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%
✖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_s]

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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_s = (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) - 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: 0.0005 Kilogram --> 0.0005 Kilogram No Conversion Required
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_s = (m*ω^2*(e+y))/y --> (0.0005*11.2^2*(0.002+0.0008))/0.0008

Evaluating ... ...

S_s = 0.21952

STEP 3: Convert Result to Output's Unit

0.21952 Newton per Meter --> No Conversion Required

FINAL ANSWER

0.21952 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 » Mechanical » Critical or Whirling Speed of Shaft » Stiffness of Shaft for Equilibrium Position

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National Institute Of Technology (NIT), Hamirpur

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< Critical or Whirling Speed of Shaft Calculators

Static Deflection of Shaft

LaTeX Go Static Deflection of Shaft = (Mass of Rotor*Acceleration Due to Gravity)/Stiffness of Shaft

Critical or Whirling Speed given Static Deflection

LaTeX Go Critical or Whirling Speed = sqrt(Acceleration Due to Gravity/Static Deflection of Shaft)

Critical or Whirling Speed given Stiffness of Shaft

LaTeX Go Critical or Whirling Speed = sqrt(Stiffness of Shaft/Mass of Rotor)

Critical or Whirling Speed in R.P.S

LaTeX Go Critical or Whirling Speed = 0.4985/sqrt(Static Deflection of Shaft)

Stiffness of Shaft for Equilibrium Position Formula

LaTeX Go

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, 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 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 -> 0.21952 = (0.0005*11.2^2*(0.002+0.0008))/0.0008.

FAQ

What is Stiffness of Shaft for Equilibrium Position?

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 and is represented as S_s = (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, 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?

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 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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