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Stiffness of Shaft for Equilibrium Position Formula

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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. Check FAQs

S s = \frac{m \cdot ω^{2} \cdot (e + y)}{y}

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

Stiffness of Shaft for Equilibrium Position Example

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Here is how the Stiffness of Shaft for Equilibrium Position equation looks like with Values.

Here is how the Stiffness of Shaft for Equilibrium Position equation looks like with Units.

Here is how the Stiffness of Shaft for Equilibrium Position equation looks like.

0.2195 = \frac{0.0005 \cdot {11.2}^{2} \cdot (2 + 0.8)}{0.8}

0.2195N/m = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot (2mm + 0.8mm)}{0.8mm}

0.2195 = \frac{0.0005 \cdot {11.2}^{2} \cdot (2 + 0.8)}{0.8}

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Stiffness of Shaft for Equilibrium Position Solution

Follow our step by step solution on how to calculate Stiffness of Shaft for Equilibrium Position?

FIRST Step Consider the formula

S s = \frac{m \cdot ω^{2} \cdot (e + y)}{y}

Next Step Substitute values of Variables

∴

S s = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot (2mm + 0.8mm)}{0.8mm}

Next Step Convert Units

∴

S s = \frac{0.0005kg \cdot {11.2rad/s}^{2} \cdot (0.002m + 0.0008m)}{0.0008m}

Next Step Prepare to Evaluate

∴

S s = \frac{0.0005 \cdot {11.2}^{2} \cdot (0.002 + 0.0008)}{0.0008}

Next Step Evaluate

∴

S s = 0.21952N/m

LAST Step Rounding Answer

∴

S s = 0.2195N/m

Stiffness of Shaft for Equilibrium Position Formula Elements

Variables

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

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

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

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 Stiffness of Shaft for Equilibrium Position?

Stiffness of Shaft for Equilibrium Position evaluator uses 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 to evaluate the Stiffness of Shaft, Stiffness of Shaft for Equilibrium Position formula is defined as a measure of the shaft's ability to resist deformation when subjected to external forces, providing a critical value for the whirling speed of the shaft in rotational motion. Stiffness of Shaft is denoted by S_s symbol.

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

FAQs on Stiffness of Shaft for Equilibrium Position

What is the formula to find Stiffness of Shaft for Equilibrium Position?

The formula of Stiffness of Shaft for Equilibrium Position is expressed as 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. Here is an example- 0.21952 = (0.0005*11.2^2*(0.002+0.0008))/0.0008.

How to calculate Stiffness of Shaft for Equilibrium Position?

With Mass of Rotor (m), Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Additional Deflection of C.G of Rotor (y) we can find Stiffness of Shaft for Equilibrium Position using the formula - 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.

Can the Stiffness of Shaft for Equilibrium Position be negative?

No, the Stiffness of Shaft for Equilibrium Position, measured in Surface Tension cannot be negative.

Which unit is used to measure Stiffness of Shaft for Equilibrium Position?

Stiffness of Shaft for Equilibrium Position is usually measured using the Newton per Meter[N/m] for Surface Tension. Millinewton per Meter[N/m], Gram-Force per Centimeter[N/m], Dyne per Centimeter[N/m] are the few other units in which Stiffness of Shaft for Equilibrium Position can be measured.

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Stiffness of Shaft for Equilibrium Position Formula

Stiffness of Shaft for Equilibrium Position Example

Stiffness of Shaft for Equilibrium Position Solution

Stiffness of Shaft for Equilibrium Position Formula Elements

Other formulas in Critical or Whirling Speed of Shaft category

How to Evaluate Stiffness of Shaft for Equilibrium Position?

FAQs on Stiffness of Shaft for Equilibrium Position

Variable Name