Permissible Bending Stress in Gear Teeth Calculator

⤿

Design of Gears

Basics Of Machine Design

Design of Coupling

⤿

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%
✖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]

⎘ Copy

👎

Formula

✖

Permissible Bending Stress in Gear Teeth

Formula

`"σ"_{"b"} = "S"_{"b"}/("m"*"b"*"Y")`

Example

`"156.3477N/mm²"="8500N"/("4.1mm"*"34mm"*"0.39")`

Calculator

LaTeX

Reset

👍

Download Design of Spur Gears Formulas PDF PDF Image

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 is the unit of size that indicates how big or small is a 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)

You are here -

Home » Physics » Design of Machine Elements » Design of Gears » Design of Spur Gears » Permissible Bending Stress in Gear Teeth

Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

Chilvera Bhanu Teja has verified this Calculator and 200+ more calculators!

< 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

Permissible Bending Stress in Gear Teeth Formula

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 is the unit of size that indicates how big or small is a 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.

Home

FREE PDFs

🔍 Search