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Beam Strength of Gear Tooth Formula

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Beam Strength of Spur Gear Teeth is the maximum value of the tangential force that the tooth can transmit without bending failure. Check FAQs

S b = m \cdot b \cdot Y \cdot σ b

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?σ_b - Bending Stress in Spur Gear Teeth?

Beam Strength of Gear Tooth Example

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

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

Here is how the Beam Strength of Gear Tooth equation looks like.

8481.096 = 4.1 \cdot 34 \cdot 0.39 \cdot 156

8481.096N = 4.1mm \cdot 34mm \cdot 0.39 \cdot 156N/mm²

8481.096 = 4.1 \cdot 34 \cdot 0.39 \cdot 156

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Beam Strength of Gear Tooth Solution

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

FIRST Step Consider the formula

S b = m \cdot b \cdot Y \cdot σ b

Next Step Substitute values of Variables

∴

S b = 4.1mm \cdot 34mm \cdot 0.39 \cdot 156N/mm²

Next Step Convert Units

∴

S b = 0.0041m \cdot 0.034m \cdot 0.39 \cdot 1.6E+8Pa

Next Step Prepare to Evaluate

∴

S b = 0.0041 \cdot 0.034 \cdot 0.39 \cdot 1.6E+8

LAST Step Evaluate

∴

S b = 8481.096N

Beam Strength of Gear Tooth Formula Elements

Variables

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

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 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 Beam Strength of Gear Tooth?

Beam Strength of Gear Tooth evaluator uses Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth to evaluate the Beam Strength of Spur Gear Teeth, Beam Strength of Gear Tooth is the strength of the bear tooth considered as a cantilever beam. The tangential component of force on the tooth causes the bending moment about the base of the tooth. So actually the beam strength of the maximum value of the tangential force that the tooth can transmit without bending failure. Beam Strength of Spur Gear Teeth is denoted by S_b symbol.

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

FAQs on Beam Strength of Gear Tooth

What is the formula to find Beam Strength of Gear Tooth?

The formula of Beam Strength of Gear Tooth is expressed as Beam Strength of Spur Gear Teeth = Module of Spur Gear*Face Width of Spur Gear Tooth*Lewis Form Factor for Spur Gear*Bending Stress in Spur Gear Teeth. Here is an example- 8481.096 = 0.0041*0.034*0.39*156000000.

How to calculate Beam Strength of Gear Tooth?

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

Can the Beam Strength of Gear Tooth be negative?

No, the Beam Strength of Gear Tooth, measured in Force cannot be negative.

Which unit is used to measure Beam Strength of Gear Tooth?

Beam Strength of Gear Tooth is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Beam Strength of Gear Tooth can be measured.

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Beam Strength of Gear Tooth Formula

Beam Strength of Gear Tooth Example

Beam Strength of Gear Tooth Solution

Beam Strength of Gear Tooth Formula Elements

Other formulas in Dynamics of Spur Gear category

How to Evaluate Beam Strength of Gear Tooth?

FAQs on Beam Strength of Gear Tooth

Variable Name