Pitch Circle Diameter of Gear given Radius of Curvature at Point Calculator

✖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 Circle Diameter of Gear given Radius of Curvature at Point [d]

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Pitch Circle Diameter of Gear given Radius of Curvature at Point 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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Home » Physics » Design of Machine Elements » Design of Gears » Design of Helical Gears » Mechanical » Core Design Parameters » Pitch Circle Diameter of Gear given Radius of Curvature at Point

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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

Pitch Circle Diameter of Gear given Radius of Curvature at Point Formula

LaTeX Go

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 Circle Diameter of Gear given Radius of Curvature at Point?

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

FAQ

What is Pitch Circle Diameter of Gear given Radius of Curvature at Point?

Pitch Circle Diameter of Gear given Radius of Curvature at Point 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 Circle Diameter of Gear given Radius of Curvature at Point?

Pitch Circle Diameter of Gear given Radius of Curvature at Point 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 Circle Diameter of Gear given Radius of Curvature at Point, 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 3 other way(s) to calculate the same, which is/are as follows -

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

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