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Actual number of teeth on Bevel Gear Solution

STEP 0: Pre-Calculation Summary
Formula Used
number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle)
zg = (z')/cos(γ)
This formula uses 1 Functions, 2 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Virtual or formative number of teeth- Virtual or formative number of teeth is imagninary spur gear teeth which is considered in plane perpendicular to the tooth at large end. Where rb is pitch circle radius for it.
Pitch angle - Pitch angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear, is called the pitch angle. The pitch angle is also called centre angle. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Virtual or formative number of teeth: 24 --> No Conversion Required
Pitch angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
zg = (z')/cos(γ) --> (24)/cos(0.5235987755982)
Evaluating ... ...
zg = 27.712812921102
STEP 3: Convert Result to Output's Unit
27.712812921102 --> No Conversion Required
FINAL ANSWER
27.712812921102 <-- Number of teeth on gear
(Calculation completed in 00.000 seconds)

10+ Design of Bevel Gear Calculators

Wear strength of the Bevel Gear
Wear_Strength = (0.75*Face width*Ratio factor*Pitch circle diameter of pinion*Material Constant)/cos(Pitch angle) Go
Beam Strength of tooth of Bevel Gear
beam_strength = ((Module*Face width*Bending Stress*Lewis Form Factor)*(1-(Face width/Cone distance))) Go
Ratio factor for Bevel gear
Ratio_factor_ = (2*Number of teeth on gear)/(Number of teeth on gear+(Number of teeth of the pinion*tan(Pitch angle))) Go
Radial force component acting on Bevel Gear
radial_force = (Tangential force*tan(Pressure angle)*cos(Pitch angle)) Go
Radius of pinion at midpoint along face width
Radius_at_midpoint = ((Pitch circle diameter of pinion/2)-(Face width*sin(Pitch angle))/2) Go
Cone Distance
Cone_Distance = sqrt(((Pitch circle diameter of pinion/2)^2)+((Pitch circle diameter of gear/2)^2)) Go
Actual number of teeth on Bevel Gear
number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle) Go
Tangential force component
Tangential_force_due_to_rated_torque = (Torque Transmitted/Radius at midpoint) Go
Virtual or formative number of teeth of Bevel Gear
Virtual_or_formative_number_of_teeth = (2*Back cone radius)/Module Go
Bevel Factor
Bevel_Factor = (1-(Face width/Cone distance)) Go

Actual number of teeth on Bevel Gear Formula

number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle)
zg = (z')/cos(γ)

Why we use virtual number of teeth ?

The actual reason is for the ease of calculation and analysis of various parameters we use Spur Gear profile as a reference.

How to Calculate Actual number of teeth on Bevel Gear?

Actual number of teeth on Bevel Gear calculator uses number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle) to calculate the Number of teeth on gear, The actual number of teeth on Bevel Gear is calculated with reference to the Spur Gear profile. Number of teeth on gear is denoted by zg symbol.

How to calculate Actual number of teeth on Bevel Gear using this online calculator? To use this online calculator for Actual number of teeth on Bevel Gear, enter Virtual or formative number of teeth (z') & Pitch angle (γ) and hit the calculate button. Here is how the Actual number of teeth on Bevel Gear calculation can be explained with given input values -> 27.71281 = (24)/cos(0.5235987755982).

FAQ

What is Actual number of teeth on Bevel Gear?
The actual number of teeth on Bevel Gear is calculated with reference to the Spur Gear profile and is represented as zg = (z')/cos(γ) or number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle). Virtual or formative number of teeth is imagninary spur gear teeth which is considered in plane perpendicular to the tooth at large end. Where rb is pitch circle radius for it & Pitch angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear, is called the pitch angle. The pitch angle is also called centre angle.
How to calculate Actual number of teeth on Bevel Gear?
The actual number of teeth on Bevel Gear is calculated with reference to the Spur Gear profile is calculated using number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle). To calculate Actual number of teeth on Bevel Gear, you need Virtual or formative number of teeth (z') & Pitch angle (γ). With our tool, you need to enter the respective value for Virtual or formative number of teeth & Pitch angle 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 on gear?
In this formula, Number of teeth on gear uses Virtual or formative number of teeth & Pitch angle. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Virtual_or_formative_number_of_teeth = (2*Back cone radius)/Module
  • number_of_teeth_on_gear = (Virtual or formative number of teeth)/cos(Pitch angle)
  • Cone_Distance = sqrt(((Pitch circle diameter of pinion/2)^2)+((Pitch circle diameter of gear/2)^2))
  • Radius_at_midpoint = ((Pitch circle diameter of pinion/2)-(Face width*sin(Pitch angle))/2)
  • Tangential_force_due_to_rated_torque = (Torque Transmitted/Radius at midpoint)
  • radial_force = (Tangential force*tan(Pressure angle)*cos(Pitch angle))
  • Bevel_Factor = (1-(Face width/Cone distance))
  • beam_strength = ((Module*Face width*Bending Stress*Lewis Form Factor)*(1-(Face width/Cone distance)))
  • Wear_Strength = (0.75*Face width*Ratio factor*Pitch circle diameter of pinion*Material Constant)/cos(Pitch angle)
  • Ratio_factor_ = (2*Number of teeth on gear)/(Number of teeth on gear+(Number of teeth of the pinion*tan(Pitch angle)))
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