Wear Strength of Bevel Gear by Buckingham's Equation 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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✖Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis.ⓘ Face Width of Bevel Gear Tooth [b]			+10% -10%
✖Ratio Factor for bevel gear is defined as the ratio used in the design of a Bevel Gear.ⓘ Ratio Factor for Bevel Gear [Q_b]			+10% -10%
✖Pitch circle diameter of bevel pinion is twice the distance from the centre of the gear to the pitch point. This is where the gear's speed is measured.ⓘ Pitch Circle Diameter of Bevel Pinion [D_p]			+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 [K]			+10% -10%
✖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.ⓘ Pitch Angle for Bevel Gear [γ]			+10% -10%

✖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.ⓘ Wear Strength of Bevel Gear by Buckingham's Equation [S_w]

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Formula

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Wear Strength of Bevel Gear by Buckingham's Equation

Formula

`"S"_{"w"} = (0.75*"b"*"Q"_{"b"}*"D"_{"p"}*"K")/cos("γ")`

Example

`"15060.94N"=(0.75*"35mm"*"1.5"*"76.5mm"*"2.5N/mm²")/cos("60°")`

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Wear Strength of Bevel Gear by Buckingham's Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
S_w = (0.75*b*Q_b*D_p*K)/cos(γ)
This formula uses 1 Functions, 6 Variables

Functions Used

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

Wear Strength of Bevel Gear Tooth - (Measured in Newton) - 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.
Face Width of Bevel Gear Tooth - (Measured in Meter) - Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis.
Ratio Factor for Bevel Gear - Ratio Factor for bevel gear is defined as the ratio used in the design of a Bevel Gear.
Pitch Circle Diameter of Bevel Pinion - (Measured in Meter) - Pitch circle diameter of bevel pinion is twice the distance from the centre of the gear to the pitch point. This is where the gear's speed is measured.
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.
Pitch Angle for Bevel Gear - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Face Width of Bevel Gear Tooth: 35 Millimeter --> 0.035 Meter (Check conversion here)
Ratio Factor for Bevel Gear: 1.5 --> No Conversion Required
Pitch Circle Diameter of Bevel Pinion: 76.5 Millimeter --> 0.0765 Meter (Check conversion here)
Material Constant: 2.5 Newton per Square Millimeter --> 2500000 Pascal (Check conversion here)
Pitch Angle for Bevel Gear: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_w = (0.75*b*Q_b*D_p*K)/cos(γ) --> (0.75*0.035*1.5*0.0765*2500000)/cos(1.0471975511964)

Evaluating ... ...

S_w = 15060.9374999948

STEP 3: Convert Result to Output's Unit

15060.9374999948 Newton --> No Conversion Required

FINAL ANSWER

15060.9374999948 ≈ 15060.94 Newton <-- Wear Strength of Bevel Gear Tooth

(Calculation completed in 00.020 seconds)

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Created by Akshay Talbar

Vishwakarma University (VU), Pune

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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

Wear Strength of Bevel Gear by Buckingham's Equation Formula

Why wear strength is calculated?

The wear strength is calculated to avoid the failure of the gear due to pitting. And can be sued to calculate the terms of gear like module, a factor of safety.

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

Wear Strength of Bevel Gear by Buckingham's Equation calculator 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 calculate 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 calculate Wear Strength of Bevel Gear by Buckingham's Equation using this online calculator? To use this online calculator 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. Here is how the Wear Strength of Bevel Gear by Buckingham's Equation calculation can be explained with given input values -> 15060.94 = (0.75*0.035*1.5*0.0765*2500000)/cos(1.0471975511964).

FAQ

What is Wear Strength of Bevel Gear by Buckingham's Equation?

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 and is represented as S_w = (0.75*b*Q_b*D_p*K)/cos(γ) or 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). Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis, Ratio Factor for bevel gear is defined as the ratio used in the design of a Bevel Gear, Pitch circle diameter of bevel pinion is twice the distance from the centre of the gear to the pitch point. This is where the gear's speed is measured, 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 & 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.

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

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 is calculated using 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 calculate Wear Strength of Bevel Gear by Buckingham's Equation, you need 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). With our tool, you need to enter the respective value for Face Width of Bevel Gear Tooth, Ratio Factor for Bevel Gear, Pitch Circle Diameter of Bevel Pinion, Material Constant & Pitch Angle for Bevel Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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