Additional Deflection of Centre of Gravity of Rotor using Whirling Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Additional Deflection of C.G of Rotor = Initial Distance of Centre of Gravity of Rotor/((Angular Velocity/Critical or Whirling Speed)^2-1)
y = e/((ω/ωc)^2-1)
This formula uses 4 Variables
Variables Used
Additional Deflection of C.G of Rotor - (Measured in Meter) - Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load.
Initial Distance of Centre of Gravity of Rotor - (Measured in Meter) - The Initial Distance of Centre of Gravity of Rotor is a numerical measurement of how far apart objects or points are.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Critical or Whirling Speed - Critical or whirling speed is the speed at which unwanted vibration happens when a vessel is rotating.
STEP 1: Convert Input(s) to Base Unit
Initial Distance of Centre of Gravity of Rotor: 2 Millimeter --> 0.002 Meter (Check conversion here)
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Critical or Whirling Speed: 6 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
y = e/((ω/ωc)^2-1) --> 0.002/((11.2/6)^2-1)
Evaluating ... ...
y = 0.000805008944543829
STEP 3: Convert Result to Output's Unit
0.000805008944543829 Meter -->0.805008944543829 Millimeter (Check conversion here)
FINAL ANSWER
0.805008944543829 0.805009 Millimeter <-- Additional Deflection of C.G of Rotor
(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

Additional Deflection of Centre of Gravity of Rotor using Whirling Speed Formula

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

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 Additional Deflection of Centre of Gravity of Rotor using Whirling Speed?

Additional Deflection of Centre of Gravity of Rotor using Whirling Speed calculator uses Additional Deflection of C.G of Rotor = Initial Distance of Centre of Gravity of Rotor/((Angular Velocity/Critical or Whirling Speed)^2-1) to calculate the Additional Deflection of C.G of Rotor, The Additional deflection of centre of gravity of rotor using whirling speed formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied. Additional Deflection of C.G of Rotor is denoted by y symbol.

How to calculate Additional Deflection of Centre of Gravity of Rotor using Whirling Speed using this online calculator? To use this online calculator for Additional Deflection of Centre of Gravity of Rotor using Whirling Speed, enter Initial Distance of Centre of Gravity of Rotor (e), Angular Velocity (ω) & Critical or Whirling Speed c) and hit the calculate button. Here is how the Additional Deflection of Centre of Gravity of Rotor using Whirling Speed calculation can be explained with given input values -> 805.0089 = 0.002/((11.2/6)^2-1).

FAQ

What is Additional Deflection of Centre of Gravity of Rotor using Whirling Speed?
The Additional deflection of centre of gravity of rotor using whirling speed formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied and is represented as y = e/((ω/ωc)^2-1) or Additional Deflection of C.G of Rotor = Initial Distance of Centre of Gravity of Rotor/((Angular Velocity/Critical or Whirling Speed)^2-1). The Initial Distance of Centre of Gravity of Rotor is a numerical measurement of how far apart objects or points are, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time & Critical or whirling speed is the speed at which unwanted vibration happens when a vessel is rotating.
How to calculate Additional Deflection of Centre of Gravity of Rotor using Whirling Speed?
The Additional deflection of centre of gravity of rotor using whirling speed formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied is calculated using Additional Deflection of C.G of Rotor = Initial Distance of Centre of Gravity of Rotor/((Angular Velocity/Critical or Whirling Speed)^2-1). To calculate Additional Deflection of Centre of Gravity of Rotor using Whirling Speed, you need Initial Distance of Centre of Gravity of Rotor (e), Angular Velocity (ω) & Critical or Whirling Speed c). With our tool, you need to enter the respective value for Initial Distance of Centre of Gravity of Rotor, Angular Velocity & Critical or Whirling Speed 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 Additional Deflection of C.G of Rotor?
In this formula, Additional Deflection of C.G of Rotor uses Initial Distance of Centre of Gravity of Rotor, Angular Velocity & Critical or Whirling Speed. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!