Number of Teeth on Gear given Pitch Circle Diameter Calculator

✖Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.ⓘ Diameter of Pitch Circle of Helical Gear [d]			+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%
✖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%

✖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 Pitch Circle Diameter [z]

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Number of Teeth on Gear given Pitch Circle Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear
z = d*cos(ψ)/m_n
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.
Diameter of Pitch Circle of Helical Gear - (Measured in Meter) - Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Diameter of Pitch Circle of Helical Gear: 118 Millimeter --> 0.118 Meter (Check conversion here)
Helix Angle of Helical Gear: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = d*cos(ψ)/m_n --> 0.118*cos(0.4363323129985)/0.003

Evaluating ... ...

z = 35.6481062901096

STEP 3: Convert Result to Output's Unit

35.6481062901096 --> No Conversion Required

FINAL ANSWER

35.6481062901096 ≈ 35.64811 <-- 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 Pitch Circle Diameter

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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

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 Pitch Circle Diameter Formula

LaTeX Go

Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear
z = d*cos(ψ)/m_n

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 Number of Teeth on Gear given Pitch Circle Diameter?

Number of Teeth on Gear given Pitch Circle Diameter calculator uses Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear to calculate the Number of Teeth on Helical Gear, The Number of Teeth on Gear given Pitch 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 Pitch Circle Diameter using this online calculator? To use this online calculator for Number of Teeth on Gear given Pitch Circle Diameter, enter Diameter of Pitch Circle of Helical Gear (d), Helix Angle of Helical Gear (ψ) & Normal Module of Helical Gear (m_n) and hit the calculate button. Here is how the Number of Teeth on Gear given Pitch Circle Diameter calculation can be explained with given input values -> 35.64811 = 0.118*cos(0.4363323129985)/0.003.

FAQ

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

The Number of Teeth on Gear given Pitch 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*cos(ψ)/m_n or Number of Teeth on Helical Gear = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear. Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle, Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone & The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.

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

The Number of Teeth on Gear given Pitch 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 = Diameter of Pitch Circle of Helical Gear*cos(Helix Angle of Helical Gear)/Normal Module of Helical Gear. To calculate Number of Teeth on Gear given Pitch Circle Diameter, you need Diameter of Pitch Circle of Helical Gear (d), Helix Angle of Helical Gear (ψ) & Normal Module of Helical Gear (m_n). With our tool, you need to enter the respective value for Diameter of Pitch Circle of Helical Gear, Helix Angle of Helical Gear & Normal Module 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 Diameter of Pitch Circle of Helical Gear, Helix Angle of Helical Gear & Normal Module 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 = 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)
Number of Teeth on Helical Gear = (cos(Helix Angle of Helical Gear))^(3)*Virtual Number of Teeth on Helical Gear

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