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

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

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

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

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

y - Additional Deflection of C.G of Rotor?m - Mass of Rotor?ω - Angular Velocity?e - Initial Distance of Centre of Gravity of Rotor?S_s - Stiffness of Shaft?

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

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Here is how the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating equation looks like with Values.

Here is how the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating equation looks like with Units.

Here is how the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating equation looks like.

0.0561 = \frac{0.0005 \cdot {11.2}^{2} \cdot 2}{2.3 - 0.0005 \cdot {11.2}^{2}}

0.0561mm = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot 2mm}{2.3N/m - 0.0005kg \cdot {11.2rad/s}^{2}}

0.0561 = \frac{0.0005 \cdot {11.2}^{2} \cdot 2}{2.3 - 0.0005 \cdot {11.2}^{2}}

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

Follow our step by step solution on how to calculate Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

y = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot 2mm}{2.3N/m - 0.0005kg \cdot {11.2rad/s}^{2}}

Next Step Convert Units

∴

y = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot 0.002m}{2.3N/m - 0.0005kg \cdot {11.2rad/s}^{2}}

Next Step Prepare to Evaluate

∴

y = \frac{0.0005 \cdot {11.2}^{2} \cdot 0.002}{2.3 - 0.0005 \cdot {11.2}^{2}}

Next Step Evaluate

∴

y = 5.60680826718158E-05m

Next Step Convert to Output's Unit

∴

y = 0.0560680826718158mm

LAST Step Rounding Answer

∴

y = 0.0561mm

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

Mass of Rotor

Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass 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

Stiffness of Shaft

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.

Symbol: S_s

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Shaft

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 using Natural Circular Frequency

y = \frac{ω^{2} \cdot e}{{ω n}^{2} - 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 when Shaft Starts Rotating?

Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating evaluator uses 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) to evaluate the Additional Deflection of C.G of Rotor, Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating formula is defined as the measure of the shift in the centre of gravity of a rotor when it starts rotating, which is critical in determining the whirling speed of a shaft and ensuring the stability of the system. Additional Deflection of C.G of Rotor is denoted by y symbol.

How to evaluate Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating using this online evaluator? To use this online evaluator for Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating, enter Mass of Rotor (m), Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Stiffness of Shaft (S_s) and hit the calculate button.

FAQs on Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating

What is the formula to find Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating?

The formula of Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating is expressed as 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). Here is an example- 56.06808 = (0.0005*11.2^2*0.002)/(2.3-0.0005*11.2^2).

How to calculate Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating?

With Mass of Rotor (m), Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Stiffness of Shaft (S_s) we can find Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating using the formula - 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).

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=(Angular Velocity^2*Initial Distance of Centre of Gravity of Rotor)/(Natural Circular Frequency^2-Angular Velocity^2)

Can the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating be negative?

Yes, the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating, measured in Length can be negative.

Which unit is used to measure Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating?

Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating 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 when Shaft Starts Rotating can be measured.

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

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

​GoAdditional Deflection of Centre of Gravity of Rotor using Natural Circular Frequency Formula

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

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

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

FAQs on Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating

Variable Name

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

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