Stiffness of Shaft for Equilibrium Position Calculator

✖Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.ⓘ Mass of Rotor [m]			+10% -10%
✖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%
✖Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load.ⓘ Additional Deflection of C.G of Rotor [y]			+10% -10%

✖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.ⓘ Stiffness of Shaft for Equilibrium Position [S_shaft]

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Formula

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Stiffness of Shaft for Equilibrium Position

Formula

`"S"_{"shaft"} = ("m"*"ω"^2*("e"+"y"))/"y"`

Example

`"2.1952N/m"=("5g"*("11.2rad/s")^2*("2mm"+"0.8mm"))/"0.8mm"`

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Download Critical or Whirling Speed of Shaft Formulas PDF

Stiffness of Shaft for Equilibrium Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
S_shaft = (m*ω^2*(e+y))/y
This formula uses 5 Variables

Variables Used

Stiffness of Shaft - (Measured in Newton per Meter) - 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.
Mass of Rotor - (Measured in Kilogram) - Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Mass of Rotor: 5 Gram --> 0.005 Kilogram (Check conversion here)
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)
Additional Deflection of C.G of Rotor: 0.8 Millimeter --> 0.0008 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_shaft = (m*ω^2*(e+y))/y --> (0.005*11.2^2*(0.002+0.0008))/0.0008

Evaluating ... ...

S_shaft = 2.1952

STEP 3: Convert Result to Output's Unit

2.1952 Newton per Meter --> No Conversion Required

FINAL ANSWER

2.1952 Newton per Meter <-- Stiffness of Shaft

(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 » Stiffness of Shaft for Equilibrium Position

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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

Stiffness of Shaft for Equilibrium Position Formula

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 Stiffness of Shaft for Equilibrium Position?

Stiffness of Shaft for Equilibrium Position calculator 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 calculate the Stiffness of Shaft, The Stiffness of shaft for equilibrium position formula is defined as the extent to which an object resists deformation in response to an applied force. Stiffness of Shaft is denoted by S_shaft symbol.

How to calculate Stiffness of Shaft for Equilibrium Position using this online calculator? To use this online calculator 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. Here is how the Stiffness of Shaft for Equilibrium Position calculation can be explained with given input values -> 2.1952 = (0.005*11.2^2*(0.002+0.0008))/0.0008.

FAQ

What is Stiffness of Shaft for Equilibrium Position?

The Stiffness of shaft for equilibrium position formula is defined as the extent to which an object resists deformation in response to an applied force and is represented as S_shaft = (m*ω^2*(e+y))/y or 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. Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration, 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 & Additional Deflection of C.G of Rotor is the degree to which a structural element is displaced under a load.

How to calculate Stiffness of Shaft for Equilibrium Position?

The Stiffness of shaft for equilibrium position formula is defined as the extent to which an object resists deformation in response to an applied force is calculated using 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 calculate Stiffness of Shaft for Equilibrium Position, you need Mass of Rotor (m), Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Additional Deflection of C.G of Rotor (y). With our tool, you need to enter the respective value for Mass of Rotor, Angular Velocity, Initial Distance of Centre of Gravity of Rotor & Additional Deflection of C.G of Rotor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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