Number of Teeth given Minimum Tooth Flank Radius Calculator

✖Minimum Tooth Flank Radius is the smallest radius of the tooth flank of a sprocket wheel, which affects the wheel's overall strength and durability.ⓘ Minimum Tooth Flank Radius [re_min]			+10% -10%
✖Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.ⓘ Roller Radius of Chain [R]			+10% -10%

✖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.ⓘ Number of Teeth given Minimum Tooth Flank Radius [z]

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Formula

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Number of Teeth given Minimum Tooth Flank Radius

Formula

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

Example

17.99105 = (\frac{28.6 mm}{0.24 \cdot 5.961 mm}) - 2

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Number of Teeth given Minimum Tooth Flank Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2
z = (re_min/(0.24*R))-2
This formula uses 3 Variables

Variables Used

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.
Minimum Tooth Flank Radius - (Measured in Meter) - Minimum Tooth Flank Radius is the smallest radius of the tooth flank of a sprocket wheel, which affects the wheel's overall strength and durability.
Roller Radius of Chain - (Measured in Meter) - Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.

STEP 1: Convert Input(s) to Base Unit

Minimum Tooth Flank Radius: 28.6 Millimeter --> 0.0286 Meter (Check conversion here)
Roller Radius of Chain: 5.961 Millimeter --> 0.005961 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = (re_min/(0.24*R))-2 --> (0.0286/(0.24*0.005961))-2

Evaluating ... ...

z = 17.9910529553207

STEP 3: Convert Result to Output's Unit

17.9910529553207 --> No Conversion Required

FINAL ANSWER

17.9910529553207 ≈ 17.99105 <-- Number of Teeth on Sprocket

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Chain Drives » Mechanical » Proportions of the Sprocket Wheel » Number of Teeth given Minimum Tooth Flank Radius

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Proportions of the Sprocket Wheel Calculators

Top Diameter of Sprocket Wheel

Go Top Diameter of Sprocket Wheel = Sproket Diameter of Pitch Circle+Pitch of Chain*(1-(1.6/Number of Teeth on Sprocket))-2*Roller Radius of Chain

Pitch Circle Diameter given Pitch

Go Sproket Diameter of Pitch Circle = Pitch of Chain/sin(3.035/Number of Teeth on Sprocket)

Number of Teeth on Sprocket given Pitch Angle of Sprocket

Go Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi))

Pitch Angle of Sprocket

Go Pitch Angle of Sprocket = (360/Number of Teeth on Sprocket)/57.24

Number of Teeth given Minimum Tooth Flank Radius Formula

Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2
z = (re_min/(0.24*R))-2

What is Minimum Tooth Flank Radius?

The minimum tooth flank radius is the smallest radius of curvature on the side surface of a sprocket or gear tooth where it contacts the chain or another gear. This radius is designed to ensure smooth engagement and minimize stress concentrations, reducing wear and prolonging the life of both the sprocket and the chain.

How to Calculate Number of Teeth given Minimum Tooth Flank Radius?

Number of Teeth given Minimum Tooth Flank Radius calculator uses Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2 to calculate the Number of Teeth on Sprocket, Number of Teeth given Minimum Tooth Flank Radius formula is defined as a method to determine the number of teeth on a gear based on the minimum tooth flank radius, which is a critical parameter in gear design that affects the gear's strength and durability. Number of Teeth on Sprocket is denoted by z symbol.

How to calculate Number of Teeth given Minimum Tooth Flank Radius using this online calculator? To use this online calculator for Number of Teeth given Minimum Tooth Flank Radius, enter Minimum Tooth Flank Radius (re_min) & Roller Radius of Chain (R) and hit the calculate button. Here is how the Number of Teeth given Minimum Tooth Flank Radius calculation can be explained with given input values -> 17.86111 = (0.0286/(0.24*0.005961))-2.

FAQ

What is Number of Teeth given Minimum Tooth Flank Radius?

Number of Teeth given Minimum Tooth Flank Radius formula is defined as a method to determine the number of teeth on a gear based on the minimum tooth flank radius, which is a critical parameter in gear design that affects the gear's strength and durability and is represented as z = (re_min/(0.24*R))-2 or Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2. Minimum Tooth Flank Radius is the smallest radius of the tooth flank of a sprocket wheel, which affects the wheel's overall strength and durability & Roller Radius of Chain Sprocket Wheel is the radius of the roller of the chain sprocket wheel, which is a critical component in a bicycle's gear system.

How to calculate Number of Teeth given Minimum Tooth Flank Radius?

Number of Teeth given Minimum Tooth Flank Radius formula is defined as a method to determine the number of teeth on a gear based on the minimum tooth flank radius, which is a critical parameter in gear design that affects the gear's strength and durability is calculated using Number of Teeth on Sprocket = (Minimum Tooth Flank Radius/(0.24*Roller Radius of Chain))-2. To calculate Number of Teeth given Minimum Tooth Flank Radius, you need Minimum Tooth Flank Radius (re_min) & Roller Radius of Chain (R). With our tool, you need to enter the respective value for Minimum Tooth Flank Radius & Roller Radius of Chain 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 Number of Teeth on Sprocket?

In this formula, Number of Teeth on Sprocket uses Minimum Tooth Flank Radius & Roller Radius of Chain. We can use 3 other way(s) to calculate the same, which is/are as follows -

Number of Teeth on Sprocket = 360/(Pitch Angle of Sprocket*(180/pi))
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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