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)/(Sshaft-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) - 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.
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)
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)/(Sshaft-m*ω^2) --> (0.005*11.2^2*0.002)/(2.3-0.005*11.2^2)
Evaluating ... ...
y = 0.00074988043998087
STEP 3: Convert Result to Output's Unit
0.00074988043998087 Meter -->0.74988043998087 Millimeter (Check conversion here)
FINAL ANSWER
0.74988043998087 0.74988 Millimeter <-- Additional Deflection of C.G of Rotor
(Calculation completed in 00.004 seconds)

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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

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

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)/(Sshaft-m*ω^2)

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, The Additional deflection of centre of gravity of rotor when shaft starts rotating formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied. 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 (Sshaft) 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 -> 36.49397 = (0.005*11.2^2*0.002)/(2.3-0.005*11.2^2).

FAQ

What is Additional Deflection of Centre of Gravity of Rotor when Shaft Starts Rotating?
The Additional deflection of centre of gravity of rotor when shaft starts rotating formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied and is represented as y = (m*ω^2*e)/(Sshaft-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, 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 & 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?
The Additional deflection of centre of gravity of rotor when shaft starts rotating formula is defined as the movement of a beam or node from its original position due to the forces and loads being applied 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 (Sshaft). 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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