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Beam Strength of Tooth of Bevel Gear Formula

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Beam strength of bevel 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 σ b \cdot Y \cdot (1 - \frac{b}{A 0})

S_b - Beam Strength of Bevel Gear Teeth?m - Module of Bevel Gear?b - Face Width of Bevel Gear Tooth?σ_b - Bending Stress in Bevel Gear Teeth?Y - Lewis Form Factor?A₀ - Cone Distance?

Beam Strength of Tooth of Bevel Gear Example

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

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

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

5700.072 = 5.502 \cdot 35 \cdot 185 \cdot 0.32 \cdot (1 - \frac{35}{70})

5700.072N = 5.502mm \cdot 35mm \cdot 185N/mm² \cdot 0.32 \cdot (1 - \frac{35mm}{70mm})

5700.072 = 5.502 \cdot 35 \cdot 185 \cdot 0.32 \cdot (1 - \frac{35}{70})

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Beam Strength of Tooth of Bevel Gear Solution

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

FIRST Step Consider the formula

S b = m \cdot b \cdot σ b \cdot Y \cdot (1 - \frac{b}{A 0})

Next Step Substitute values of Variables

∴

S b = 5.502mm \cdot 35mm \cdot 185N/mm² \cdot 0.32 \cdot (1 - \frac{35mm}{70mm})

Next Step Convert Units

∴

S b = 0.0055m \cdot 0.035m \cdot 1.9E+8Pa \cdot 0.32 \cdot (1 - \frac{0.035m}{0.07m})

Next Step Prepare to Evaluate

∴

S b = 0.0055 \cdot 0.035 \cdot 1.9E+8 \cdot 0.32 \cdot (1 - \frac{0.035}{0.07})

LAST Step Evaluate

∴

S b = 5700.072N

Beam Strength of Tooth of Bevel Gear Formula Elements

Variables

Beam Strength of Bevel Gear Teeth

Beam strength of bevel 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 Bevel Gear Teeth

Module of Bevel Gear

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

Symbol: m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Module of Bevel Gear

Face Width of Bevel Gear Tooth

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

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Face Width of Bevel Gear Tooth

Bending Stress in Bevel Gear Teeth

Bending stress in bevel gear teeth is the normal stress that is induced at a point in a gear tooth 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 Bevel Gear Teeth

Lewis Form Factor

The Lewis Form Factor 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

Cone Distance

Cone distance is the length of the pitch-cone element and is also called the pitch-cone radius.

Symbol: A₀

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Cone Distance

Other formulas in Material Properties category

Go Wear Strength of Bevel Gear by Buckingham's Equation

S w = \frac{0.75 \cdot b \cdot Q b \cdot D p \cdot K}{\cos (γ)}

Go Material Constant for Bevel Gear Wear Strength given Brinell Hardness Number

K = 0.16 \cdot {(\frac{BHN}{100})}^{2}

Go Material Constant for Bevel Gear Wear Strength

K = \frac{{σ c}^{2} \cdot \sin (α Bevel) \cdot \cos (α Bevel) \cdot (\frac{1}{E p} + \frac{1}{E g})}{1.4}

How to Evaluate Beam Strength of Tooth of Bevel Gear?

Beam Strength of Tooth of Bevel Gear evaluator uses Beam Strength of Bevel Gear Teeth = Module of Bevel Gear*Face Width of Bevel Gear Tooth*Bending Stress in Bevel Gear Teeth*Lewis Form Factor*(1-Face Width of Bevel Gear Tooth/Cone Distance) to evaluate the Beam Strength of Bevel Gear Teeth, The Beam Strength of Tooth of Bevel Gear is one of the essential terms used to calculate the parameters of the gear. The failure of the gear due to bending can be verified. Beam strength indicates the maximum value of the force at the large end of the tooth that the tooth can transmit without bending. Beam Strength of Bevel Gear Teeth is denoted by S_b symbol.

How to evaluate Beam Strength of Tooth of Bevel Gear using this online evaluator? To use this online evaluator for Beam Strength of Tooth of Bevel Gear, enter Module of Bevel Gear (m), Face Width of Bevel Gear Tooth (b), Bending Stress in Bevel Gear Teeth (σ_b), Lewis Form Factor (Y) & Cone Distance (A₀) and hit the calculate button.

FAQs on Beam Strength of Tooth of Bevel Gear

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

The formula of Beam Strength of Tooth of Bevel Gear is expressed as Beam Strength of Bevel Gear Teeth = Module of Bevel Gear*Face Width of Bevel Gear Tooth*Bending Stress in Bevel Gear Teeth*Lewis Form Factor*(1-Face Width of Bevel Gear Tooth/Cone Distance). Here is an example- 5700.072 = 0.005502*0.035*185000000*0.32*(1-0.035/0.07).

How to calculate Beam Strength of Tooth of Bevel Gear?

With Module of Bevel Gear (m), Face Width of Bevel Gear Tooth (b), Bending Stress in Bevel Gear Teeth (σ_b), Lewis Form Factor (Y) & Cone Distance (A₀) we can find Beam Strength of Tooth of Bevel Gear using the formula - Beam Strength of Bevel Gear Teeth = Module of Bevel Gear*Face Width of Bevel Gear Tooth*Bending Stress in Bevel Gear Teeth*Lewis Form Factor*(1-Face Width of Bevel Gear Tooth/Cone Distance).

Can the Beam Strength of Tooth of Bevel Gear be negative?

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

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

Beam Strength of Tooth of Bevel Gear 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 Tooth of Bevel Gear can be measured.

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Beam Strength of Tooth of Bevel Gear Formula

Beam Strength of Tooth of Bevel Gear Example

Beam Strength of Tooth of Bevel Gear Solution

Beam Strength of Tooth of Bevel Gear Formula Elements

Other formulas in Material Properties category

How to Evaluate Beam Strength of Tooth of Bevel Gear?

FAQs on Beam Strength of Tooth of Bevel Gear

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