Permissible Bending Stress in Gear Teeth 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 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.ⓘ Permissible Bending Stress in Gear Teeth [σ_b]

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Permissible Bending Stress in Gear Teeth Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

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)
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_b = S_b/(m*b*Y) --> 8500/(0.0041*0.034*0.39)

Evaluating ... ...

σ_b = 156347717.323327

STEP 3: Convert Result to Output's Unit

156347717.323327 Pascal -->156.347717323327 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

156.347717323327 ≈ 156.3477 Newton per Square Millimeter <-- Bending Stress in 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 » Permissible Bending Stress in Gear Teeth

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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

Permissible Bending Stress in Gear Teeth Formula

LaTeX Go

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

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 Permissible Bending Stress in Gear Teeth?

Permissible Bending Stress in Gear Teeth calculator uses Bending Stress in Spur Gear Teeth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear) to calculate the Bending Stress in Spur Gear Teeth, Permissible Bending Stress in Gear Teeth is the allowable amount of bending stress in the gear tooth until it reaches its calculated failure. Bending Stress in Spur Gear Teeth is denoted by σ_b symbol.

How to calculate Permissible Bending Stress in Gear Teeth using this online calculator? To use this online calculator for Permissible Bending Stress in Gear Teeth, enter Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Face Width of Spur Gear Tooth (b) & Lewis Form Factor for Spur Gear (Y) and hit the calculate button. Here is how the Permissible Bending Stress in Gear Teeth calculation can be explained with given input values -> 0.000156 = 8500/(0.0041*0.034*0.39).

FAQ

What is Permissible Bending Stress in Gear Teeth?

Permissible Bending Stress in Gear Teeth is the allowable amount of bending stress in the gear tooth until it reaches its calculated failure and is represented as σ_b = S_b/(m*b*Y) or Bending Stress in Spur Gear Teeth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear). 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 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.

How to calculate Permissible Bending Stress in Gear Teeth?

Permissible Bending Stress in Gear Teeth is the allowable amount of bending stress in the gear tooth until it reaches its calculated failure is calculated using Bending Stress in Spur Gear Teeth = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear). To calculate Permissible Bending Stress in Gear Teeth, you need Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Face Width of Spur Gear Tooth (b) & Lewis Form Factor for Spur Gear (Y). With our tool, you need to enter the respective value for Beam Strength of Spur Gear Teeth, Module of Spur Gear, Face Width of Spur Gear Tooth & Lewis Form Factor for Spur Gear 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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