Actual Number of Teeth on Gear given Virtual Number of Teeth Calculator

✖Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.ⓘ Helix Angle of Helical Gear [ψ]			+10% -10%
✖The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.ⓘ Virtual Number of Teeth on Helical Gear [z']			+10% -10%

✖Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.ⓘ Actual Number of Teeth on Gear given Virtual Number of Teeth [z]

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Formula

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Actual Number of Teeth on Gear given Virtual Number of Teeth

Formula

z = {(\cos (ψ))}^{3} \cdot z'

Example

40.19952 = {(\cos (25 °))}^{3} \cdot 54

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Actual Number of Teeth on Gear given Virtual Number of Teeth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear
z = (cos(ψ))^(3)*z'
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 Helical Gear - Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.
Helix Angle of Helical Gear - (Measured in Radian) - Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.
Virtual Number of Teeth on Helical Gear - The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.

STEP 1: Convert Input(s) to Base Unit

Helix Angle of Helical Gear: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Virtual Number of Teeth on Helical Gear: 54 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = (cos(ψ))^(3)*z' --> (cos(0.4363323129985))^(3)*54

Evaluating ... ...

z = 40.199522483873

STEP 3: Convert Result to Output's Unit

40.199522483873 --> No Conversion Required

FINAL ANSWER

40.199522483873 ≈ 40.19952 <-- Number of Teeth on Helical Gear

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Helical Gears » Mechanical » Core Design Parameters » Actual Number of Teeth on Gear given Virtual Number of Teeth

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Core Design Parameters Calculators

Pitch Circle Diameter of Helical Gear

Go Diameter of Pitch Circle of Helical Gear = Number of Teeth on Helical Gear*Normal Module of Helical Gear/cos(Helix Angle of Helical Gear)

Transverse Module of Helical Gear given Normal Module

Go Transverse Module of Helical Gear = Normal Module of Helical Gear/cos(Helix Angle of Helical Gear)

Normal Module of Helical Gear

Go Normal Module of Helical Gear = Transverse Module of Helical Gear*cos(Helix Angle of Helical Gear)

Transverse Module of Helical Gear given Transverse Diametrical Pitch

Go Transverse Module of Helical Gear = 1/Transverse Diametrical Pitch of Helical Gear

Actual Number of Teeth on Gear given Virtual Number of Teeth Formula

Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear
z = (cos(ψ))^(3)*z'

Define Helical Gears

A helical gear has a cylindrical pitch surface and teeth that follow a helix on the pitch cylinder. External helical gears have teeth that project outwards, whereas internal helical gears have teeth that project inwards.

How to Calculate Actual Number of Teeth on Gear given Virtual Number of Teeth?

Actual Number of Teeth on Gear given Virtual Number of Teeth calculator uses Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear to calculate the Number of Teeth on Helical Gear, Actual Number of Teeth on Gear given Virtual Number of Teeth formula is defined as the actual number of Gear Teeth that are present on the Gear. Number of Teeth on Helical Gear is denoted by z symbol.

How to calculate Actual Number of Teeth on Gear given Virtual Number of Teeth using this online calculator? To use this online calculator for Actual Number of Teeth on Gear given Virtual Number of Teeth, enter Helix Angle of Helical Gear (ψ) & Virtual Number of Teeth on Helical Gear (z') and hit the calculate button. Here is how the Actual Number of Teeth on Gear given Virtual Number of Teeth calculation can be explained with given input values -> 40.19952 = (cos(0.4363323129985))^(3)*54.

FAQ

What is Actual Number of Teeth on Gear given Virtual Number of Teeth?

Actual Number of Teeth on Gear given Virtual Number of Teeth formula is defined as the actual number of Gear Teeth that are present on the Gear and is represented as z = (cos(ψ))^(3)*z' or Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear. Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone & The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.

How to calculate Actual Number of Teeth on Gear given Virtual Number of Teeth?

Actual Number of Teeth on Gear given Virtual Number of Teeth formula is defined as the actual number of Gear Teeth that are present on the Gear is calculated using Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear. To calculate Actual Number of Teeth on Gear given Virtual Number of Teeth, you need Helix Angle of Helical Gear (ψ) & Virtual Number of Teeth on Helical Gear (z'). With our tool, you need to enter the respective value for Helix Angle of Helical Gear & Virtual Number of Teeth on Helical 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 Number of Teeth on Helical Gear?

In this formula, Number of Teeth on Helical Gear uses Helix Angle of Helical Gear & Virtual Number of Teeth on Helical Gear. We can use 3 other way(s) to calculate the same, which is/are as follows -

Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear
Number of Teeth on Helical Gear = Number of Teeth on Helical Pinion*Helical Gear Speed Ratio
Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear)

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