Centrifugal Force Causing Shaft Deflection Calculator

✖Maximum Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.ⓘ Maximum Mass of Rotor [m_max]			+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%

✖Centrifugal Force is the apparent outward force on a mass when it is rotated.ⓘ Centrifugal Force Causing Shaft Deflection [F_c]

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Centrifugal Force Causing Shaft Deflection

Formula

`"F"_{"c"} = "m"_{"max"}*"ω"^2*("e"+"y")`

Example

`"35.1232N"="100kg"*("11.2rad/s")^2*("2mm"+"0.8mm")`

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Download Critical or Whirling Speed of Shaft Formulas PDF

Centrifugal Force Causing Shaft Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor)
F_c = m_max*ω^2*(e+y)
This formula uses 5 Variables

Variables Used

Centrifugal Force - (Measured in Newton) - Centrifugal Force is the apparent outward force on a mass when it is rotated.
Maximum Mass of Rotor - (Measured in Kilogram) - Maximum 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

Maximum Mass of Rotor: 100 Kilogram --> 100 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

F_c = m_max*ω^2*(e+y) --> 100*11.2^2*(0.002+0.0008)

Evaluating ... ...

F_c = 35.1232

STEP 3: Convert Result to Output's Unit

35.1232 Newton --> No Conversion Required

FINAL ANSWER

35.1232 Newton <-- Centrifugal Force

(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 » Centrifugal Force Causing Shaft Deflection

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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

Centrifugal Force Causing Shaft Deflection Formula

Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor)
F_c = m_max*ω^2*(e+y)

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 Centrifugal Force Causing Shaft Deflection?

Centrifugal Force Causing Shaft Deflection calculator uses Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor) to calculate the Centrifugal Force, The Centrifugal Force Causing Shaft Deflection formula is defined as a force that arises from the body's inertia and appears to act on a body that is moving in a circular path that is directed away from the center around which the body is moving. Centrifugal Force is denoted by F_c symbol.

How to calculate Centrifugal Force Causing Shaft Deflection using this online calculator? To use this online calculator for Centrifugal Force Causing Shaft Deflection, enter Maximum Mass of Rotor (m_max), 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 Centrifugal Force Causing Shaft Deflection calculation can be explained with given input values -> 0.001756 = 100*11.2^2*(0.002+0.0008).

FAQ

What is Centrifugal Force Causing Shaft Deflection?

The Centrifugal Force Causing Shaft Deflection formula is defined as a force that arises from the body's inertia and appears to act on a body that is moving in a circular path that is directed away from the center around which the body is moving and is represented as F_c = m_max*ω^2*(e+y) or Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor). Maximum 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 Centrifugal Force Causing Shaft Deflection?

The Centrifugal Force Causing Shaft Deflection formula is defined as a force that arises from the body's inertia and appears to act on a body that is moving in a circular path that is directed away from the center around which the body is moving is calculated using Centrifugal Force = Maximum Mass of Rotor*Angular Velocity^2*(Initial Distance of Centre of Gravity of Rotor+Additional Deflection of C.G of Rotor). To calculate Centrifugal Force Causing Shaft Deflection, you need Maximum Mass of Rotor (m_max), 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 Maximum 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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