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Permissible Bending Stress in Gear Teeth Formula

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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. Check FAQs

σ b = \frac{S b}{m \cdot b \cdot Y}

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

Permissible Bending Stress in Gear Teeth Example

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Here is how the Permissible Bending Stress in Gear Teeth equation looks like with Values.

Here is how the Permissible Bending Stress in Gear Teeth equation looks like with Units.

Here is how the Permissible Bending Stress in Gear Teeth equation looks like.

156.3477 = \frac{8500}{4.1 \cdot 34 \cdot 0.39}

156.3477N/mm² = \frac{8500N}{4.1mm \cdot 34mm \cdot 0.39}

156.3477 = \frac{8500}{4.1 \cdot 34 \cdot 0.39}

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Permissible Bending Stress in Gear Teeth Solution

Follow our step by step solution on how to calculate Permissible Bending Stress in Gear Teeth?

FIRST Step Consider the formula

σ b = \frac{S b}{m \cdot b \cdot Y}

Next Step Substitute values of Variables

∴

σ b = \frac{8500N}{4.1mm \cdot 34mm \cdot 0.39}

Next Step Convert Units

∴

σ b = \frac{8500N}{0.0041m \cdot 0.034m \cdot 0.39}

Next Step Prepare to Evaluate

∴

σ b = \frac{8500}{0.0041 \cdot 0.034 \cdot 0.39}

Next Step Evaluate

∴

σ b = 156347717.323327Pa

Next Step Convert to Output's Unit

∴

σ b = 156.347717323327N/mm²

LAST Step Rounding Answer

∴

σ b = 156.3477N/mm²

Permissible Bending Stress in Gear Teeth Formula Elements

Variables

Bending Stress in Spur Gear Teeth

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.

Symbol: σ_b

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress in Spur Gear Teeth

Beam Strength of 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.

Symbol: S_b

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Beam Strength of Spur Gear Teeth

Module of Spur Gear

Module of spur gear in mm is the unit of size that indicates how big or small is the spur gear.

Symbol: m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Module of Spur Gear

Face Width of Spur Gear Tooth

Face Width of Spur Gear Tooth is the length of the gear tooth parallel to the gear axis.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Face Width of Spur Gear Tooth

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.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lewis Form Factor for Spur Gear

Other formulas in Dynamics of Spur Gear category

Go Torque Transmitted by Gear given Tangential Force and Pitch Circle Diameter

M t = P t \cdot \frac{d}{2}

Go Tangential Force on Gear given Torque and Pitch Circle Diameter

P t = 2 \cdot \frac{M t}{d}

Go Radial Force of Gear given Tangential Force and Pressure Angle

P r = P t \cdot \tan (Φ)

Go Tangential Force on Gear given Radial Force and Pressure Angle

P t = P r \cdot \cot (Φ)

How to Evaluate Permissible Bending Stress in Gear Teeth?

Permissible Bending Stress in Gear Teeth evaluator 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 evaluate 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 evaluate Permissible Bending Stress in Gear Teeth using this online evaluator? To use this online evaluator 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.

FAQs on Permissible Bending Stress in Gear Teeth

What is the formula to find Permissible Bending Stress in Gear Teeth?

The formula of Permissible Bending Stress in Gear Teeth is expressed as 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). Here is an example- 0.000156 = 8500/(0.0041*0.034*0.39).

How to calculate Permissible Bending Stress in Gear Teeth?

With 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) we can find Permissible Bending Stress in Gear Teeth using the 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).

Can the Permissible Bending Stress in Gear Teeth be negative?

No, the Permissible Bending Stress in Gear Teeth, measured in Stress cannot be negative.

Which unit is used to measure Permissible Bending Stress in Gear Teeth?

Permissible Bending Stress in Gear Teeth is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Permissible Bending Stress in Gear Teeth can be measured.

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Permissible Bending Stress in Gear Teeth Formula

Permissible Bending Stress in Gear Teeth Example

Permissible Bending Stress in Gear Teeth Solution

Permissible Bending Stress in Gear Teeth Formula Elements

Other formulas in Dynamics of Spur Gear category

How to Evaluate Permissible Bending Stress in Gear Teeth?

FAQs on Permissible Bending Stress in Gear Teeth

Variable Name