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Number of Teeth on Gear When Pitch Circle Diameter is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
number_of_teeth = Pitch Circle Diameter*cos(Helix Angle)/Normal Module
z = D*cos(α)/mn
This formula uses 1 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Pitch Circle Diameter - Pitch Circle Diameter is the diameter of the pitch circle. (Measured in Millimeter)
Helix Angle - Helix Angle denotes the standard pitch circle unless otherwise specified. Application of the helix angle typically employs a magnitude ranging from 15° to 30° for helical gears, with 45° capping the safe operation limit. (Measured in Degree)
Normal Module - Normal Module is deifined as the unit of size that indicates how big or small a gear is. It is the ratio of the reference diameter of the gear divided by the number of teeth. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Pitch Circle Diameter: 0.001 Millimeter --> 1E-06 Meter (Check conversion here)
Helix Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Normal Module: 0.001 Millimeter --> 1E-06 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
z = D*cos(α)/mn --> 1E-06*cos(0.5235987755982)/1E-06
Evaluating ... ...
z = 0.866025403784439
STEP 3: Convert Result to Output's Unit
0.866025403784439 --> No Conversion Required
FINAL ANSWER
0.866025403784439 <-- Number of teeth
(Calculation completed in 00.015 seconds)

10+ Design of Helical Gears Calculators

Helix Angle When Normal Circular pitch is Given
helix_angle = acos(Transverse Diametrical Pitch/Circular pitch) Go
Transverse Diametrical Pitch When Normal Circular Pitch is Given
transverse_diametrical_pitch = Circular pitch*cos(Helix Angle) Go
Normal Circular Pitch of Helical Gear
circular_pitch = Transverse Diametrical Pitch/cos(Helix Angle) Go
Transverse Diametrical Pitch When Axial Pitch is Given
transverse_diametrical_pitch = Axial Pitch*tan(Helix Angle) Go
Axial Pitch in terms of helix angle
axial_pitch = Transverse Diametrical Pitch/tan(Helix Angle) Go
Helix Angle When Normal Module is Given
helix_angle = acos(Normal Module/Transverse Module) Go
Transverse Module When Normal Module is Given
transverse_module = Normal Module/cos(Helix Angle) Go
Normal Module
normal_module = Transverse Module*cos(Helix Angle) Go
Transverse Module When Transverse Diametrical Pitch is Given
transverse_module = 1/Transverse Diametrical Pitch Go
Transverse Diametrical Pitch in Terms of Transverse Module
transverse_diametrical_pitch = 1/Transverse Module Go

Number of Teeth on Gear When Pitch Circle Diameter is Given Formula

number_of_teeth = Pitch Circle Diameter*cos(Helix Angle)/Normal Module
z = D*cos(α)/mn

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 Number of Teeth on Gear When Pitch Circle Diameter is Given?

Number of Teeth on Gear When Pitch Circle Diameter is Given calculator uses number_of_teeth = Pitch Circle Diameter*cos(Helix Angle)/Normal Module to calculate the Number of teeth, The Number of Teeth on Gear When Pitch Circle Diameter is Given formula is defined as the number of indentations that are present on the gears to transmit the torque. Number of teeth and is denoted by z symbol.

How to calculate Number of Teeth on Gear When Pitch Circle Diameter is Given using this online calculator? To use this online calculator for Number of Teeth on Gear When Pitch Circle Diameter is Given, enter Pitch Circle Diameter (D), Helix Angle (α) and Normal Module (mn) and hit the calculate button. Here is how the Number of Teeth on Gear When Pitch Circle Diameter is Given calculation can be explained with given input values -> 0.866025 = 1E-06*cos(0.5235987755982)/1E-06.

FAQ

What is Number of Teeth on Gear When Pitch Circle Diameter is Given?
The Number of Teeth on Gear When Pitch Circle Diameter is Given formula is defined as the number of indentations that are present on the gears to transmit the torque and is represented as z = D*cos(α)/mn or number_of_teeth = Pitch Circle Diameter*cos(Helix Angle)/Normal Module. Pitch Circle Diameter is the diameter of the pitch circle, Helix Angle denotes the standard pitch circle unless otherwise specified. Application of the helix angle typically employs a magnitude ranging from 15° to 30° for helical gears, with 45° capping the safe operation limit and Normal Module is deifined as the unit of size that indicates how big or small a gear is. It is the ratio of the reference diameter of the gear divided by the number of teeth.
How to calculate Number of Teeth on Gear When Pitch Circle Diameter is Given?
The Number of Teeth on Gear When Pitch Circle Diameter is Given formula is defined as the number of indentations that are present on the gears to transmit the torque is calculated using number_of_teeth = Pitch Circle Diameter*cos(Helix Angle)/Normal Module. To calculate Number of Teeth on Gear When Pitch Circle Diameter is Given, you need Pitch Circle Diameter (D), Helix Angle (α) and Normal Module (mn). With our tool, you need to enter the respective value for Pitch Circle Diameter, Helix Angle and Normal Module 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 Number of teeth?
In this formula, Number of teeth uses Pitch Circle Diameter, Helix Angle and Normal Module. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • circular_pitch = Transverse Diametrical Pitch/cos(Helix Angle)
  • transverse_diametrical_pitch = Circular pitch*cos(Helix Angle)
  • helix_angle = acos(Transverse Diametrical Pitch/Circular pitch)
  • transverse_diametrical_pitch = 1/Transverse Module
  • transverse_module = 1/Transverse Diametrical Pitch
  • normal_module = Transverse Module*cos(Helix Angle)
  • transverse_module = Normal Module/cos(Helix Angle)
  • helix_angle = acos(Normal Module/Transverse Module)
  • axial_pitch = Transverse Diametrical Pitch/tan(Helix Angle)
  • transverse_diametrical_pitch = Axial Pitch*tan(Helix Angle)
Where is the Number of Teeth on Gear When Pitch Circle Diameter is Given calculator used?
Among many, Number of Teeth on Gear When Pitch Circle Diameter is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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