Helix Angle of Helical Gear given Pressure Angle Calculator

✖The Normal Pressure Angle of Helical Gear is defined as the angle between the tooth face and the gear wheel tangent.ⓘ Normal Pressure Angle of Helical Gear [α_n]			+10% -10%
✖The Transverse Pressure Angle of Helical Gear is defined as the pressure angle for the gear measured in the plane of rotation.ⓘ Transverse Pressure Angle of Helical Gear [α]			+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 Pressure Angle [ψ]

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Formula

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Helix Angle of Helical Gear given Pressure Angle

Formula

ψ = a \cos (\frac{\tan (α n)}{\tan (α)})

Example

25.07509 ° = a \cos (\frac{\tan (20.1 °)}{\tan (22 °)})

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Helix Angle of Helical Gear given Pressure Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear))
ψ = acos(tan(α_n)/tan(α))
This formula uses 3 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)
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)
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 Pressure Angle of Helical Gear - (Measured in Radian) - The Normal Pressure Angle of Helical Gear is defined as the angle between the tooth face and the gear wheel tangent.
Transverse Pressure Angle of Helical Gear - (Measured in Radian) - The Transverse Pressure Angle of Helical Gear is defined as the pressure angle for the gear measured in the plane of rotation.

STEP 1: Convert Input(s) to Base Unit

Normal Pressure Angle of Helical Gear: 20.1 Degree --> 0.350811179650794 Radian (Check conversion here)
Transverse Pressure Angle of Helical Gear: 22 Degree --> 0.38397243543868 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = acos(tan(α_n)/tan(α)) --> acos(tan(0.350811179650794)/tan(0.38397243543868))

Evaluating ... ...

ψ = 0.437642816760259

STEP 3: Convert Result to Output's Unit

0.437642816760259 Radian -->25.0750863345848 Degree (Check conversion here)

FINAL ANSWER

25.0750863345848 ≈ 25.07509 Degree <-- Helix Angle of Helical Gear

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Helical Gears » Mechanical » Helix Geometry » Helix Angle of Helical Gear given Pressure Angle

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Helix Geometry Calculators

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)

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 Pressure Angle Formula

Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear))
ψ = acos(tan(α_n)/tan(α))

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 Pressure Angle?

Helix Angle of Helical Gear given Pressure Angle calculator uses Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear)) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given Pressure Angle 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 Pressure Angle using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Pressure Angle, enter Normal Pressure Angle of Helical Gear (α_n) & Transverse Pressure Angle of Helical Gear (α) and hit the calculate button. Here is how the Helix Angle of Helical Gear given Pressure Angle calculation can be explained with given input values -> 1436.697 = acos(tan(0.350811179650794)/tan(0.38397243543868)).

FAQ

What is Helix Angle of Helical Gear given Pressure Angle?

Helix Angle of Helical Gear given Pressure Angle 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 = acos(tan(α_n)/tan(α)) or Helix Angle of Helical Gear = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear)). The Normal Pressure Angle of Helical Gear is defined as the angle between the tooth face and the gear wheel tangent & The Transverse Pressure Angle of Helical Gear is defined as the pressure angle for the gear measured in the plane of rotation.

How to calculate Helix Angle of Helical Gear given Pressure Angle?

Helix Angle of Helical Gear given Pressure Angle 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 = acos(tan(Normal Pressure Angle of Helical Gear)/tan(Transverse Pressure Angle of Helical Gear)). To calculate Helix Angle of Helical Gear given Pressure Angle, you need Normal Pressure Angle of Helical Gear (α_n) & Transverse Pressure Angle of Helical Gear (α). With our tool, you need to enter the respective value for Normal Pressure Angle of Helical Gear & Transverse Pressure 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 Helix Angle of Helical Gear?

In this formula, Helix Angle of Helical Gear uses Normal Pressure Angle of Helical Gear & Transverse Pressure Angle of Helical Gear. We can use 3 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 = atan(Pitch of Helical Gear/Axial Pitch of Helical Gear)

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