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)
ωc = sqrt(Sshaft/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: 5 Gram --> 0.005 Kilogram (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ωc = sqrt(Sshaft/m) --> sqrt(2.3/0.005)
Evaluating ... ...
ωc = 21.4476105895272
STEP 3: Convert Result to Output's Unit
21.4476105895272 --> No Conversion Required
FINAL ANSWER
21.4476105895272 21.44761 <-- Critical or Whirling Speed
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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

Critical or Whirling Speed given Stiffness of Shaft Formula

Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor)
ωc = sqrt(Sshaft/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, The Critical or whirling Speed given Stiffness of Shaft formula is defined as the speed at which unwanted vibration happens when shaft is rotating. Critical or Whirling Speed is denoted by ωc 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 (Sshaft) & 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 -> 83.666 = sqrt(2.3/0.005).

FAQ

What is Critical or Whirling Speed given Stiffness of Shaft?
The Critical or whirling Speed given Stiffness of Shaft formula is defined as the speed at which unwanted vibration happens when shaft is rotating and is represented as ωc = sqrt(Sshaft/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?
The Critical or whirling Speed given Stiffness of Shaft formula is defined as the speed at which unwanted vibration happens when shaft is rotating 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 (Sshaft) & 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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