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Material Constant for Bevel Gear Wear Strength Formula

GoMaterial Constant for Bevel Gear Wear Strength given Brinell Hardness Number Formula

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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. Check FAQs

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

K - Material Constant?σ_c - Compressive Stress in Bevel Gear Tooth?α_Bevel - Pressure Angle?E_p - Modulus of Elasticity of Spur Pinion?E_g - Modulus of Elasticity of Spur Gear?

Material Constant for Bevel Gear Wear Strength Example

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Here is how the Material Constant for Bevel Gear Wear Strength equation looks like with Values.

Here is how the Material Constant for Bevel Gear Wear Strength equation looks like with Units.

Here is how the Material Constant for Bevel Gear Wear Strength equation looks like.

2.5055 = \frac{350^{2} \cdot \sin (22) \cdot \cos (22) \cdot (\frac{1}{20600} + \frac{1}{29500})}{1.4}

2.5055N/mm² = \frac{{350N/mm²}^{2} \cdot \sin (22°) \cdot \cos (22°) \cdot (\frac{1}{20600N/mm²} + \frac{1}{29500N/mm²})}{1.4}

2.5055 = \frac{350^{2} \cdot \sin (22) \cdot \cos (22) \cdot (\frac{1}{20600} + \frac{1}{29500})}{1.4}

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Material Constant for Bevel Gear Wear Strength Solution

Follow our step by step solution on how to calculate Material Constant for Bevel Gear Wear Strength?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

K = \frac{{350N/mm²}^{2} \cdot \sin (22°) \cdot \cos (22°) \cdot (\frac{1}{20600N/mm²} + \frac{1}{29500N/mm²})}{1.4}

Next Step Convert Units

∴

K = \frac{{3.5E+8Pa}^{2} \cdot \sin (0.384rad) \cdot \cos (0.384rad) \cdot (\frac{1}{2.1E+10Pa} + \frac{1}{3E+10Pa})}{1.4}

Next Step Prepare to Evaluate

∴

K = \frac{{3.5E+8}^{2} \cdot \sin (0.384) \cdot \cos (0.384) \cdot (\frac{1}{2.1E+10} + \frac{1}{3E+10})}{1.4}

Next Step Evaluate

∴

K = 2505519.69022476Pa

Next Step Convert to Output's Unit

∴

K = 2.50551969022476N/mm²

LAST Step Rounding Answer

∴

K = 2.5055N/mm²

Material Constant for Bevel Gear Wear Strength Formula Elements

Variables

Functions

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

Compressive Stress in Bevel Gear Tooth

Compressive stress in bevel gear tooth is the force per unit area that is responsible for the deformation of the material such that the volume of the material reduces.

Symbol: σ_c

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Compressive Stress in Bevel Gear Tooth

Pressure Angle

The Pressure Angle for Bevel Gear is the angle between the pressure line and the common tangent to the pitch circles.

Symbol: α_Bevel

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle

Modulus of Elasticity of Spur Pinion

Modulus of Elasticity of Spur Pinion is the measure of the stiffness of pinion gear material. It is a measure of how easily the pinion can be bent or stretched.

Symbol: E_p

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Spur Pinion

Modulus of Elasticity of Spur Gear

Modulus of Elasticity of Spur Gear is the measure of the stiffness of gear material. It is a measure of how easily the gear can be bent or stretched.

Symbol: E_g

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Spur Gear

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 to find Material Constant

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

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

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 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)}

How to Evaluate Material Constant for Bevel Gear Wear Strength?

Material Constant for Bevel Gear Wear Strength evaluator uses Material Constant = (Compressive Stress in Bevel Gear Tooth^2*sin(Pressure Angle)*cos(Pressure Angle)*(1/Modulus of Elasticity of Spur Pinion+1/Modulus of Elasticity of Spur Gear))/1.4 to evaluate the Material Constant, Material constant for Bevel Gear wear strength is defined as the ratio of the product of compressive stress and modulus of elasticity. It is constant for the bevel gear material. It is defined as the constant depending on the bevel gear material and determines the wear strength of that material. Material Constant is denoted by K symbol.

How to evaluate Material Constant for Bevel Gear Wear Strength using this online evaluator? To use this online evaluator for Material Constant for Bevel Gear Wear Strength, enter Compressive Stress in Bevel Gear Tooth (σ_c), Pressure Angle (α_Bevel), Modulus of Elasticity of Spur Pinion (E_p) & Modulus of Elasticity of Spur Gear (E_g) and hit the calculate button.

FAQs on Material Constant for Bevel Gear Wear Strength

What is the formula to find Material Constant for Bevel Gear Wear Strength?

The formula of Material Constant for Bevel Gear Wear Strength is expressed as Material Constant = (Compressive Stress in Bevel Gear Tooth^2*sin(Pressure Angle)*cos(Pressure Angle)*(1/Modulus of Elasticity of Spur Pinion+1/Modulus of Elasticity of Spur Gear))/1.4. Here is an example- 2.5E-6 = (350000000^2*sin(0.38397243543868)*cos(0.38397243543868)*(1/20600000000+1/29500000000))/1.4.

How to calculate Material Constant for Bevel Gear Wear Strength?

With Compressive Stress in Bevel Gear Tooth (σ_c), Pressure Angle (α_Bevel), Modulus of Elasticity of Spur Pinion (E_p) & Modulus of Elasticity of Spur Gear (E_g) we can find Material Constant for Bevel Gear Wear Strength using the formula - Material Constant = (Compressive Stress in Bevel Gear Tooth^2*sin(Pressure Angle)*cos(Pressure Angle)*(1/Modulus of Elasticity of Spur Pinion+1/Modulus of Elasticity of Spur Gear))/1.4. This formula also uses Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Material Constant?

Here are the different ways to Calculate Material Constant-

Material Constant=0.16*(Brinell Hardness Number for Bevel Gear/100)^2

Can the Material Constant for Bevel Gear Wear Strength be negative?

No, the Material Constant for Bevel Gear Wear Strength, measured in Stress cannot be negative.

Which unit is used to measure Material Constant for Bevel Gear Wear Strength?

Material Constant for Bevel Gear Wear Strength is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Material Constant for Bevel Gear Wear Strength can be measured.

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Material Constant for Bevel Gear Wear Strength Formula

​GoMaterial Constant for Bevel Gear Wear Strength given Brinell Hardness Number Formula

Material Constant for Bevel Gear Wear Strength Example

Material Constant for Bevel Gear Wear Strength Solution

Material Constant for Bevel Gear Wear Strength Formula Elements

Other Formulas to find Material Constant

Other formulas in Material Properties category

How to Evaluate Material Constant for Bevel Gear Wear Strength?

FAQs on Material Constant for Bevel Gear Wear Strength

Variable Name

GoMaterial Constant for Bevel Gear Wear Strength given Brinell Hardness Number Formula