Helix Angle of Helical Gear given Actual and Virtual Number of Teeth Calculator

✖Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.ⓘ Number of Teeth on Helical Gear [z]			+10% -10%
✖The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.ⓘ Virtual Number of Teeth on Helical Gear [z']			+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 Actual and Virtual Number of Teeth [ψ]

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Helix Angle of Helical Gear given Actual and Virtual Number of Teeth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helix Angle of Helical Gear = acos((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3))
ψ = acos((z/z')^(1/3))
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.
Number of Teeth on Helical Gear - Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.
Virtual Number of Teeth on Helical Gear - The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.

STEP 1: Convert Input(s) to Base Unit

Number of Teeth on Helical Gear: 37 --> No Conversion Required
Virtual Number of Teeth on Helical Gear: 54 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = acos((z/z')^(1/3)) --> acos((37/54)^(1/3))

Evaluating ... ...

ψ = 0.491564654166394

STEP 3: Convert Result to Output's Unit

0.491564654166394 Radian -->28.1645800415475 Degree (Check conversion here)

FINAL ANSWER

28.1645800415475 ≈ 28.16458 Degree <-- Helix Angle 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 » Helix Geometry » Helix Angle of Helical Gear given Actual and Virtual Number of Teeth

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Helix Geometry Calculators

Helix Angle of Helical Gear given Normal Circular Pitch

LaTeX 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

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

Normal Circular Pitch of Helical Gear

LaTeX 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

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

Helix Angle of Helical Gear given Actual and Virtual Number of Teeth Formula

LaTeX Go

Helix Angle of Helical Gear = acos((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3))
ψ = acos((z/z')^(1/3))

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 Actual and Virtual Number of Teeth?

Helix Angle of Helical Gear given Actual and Virtual Number of Teeth calculator uses Helix Angle of Helical Gear = acos((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3)) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given Actual and Virtual Number of Teeth 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 Actual and Virtual Number of Teeth using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Actual and Virtual Number of Teeth, enter Number of Teeth on Helical Gear (z) & Virtual Number of Teeth on Helical Gear (z') and hit the calculate button. Here is how the Helix Angle of Helical Gear given Actual and Virtual Number of Teeth calculation can be explained with given input values -> 1613.712 = acos((37/54)^(1/3)).

FAQ

What is Helix Angle of Helical Gear given Actual and Virtual Number of Teeth?

Helix Angle of Helical Gear given Actual and Virtual Number of Teeth 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((z/z')^(1/3)) or Helix Angle of Helical Gear = acos((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3)). Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration & The Virtual Number of Teeth on Helical Gear is defined as the number of teeth that are present on the virtual helical gear.

How to calculate Helix Angle of Helical Gear given Actual and Virtual Number of Teeth?

Helix Angle of Helical Gear given Actual and Virtual Number of Teeth 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((Number of Teeth on Helical Gear/Virtual Number of Teeth on Helical Gear)^(1/3)). To calculate Helix Angle of Helical Gear given Actual and Virtual Number of Teeth, you need Number of Teeth on Helical Gear (z) & Virtual Number of Teeth on Helical Gear (z'). With our tool, you need to enter the respective value for Number of Teeth on Helical Gear & Virtual Number of Teeth on 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 Number of Teeth on Helical Gear & Virtual Number of Teeth on 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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