Helix Angle of Helical Gear given Radius of Curvature at Point Calculator

✖Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.ⓘ Diameter of Pitch Circle of Helical Gear [d]			+10% -10%
✖Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.ⓘ Radius of Curvature of Helical Gear [r']			+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 Radius of Curvature at Point [ψ]

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Helix Angle of Helical Gear given Radius of Curvature at Point Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear)))
ψ = sqrt(acos(d/(2*r')))
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)
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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(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.
Diameter of Pitch Circle of Helical Gear - (Measured in Meter) - Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.
Radius of Curvature of Helical Gear - (Measured in Meter) - Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.

STEP 1: Convert Input(s) to Base Unit

Diameter of Pitch Circle of Helical Gear: 118 Millimeter --> 0.118 Meter (Check conversion here)
Radius of Curvature of Helical Gear: 72 Millimeter --> 0.072 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = sqrt(acos(d/(2*r'))) --> sqrt(acos(0.118/(2*0.072)))

Evaluating ... ...

ψ = 0.781252371742426

STEP 3: Convert Result to Output's Unit

0.781252371742426 Radian -->44.7624636354351 Degree (Check conversion here)

FINAL ANSWER

44.7624636354351 ≈ 44.76246 Degree <-- Helix Angle of Helical Gear

(Calculation completed in 00.010 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 Radius of Curvature at Point

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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

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 Radius of Curvature at Point Formula

LaTeX Go

Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear)))
ψ = sqrt(acos(d/(2*r')))

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 Radius of Curvature at Point?

Helix Angle of Helical Gear given Radius of Curvature at Point calculator uses Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear))) to calculate the Helix Angle of Helical Gear, Helix Angle of Helical Gear given Radius of Curvature at Point 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 Radius of Curvature at Point using this online calculator? To use this online calculator for Helix Angle of Helical Gear given Radius of Curvature at Point, enter Diameter of Pitch Circle of Helical Gear (d) & Radius of Curvature of Helical Gear (r') and hit the calculate button. Here is how the Helix Angle of Helical Gear given Radius of Curvature at Point calculation can be explained with given input values -> 2564.7 = sqrt(acos(0.118/(2*0.072))).

FAQ

What is Helix Angle of Helical Gear given Radius of Curvature at Point?

Helix Angle of Helical Gear given Radius of Curvature at Point 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 = sqrt(acos(d/(2*r'))) or Helix Angle of Helical Gear = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear))). Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle & Radius of Curvature of Helical Gear is the radius of a circle that touches a curve at a given point and has the same tangent and curvature at that point.

How to calculate Helix Angle of Helical Gear given Radius of Curvature at Point?

Helix Angle of Helical Gear given Radius of Curvature at Point 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 = sqrt(acos(Diameter of Pitch Circle of Helical Gear/(2*Radius of Curvature of Helical Gear))). To calculate Helix Angle of Helical Gear given Radius of Curvature at Point, you need Diameter of Pitch Circle of Helical Gear (d) & Radius of Curvature of Helical Gear (r'). With our tool, you need to enter the respective value for Diameter of Pitch Circle of Helical Gear & Radius of Curvature 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 Diameter of Pitch Circle of Helical Gear & Radius of Curvature 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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