Helix Angle of Helical Gear given Normal Module 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

✖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 Transverse Module of Helical Gear is the module of the helical gear measured in the plane of rotation.ⓘ Transverse Module of Helical Gear [m]			+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 Normal Module [ψ]

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Formula

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Helix Angle of Helical Gear given Normal Module

Formula

`"ψ" = acos("m"_{"n"}/"m")`

Example

`"28.07249°"=acos("3mm"/"3.4mm")`

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Download Design of Helical Gears Formulas PDF

Helix Angle of Helical Gear given Normal Module Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear)
ψ = acos(m_n/m)
This formula uses 2 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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(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.
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.
Transverse Module of Helical Gear - (Measured in Meter) - The Transverse Module of Helical Gear is the module of the helical gear measured in the plane of rotation.

STEP 1: Convert Input(s) to Base Unit

Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)
Transverse Module of Helical Gear: 3.4 Millimeter --> 0.0034 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = acos(m_n/m) --> acos(0.003/0.0034)

Evaluating ... ...

ψ = 0.489957326253728

STEP 3: Convert Result to Output's Unit

0.489957326253728 Radian -->28.0724869358582 Degree (Check conversion here)

FINAL ANSWER

28.0724869358582 ≈ 28.07249 Degree <-- Helix Angle of Helical Gear

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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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 Normal Module Formula

Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear)
ψ = acos(m_n/m)

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 Normal Module?

Helix Angle of Helical Gear given Normal Module calculator uses Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given Normal Module formula is defined as the angle between the axis of the shaft and the centerline 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 Normal Module using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Normal Module, enter Normal Module of Helical Gear (m_n) & Transverse Module of Helical Gear (m) and hit the calculate button. Here is how the Helix Angle of Helical Gear given Normal Module calculation can be explained with given input values -> 1608.435 = acos(0.003/0.0034).

FAQ

What is Helix Angle of Helical Gear given Normal Module?

Helix Angle of Helical Gear given Normal Module formula is defined as the angle between the axis of the shaft and the centerline of the tooth taken on the pitch plane and is represented as ψ = acos(m_n/m) or Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear). The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear & The Transverse Module of Helical Gear is the module of the helical gear measured in the plane of rotation.

How to calculate Helix Angle of Helical Gear given Normal Module?

Helix Angle of Helical Gear given Normal Module formula is defined as the angle between the axis of the shaft and the centerline of the tooth taken on the pitch plane is calculated using Helix Angle of Helical Gear = acos(Normal Module of Helical Gear/Transverse Module of Helical Gear). To calculate Helix Angle of Helical Gear given Normal Module, you need Normal Module of Helical Gear (m_n) & Transverse Module of Helical Gear (m). With our tool, you need to enter the respective value for Normal Module of Helical Gear & Transverse 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 Helix Angle of Helical Gear?

In this formula, Helix Angle of Helical Gear uses Normal Module of Helical Gear & Transverse Module 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 = atan(Pitch of Helical Gear/Axial Pitch 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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