Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
D = vmin*60/(pi*N*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
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.
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.
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).
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
Speed of chain drive shaft in rpm: 500 --> No Conversion Required
Pitch Angle of Sprocket: 18 Degree --> 0.31415926535892 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
D = vmin*60/(pi*N*cos(α/2)) --> 4.2*60/(pi*500*cos(0.31415926535892/2))
Evaluating ... ...
D = 0.162427940113136
STEP 3: Convert Result to Output's Unit
0.162427940113136 Meter -->162.427940113136 Millimeter (Check conversion here)
FINAL ANSWER
162.427940113136 162.4279 Millimeter <-- Pitch Circle Diameter of Sprocket
(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

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket Formula

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))
D = vmin*60/(pi*N*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 Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket calculator uses 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)) to calculate the Pitch Circle Diameter of Sprocket, The Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes. Pitch Circle Diameter of Sprocket is denoted by D symbol.

How to calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket using this online calculator? To use this online calculator for Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, enter Minimum Linear Velocity of Sprocket (vmin), Speed of chain drive shaft in rpm (N) & Pitch Angle of Sprocket (α) and hit the calculate button. Here is how the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket calculation can be explained with given input values -> 162427.9 = 4.2*60/(pi*500*cos(0.31415926535892/2)).

FAQ

What is Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?
The Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes and is represented as D = vmin*60/(pi*N*cos(α/2)) or 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)). The Minimum Linear Velocity of Sprocket is defined as the lowest possible velocity of the sprocket when it is moving, Speed of chain drive shaft in rpm is the number of turns of the shaft divided by time, specified as revolutions per minute (rpm) & 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 Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?
The Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as the diameter of the circle which passes through the centre of all the studs, wheel bolts or wheel rim holes is calculated using 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)). To calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, you need Minimum Linear Velocity of Sprocket (vmin), Speed of chain drive shaft in rpm (N) & Pitch Angle of Sprocket (α). With our tool, you need to enter the respective value for Minimum Linear Velocity of Sprocket, Speed of chain drive shaft in rpm & 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 Pitch Circle Diameter of Sprocket?
In this formula, Pitch Circle Diameter of Sprocket uses Minimum Linear Velocity of Sprocket, Speed of chain drive shaft in rpm & Pitch Angle of Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Pitch Circle Diameter of Sprocket = Linear Velocity of Sprocket*60/(pi*Speed of chain drive shaft in rpm)
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