Pitch Circular Diameter of Gear given Virtual Gear Calculator

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Design of Gears

Basics Of Machine Design

Design of Coupling

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Design of Helical Gears

Design of Bevel Gears

Design of Spur Gears

Design of Worm Gears

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Helix Geometry

Core Design Parameters

✖Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.ⓘ Radius of Curvature of Helical Gear [r']			+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 Gear [d]

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Formula

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Pitch Circular Diameter of Gear given Virtual Gear

Formula

`"d" = 2*"r'"*(cos("ψ"))^2`

Example

`"118.2807mm"=2*"72mm"*(cos("25°"))^2`

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Download Design of Helical Gears Formulas PDF

Pitch Circular Diameter of Gear given Virtual Gear Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Radius of Curvature of Helical Gear - (Measured in Meter) - Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.
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

Radius of Curvature of Helical Gear: 72 Millimeter --> 0.072 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

d = 2*r'*(cos(ψ))^2 --> 2*0.072*(cos(0.4363323129985))^2

Evaluating ... ...

d = 0.11828070789744

STEP 3: Convert Result to Output's Unit

0.11828070789744 Meter -->118.28070789744 Millimeter (Check conversion here)

FINAL ANSWER

118.28070789744 ≈ 118.2807 Millimeter <-- Diameter of Pitch Circle of Helical Gear

(Calculation completed in 00.004 seconds)

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< 25 Helix Geometry Calculators

Helix Angle of Helical Gear given Center to Center Distance between Two Gears

Go Helix Angle of Helical Gear = acos(Normal Module of Helical Gear*(Number of Teeth on 1st Helical Gear+Number of Teeth on 2nd Helical Gear)/(2*Center to Center Distance of Helical Gears))

Helix Angle of Helical Gear given Virtual Number of Teeth

Go Helix Angle of Helical Gear = acos((Diameter of Pitch Circle of Helical Gear/(Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear))^(1/2))

Transverse Pressure Angle of Helical Gear given Helix Angle

Go Transverse Pressure Angle of Helical Gear = atan(tan(Normal Pressure Angle of Helical Gear)/cos(Helix Angle of Helical Gear))

Normal Pressure Angle of Helical Gear given Helix Angle

Go Normal Pressure Angle of Helical Gear = atan(tan(Transverse Pressure Angle of Helical Gear)*cos(Helix Angle of Helical Gear))

Helix Angle of Helical Gear given Pressure Angle

Go Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear))

Pitch Circular Diameter of Gear given Virtual Number of Teeth

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)

Helix Angle of Helical Gear given Pitch Circle Diameter

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

Helix Angle of Helical Gear given Radius of Curvature at Point

Go Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear)))

Radius of Curvature of Virtual Gear given Virtual Number of Teeth

Go Virtual Pitch Circle Radius for Helical Gear = Virtual Number of Teeth on Helical Gear*Normal Circular Pitch of Helical Gear/(2*pi)

Normal Circular Pitch of Helical Gear given Virtual Number of Teeth

Go Normal Circular Pitch of Helical Gear = 2*pi*Virtual Pitch Circle Radius for Helical Gear/Virtual Number of Teeth on Helical Gear

Semi Major Axis of Elliptical Profile given Radius of Curvature at Point

Go Semi Major Axis of Helical Gear Teeth = sqrt(Radius of Curvature of Helical Gear*Semi Minor Axis of Helical Gear Teeth)

Radius of Curvature at Point on Virtual Gear

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

Pitch Circular Diameter of Gear given Virtual Gear

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

Helix Angle of Helical Gear given Normal Module

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

Helix Angle of Helical Gear given Normal Circular Pitch

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

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

Normal Circular Pitch of Helical Gear

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

Semi Minor Axis of Elliptical Profile given Radius of Curvature at Point

Go Semi Minor Axis of Helical Gear Teeth = Semi Major Axis of Helical Gear Teeth^2/Radius of Curvature of Helical Gear

Helix Angle of Helical Gear given Axial Pitch

Go Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear)

Radius of Curvature at Point on Helical Gear

Go Radius of Curvature of Helical Gear = Semi Major Axis of Helical Gear Teeth^2/Semi Minor Axis of Helical Gear Teeth

Axial Pitch of Helical Gear given Helix Angle

Go Axial Pitch of Helical Gear = Pitch of Helical Gear/tan(Helix Angle of Helical Gear)

Pitch of Helical Gear given Axial Pitch

Go Pitch of Helical Gear = Axial Pitch of Helical Gear*tan(Helix Angle of Helical Gear)

Radius of Curvature of Virtual Gear given Pitch Circular Diameter

Go Radius of Curvature of Helical Gear = Pitch Circular Diameter of Helical Virtual Gear/2

Pitch Circular Diameter of Gear given Radius of Curvature

Go Pitch Circular Diameter of Helical Virtual Gear = 2*Radius of Curvature of Helical Gear

Transverse Diametrical Pitch of Helical Gear given Transverse Module

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

Pitch Circular Diameter of Gear given Virtual Gear Formula

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

Pitch Circular Diameter of Gear given Virtual Gear calculator uses Diameter of Pitch Circle of Helical Gear = 2*Radius of Curvature of 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 Gear 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 Gear using this online calculator? To use this online calculator for Pitch Circular Diameter of Gear given Virtual Gear, enter Radius of Curvature of Helical Gear (r') & Helix Angle of Helical Gear (ψ) and hit the calculate button. Here is how the Pitch Circular Diameter of Gear given Virtual Gear calculation can be explained with given input values -> 118280.7 = 2*0.072*(cos(0.4363323129985))^2.

FAQ

What is Pitch Circular Diameter of Gear given Virtual Gear?

The Pitch Circular Diameter of Gear given Virtual Gear 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 = 2*r'*(cos(ψ))^2 or Diameter of Pitch Circle of Helical Gear = 2*Radius of Curvature of Helical Gear*(cos(Helix Angle of Helical Gear))^2. Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point & 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 Gear?

The Pitch Circular Diameter of Gear given Virtual Gear 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 = 2*Radius of Curvature of Helical Gear*(cos(Helix Angle of Helical Gear))^2. To calculate Pitch Circular Diameter of Gear given Virtual Gear, you need Radius of Curvature of Helical Gear (r') & Helix Angle of Helical Gear (ψ). With our tool, you need to enter the respective value for Radius of Curvature 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 Diameter of Pitch Circle of Helical Gear?

In this formula, Diameter of Pitch Circle of Helical Gear uses Radius of Curvature of 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 = Normal Module of Helical Gear*Virtual Number of Teeth on Helical Gear*(cos(Helix Angle of Helical Gear)^2)

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