Material Constant for Bevel Gear Wear Strength Calculator

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Design of Gears

Basics Of Machine Design

Design of Coupling

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Design of Bevel Gears

Design of Helical Gears

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✖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.ⓘ Compressive Stress in Bevel Gear Tooth [σ_c]			+10% -10%
✖The Pressure Angle for Bevel Gear is the angle between the pressure line and the common tangent to the pitch circles.ⓘ Pressure Angle [α_Bevel]			+10% -10%
✖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.ⓘ Modulus of Elasticity of Spur Pinion [E_p]			+10% -10%
✖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.ⓘ Modulus of Elasticity of Spur Gear [E_g]			+10% -10%

✖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.ⓘ Material Constant for Bevel Gear Wear Strength [K]

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Formula

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Material Constant for Bevel Gear Wear Strength

Formula

`"K" = ("σ"_{"c"}^2*sin("α"_{"Bevel"})*cos("α"_{"Bevel"})*(1/"E"_{"p"}+1/"E"_{"g"}))/1.4`

Example

`"2.50552N/mm²"=(("350N/mm²")^2*sin("22°")*cos("22°")*(1/"20600N/mm²"+1/"29500N/mm²"))/1.4`

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Material Constant for Bevel Gear Wear Strength Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
K = (σ_c^2*sin(α_Bevel)*cos(α_Bevel)*(1/E_p+1/E_g))/1.4
This formula uses 2 Functions, 5 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Material Constant - (Measured in Pascal) - 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.
Compressive Stress in Bevel Gear Tooth - (Measured in Pascal) - 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.
Pressure Angle - (Measured in Radian) - The Pressure Angle for Bevel Gear is the angle between the pressure line and the common tangent to the pitch circles.
Modulus of Elasticity of Spur Pinion - (Measured in Pascal) - 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.
Modulus of Elasticity of Spur Gear - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Compressive Stress in Bevel Gear Tooth: 350 Newton per Square Millimeter --> 350000000 Pascal (Check conversion here)
Pressure Angle: 22 Degree --> 0.38397243543868 Radian (Check conversion here)
Modulus of Elasticity of Spur Pinion: 20600 Newton per Square Millimeter --> 20600000000 Pascal (Check conversion here)
Modulus of Elasticity of Spur Gear: 29500 Newton per Square Millimeter --> 29500000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K = (σ_c^2*sin(α_Bevel)*cos(α_Bevel)*(1/E_p+1/E_g))/1.4 --> (350000000^2*sin(0.38397243543868)*cos(0.38397243543868)*(1/20600000000+1/29500000000))/1.4

Evaluating ... ...

K = 2505519.69022476

STEP 3: Convert Result to Output's Unit

2505519.69022476 Pascal -->2.50551969022476 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

2.50551969022476 ≈ 2.50552 Newton per Square Millimeter <-- Material Constant

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Bevel Gears » Material Properties » Material Constant for Bevel Gear Wear Strength

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Created by Akshay Talbar

Vishwakarma University (VU), Pune

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National Institute Of Technology (NIT), Hamirpur

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< 4 Material Properties Calculators

Material Constant for Bevel Gear Wear Strength

Go 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

Wear Strength of Bevel Gear by Buckingham's Equation

Go 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)

Beam Strength of Tooth of Bevel Gear

Go 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)

Material Constant for Bevel Gear Wear Strength given Brinell Hardness Number

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

Material Constant for Bevel Gear Wear Strength Formula

Why load stress factor is used ?

Load stress factor is used to calculate the wear strength of the material. The formula can be further simplified to a certain extent by putting the values of pressure angle and modulus of elasticity for some material.

How to Calculate Material Constant for Bevel Gear Wear Strength?

Material Constant for Bevel Gear Wear Strength calculator 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 calculate 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 calculate Material Constant for Bevel Gear Wear Strength using this online calculator? To use this online calculator 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. Here is how the Material Constant for Bevel Gear Wear Strength calculation can be explained with given input values -> 2.5E-6 = (350000000^2*sin(0.38397243543868)*cos(0.38397243543868)*(1/20600000000+1/29500000000))/1.4.

FAQ

What is Material Constant for Bevel Gear Wear Strength?

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 and is represented as K = (σ_c^2*sin(α_Bevel)*cos(α_Bevel)*(1/E_p+1/E_g))/1.4 or 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. 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, The Pressure Angle for Bevel Gear is the angle between the pressure line and the common tangent to the pitch circles, 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 & 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.

How to calculate Material Constant for Bevel Gear Wear Strength?

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 is calculated using 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 calculate Material Constant for Bevel Gear Wear Strength, you need 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). With our tool, you need to enter the respective value for Compressive Stress in Bevel Gear Tooth, Pressure Angle, Modulus of Elasticity of Spur Pinion & Modulus of Elasticity of Spur Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Material Constant?

In this formula, Material Constant uses Compressive Stress in Bevel Gear Tooth, Pressure Angle, Modulus of Elasticity of Spur Pinion & Modulus of Elasticity of Spur Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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