Beam Strength of Gear Tooth Calculator

✖Module of spur gear in mm is the unit of size that indicates how big or small is the spur gear.ⓘ Module of Spur Gear [m]			+10% -10%
✖Face Width of Spur Gear Tooth is the length of the gear tooth parallel to the gear axis.ⓘ Face Width of Spur Gear Tooth [b]			+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%

✖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 Gear Tooth [S_b]

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Beam Strength of Gear Tooth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth
S_b = m*b*Y*σ_b
This formula uses 5 Variables

Variables Used

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 in mm is the unit of size that indicates how big or small is the spur gear.
Face Width of Spur Gear Tooth - (Measured in Meter) - Face Width of Spur Gear Tooth is the length of the gear tooth parallel to the gear axis.
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

Module of Spur Gear: 4.1 Millimeter --> 0.0041 Meter (Check conversion here)
Face Width of Spur Gear Tooth: 34 Millimeter --> 0.034 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

S_b = m*b*Y*σ_b --> 0.0041*0.034*0.39*156000000

Evaluating ... ...

S_b = 8481.096

STEP 3: Convert Result to Output's Unit

8481.096 Newton --> No Conversion Required

FINAL ANSWER

8481.096 Newton <-- Beam Strength of Spur Gear Teeth

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Spur Gears » Mechanical » Dynamics of Spur Gear » Beam Strength of Gear Tooth

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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< Dynamics of Spur Gear Calculators

Radial Force of Gear given Tangential Force and Pressure Angle

LaTeX 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

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

Torque Transmitted by Gear given Tangential Force and Pitch Circle Diameter

LaTeX Go Torque Transmitted by Spur Gear = Tangential Force on Spur Gear*Pitch Circle Diameter of Spur Gear/2

Tangential Force on Gear given Torque and Pitch Circle Diameter

LaTeX Go Tangential Force on Spur Gear = 2*Torque Transmitted by Spur Gear/Pitch Circle Diameter of Spur Gear

Beam Strength of Gear Tooth Formula

LaTeX Go

Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth
S_b = m*b*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 Beam Strength of Gear Tooth?

Beam Strength of Gear Tooth calculator uses Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth to calculate the Beam Strength of Spur Gear Teeth, Beam Strength of Gear Tooth is the strength of the bear tooth considered as a cantilever beam. The tangential component of force on the tooth causes the bending moment about the base of the tooth. So actually the beam strength of the maximum value of the tangential force that the tooth can transmit without bending failure. Beam Strength of Spur Gear Teeth is denoted by S_b symbol.

How to calculate Beam Strength of Gear Tooth using this online calculator? To use this online calculator for Beam Strength of Gear Tooth, enter Module of Spur Gear (m), Face Width of Spur Gear Tooth (b), Lewis Form Factor for Spur Gear (Y) & Bending Stress in Spur Gear Teeth (σ_b) and hit the calculate button. Here is how the Beam Strength of Gear Tooth calculation can be explained with given input values -> 8481.096 = 0.0041*0.034*0.39*156000000.

FAQ

What is Beam Strength of Gear Tooth?

Beam Strength of Gear Tooth is the strength of the bear tooth considered as a cantilever beam. The tangential component of force on the tooth causes the bending moment about the base of the tooth. So actually the beam strength of the maximum value of the tangential force that the tooth can transmit without bending failure and is represented as S_b = m*b*Y*σ_b or Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth. Module of spur gear in mm is the unit of size that indicates how big or small is the spur gear, Face Width of Spur Gear Tooth is the length of the gear tooth parallel to the gear axis, 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 Beam Strength of Gear Tooth?

Beam Strength of Gear Tooth is the strength of the bear tooth considered as a cantilever beam. The tangential component of force on the tooth causes the bending moment about the base of the tooth. So actually the beam strength of the maximum value of the tangential force that the tooth can transmit without bending failure is calculated using Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth. To calculate Beam Strength of Gear Tooth, you need Module of Spur Gear (m), Face Width of Spur Gear Tooth (b), 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 Module of Spur Gear, Face Width of Spur Gear Tooth, 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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