

21.4476105895272 ≈ 21.44761 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.007 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Critical or Whirling Speed of Shaft » Natural Circular Frequency of Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 12 Critical or Whirling Speed of Shaft Calculators

Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating

Go Additional Deflection of C.G of Rotor = (Mass of Rotor*Angular Velocity^2*Initial Distance of Centre of Gravity of Rotor)/(Stiffness of Shaft-Mass of Rotor*Angular Velocity^2)

Stiffness of Shaft for Equilibrium Position

Go Stiffness of Shaft = (Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor))/Additional Deflection of C.G of Rotor

Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency

Go Additional Deflection of C.G of Rotor = (Angular Velocity^2*Initial Distance of Centre of Gravity of Rotor)/(Natural Circular Frequency^2-Angular Velocity^2)

Mass of Rotor given Centrifugal Force

Go Maximum Mass of Rotor = Centrifugal Force/(Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor))

Centrifugal Force Causing Shaft Deflection

Go Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor)

Additional Deflection of Centre of Gravity of Rotor using Whirling Speed

Go Additional Deflection of C.G of Rotor = Initial Distance of Centre of Gravity of Rotor/((Angular Velocity/Critical or Whirling Speed)^2-1)

Static Deflection of Shaft

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

Critical or Whirling Speed given Static Deflection

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

Critical or Whirling Speed given Stiffness of Shaft

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

Natural Circular Frequency of Shaft

Go Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor)

Critical or Whirling Speed in R.P.S

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

Force Resisting Additional Deflection of Centre of Gravity of Rotor

Go Force = Stiffness of Spring*Additional Deflection of C.G of Rotor

Natural Circular Frequency of Shaft Formula

Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor)
ω_n = sqrt(S_shaft/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 Natural Circular Frequency of Shaft?

Natural Circular Frequency of Shaft calculator uses Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor) to calculate the Natural Circular Frequency, The Natural circular frequency of shaft formula is defined as a scalar measure of rotation rate. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Natural Circular Frequency of Shaft using this online calculator? To use this online calculator for Natural Circular Frequency of Shaft, enter Stiffness of Shaft (S_shaft) & Mass of Rotor (m) and hit the calculate button. Here is how the Natural Circular Frequency of Shaft calculation can be explained with given input values -> 83.666 = sqrt(2.3/0.005).

FAQ

What is Natural Circular Frequency of Shaft?

The Natural circular frequency of shaft formula is defined as a scalar measure of rotation rate and is represented as ω_n = sqrt(S_shaft/m) or Natural Circular Frequency = 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 Natural Circular Frequency of Shaft?

The Natural circular frequency of shaft formula is defined as a scalar measure of rotation rate is calculated using Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor). To calculate Natural Circular Frequency of Shaft, you need Stiffness of Shaft (S_shaft) & 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.

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