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

GoPitch Circle Diameter of Sprocket given Linear Velocity of Sprocket Formula

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Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the centers of the sprocket's teeth. Check FAQs

D = v min \cdot \frac{60}{π \cdot N \cdot \cos (\frac{α}{2})}

D - Pitch Circle Diameter of Sprocket?v_min - Minimum Linear Velocity of Sprocket?N - Speed of Chain Drive Shaft in RPM?α - Pitch Angle of Sprocket?π - Archimedes' constant?

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

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Here is how the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket equation looks like with Values.

Here is how the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket equation looks like with Units.

Here is how the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket equation looks like.

164.2479 = 2.8773 \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{96}{2})}

164.2479mm = 2.8773m/s \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{96°}{2})}

164.2479 = 2.8773 \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{96}{2})}

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

Follow our step by step solution on how to calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

FIRST Step Consider the formula

D = v min \cdot \frac{60}{π \cdot N \cdot \cos (\frac{α}{2})}

Next Step Substitute values of Variables

∴

D = 2.8773m/s \cdot \frac{60}{π \cdot 500 \cdot \cos (\frac{96°}{2})}

Next Step Substitute values of Constants

∴

D = 2.8773m/s \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{96°}{2})}

Next Step Convert Units

∴

D = 2.8773m/s \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{1.6755rad}{2})}

Next Step Prepare to Evaluate

∴

D = 2.8773 \cdot \frac{60}{3.1416 \cdot 500 \cdot \cos (\frac{1.6755}{2})}

Next Step Evaluate

∴

D = 0.164247923685548m

Next Step Convert to Output's Unit

∴

D = 164.247923685548mm

LAST Step Rounding Answer

∴

D = 164.2479mm

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

Variables

Constants

Functions

Pitch Circle Diameter of Sprocket

Pitch Circle Diameter of Sprocket is the diameter of the circle that passes through the centers of the sprocket's teeth.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch Circle Diameter of Sprocket

Minimum Linear Velocity of Sprocket

Minimum Linear Velocity of Sprocket is the slowest speed at which a point on the sprocket's circumference moves. It depends on the sprocket's smallest rotational speed and radius.

Symbol: v_min

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Minimum Linear Velocity of Sprocket

Speed of Chain Drive Shaft in RPM

Speed of Chain Drive Shaft in RPM is the number of revolutions the shaft completes in one minute. It indicates the rotational speed at which the chain drive operates.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Speed of Chain Drive Shaft in RPM

Pitch Angle of Sprocket

Pitch Angle of Sprocket is the angle between the line connecting the centers of two consecutive teeth and the radial line through the center of the sprocket.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pitch Angle of Sprocket

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Pitch Circle Diameter of Sprocket

Go Pitch Circle Diameter of Sprocket given Linear Velocity of Sprocket

D = v s \cdot \frac{60}{π \cdot N}

Other formulas in Polygonal Effect category

Go Linear Velocity of Sprocket

v s = π \cdot D \cdot \frac{N}{60}

Go Speed of Rotation of Shaft given Linear Velocity of Sprocket

N = v s \cdot \frac{60}{π \cdot D}

Go Minimum Linear Velocity of Sprocket

v min = π \cdot D \cdot N \cdot \frac{\cos (\frac{α}{2})}{60}

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

N = 60 \cdot \frac{v min}{D \cdot π \cdot \cos (\frac{α}{2})}

How to Evaluate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket evaluator 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 evaluate the Pitch Circle Diameter of Sprocket, Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket formula is defined as a measure of the diameter of the pitch circle of a sprocket, which is a critical parameter in designing and optimizing sprocket-based mechanical systems, particularly in power transmission and conveyor systems. Pitch Circle Diameter of Sprocket is denoted by D symbol.

How to evaluate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket using this online evaluator? To use this online evaluator for Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, enter Minimum Linear Velocity of Sprocket (v_min), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α) and hit the calculate button.

FAQs on Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket

What is the formula to find Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

The formula of Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket is expressed as 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)). Here is an example- 158274.5 = 2.877262*60/(pi*500*cos(1.67551608191424/2)).

How to calculate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

With Minimum Linear Velocity of Sprocket (v_min), Speed of Chain Drive Shaft in RPM (N) & Pitch Angle of Sprocket (α) we can find Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket using the 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)). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Pitch Circle Diameter of Sprocket?

Here are the different ways to Calculate Pitch Circle Diameter of Sprocket-

Pitch Circle Diameter of Sprocket=Linear Velocity of Sprocket*60/(pi*Speed of Chain Drive Shaft in RPM)

Can the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket be negative?

No, the Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket, measured in Length cannot be negative.

Which unit is used to measure Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket can be measured.

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

​GoPitch Circle Diameter of Sprocket given Linear Velocity of Sprocket Formula

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

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

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

Other Formulas to find Pitch Circle Diameter of Sprocket

Other formulas in Polygonal Effect category

How to Evaluate Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket?

FAQs on Diameter of Pitch Circle of Sprocket given Minimum Linear Velocity of Sprocket

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GoPitch Circle Diameter of Sprocket given Linear Velocity of Sprocket Formula