Critical or Whirling Speed given Static Deflection Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical or Whirling Speed = sqrt(Acceleration due to Gravity/Static Deflection of Shaft)
ωc = sqrt(g/δ)
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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Static Deflection of Shaft - (Measured in Meter) - Static Deflection of Shaft is the extension or compression of the constraint.
STEP 1: Convert Input(s) to Base Unit
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Static Deflection of Shaft: 0.66 Millimeter --> 0.00066 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ωc = sqrt(g/δ) --> sqrt(9.8/0.00066)
Evaluating ... ...
ωc = 121.854359168988
STEP 3: Convert Result to Output's Unit
121.854359168988 --> No Conversion Required
FINAL ANSWER
121.854359168988 121.8544 <-- Critical or Whirling Speed
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
Dipto Mandal has verified this Calculator and 400+ more calculators!

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 Static Deflection Formula

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

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 Static Deflection?

Critical or Whirling Speed given Static Deflection calculator uses Critical or Whirling Speed = sqrt(Acceleration due to Gravity/Static Deflection of Shaft) to calculate the Critical or Whirling Speed, The Critical or Whirling Speed given Static Deflection 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 Static Deflection using this online calculator? To use this online calculator for Critical or Whirling Speed given Static Deflection, enter Acceleration due to Gravity (g) & Static Deflection of Shaft (δ) and hit the calculate button. Here is how the Critical or Whirling Speed given Static Deflection calculation can be explained with given input values -> 121.8544 = sqrt(9.8/0.00066).

FAQ

What is Critical or Whirling Speed given Static Deflection?
The Critical or Whirling Speed given Static Deflection formula is defined as the speed at which unwanted vibration happens when shaft is rotating and is represented as ωc = sqrt(g/δ) or Critical or Whirling Speed = sqrt(Acceleration due to Gravity/Static Deflection of Shaft). Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Static Deflection of Shaft is the extension or compression of the constraint.
How to calculate Critical or Whirling Speed given Static Deflection?
The Critical or Whirling Speed given Static Deflection formula is defined as the speed at which unwanted vibration happens when shaft is rotating is calculated using Critical or Whirling Speed = sqrt(Acceleration due to Gravity/Static Deflection of Shaft). To calculate Critical or Whirling Speed given Static Deflection, you need Acceleration due to Gravity (g) & Static Deflection of Shaft (δ). With our tool, you need to enter the respective value for Acceleration due to Gravity & Static Deflection of Shaft 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 Acceleration due to Gravity & Static Deflection of Shaft. 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(Stiffness of Shaft/Mass of Rotor)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!