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Lewis Form Factor of Gear Tooth Formula

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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. Check FAQs

Y = \frac{S b}{m \cdot σ b \cdot b}

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

Lewis Form Factor of Gear Tooth Example

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Here is how the Lewis Form Factor of Gear Tooth equation looks like with Values.

Here is how the Lewis Form Factor of Gear Tooth equation looks like with Units.

Here is how the Lewis Form Factor of Gear Tooth equation looks like.

0.3909 = \frac{8500}{4.1 \cdot 156 \cdot 34}

0.3909 = \frac{8500N}{4.1mm \cdot 156N/mm² \cdot 34mm}

0.3909 = \frac{8500}{4.1 \cdot 156 \cdot 34}

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Lewis Form Factor of Gear Tooth Solution

Follow our step by step solution on how to calculate Lewis Form Factor of Gear Tooth?

FIRST Step Consider the formula

Y = \frac{S b}{m \cdot σ b \cdot b}

Next Step Substitute values of Variables

∴

Y = \frac{8500N}{4.1mm \cdot 156N/mm² \cdot 34mm}

Next Step Convert Units

∴

Y = \frac{8500N}{0.0041m \cdot 1.6E+8Pa \cdot 0.034m}

Next Step Prepare to Evaluate

∴

Y = \frac{8500}{0.0041 \cdot 1.6E+8 \cdot 0.034}

Next Step Evaluate

∴

Y = 0.390869293308318

LAST Step Rounding Answer

∴

Y = 0.3909

Lewis Form Factor of Gear Tooth Formula Elements

Variables

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

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

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

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

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 Lewis Form Factor of Gear Tooth?

Lewis Form Factor of Gear Tooth evaluator uses Lewis Form Factor for Spur Gear = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Bending Stress in Spur Gear Teeth*Face Width of Spur Gear Tooth) to evaluate the Lewis Form Factor for Spur Gear, Lewis Form Factor of Gear Tooth is a factor used in the beam strength of gear equation. It is a function of the number of teeth, pressure angle, and involute depth of the gear. Lewis Form Factor for Spur Gear is denoted by Y symbol.

How to evaluate Lewis Form Factor of Gear Tooth using this online evaluator? To use this online evaluator for Lewis Form Factor of Gear Tooth, enter Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Bending Stress in Spur Gear Teeth (σ_b) & Face Width of Spur Gear Tooth (b) and hit the calculate button.

FAQs on Lewis Form Factor of Gear Tooth

What is the formula to find Lewis Form Factor of Gear Tooth?

The formula of Lewis Form Factor of Gear Tooth is expressed as Lewis Form Factor for Spur Gear = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Bending Stress in Spur Gear Teeth*Face Width of Spur Gear Tooth). Here is an example- 0.390869 = 8500/(0.0041*156000000*0.034).

How to calculate Lewis Form Factor of Gear Tooth?

With Beam Strength of Spur Gear Teeth (S_b), Module of Spur Gear (m), Bending Stress in Spur Gear Teeth (σ_b) & Face Width of Spur Gear Tooth (b) we can find Lewis Form Factor of Gear Tooth using the formula - Lewis Form Factor for Spur Gear = Beam Strength of Spur Gear Teeth/(Module of Spur Gear*Bending Stress in Spur Gear Teeth*Face Width of Spur Gear Tooth).

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Lewis Form Factor of Gear Tooth Formula

Lewis Form Factor of Gear Tooth Example

Lewis Form Factor of Gear Tooth Solution

Lewis Form Factor of Gear Tooth Formula Elements

Other formulas in Parameters of Spur Gear category

How to Evaluate Lewis Form Factor of Gear Tooth?

FAQs on Lewis Form Factor of Gear Tooth

Variable Name