Helix Angle of Helical Gear given Center to Center Distance between Two Gears Calculator

✖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 Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1.ⓘ Number of Teeth on 1st Helical Gear [z₁]			+10% -10%
✖The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2.ⓘ Number of Teeth on 2nd Helical Gear [z₂]			+10% -10%
✖Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration.ⓘ Center to Center Distance of Helical Gears [a_c]			+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 Center to Center Distance between Two Gears [ψ]

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Helix Angle of Helical Gear given Center to Center Distance between Two Gears Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ψ = acos(m_n*(z₁+z₂)/(2*a_c))
This formula uses 2 Functions, 5 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.
Number of Teeth on 1st Helical Gear - The Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1.
Number of Teeth on 2nd Helical Gear - The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2.
Center to Center Distance of Helical Gears - (Measured in Meter) - Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration.

STEP 1: Convert Input(s) to Base Unit

Normal Module of Helical Gear: 3 Millimeter --> 0.003 Meter (Check conversion here)
Number of Teeth on 1st Helical Gear: 18 --> No Conversion Required
Number of Teeth on 2nd Helical Gear: 42 --> No Conversion Required
Center to Center Distance of Helical Gears: 99.3 Millimeter --> 0.0993 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = acos(m_n*(z₁+z₂)/(2*a_c)) --> acos(0.003*(18+42)/(2*0.0993))

Evaluating ... ...

ψ = 0.436245645557549

STEP 3: Convert Result to Output's Unit

0.436245645557549 Radian -->24.9950343214123 Degree (Check conversion here)

FINAL ANSWER

24.9950343214123 ≈ 24.99503 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 Center to Center Distance between Two Gears

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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 Center to Center Distance between Two Gears Formula

LaTeX Go

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 Center to Center Distance between Two Gears?

Helix Angle of Helical Gear given Center to Center Distance between Two Gears calculator uses 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)) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given center to center distance between two Gears 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 Center to Center Distance between Two Gears using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Center to Center Distance between Two Gears, enter Normal Module of Helical Gear (m_n), Number of Teeth on 1st Helical Gear (z₁), Number of Teeth on 2nd Helical Gear (z₂) & Center to Center Distance of Helical Gears (a_c) and hit the calculate button. Here is how the Helix Angle of Helical Gear given Center to Center Distance between Two Gears calculation can be explained with given input values -> 1432.11 = acos(0.003*(18+42)/(2*0.0993)).

FAQ

What is Helix Angle of Helical Gear given Center to Center Distance between Two Gears?

Helix Angle of Helical Gear given center to center distance between two Gears 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*(z₁+z₂)/(2*a_c)) or 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)). The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear, The Number of Teeth on 1st Helical Gear is defined as the number of teeth that are present on gear 1, The Number of Teeth on 2nd Helical Gear is defined as the number of teeth that are present on gear 2 & Center to Center Distance of Helical Gears is defined as the distance in between the centers of the two helical gears that are taken in consideration.

How to calculate Helix Angle of Helical Gear given Center to Center Distance between Two Gears?

Helix Angle of Helical Gear given center to center distance between two Gears 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*(Number of Teeth on 1st Helical Gear+Number of Teeth on 2nd Helical Gear)/(2*Center to Center Distance of Helical Gears)). To calculate Helix Angle of Helical Gear given Center to Center Distance between Two Gears, you need Normal Module of Helical Gear (m_n), Number of Teeth on 1st Helical Gear (z₁), Number of Teeth on 2nd Helical Gear (z₂) & Center to Center Distance of Helical Gears (a_c). With our tool, you need to enter the respective value for Normal Module of Helical Gear, Number of Teeth on 1st Helical Gear, Number of Teeth on 2nd Helical Gear & Center to Center Distance of Helical Gears 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, Number of Teeth on 1st Helical Gear, Number of Teeth on 2nd Helical Gear & Center to Center Distance of Helical Gears. 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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