Critical Speed for Each Deflection Calculator

✖Critical Speed its unbalanced mass of the rotating object causes deflection that will create resonant vibration.ⓘ Critical Speed for Each Deflection [N_c]

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Critical Speed for Each Deflection

Formula

`"N"_{"c"} = 946/sqrt("δ"_{"s"})`

Example

`"13378.46rev/min"=946/sqrt("0.005mm")`

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Download Design of Agitation System Components Formulas PDF

Critical Speed for Each Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Speed = 946/sqrt(Deflection)
N_c = 946/sqrt(δ_s)
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Critical Speed - (Measured in Revolution per Minute) - Critical Speed its unbalanced mass of the rotating object causes deflection that will create resonant vibration.
Deflection - (Measured in Millimeter) - Deflection is the degree to which a structural element is displaced under a load (due to its deformation).

STEP 1: Convert Input(s) to Base Unit

Deflection: 0.005 Millimeter --> 0.005 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_c = 946/sqrt(δ_s) --> 946/sqrt(0.005)

Evaluating ... ...

N_c = 13378.4603000495

STEP 3: Convert Result to Output's Unit

1400.98908642793 Radian per Second -->13378.4603000495 Revolution per Minute (Check conversion here)

FINAL ANSWER

13378.4603000495 ≈ 13378.46 Revolution per Minute <-- Critical Speed

(Calculation completed in 00.004 seconds)

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< 18 Design of Agitation System Components Calculators

Outside Diameter of Hollow Shaft based on Equivalent Twisting Moment

Go Hollow Shaft Outer Diameter = ((Equivalent Twisting Moment)*(16/pi)*(1)/((Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Maximum Deflection due to Shaft with Uniform Weight

Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Maximum Torque for Hollow Shaft

Go Maximum Torque for Hollow Shaft = ((pi/16)*(Hollow Shaft Outer Diameter^3)*(Torsional Shear Stress in Shaft)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2))

Outside Diameter of Hollow Shaft based on Equivalent Bending Moment

Go Diameter of Hollow Shaft for Agitator = ((Equivalent Bending Moment)*(32/pi)*(1)/((Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)))^(1/3)

Maximum Deflection due to Each Load

Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Equivalent Twisting Moment for Hollow Shaft

Go Equivalent Twisting Moment for Hollow Shaft = (pi/16)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)

Equivalent Bending Moment for Hollow Shaft

Go Equivalent Bending Moment for Hollow Shaft = (pi/32)*(Bending Stress)*(Hollow Shaft Outer Diameter ^3)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^4)

Diameter of Hollow Shaft Subjected to Maximum Bending Moment

Go Hollow Shaft Outer Diameter = (Maximum Bending Moment/((pi/32)*(Bending Stress)*(1-Ratio of Inner to Outer Diameter of Hollow Shaft^2)))^(1/3)

Equivalent Bending Moment for Solid Shaft

Go Equivalent Bending Moment for Solid Shaft = (1/2)*(Maximum Bending Moment+sqrt(Maximum Bending Moment^2+Maximum Torque for Agitator^2))

Diameter of Solid Shaft Subjected to Maximum Bending Moment

Go Diameter of Solid Shaft for Agitator = ((Maximum Bending Moment for Solid Shaft)/((pi/32)*Bending Stress))^(1/3)

Maximum Torque for Solid Shaft

Go Maximum Torque for Solid Shaft = ((pi/16)*(Diameter of Shaft for Agitator^3)*(Torsional Shear Stress in Shaft))

Equivalent Twisting Moment for Solid Shaft

Go Equivalent Twisting Moment for Solid Shaft = (sqrt((Maximum Bending Moment^2)+(Maximum Torque for Agitator^2)))

Diameter of Solid Shaft based on Equivalent Twisting Moment

Go Diameter of Solid Shaft = (Equivalent Twisting Moment*16/pi*1/Torsional Shear Stress in Shaft)^(1/3)

Diameter of Solid Shaft based on Equivalent Bending Moment

Go Diameter of Solid Shaft for Agitator = (Equivalent Bending Moment*32/pi*1/Bending Stress)^(1/3)

Rated Motor Torque

Go Rated Motor Torque = ((Power*4500)/(2*pi*Speed of Agitator))

Force for Design of Shaft Based on Pure Bending

Go Force = Maximum Torque for Agitator/(0.75*Height of Manometer Liquid)

Maximum Bending Moment subject to Shaft

Go Maximum Bending Moment = Length of Shaft*Force

Critical Speed for Each Deflection

Go Critical Speed = 946/sqrt(Deflection)

< 3 Design of Shaft Based on Critical Speed Calculators

Maximum Deflection due to Shaft with Uniform Weight

Go Deflection = (Uniformly Distributed Load per Unit Length*Length^(4))/((8*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Maximum Deflection due to Each Load

Go Deflection due to each Load = (Concentrated Load*Length^(3))/((3*Modulus of Elasticity)*(pi/64)*Diameter of Shaft for Agitator^(4))

Critical Speed for Each Deflection

Go Critical Speed = 946/sqrt(Deflection)

Critical Speed for Each Deflection Formula

Critical Speed = 946/sqrt(Deflection)
N_c = 946/sqrt(δ_s)

What is Critical Speed?

An object is said to reach critical speed when the speed of its rotation corresponds to one of its natural frequencies. This type of speed is studied in a branch of physics known as rotordynamics, which deals with rotational, or angular, motion. A rotating object, such as a propeller or a centrifugal pump, must often pass through one or more of its critical speeds as it accelerates or decelerates. While operating at critical speed, these objects vibrate at a high amplitude, which can cause damage.

How to Calculate Critical Speed for Each Deflection?

Critical Speed for Each Deflection calculator uses Critical Speed = 946/sqrt(Deflection) to calculate the Critical Speed, Critical Speed for Each Deflection is defined as the deflection of the shaft due to transverse vibration because the centrifugal forces change direction rapidly as the shaft turns. Critical Speed is denoted by N_c symbol.

How to calculate Critical Speed for Each Deflection using this online calculator? To use this online calculator for Critical Speed for Each Deflection, enter Deflection (δ_s) and hit the calculate button. Here is how the Critical Speed for Each Deflection calculation can be explained with given input values -> 127754.9 = 946/sqrt(5E-06).

FAQ

What is Critical Speed for Each Deflection?

Critical Speed for Each Deflection is defined as the deflection of the shaft due to transverse vibration because the centrifugal forces change direction rapidly as the shaft turns and is represented as N_c = 946/sqrt(δ_s) or Critical Speed = 946/sqrt(Deflection). Deflection is the degree to which a structural element is displaced under a load (due to its deformation).

How to calculate Critical Speed for Each Deflection?

Critical Speed for Each Deflection is defined as the deflection of the shaft due to transverse vibration because the centrifugal forces change direction rapidly as the shaft turns is calculated using Critical Speed = 946/sqrt(Deflection). To calculate Critical Speed for Each Deflection, you need Deflection (δ_s). With our tool, you need to enter the respective value for Deflection 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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