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Number of Teeth on Sprocket given Pitch Angle of Sprocket Formula

GoNumber of Teeth given Minimum Tooth Flank Radius Formula

GoNumber of Teeth given Maximum Roller Seating Angle Formula

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Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism. Check FAQs

z = \frac{360}{α \cdot (\frac{180}{π})}

z - Number of Teeth on Sprocket?α - Pitch Angle of Sprocket?π - Archimedes' constant?

Number of Teeth on Sprocket given Pitch Angle of Sprocket Example

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Here is how the Number of Teeth on Sprocket given Pitch Angle of Sprocket equation looks like with Values.

Here is how the Number of Teeth on Sprocket given Pitch Angle of Sprocket equation looks like with Units.

Here is how the Number of Teeth on Sprocket given Pitch Angle of Sprocket equation looks like.

18 = \frac{360}{20 \cdot (\frac{180}{3.1416})}

18 = \frac{360}{20° \cdot (\frac{180}{3.1416})}

18 = \frac{360}{20 \cdot (\frac{180}{3.1416})}

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Design of Automobile Elements » fx Number of Teeth on Sprocket given Pitch Angle of Sprocket

Number of Teeth on Sprocket given Pitch Angle of Sprocket Solution

Follow our step by step solution on how to calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket?

FIRST Step Consider the formula

z = \frac{360}{α \cdot (\frac{180}{π})}

Next Step Substitute values of Variables

∴

z = \frac{360}{20° \cdot (\frac{180}{π})}

Next Step Substitute values of Constants

∴

z = \frac{360}{20° \cdot (\frac{180}{3.1416})}

Next Step Convert Units

∴

z = \frac{360}{0.3491rad \cdot (\frac{180}{3.1416})}

Next Step Prepare to Evaluate

∴

z = \frac{360}{0.3491 \cdot (\frac{180}{3.1416})}

Next Step Evaluate

∴

z = 18.0000000000034

LAST Step Rounding Answer

∴

z = 18

Number of Teeth on Sprocket given Pitch Angle of Sprocket Formula Elements

Variables

Constants

Number of Teeth on Sprocket

Number of teeth on sprocket is the total count of teeth present on the circumference of the sprocket wheel, which affects the gear ratio and overall mechanism.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Sprocket

Pitch Angle of Sprocket

Pitch Angle of Sprocket is the angle between the sprocket's rotational axis and the plane of the sprocket wheel, affecting the chain's movement and overall mechanism.

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

Other Formulas to find Number of Teeth on Sprocket

Go Number of Teeth given Minimum Tooth Flank Radius

z = (\frac{re min}{0.24 \cdot R}) - 2

Go Number of Teeth given Maximum Roller Seating Angle

z = \frac{90}{120 - (α max \cdot \frac{180}{π})}

Go Number of Teeth given Minimum Roller Seating Angle

z = \frac{90}{140 - (α min \cdot \frac{180}{π})}

Go Number of Teeth given Maximum Tooth Height above Pitch Polygon

z = 0.8 \cdot \frac{P}{ha max - 0.625 \cdot P + R}

Other formulas in Proportions of the Sprocket Wheel category

Go Pitch Angle of Sprocket

α = \frac{\frac{360}{z}}{57.24}

Go Pitch Circle Diameter given Pitch

D s = \frac{P}{\sin (\frac{3.035}{z})}

Go Top Diameter of Sprocket Wheel

d a = D s + P \cdot (1 - (\frac{1.6}{z})) - 2 \cdot R

Go Pitch Circle Diameter given Top Diameter of Sprocket Wheel

D s = d a - P \cdot (1 - (\frac{1.6}{z})) + 2 \cdot R

How to Evaluate Number of Teeth on Sprocket given Pitch Angle of Sprocket?

Number of Teeth on Sprocket given Pitch Angle of Sprocket evaluator uses Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi)) to evaluate the Number of Teeth on Sprocket, Number of Teeth on Sprocket given Pitch Angle of Sprocket formula is defined as a measure that determines the total number of teeth present on a sprocket, which is a critical component in a transmission system, based on the pitch angle of the sprocket, providing essential information for designing and building mechanical systems. Number of Teeth on Sprocket is denoted by z symbol.

How to evaluate Number of Teeth on Sprocket given Pitch Angle of Sprocket using this online evaluator? To use this online evaluator for Number of Teeth on Sprocket given Pitch Angle of Sprocket, enter Pitch Angle of Sprocket (α) and hit the calculate button.

FAQs on Number of Teeth on Sprocket given Pitch Angle of Sprocket

What is the formula to find Number of Teeth on Sprocket given Pitch Angle of Sprocket?

The formula of Number of Teeth on Sprocket given Pitch Angle of Sprocket is expressed as Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi)). Here is an example- 20 = 360/(0.3490658503988*(180/pi)).

How to calculate Number of Teeth on Sprocket given Pitch Angle of Sprocket?

With Pitch Angle of Sprocket (α) we can find Number of Teeth on Sprocket given Pitch Angle of Sprocket using the formula - Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Number of Teeth on Sprocket?

Here are the different ways to Calculate Number of Teeth on Sprocket-

Number of Teeth on Sprocket=(Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2
Number of Teeth on Sprocket=90/(120-(Maximum Roller Seating Angle*180/pi))
Number of Teeth on Sprocket=90/(140-(Minimum Roller Seating Angle*180/pi))

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