Length of Gear Tooth Calculator

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Design of Gears

Basics Of Machine Design

Design of Coupling

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Design of Spur Gears

Design of Bevel Gears

Design of Helical Gears

Design of Worm Gears

✖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]

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Formula

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Length of Gear Tooth

Formula

`"b" = "S"_{"b"}/("m"*"Y"*"σ"_{"b"})`

Example

`"34.07578mm"="8500N"/("4.1mm"*"0.39"*"156N/mm²")`

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Download Design of Spur Gears Formulas PDF

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

Evaluating ... ...

b = 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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< 25 Design of Spur Gears Calculators

Center to Center Distance between Spur Gears

Go Distance between Spur Gear Centres = Module of Spur Gear*((Number of Teeth on Pinion+Number of Teeth on Spur Gear)/2)

Circular Pitch of Gear given Diameter and Number of Teeth

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

Resultant Force on Gear

Go Resultant Force on Spur Gear = Tangential Force on Spur Gear/cos(Pressure Angle of Spur Gear)

Radial Force of Gear given Tangential Force and Pressure Angle

Go Radial Force on Spur Gear = Tangential Force on Spur Gear*tan(Pressure Angle of Spur Gear)

Tangential Force on Gear given Radial Force and Pressure Angle

Go Tangential Force on Spur Gear = Radial Force on Spur Gear*cot(Pressure Angle of Spur Gear)

Pitch Circle Diameter of holes of Medium Size Gear

Go Pitch Circle Diameter of Holes in Gear = (Inner Diameter of Rim of Spur Gear+Outer Diameter of Spur Gear Hub)/2

Diameter of Holes in Gear Web of Medium Size Diameter

Go Diameter of Holes in Spur Gear Web = (Inner Diameter of Rim of Spur Gear-Outer Diameter of Spur Gear Hub)/4

Inner Diameter of Rim of Large Size Gear

Go Inner Diameter of Rim of Spur Gear = Dedendum Circle Diameter of Spur Gear-2*Thickness of Spur Gear Rim

Torque Transmitted by Gear given Tangential Force and Pitch Circle Diameter

Go Torque transmitted by spur gear = Tangential Force on Spur Gear*Pitch Circle Diameter of Spur Gear/2

Addendum Circle Diameter of Medium Size Gear Diameter given Addendum

Go Addendum Circle Diameter of Spur Gear = Pitch Circle Diameter of Spur Gear+(2*Addendum of spur gear)

Tangential Force on Gear given Torque and Pitch Circle Diameter

Go Tangential Force on Spur Gear = 2*Torque transmitted by spur gear/Pitch Circle Diameter of Spur Gear

Dedendum Circle Diameter of Medium Size Gear given Dedundum

Go Dedendum Circle Diameter of Spur Gear = Pitch Circle Diameter of Spur Gear-(2*Dedundum of Spur Gear)

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

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

Dedendum Circle Diameter of Large Size Gear

Go Dedendum Circle Diameter of Spur Gear = Module of Spur Gear*(Number of Teeth on Spur Gear-2.5)

Addendum Circle Diameter of Large Size Gear

Go Addendum Circle Diameter of Spur Gear = Module of Spur Gear*(Number of Teeth on Spur Gear+2)

Pitch Circle Diameter of Gear given Module and Number of Teeth

Go Pitch Circle Diameter of Spur Gear = Module of Spur Gear*Number of Teeth on Spur Gear

Module of Gear given Pitch Circle Diameter

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

Maximum Torque of Gear given Service Factor

Go Maximum Torque on Spur Gear = Service Factor for Spur Gear*Rated Torque of Spur Gear

Service Factor for Gear given Torque

Go Service Factor for Spur Gear = Maximum Torque on Spur Gear/Rated Torque of Spur Gear

Gear Ratio given Number of Teeth

Go Gear Ratio of Spur Gear = Number of Teeth on Spur Gear/Number of Teeth on Pinion

Gear Ratio given Speed

Go Gear Ratio of Spur Gear = Speed of Spur Pinion/Speed of Spur Gear

Diametral Pitch of Gear given Circular Pitch

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

Outer Diameter of Hub of Large Size Gear

Go Outer Diameter of Spur Gear Hub = 2*Diameter of Spur Gear Shaft

Thickness of Rim of Large Size Gear

Go Thickness of Spur Gear Rim = 0.56*Circular Pitch of Spur Gear

Module of Gear given Diametral Pitch

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

Length of Gear Tooth Formula

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 = 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 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 = 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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