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Minimum Linear Velocity of Sprocket Formula

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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. Check FAQs

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

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

Minimum Linear Velocity of Sprocket Example

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Here is how the Minimum Linear Velocity of Sprocket equation looks like with Values.

Here is how the Minimum Linear Velocity of Sprocket equation looks like with Units.

Here is how the Minimum Linear Velocity of Sprocket equation looks like.

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

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

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

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Minimum Linear Velocity of Sprocket Solution

Follow our step by step solution on how to calculate Minimum Linear Velocity of Sprocket?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

v min = π \cdot 164.2479mm \cdot 500 \cdot \frac{\cos (\frac{96°}{2})}{60}

Next Step Substitute values of Constants

∴

v min = 3.1416 \cdot 164.2479mm \cdot 500 \cdot \frac{\cos (\frac{96°}{2})}{60}

Next Step Convert Units

∴

v min = 3.1416 \cdot 0.1642m \cdot 500 \cdot \frac{\cos (\frac{1.6755rad}{2})}{60}

Next Step Prepare to Evaluate

∴

v min = 3.1416 \cdot 0.1642 \cdot 500 \cdot \frac{\cos (\frac{1.6755}{2})}{60}

Next Step Evaluate

∴

v min = 2.87726158508135m/s

LAST Step Rounding Answer

∴

v min = 2.8773m/s

Minimum Linear Velocity of Sprocket Formula Elements

Variables

Constants

Functions

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

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 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 Speed of Rotation of Shaft given Linear Velocity of Sprocket

N = v s \cdot \frac{60}{π \cdot D}

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 Minimum Linear Velocity of Sprocket?

Minimum Linear Velocity of Sprocket evaluator uses 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 to evaluate the Minimum Linear Velocity of Sprocket, Minimum Linear Velocity of Sprocket formula is defined as the lowest velocity at which a sprocket can rotate without slipping, considering the diameter of the sprocket, the rotational speed, and the angle of engagement, providing a critical value for designing and optimizing mechanical systems. Minimum Linear Velocity of Sprocket is denoted by v_min symbol.

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

FAQs on Minimum Linear Velocity of Sprocket

What is the formula to find Minimum Linear Velocity of Sprocket?

The formula of Minimum Linear Velocity of Sprocket is expressed as 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. Here is an example- 2.877262 = pi*0.1642479*500*cos(1.67551608191424/2)/60.

How to calculate Minimum Linear Velocity of Sprocket?

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

Can the Minimum Linear Velocity of Sprocket be negative?

No, the Minimum Linear Velocity of Sprocket, measured in Speed cannot be negative.

Which unit is used to measure Minimum Linear Velocity of Sprocket?

Minimum Linear Velocity of Sprocket is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Minimum Linear Velocity of Sprocket can be measured.

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Minimum Linear Velocity of Sprocket Formula

Minimum Linear Velocity of Sprocket Example

Minimum Linear Velocity of Sprocket Solution

Minimum Linear Velocity of Sprocket Formula Elements

Other formulas in Polygonal Effect category

How to Evaluate Minimum Linear Velocity of Sprocket?

FAQs on Minimum Linear Velocity of Sprocket

Variable Name