Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket Solution

STEP 0: Pre-Calculation Summary
Formula Used
Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2))
N = 60*vmin/(D*pi*cos(α/2))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Speed of chain drive shaft in rpm - Speed of chain drive shaft in rpm is the number of turns of the shaft divided by time, specified as revolutions per minute (rpm).
Minimum Linear Velocity of Sprocket - (Measured in Meter per Second) - The Minimum Linear Velocity of Sprocket is defined as the lowest possible velocity of the sprocket when it is moving.
Pitch Circle Diameter of Sprocket - (Measured in Meter) - Pitch Circle Diameter of Sprocket is the diameter of the pitch circle (passing through rollers centre) of the sprocket.
Pitch Angle of Sprocket - (Measured in Radian) - The Pitch Angle of Sprocket is generally the angle subtended by a small line called pitch. It is generally used in sprockets.
STEP 1: Convert Input(s) to Base Unit
Minimum Linear Velocity of Sprocket: 4.2 Meter per Second --> 4.2 Meter per Second No Conversion Required
Pitch Circle Diameter of Sprocket: 110 Millimeter --> 0.11 Meter (Check conversion here)
Pitch Angle of Sprocket: 18 Degree --> 0.31415926535892 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
N = 60*vmin/(D*pi*cos(α/2)) --> 60*4.2/(0.11*pi*cos(0.31415926535892/2))
Evaluating ... ...
N = 738.308818696073
STEP 3: Convert Result to Output's Unit
738.308818696073 --> No Conversion Required
FINAL ANSWER
738.308818696073 738.3088 <-- Speed of chain drive shaft in rpm
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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6 Polygonal Effect Calculators

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket
Go Pitch Circle Diameter of Sprocket = Minimum Linear Velocity of Sprocket*60/(pi*Speed of chain drive shaft in rpm*cos(Pitch Angle of Sprocket/2))
Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket
Go Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2))
Minimum Linear Velocity of Sprocket
Go Minimum Linear Velocity of Sprocket = pi*Pitch Circle Diameter of Sprocket*Speed of chain drive shaft in rpm*cos(Pitch Angle of Sprocket/2)/60
Pitch Circle Diameter of Sprocket given Linear Velocity of Sprocket
Go Pitch Circle Diameter of Sprocket = Linear Velocity of Sprocket*60/(pi*Speed of chain drive shaft in rpm)
Speed of Rotation of Shaft given Linear Velocity of Sprocket
Go Speed of chain drive shaft in rpm = Linear Velocity of Sprocket*60/(pi*Pitch Circle Diameter of Sprocket)
Linear Velocity of Sprocket
Go Linear Velocity of Sprocket = pi*Pitch Circle Diameter of Sprocket*Speed of chain drive shaft in rpm/60

Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket Formula

Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2))
N = 60*vmin/(D*pi*cos(α/2))

Define Linear velocity?

Linear velocity is the measure of “the rate of change of displacement with respect to time when the object moves along a straight path.”

How to Calculate Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket?

Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket calculator uses Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2)) to calculate the Speed of chain drive shaft in rpm, The Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket formula is defined as the speed at which the shaft is rotating . Speed of chain drive shaft in rpm is denoted by N symbol.

How to calculate Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket using this online calculator? To use this online calculator for Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket, enter Minimum Linear Velocity of Sprocket (vmin), Pitch Circle Diameter of Sprocket (D) & Pitch Angle of Sprocket (α) and hit the calculate button. Here is how the Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket calculation can be explained with given input values -> 738.3088 = 60*4.2/(0.11*pi*cos(0.31415926535892/2)).

FAQ

What is Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket?
The Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket formula is defined as the speed at which the shaft is rotating and is represented as N = 60*vmin/(D*pi*cos(α/2)) or Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2)). The Minimum Linear Velocity of Sprocket is defined as the lowest possible velocity of the sprocket when it is moving, Pitch Circle Diameter of Sprocket is the diameter of the pitch circle (passing through rollers centre) of the sprocket & The Pitch Angle of Sprocket is generally the angle subtended by a small line called pitch. It is generally used in sprockets.
How to calculate Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket?
The Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket formula is defined as the speed at which the shaft is rotating is calculated using Speed of chain drive shaft in rpm = 60*Minimum Linear Velocity of Sprocket/(Pitch Circle Diameter of Sprocket*pi*cos(Pitch Angle of Sprocket/2)). To calculate Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket, you need Minimum Linear Velocity of Sprocket (vmin), Pitch Circle Diameter of Sprocket (D) & Pitch Angle of Sprocket (α). With our tool, you need to enter the respective value for Minimum Linear Velocity of Sprocket, Pitch Circle Diameter of Sprocket & Pitch Angle of Sprocket 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 Speed of chain drive shaft in rpm?
In this formula, Speed of chain drive shaft in rpm uses Minimum Linear Velocity of Sprocket, Pitch Circle Diameter of Sprocket & Pitch Angle of Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Speed of chain drive shaft in rpm = Linear Velocity of Sprocket*60/(pi*Pitch Circle Diameter of Sprocket)
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