Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating 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%
✖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 [S_s]			+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 Centre of Gravity of Rotor when Shaft Starts Rotating [y]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.

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)
Stiffness of Shaft: 2.3 Newton per Meter --> 2.3 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y = (m*ω^2*e)/(S_s-m*ω^2) --> (0.0005*11.2^2*0.002)/(2.3-0.0005*11.2^2)

Evaluating ... ...

y = 5.60680826718158E-05

STEP 3: Convert Result to Output's Unit

5.60680826718158E-05 Meter -->0.0560680826718158 Millimeter (Check conversion here)

FINAL ANSWER

0.0560680826718158 ≈ 0.056068 Millimeter <-- Additional Deflection of C.G of Rotor

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

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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)

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

Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating calculator 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 calculate 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 calculate Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating using this online calculator? To use this online calculator 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. Here is how the Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating calculation can be explained with given input values -> 56.06808 = (0.0005*11.2^2*0.002)/(2.3-0.0005*11.2^2).

FAQ

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

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 and is represented as y = (m*ω^2*e)/(S_s-m*ω^2) or 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). 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 & 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.

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

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 is calculated using 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 calculate Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating, you need Mass of Rotor (m), Angular Velocity (ω), Initial Distance of Centre of Gravity of Rotor (e) & Stiffness of Shaft (S_s). With our tool, you need to enter the respective value for Mass of Rotor, Angular Velocity, Initial Distance of Centre of Gravity of Rotor & Stiffness of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Additional Deflection of C.G of Rotor?

In this formula, Additional Deflection of C.G of Rotor uses Mass of Rotor, Angular Velocity, Initial Distance of Centre of Gravity of Rotor & Stiffness of Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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