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Wear Strength of Bevel Gear by Buckingham's Equation Formula

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Wear Strength of Bevel Gear Tooth indicates the maximum value of radial force at the large end of the tooth that the tooth can transmit without pitting failure. Check FAQs

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

S_w - Wear Strength of Bevel Gear Tooth?b - Face Width of Bevel Gear Tooth?Q_b - Ratio Factor for Bevel Gear?D_p - Pitch Circle Diameter of Bevel Pinion?K - Material Constant?γ - Pitch Angle for Bevel Gear?

Wear Strength of Bevel Gear by Buckingham's Equation Example

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Here is how the Wear Strength of Bevel Gear by Buckingham's Equation equation looks like with Values.

Here is how the Wear Strength of Bevel Gear by Buckingham's Equation equation looks like with Units.

Here is how the Wear Strength of Bevel Gear by Buckingham's Equation equation looks like.

15060.9375 = \frac{0.75 \cdot 35 \cdot 1.5 \cdot 76.5 \cdot 2.5}{\cos (60)}

15060.9375N = \frac{0.75 \cdot 35mm \cdot 1.5 \cdot 76.5mm \cdot 2.5N/mm²}{\cos (60°)}

15060.9375 = \frac{0.75 \cdot 35 \cdot 1.5 \cdot 76.5 \cdot 2.5}{\cos (60)}

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Wear Strength of Bevel Gear by Buckingham's Equation Solution

Follow our step by step solution on how to calculate Wear Strength of Bevel Gear by Buckingham's Equation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S w = \frac{0.75 \cdot 35mm \cdot 1.5 \cdot 76.5mm \cdot 2.5N/mm²}{\cos (60°)}

Next Step Convert Units

∴

S w = \frac{0.75 \cdot 0.035m \cdot 1.5 \cdot 0.0765m \cdot 2.5E+6Pa}{\cos (1.0472rad)}

Next Step Prepare to Evaluate

∴

S w = \frac{0.75 \cdot 0.035 \cdot 1.5 \cdot 0.0765 \cdot 2.5E+6}{\cos (1.0472)}

Next Step Evaluate

∴

S w = 15060.9374999948N

LAST Step Rounding Answer

∴

S w = 15060.9375N

Wear Strength of Bevel Gear by Buckingham's Equation Formula Elements

Variables

Functions

Wear Strength of Bevel Gear Tooth

Wear Strength of Bevel Gear Tooth indicates the maximum value of radial force at the large end of the tooth that the tooth can transmit without pitting failure.

Symbol: S_w

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Wear Strength of Bevel Gear Tooth

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

Ratio Factor for Bevel Gear

Ratio Factor for bevel gear is defined as the ratio used in the design of a Bevel Gear.

Symbol: Q_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Ratio Factor for Bevel Gear

Pitch Circle Diameter of Bevel Pinion

Pitch circle diameter of bevel pinion is twice the distance from the center of the gear to the pitch point. This is where the gear's speed is measured.

Symbol: D_p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch Circle Diameter of Bevel Pinion

Material Constant

The Material Constant is used to calculate the wear strength of the gear teeth and can be further simplified by fixed values of pressure angle and modulus of elasticity of the material.

Symbol: K

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Material Constant

Pitch Angle for Bevel Gear

Pitch Angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear. The pitch angle is also known as center angle.

Symbol: γ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pitch Angle for Bevel Gear

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Material Properties category

Go Beam Strength of Tooth of Bevel Gear

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

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 Wear Strength of Bevel Gear by Buckingham's Equation?

Wear Strength of Bevel Gear by Buckingham's Equation evaluator uses Wear Strength of Bevel Gear Tooth = (0.75*Face Width of Bevel Gear Tooth*Ratio Factor for Bevel Gear*Pitch Circle Diameter of Bevel Pinion*Material Constant)/cos(Pitch Angle for Bevel Gear) to evaluate the Wear Strength of Bevel Gear Tooth, Wear strength of Bevel Gear by Buckingham's equation is used to verify the term of failure of gear due to pitting. It indicates the maximum value of radial force at the large end of the tooth that the tooth can transmit without pitting failure. Wear Strength of Bevel Gear Tooth is denoted by S_w symbol.

How to evaluate Wear Strength of Bevel Gear by Buckingham's Equation using this online evaluator? To use this online evaluator for Wear Strength of Bevel Gear by Buckingham's Equation, enter Face Width of Bevel Gear Tooth (b), Ratio Factor for Bevel Gear (Q_b), Pitch Circle Diameter of Bevel Pinion (D_p), Material Constant (K) & Pitch Angle for Bevel Gear (γ) and hit the calculate button.

FAQs on Wear Strength of Bevel Gear by Buckingham's Equation

What is the formula to find Wear Strength of Bevel Gear by Buckingham's Equation?

The formula of Wear Strength of Bevel Gear by Buckingham's Equation is expressed as Wear Strength of Bevel Gear Tooth = (0.75*Face Width of Bevel Gear Tooth*Ratio Factor for Bevel Gear*Pitch Circle Diameter of Bevel Pinion*Material Constant)/cos(Pitch Angle for Bevel Gear). Here is an example- 15060.94 = (0.75*0.035*1.5*0.0765*2500000)/cos(1.0471975511964).

How to calculate Wear Strength of Bevel Gear by Buckingham's Equation?

With Face Width of Bevel Gear Tooth (b), Ratio Factor for Bevel Gear (Q_b), Pitch Circle Diameter of Bevel Pinion (D_p), Material Constant (K) & Pitch Angle for Bevel Gear (γ) we can find Wear Strength of Bevel Gear by Buckingham's Equation using the formula - Wear Strength of Bevel Gear Tooth = (0.75*Face Width of Bevel Gear Tooth*Ratio Factor for Bevel Gear*Pitch Circle Diameter of Bevel Pinion*Material Constant)/cos(Pitch Angle for Bevel Gear). This formula also uses Cosine (cos) function(s).

Can the Wear Strength of Bevel Gear by Buckingham's Equation be negative?

No, the Wear Strength of Bevel Gear by Buckingham's Equation, measured in Force cannot be negative.

Which unit is used to measure Wear Strength of Bevel Gear by Buckingham's Equation?

Wear Strength of Bevel Gear by Buckingham's Equation is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Wear Strength of Bevel Gear by Buckingham's Equation can be measured.

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Wear Strength of Bevel Gear by Buckingham's Equation Formula

Wear Strength of Bevel Gear by Buckingham's Equation Example

Wear Strength of Bevel Gear by Buckingham's Equation Solution

Wear Strength of Bevel Gear by Buckingham's Equation Formula Elements

Other formulas in Material Properties category

How to Evaluate Wear Strength of Bevel Gear by Buckingham's Equation?

FAQs on Wear Strength of Bevel Gear by Buckingham's Equation

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