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Length of Gear Tooth Formula

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The Length of Spur Gear Tooth is basically the summation of the addendum and the dedendum of a gear. Check FAQs

b g = \frac{S b}{m \cdot Y \cdot σ b}

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

Length of Gear Tooth Example

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Here is how the Length of Gear Tooth equation looks like with Values.

Here is how the Length of Gear Tooth equation looks like with Units.

Here is how the Length of Gear Tooth equation looks like.

34.0758 = \frac{8500}{4.1 \cdot 0.39 \cdot 156}

34.0758mm = \frac{8500N}{4.1mm \cdot 0.39 \cdot 156N/mm²}

34.0758 = \frac{8500}{4.1 \cdot 0.39 \cdot 156}

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Length of Gear Tooth Solution

Follow our step by step solution on how to calculate Length of Gear Tooth?

FIRST Step Consider the formula

b g = \frac{S b}{m \cdot Y \cdot σ b}

Next Step Substitute values of Variables

∴

b g = \frac{8500N}{4.1mm \cdot 0.39 \cdot 156N/mm²}

Next Step Convert Units

∴

b g = \frac{8500N}{0.0041m \cdot 0.39 \cdot 1.6E+8Pa}

Next Step Prepare to Evaluate

∴

b g = \frac{8500}{0.0041 \cdot 0.39 \cdot 1.6E+8}

Next Step Evaluate

∴

b g = 0.0340757845448277m

Next Step Convert to Output's Unit

∴

b g = 34.0757845448277mm

LAST Step Rounding Answer

∴

b g = 34.0758mm

Length of Gear Tooth Formula Elements

Variables

Length of Spur Gear Tooth

The Length of Spur Gear Tooth is basically the summation of the addendum and the dedendum of a gear.

Symbol: b_g

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Spur Gear Tooth

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

Symbol: m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Module of Spur 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.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Lewis Form Factor for Spur Gear

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

Other formulas in Parameters of Spur Gear category

Go Circular Pitch of Gear given Diameter and Number of Teeth

P c = π \cdot \frac{d}{z}

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

P d = \frac{z}{d}

Go Diametral Pitch of Gear given Circular Pitch

P d = \frac{π}{P c}

Go Module of Gear given Diametral Pitch

m = \frac{1}{P d}

How to Evaluate Length of Gear Tooth?

Length of Gear Tooth evaluator 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 evaluate 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_g symbol.

How to evaluate Length of Gear Tooth using this online evaluator? To use this online evaluator 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.

FAQs on Length of Gear Tooth

What is the formula to find Length of Gear Tooth?

The formula of Length of Gear Tooth is expressed as 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). Here is an example- 34075.78 = 8500/(0.0041*0.39*156000000).

How to calculate Length of Gear Tooth?

With 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) we can find Length of Gear Tooth using the 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).

Can the Length of Gear Tooth be negative?

No, the Length of Gear Tooth, measured in Length cannot be negative.

Which unit is used to measure Length of Gear Tooth?

Length of Gear Tooth is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Gear Tooth can be measured.

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Length of Gear Tooth Formula

Length of Gear Tooth Example

Length of Gear Tooth Solution

Length of Gear Tooth Formula Elements

Other formulas in Parameters of Spur Gear category

How to Evaluate Length of Gear Tooth?

FAQs on Length of Gear Tooth

Variable Name