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

✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖The Initial Distance of Centre of Gravity of Rotor is a numerical measurement of how far apart objects or points are.ⓘ Initial Distance of Centre of Gravity of Rotor [e]			+10% -10%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load.ⓘ Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency [y]

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Formula

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

Formula

`"y" = ("ω"^2*"e")/("ω"_{"n"}^2-"ω"^2)`

Example

`"0.795031mm"=(("11.2rad/s")^2*"2mm")/(("21rad/s")^2-("11.2rad/s")^2)`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
y = (ω^2*e)/(ω_n^2-ω^2)
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.
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.
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Initial Distance of Centre of Gravity of Rotor: 2 Millimeter --> 0.002 Meter (Check conversion here)
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = (ω^2*e)/(ω_n^2-ω^2) --> (11.2^2*0.002)/(21^2-11.2^2)

Evaluating ... ...

y = 0.000795031055900621

STEP 3: Convert Result to Output's Unit

0.000795031055900621 Meter -->0.795031055900621 Millimeter (Check conversion here)

FINAL ANSWER

0.795031055900621 ≈ 0.795031 Millimeter <-- Additional Deflection of C.G of Rotor

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Critical or Whirling Speed of Shaft » Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency

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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

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

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)
y = (ω^2*e)/(ω_n^2-ω^2)

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 Natural Circular Frequency?

Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency calculator uses 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) to calculate the Additional Deflection of C.G of Rotor, The Additional deflection of centre of gravity of rotor using natural circular frequency 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 Natural Circular Frequency using this online calculator? To use this online calculator for Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency, enter Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency calculation can be explained with given input values -> 13517.24 = (11.2^2*0.002)/(21^2-11.2^2).

FAQ

What is Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency?

The Additional deflection of centre of gravity of rotor using natural circular frequency 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 = (ω^2*e)/(ω_n^2-ω^2) or 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). 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, The Initial Distance of Centre of Gravity of Rotor is a numerical measurement of how far apart objects or points are & Natural Circular Frequency is a scalar measure of rotation rate.

How to calculate Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency?

The Additional deflection of centre of gravity of rotor using natural circular frequency 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 = (Angular Velocity^2*Initial Distance of Centre of Gravity of Rotor)/(Natural Circular Frequency^2-Angular Velocity^2). To calculate Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency, you need Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Angular Velocity, Initial Distance of Centre of Gravity of Rotor & Natural Circular Frequency 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 Angular Velocity, Initial Distance of Centre of Gravity of Rotor & Natural Circular Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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