Length of Gear Tooth Calculator

✖Beam Strength of Spur Gear Teeth is the maximum value of the tangential force that the tooth can transmit without bending failure.ⓘ Beam Strength of Spur Gear Teeth [S_b]			+10% -10%
✖Module of Spur Gear is the unit of size that indicates how big or small is a gear.ⓘ Module of Spur Gear [m]			+10% -10%
✖Lewis Form Factor for Spur Gear is defined as the ratio of the beam strength to the product of the module, bending stress, and the length of the gear tooth.ⓘ Lewis Form Factor for Spur Gear [Y]			+10% -10%
✖Bending Stress in Spur Gear Teeth is the normal stress that is induced at a point in a gear teeth subjected to loads that cause it to bend.ⓘ Bending Stress in Spur Gear Teeth [σ_b]			+10% -10%

✖The Length of Spur Gear Tooth is basically the summation of the addendum and the dedendum of a gear.ⓘ Length of Gear Tooth [b_g]

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Length of Gear Tooth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Spur Gear Tooth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth)
b_g = S_b/(m*Y*σ_b)
This formula uses 5 Variables

Variables Used

Length of Spur Gear Tooth - (Measured in Meter) - The Length of Spur Gear Tooth is basically the summation of the addendum and the dedendum of a gear.
Beam Strength of Spur Gear Teeth - (Measured in Newton) - Beam Strength of Spur Gear Teeth is the maximum value of the tangential force that the tooth can transmit without bending failure.
Module of Spur Gear - (Measured in Meter) - Module of Spur Gear is the unit of size that indicates how big or small is a gear.
Lewis Form Factor for Spur Gear - Lewis Form Factor for Spur Gear is defined as the ratio of the beam strength to the product of the module, bending stress, and the length of the gear tooth.
Bending Stress in Spur Gear Teeth - (Measured in Pascal) - Bending Stress in Spur Gear Teeth is the normal stress that is induced at a point in a gear teeth subjected to loads that cause it to bend.

STEP 1: Convert Input(s) to Base Unit

Beam Strength of Spur Gear Teeth: 8500 Newton --> 8500 Newton No Conversion Required
Module of Spur Gear: 4.1 Millimeter --> 0.0041 Meter (Check conversion here)
Lewis Form Factor for Spur Gear: 0.39 --> No Conversion Required
Bending Stress in Spur Gear Teeth: 156 Newton per Square Millimeter --> 156000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

b_g = S_b/(m*Y*σ_b) --> 8500/(0.0041*0.39*156000000)

Evaluating ... ...

b_g = 0.0340757845448277

STEP 3: Convert Result to Output's Unit

0.0340757845448277 Meter -->34.0757845448277 Millimeter (Check conversion here)

FINAL ANSWER

34.0757845448277 ≈ 34.07578 Millimeter <-- Length of Spur Gear Tooth

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Spur Gears » Mechanical » Parameters of Spur Gear » Length of Gear Tooth

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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< Parameters of Spur Gear Calculators

Circular Pitch of Gear given Diameter and Number of Teeth

LaTeX Go Circular Pitch of Spur Gear = pi*Pitch Circle Diameter of Spur Gear/Number of Teeth on Spur Gear

Diametral Pitch of Gear given Number of teeth and Pitch Circle Diameter

LaTeX Go Diametral Pitch of Spur Gear = Number of Teeth on Spur Gear/Pitch Circle Diameter of Spur Gear

Diametral Pitch of Gear given Circular Pitch

LaTeX Go Diametral Pitch of Spur Gear = pi/Circular Pitch of Spur Gear

Module of Gear given Diametral Pitch

LaTeX Go Module of Spur Gear = 1/Diametral Pitch of Spur Gear

Length of Gear Tooth Formula

LaTeX Go

Length of Spur Gear Tooth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth)
b_g = S_b/(m*Y*σ_b)

What is a gear?

Gears are defined as toothed wheels or multilobed-cams, which transmit power and motion from one shaft to another by means of successive engagement of teeth.

How to Calculate Length of Gear Tooth?

Length of Gear Tooth calculator uses Length of Spur Gear Tooth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth) to calculate the Length of Spur Gear Tooth, The Length of gear tooth formula is defined as the length of the protrusion on the circumference of a gear wheel. These teeth mesh with similar teeth of another gear and transmit motion and torque. The length of gear teeth is also equal to the sum of the addendum and the dedendum. Length of Spur Gear Tooth is denoted by b_g symbol.

How to calculate Length of Gear Tooth using this online calculator? To use this online calculator for Length of Gear Tooth, enter Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Lewis Form Factor for Spur Gear (Y) & Bending Stress in Spur Gear Teeth (σ_b) and hit the calculate button. Here is how the Length of Gear Tooth calculation can be explained with given input values -> 34075.78 = 8500/(0.0041*0.39*156000000).

FAQ

What is Length of Gear Tooth?

The Length of gear tooth formula is defined as the length of the protrusion on the circumference of a gear wheel. These teeth mesh with similar teeth of another gear and transmit motion and torque. The length of gear teeth is also equal to the sum of the addendum and the dedendum and is represented as b_g = S_b/(m*Y*σ_b) or Length of Spur Gear Tooth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth). Beam Strength of Spur Gear Teeth is the maximum value of the tangential force that the tooth can transmit without bending failure, Module of Spur Gear is the unit of size that indicates how big or small is a gear, Lewis Form Factor for Spur Gear is defined as the ratio of the beam strength to the product of the module, bending stress, and the length of the gear tooth & Bending Stress in Spur Gear Teeth is the normal stress that is induced at a point in a gear teeth subjected to loads that cause it to bend.

How to calculate Length of Gear Tooth?

The Length of gear tooth formula is defined as the length of the protrusion on the circumference of a gear wheel. These teeth mesh with similar teeth of another gear and transmit motion and torque. The length of gear teeth is also equal to the sum of the addendum and the dedendum is calculated using Length of Spur Gear Tooth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth). To calculate Length of Gear Tooth, you need Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Lewis Form Factor for Spur Gear (Y) & Bending Stress in Spur Gear Teeth (σ_b). With our tool, you need to enter the respective value for Beam Strength of Spur Gear Teeth, Module of Spur Gear, Lewis Form Factor for Spur Gear & Bending Stress in Spur Gear Teeth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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