Actual Number of Teeth on Bevel Gear 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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✖Virtual Number of Teeth for Bevel Gear is imaginary spur gear teeth that are considered in a plane perpendicular to the tooth at the large end.ⓘ Virtual Number of Teeth for Bevel Gear [z^']			+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%

✖Number of Teeth on Bevel Gear is the total number of teeth on the peripheral surface of gear and they mesh with the teeth of some other gear or toothed machine element.ⓘ Actual Number of Teeth on Bevel Gear [z_g]

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Formula

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Actual Number of Teeth on Bevel Gear

Formula

`"z"_{"g"} = "z"^{"'"}*cos("γ")`

Example

`"12"="24"*cos("60°")`

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Download Design of Bevel Gears Formulas PDF

Actual Number of Teeth on Bevel Gear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear)
z_g = z^'*cos(γ)
This formula uses 1 Functions, 3 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

Number of Teeth on Bevel Gear - Number of Teeth on Bevel Gear is the total number of teeth on the peripheral surface of gear and they mesh with the teeth of some other gear or toothed machine element.
Virtual Number of Teeth for Bevel Gear - Virtual Number of Teeth for Bevel Gear is imaginary spur gear teeth that are considered in a plane perpendicular to the tooth at the large end.
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

Virtual Number of Teeth for Bevel Gear: 24 --> No Conversion Required
Pitch Angle for Bevel Gear: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z_g = z^'*cos(γ) --> 24*cos(1.0471975511964)

Evaluating ... ...

z_g = 12.0000000000041

STEP 3: Convert Result to Output's Unit

12.0000000000041 --> No Conversion Required

FINAL ANSWER

12.0000000000041 ≈ 12 <-- Number of Teeth on Bevel Gear

(Calculation completed in 00.004 seconds)

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Created by Akshay Talbar

Vishwakarma University (VU), Pune

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< 7 Geometric Properties Calculators

Radius of Pinion at Midpoint along Face Width for Bevel Gear

Go Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2

Actual Number of Teeth on Bevel Gear

Go Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear)

Cone Distance of Bevel Gear

Go Cone Distance = sqrt((Pitch Circle Diameter of Bevel Pinion/2)^2+(Pitch Circle Diameter of Gear/2)^2)

Radius of Pinion at Midpoint given Torque and Tangential Force for Bevel Gear

Go Radius of Pinion at Midpoint = Torque Transmitted by Bevel Pinion/Tangential Force Transmitted by Bevel Gear

Geometric step ratio

Go Geometric step ratio = Range ratio in preferred Series^(1/(Quantity of product(Enter integer value only)-1))

Virtual or Formative Number of Teeth of Bevel Gear

Go Virtual Number of Teeth for Bevel Gear = (2*Back Cone Radius)/Module of Bevel Gear

Back Cone Radius of Bevel Gear

Go Back Cone Radius = (Module of Bevel Gear*Virtual Number of Teeth for Bevel Gear)/2

Actual Number of Teeth on Bevel Gear Formula

Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear)
z_g = z^'*cos(γ)

Why we use virtual number of teeth ?

The actual reason is for the ease of calculation and analysis of various parameters we use Spur Gear profile as a reference.

How to Calculate Actual Number of Teeth on Bevel Gear?

Actual Number of Teeth on Bevel Gear calculator uses Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear) to calculate the Number of Teeth on Bevel Gear, Actual Number of Teeth on Bevel Gear is defined as the number of the gear teeth that mesh with another toothed part to transmit motion or to change speed or direction. Number of Teeth on Bevel Gear is denoted by z_g symbol.

How to calculate Actual Number of Teeth on Bevel Gear using this online calculator? To use this online calculator for Actual Number of Teeth on Bevel Gear, enter Virtual Number of Teeth for Bevel Gear (z^') & Pitch Angle for Bevel Gear (γ) and hit the calculate button. Here is how the Actual Number of Teeth on Bevel Gear calculation can be explained with given input values -> 12 = 24*cos(1.0471975511964).

FAQ

What is Actual Number of Teeth on Bevel Gear?

Actual Number of Teeth on Bevel Gear is defined as the number of the gear teeth that mesh with another toothed part to transmit motion or to change speed or direction and is represented as z_g = z^'*cos(γ) or Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear). Virtual Number of Teeth for Bevel Gear is imaginary spur gear teeth that are considered in a plane perpendicular to the tooth at the large end & 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 Actual Number of Teeth on Bevel Gear?

Actual Number of Teeth on Bevel Gear is defined as the number of the gear teeth that mesh with another toothed part to transmit motion or to change speed or direction is calculated using Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear). To calculate Actual Number of Teeth on Bevel Gear, you need Virtual Number of Teeth for Bevel Gear (z^') & Pitch Angle for Bevel Gear (γ). With our tool, you need to enter the respective value for Virtual Number of Teeth for Bevel Gear & 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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