Pitch Circular Diameter of Gear given Virtual Number of Teeth Calculator

✖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%
✖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%
✖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%

✖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.ⓘ Pitch Circular Diameter of Gear given Virtual Number of Teeth [d]

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Pitch Circular Diameter of Gear given Virtual Number of Teeth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2)
d = m_n*z'*(cos(ψ)^2)
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

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.
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.
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.
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

Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)
Virtual Number of Teeth on Helical Gear: 54 --> No Conversion Required
Helix Angle of Helical Gear: 25 Degree --> 0.4363323129985 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = m_n*z'*(cos(ψ)^2) --> 0.003*54*(cos(0.4363323129985)^2)

Evaluating ... ...

d = 0.13306579638462

STEP 3: Convert Result to Output's Unit

0.13306579638462 Meter -->133.06579638462 Millimeter (Check conversion here)

FINAL ANSWER

133.06579638462 ≈ 133.0658 Millimeter <-- Diameter of Pitch Circle of 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 » Helix Geometry » Pitch Circular Diameter of Gear given Virtual Number of Teeth

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Osmania University (OU), Hyderabad

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< Helix Geometry Calculators

Helix Angle of Helical Gear given Normal Circular Pitch

LaTeX Go Helix Angle of Helical Gear = acos(Normal Circular Pitch of Helical Gear/Pitch of Helical Gear)

Pitch of Helical Gear given Normal Circular Pitch

LaTeX Go Pitch of Helical Gear = Normal Circular Pitch of Helical Gear/cos(Helix Angle of Helical Gear)

Normal Circular Pitch of Helical Gear

LaTeX Go Normal Circular Pitch of Helical Gear = Pitch of Helical Gear*cos(Helix Angle of Helical Gear)

Transverse Diametrical Pitch of Helical Gear given Transverse Module

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

Pitch Circular Diameter of Gear given Virtual Number of Teeth Formula

LaTeX Go

Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2)
d = m_n*z'*(cos(ψ)^2)

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 Pitch Circular Diameter of Gear given Virtual Number of Teeth?

Pitch Circular Diameter of Gear given Virtual Number of Teeth calculator uses Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2) to calculate the Diameter of Pitch Circle of Helical Gear, The Pitch Circular Diameter of Gear given Virtual Number of Teeth formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point. Diameter of Pitch Circle of Helical Gear is denoted by d symbol.

How to calculate Pitch Circular Diameter of Gear given Virtual Number of Teeth using this online calculator? To use this online calculator for Pitch Circular Diameter of Gear given Virtual Number of Teeth, enter Normal Module of Helical Gear (m_n), Virtual Number of Teeth on Helical Gear (z') & Helix Angle of Helical Gear (ψ) and hit the calculate button. Here is how the Pitch Circular Diameter of Gear given Virtual Number of Teeth calculation can be explained with given input values -> 133065.8 = 0.003*54*(cos(0.4363323129985)^2).

FAQ

What is Pitch Circular Diameter of Gear given Virtual Number of Teeth?

The Pitch Circular Diameter of Gear given Virtual Number of Teeth formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point and is represented as d = m_n*z'*(cos(ψ)^2) or Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2). The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the 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 & 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 Pitch Circular Diameter of Gear given Virtual Number of Teeth?

The Pitch Circular Diameter of Gear given Virtual Number of Teeth formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point is calculated using Diameter of Pitch Circle of Helical Gear = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2). To calculate Pitch Circular Diameter of Gear given Virtual Number of Teeth, you need Normal Module of Helical Gear (m_n), Virtual Number of Teeth on Helical Gear (z') & Helix Angle of Helical Gear (ψ). With our tool, you need to enter the respective value for Normal Module of Helical Gear, Virtual Number of Teeth on 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 Diameter of Pitch Circle of Helical Gear?

In this formula, Diameter of Pitch Circle of Helical Gear uses Normal Module of Helical Gear, Virtual Number of Teeth on Helical Gear & Helix Angle of Helical Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

Diameter of Pitch Circle of Helical Gear = 2*Radius of Curvature of Helical Gear*(cos(Helix Angle of Helical Gear))^2

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