Static Deflection of Shaft 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%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+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_shaft]			+10% -10%

✖Static Deflection of Shaft is the extension or compression of the constraint.ⓘ Static Deflection of Shaft [δ]

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Formula

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Static Deflection of Shaft

Formula

`"δ" = ("m"*"g")/"S"_{"shaft"}`

Example

`"21.30435mm"=("5g"*"9.8m/s²")/"2.3N/m"`

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Download Critical or Whirling Speed of Shaft Formulas PDF

Static Deflection of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection of Shaft = (Mass of Rotor*Acceleration due to Gravity)/Stiffness of Shaft
δ = (m*g)/S_shaft
This formula uses 4 Variables

Variables Used

Static Deflection of Shaft - (Measured in Meter) - Static Deflection of Shaft is the extension or compression of the constraint.
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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
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: 5 Gram --> 0.005 Kilogram (Check conversion here)
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
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

δ = (m*g)/S_shaft --> (0.005*9.8)/2.3

Evaluating ... ...

δ = 0.021304347826087

STEP 3: Convert Result to Output's Unit

0.021304347826087 Meter -->21.304347826087 Millimeter (Check conversion here)

FINAL ANSWER

21.304347826087 ≈ 21.30435 Millimeter <-- Static Deflection 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 » Static Deflection of Shaft

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National Institute Of Technology (NIT), Hamirpur

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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

Static Deflection of Shaft Formula

Static Deflection of Shaft = (Mass of Rotor*Acceleration due to Gravity)/Stiffness of Shaft
δ = (m*g)/S_shaft

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 Static Deflection of Shaft?

Static Deflection of Shaft calculator uses Static Deflection of Shaft = (Mass of Rotor*Acceleration due to Gravity)/Stiffness of Shaft to calculate the Static Deflection of Shaft, The Static deflection of shaft formula is defined as the degree to which a structural element is displaced under a load (due to its deformation). Static Deflection of Shaft is denoted by δ symbol.

How to calculate Static Deflection of Shaft using this online calculator? To use this online calculator for Static Deflection of Shaft, enter Mass of Rotor (m), Acceleration due to Gravity (g) & Stiffness of Shaft (S_shaft) and hit the calculate button. Here is how the Static Deflection of Shaft calculation can be explained with given input values -> 1400 = (0.005*9.8)/2.3.

FAQ

What is Static Deflection of Shaft?

The Static deflection of shaft formula is defined as the degree to which a structural element is displaced under a load (due to its deformation) and is represented as δ = (m*g)/S_shaft or Static Deflection of Shaft = (Mass of Rotor*Acceleration due to Gravity)/Stiffness of Shaft. Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration, Acceleration due to Gravity is acceleration gained by an object because of gravitational force & 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 Static Deflection of Shaft?

The Static deflection of shaft formula is defined as the degree to which a structural element is displaced under a load (due to its deformation) is calculated using Static Deflection of Shaft = (Mass of Rotor*Acceleration due to Gravity)/Stiffness of Shaft. To calculate Static Deflection of Shaft, you need Mass of Rotor (m), Acceleration due to Gravity (g) & Stiffness of Shaft (S_shaft). With our tool, you need to enter the respective value for Mass of Rotor, Acceleration due to Gravity & Stiffness of Shaft 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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