Helix Angle of Helical Gear given Axial Pitch Calculator

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Design of Gears

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Design of Helical Gears

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Helix Geometry

Core Design Parameters

✖Pitch of Helical Gear is defined as the distance between two identical points on two adjacent gear teeth.ⓘ Pitch of Helical Gear [p]			+10% -10%
✖Axial Pitch of Helical Gear is defined as the axial advance of a helix or screw during one complete turn (360°) The lead for a screw thread is the axial travel for a single revolution.ⓘ Axial Pitch of Helical Gear [p_a]			+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 given Axial Pitch [ψ]

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Formula

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Helix Angle of Helical Gear given Axial Pitch

Formula

`"ψ" = atan("p"/"p"_{"a"})`

Example

`"25.59087°"=atan("10.68mm"/"22.3mm")`

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Helix Angle of Helical Gear given Axial Pitch Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear)
ψ = atan(p/p_a)
This formula uses 2 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

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.
Pitch of Helical Gear - (Measured in Meter) - Pitch of Helical Gear is defined as the distance between two identical points on two adjacent gear teeth.
Axial Pitch of Helical Gear - (Measured in Meter) - Axial Pitch of Helical Gear is defined as the axial advance of a helix or screw during one complete turn (360°) The lead for a screw thread is the axial travel for a single revolution.

STEP 1: Convert Input(s) to Base Unit

Pitch of Helical Gear: 10.68 Millimeter --> 0.01068 Meter (Check conversion here)
Axial Pitch of Helical Gear: 22.3 Millimeter --> 0.0223 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = atan(p/p_a) --> atan(0.01068/0.0223)

Evaluating ... ...

ψ = 0.446644906104212

STEP 3: Convert Result to Output's Unit

0.446644906104212 Radian -->25.5908680607931 Degree (Check conversion here)

FINAL ANSWER

25.5908680607931 ≈ 25.59087 Degree <-- Helix Angle 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

Helix Angle of Helical Gear given Axial Pitch Formula

Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear)
ψ = atan(p/p_a)

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 Helix Angle of Helical Gear given Axial Pitch?

Helix Angle of Helical Gear given Axial Pitch calculator uses Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given Axial Pitch formula is defined as the angle between the axis of the shaft and the center line of the tooth taken on the pitch plane. Helix Angle of Helical Gear is denoted by ψ symbol.

How to calculate Helix Angle of Helical Gear given Axial Pitch using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Axial Pitch, enter Pitch of Helical Gear (p) & Axial Pitch of Helical Gear (p_a) and hit the calculate button. Here is how the Helix Angle of Helical Gear given Axial Pitch calculation can be explained with given input values -> 1466.249 = atan(0.01068/0.0223).

FAQ

What is Helix Angle of Helical Gear given Axial Pitch?

Helix Angle of Helical Gear given Axial Pitch formula is defined as the angle between the axis of the shaft and the center line of the tooth taken on the pitch plane and is represented as ψ = atan(p/p_a) or Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear). Pitch of Helical Gear is defined as the distance between two identical points on two adjacent gear teeth & Axial Pitch of Helical Gear is defined as the axial advance of a helix or screw during one complete turn (360°) The lead for a screw thread is the axial travel for a single revolution.

How to calculate Helix Angle of Helical Gear given Axial Pitch?

Helix Angle of Helical Gear given Axial Pitch formula is defined as the angle between the axis of the shaft and the center line of the tooth taken on the pitch plane is calculated using Helix Angle of Helical Gear = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear). To calculate Helix Angle of Helical Gear given Axial Pitch, you need Pitch of Helical Gear (p) & Axial Pitch of Helical Gear (p_a). With our tool, you need to enter the respective value for Pitch of Helical Gear & Axial Pitch 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 Helix Angle of Helical Gear?

In this formula, Helix Angle of Helical Gear uses Pitch of Helical Gear & Axial Pitch of Helical Gear. We can use 9 other way(s) to calculate the same, which is/are as follows -

Helix Angle of Helical Gear = acos(Normal Circular Pitch of Helical Gear/Pitch of Helical Gear)
Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear)
Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear))
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 = 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 = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear)))
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))
Helix Angle of Helical Gear = acos((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3))
Helix Angle of Helical Gear = acos(Number of Teeth on Helical Gear/(Addendum Circle Diameter of Helical Gear/Normal Module of Helical Gear-2))

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