Number of Teeth on Gear given Addendum Circle Diameter Calculator

✖The Addendum Circle Diameter of Helical Gear is defined as a circle touching the outermost points of the teeth of a circular gear wheel.ⓘ Addendum Circle Diameter of Helical Gear [d_a]			+10% -10%
✖The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.ⓘ Normal Module of Helical Gear [m_n]			+10% -10%
✖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%

✖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.ⓘ Number of Teeth on Gear given Addendum Circle Diameter [z]

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Number of Teeth on Gear given Addendum Circle Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear)
z = (d_a/m_n-2)*cos(ψ)
This formula uses 1 Functions, 4 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.
Addendum Circle Diameter of Helical Gear - (Measured in Meter) - The Addendum Circle Diameter of Helical Gear is defined as a circle touching the outermost points of the teeth of a circular gear wheel.
Normal Module of Helical Gear - (Measured in Meter) - The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.
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.

STEP 1: Convert Input(s) to Base Unit

Addendum Circle Diameter of Helical Gear: 138 Millimeter --> 0.138 Meter (Check conversion here)
Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)
Helix Angle of Helical Gear: 25 Degree --> 0.4363323129985 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = (d_a/m_n-2)*cos(ψ) --> (0.138/0.003-2)*cos(0.4363323129985)

Evaluating ... ...

z = 39.8775426296141

STEP 3: Convert Result to Output's Unit

39.8775426296141 --> No Conversion Required

FINAL ANSWER

39.8775426296141 ≈ 39.87754 <-- 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 » Number of Teeth on Gear given Addendum Circle Diameter

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Osmania University (OU), Hyderabad

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< Core Design Parameters Calculators

Pitch Circle Diameter of Helical Gear

LaTeX 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

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

Normal Module of Helical Gear

LaTeX 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

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

Number of Teeth on Gear given Addendum Circle Diameter Formula

LaTeX Go

Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear)
z = (d_a/m_n-2)*cos(ψ)

Define Addendum

The addendum is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line; also, the radial distance between the pitch diameter and the outside diameter.

How to Calculate Number of Teeth on Gear given Addendum Circle Diameter?

Number of Teeth on Gear given Addendum Circle Diameter calculator uses Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear) to calculate the Number of Teeth on Helical Gear, The Number of Teeth on Gear given Addendum Circle Diameter formula is defined as the number of protrusions onto the periphery of a gear that mesh with Teeth of another gear to transmit motion. Number of Teeth on Helical Gear is denoted by z symbol.

How to calculate Number of Teeth on Gear given Addendum Circle Diameter using this online calculator? To use this online calculator for Number of Teeth on Gear given Addendum Circle Diameter, enter Addendum Circle Diameter of Helical Gear (d_a), Normal Module of Helical Gear (m_n) & Helix Angle of Helical Gear (ψ) and hit the calculate button. Here is how the Number of Teeth on Gear given Addendum Circle Diameter calculation can be explained with given input values -> 39.87754 = (0.138/0.003-2)*cos(0.4363323129985).

FAQ

What is Number of Teeth on Gear given Addendum Circle Diameter?

The Number of Teeth on Gear given Addendum Circle Diameter formula is defined as the number of protrusions onto the periphery of a gear that mesh with Teeth of another gear to transmit motion and is represented as z = (d_a/m_n-2)*cos(ψ) or Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear). The Addendum Circle Diameter of Helical Gear is defined as a circle touching the outermost points of the teeth of a circular gear wheel, The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the 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.

How to calculate Number of Teeth on Gear given Addendum Circle Diameter?

The Number of Teeth on Gear given Addendum Circle Diameter formula is defined as the number of protrusions onto the periphery of a gear that mesh with Teeth of another gear to transmit motion is calculated using Number of Teeth on Helical Gear = (Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2)*cos(Helix Angle of Helical Gear). To calculate Number of Teeth on Gear given Addendum Circle Diameter, you need Addendum Circle Diameter of Helical Gear (d_a), Normal Module of Helical Gear (m_n) & Helix Angle of Helical Gear (ψ). With our tool, you need to enter the respective value for Addendum Circle Diameter of Helical Gear, Normal Module of Helical Gear & Helix Angle of 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 Addendum Circle Diameter of Helical Gear, Normal Module of Helical Gear & Helix Angle of 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 = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear

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