FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

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

GoAdditional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating Formula

Fx Copy

LaTeX Copy

Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load. Check FAQs

y = \frac{ω^{2} \cdot e}{{ω n}^{2} - ω^{2}}

y - Additional Deflection of C.G of Rotor?ω - Angular Velocity?e - Initial Distance of Centre of Gravity of Rotor?ω_n - Natural Circular Frequency?

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

With values

With units

Only example

Here is how the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency equation looks like with Values.

Here is how the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency equation looks like with Units.

Here is how the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency equation looks like.

0.795 = \frac{{11.2}^{2} \cdot 2}{21^{2} - {11.2}^{2}}

0.795mm = \frac{{11.2rad/s}^{2} \cdot 2mm}{{21rad/s}^{2} - {11.2rad/s}^{2}}

0.795 = \frac{{11.2}^{2} \cdot 2}{21^{2} - {11.2}^{2}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency

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

Follow our step by step solution on how to calculate Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency?

FIRST Step Consider the formula

y = \frac{ω^{2} \cdot e}{{ω n}^{2} - ω^{2}}

Next Step Substitute values of Variables

∴

y = \frac{{11.2rad/s}^{2} \cdot 2mm}{{21rad/s}^{2} - {11.2rad/s}^{2}}

Next Step Convert Units

∴

y = \frac{{11.2rad/s}^{2} \cdot 0.002m}{{21rad/s}^{2} - {11.2rad/s}^{2}}

Next Step Prepare to Evaluate

∴

y = \frac{{11.2}^{2} \cdot 0.002}{21^{2} - {11.2}^{2}}

Next Step Evaluate

∴

y = 0.000795031055900621m

Next Step Convert to Output's Unit

∴

y = 0.795031055900621mm

LAST Step Rounding Answer

∴

y = 0.795mm

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

Variables

Additional Deflection of C.G of Rotor

Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load.

Symbol: y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Additional Deflection of C.G of Rotor

Angular Velocity

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.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Initial Distance of Centre of Gravity of Rotor

The Initial Distance of Centre of Gravity of Rotor is a numerical measurement of how far apart objects or points are.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Initial Distance of Centre of Gravity of Rotor

Natural Circular Frequency

Natural Circular Frequency is a scalar measure of rotation rate.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Other Formulas to find Additional Deflection of C.G of Rotor

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

y = \frac{e}{{(\frac{ω}{ω c})}^{2} - 1}

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

y = \frac{m \cdot ω^{2} \cdot e}{S s - m \cdot ω^{2}}

Other formulas in Critical or Whirling Speed of Shaft category

Go Static Deflection of Shaft

δ = \frac{m \cdot g}{S s}

Go Critical or Whirling Speed in R.P.S

ω c = \frac{0.4985}{\sqrt{δ}}

Go Critical or Whirling Speed given Static Deflection

ω c = \sqrt{\frac{g}{δ}}

Go Critical or Whirling Speed given Stiffness of Shaft

ω c = \sqrt{\frac{S s}{m}}

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

Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency evaluator 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 evaluate the Additional Deflection of C.G of Rotor, Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency formula is defined as a measure of the rotor's centre of gravity displacement from its initial position when the rotor is subjected to a critical or whirling speed of shaft, which is a crucial parameter in determining the stability of rotating machines. Additional Deflection of C.G of Rotor is denoted by y symbol.

How to evaluate Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency?

The formula of Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency is expressed as 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). Here is an example- 795.0311 = (11.2^2*0.002)/(21^2-11.2^2).

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

With Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Natural Circular Frequency (ω_n) we can find Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency using the 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).

What are the other ways to Calculate Additional Deflection of C.G of Rotor?

Here are the different ways to Calculate Additional Deflection of C.G of Rotor-

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)

Can the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency be negative?

Yes, the Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency, measured in Length can be negative.

Which unit is used to measure Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency?

Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Additional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

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

​GoAdditional Deflection of Centre of Gravity of Rotor using Whirling Speed Formula

​GoAdditional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating Formula

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

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

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

Other Formulas to find Additional Deflection of C.G of Rotor

Other formulas in Critical or Whirling Speed of Shaft category

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

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

Variable Name

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

GoAdditional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating Formula