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

GoSpeed of Rotation of Shaft given Linear Velocity of Sprocket Formula

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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. Check FAQs

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

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

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

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Here is how the Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket equation looks like with Values.

Here is how the Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket equation looks like with Units.

Here is how the Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket equation looks like.

500.0001 = 60 \cdot \frac{2.8773}{164.2479 \cdot 3.1416 \cdot \cos (\frac{96}{2})}

500.0001 = 60 \cdot \frac{2.8773m/s}{164.2479mm \cdot 3.1416 \cdot \cos (\frac{96°}{2})}

500.0001 = 60 \cdot \frac{2.8773}{164.2479 \cdot 3.1416 \cdot \cos (\frac{96}{2})}

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

Follow our step by step solution on how to calculate Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

N = 60 \cdot \frac{2.8773m/s}{0.1642m \cdot 3.1416 \cdot \cos (\frac{1.6755rad}{2})}

Next Step Prepare to Evaluate

∴

N = 60 \cdot \frac{2.8773}{0.1642 \cdot 3.1416 \cdot \cos (\frac{1.6755}{2})}

Next Step Evaluate

∴

N = 500.000072103047

LAST Step Rounding Answer

∴

N = 500.0001

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

Variables

Constants

Functions

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

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

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

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 Speed of Chain Drive Shaft in RPM

Go Speed of Rotation of Shaft given Linear Velocity of Sprocket

N = v s \cdot \frac{60}{π \cdot D}

Other formulas in Polygonal Effect category

Go Linear Velocity of Sprocket

v s = π \cdot D \cdot \frac{N}{60}

Go Pitch Circle Diameter of Sprocket given Linear Velocity of Sprocket

D = v s \cdot \frac{60}{π \cdot N}

Go Minimum Linear Velocity of Sprocket

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

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

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

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

Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket evaluator 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 evaluate the Speed of Chain Drive Shaft in RPM, Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket formula is defined as the rotational speed of a shaft in relation to the minimum linear velocity of a sprocket, providing a critical parameter in mechanical systems, particularly in power transmission and conveyor belt applications. Speed of Chain Drive Shaft in RPM is denoted by N symbol.

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

FAQs on Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket

What is the formula to find Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket?

The formula of Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket is expressed as 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)). Here is an example- 481.8158 = 60*2.877262/(0.1642479*pi*cos(1.67551608191424/2)).

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

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

What are the other ways to Calculate Speed of Chain Drive Shaft in RPM?

Here are the different ways to Calculate Speed of Chain Drive Shaft in RPM-

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

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

​GoSpeed of Rotation of Shaft given Linear Velocity of Sprocket Formula

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

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

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

Other Formulas to find Speed of Chain Drive Shaft in RPM

Other formulas in Polygonal Effect category

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

FAQs on Speed of Rotation of Shaft given Minimum Linear Velocity of Sprocket

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GoSpeed of Rotation of Shaft given Linear Velocity of Sprocket Formula