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 00.004 seconds)

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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 Radius of Curvature at Point Formula

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 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 = 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)
  • 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 = 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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