Radius of Pinion at Midpoint along Face Width for Bevel Gear Calculator

✖Pitch circle diameter of bevel pinion is twice the distance from the center of the gear to the pitch point. This is where the gear's speed is measured.ⓘ Pitch Circle Diameter of Bevel Pinion [D_p]			+10% -10%
✖Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis.ⓘ Face Width of Bevel Gear Tooth [b]			+10% -10%
✖Pitch Angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear. The pitch angle is also known as center angle.ⓘ Pitch Angle for Bevel Gear [γ]			+10% -10%

✖The Radius of Pinion at Midpoint is the radius of the pinion at the midpoint along the face width.ⓘ Radius of Pinion at Midpoint along Face Width for Bevel Gear [r_m]

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Formula

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Radius of Pinion at Midpoint along Face Width for Bevel Gear

Formula

r m = \frac{D p - (b \cdot \sin (γ))}{2}

Example

23.09456 mm = \frac{76.5 mm - (35 mm \cdot \sin (60 °))}{2}

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Radius of Pinion at Midpoint along Face Width for Bevel Gear Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2
r_m = (D_p-(b*sin(γ)))/2
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Radius of Pinion at Midpoint - (Measured in Meter) - The Radius of Pinion at Midpoint is the radius of the pinion at the midpoint along the face width.
Pitch Circle Diameter of Bevel Pinion - (Measured in Meter) - Pitch circle diameter of bevel pinion is twice the distance from the center of the gear to the pitch point. This is where the gear's speed is measured.
Face Width of Bevel Gear Tooth - (Measured in Meter) - Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis.
Pitch Angle for Bevel Gear - (Measured in Radian) - Pitch Angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear. The pitch angle is also known as center angle.

STEP 1: Convert Input(s) to Base Unit

Pitch Circle Diameter of Bevel Pinion: 76.5 Millimeter --> 0.0765 Meter (Check conversion here)
Face Width of Bevel Gear Tooth: 35 Millimeter --> 0.035 Meter (Check conversion here)
Pitch Angle for Bevel Gear: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (D_p-(b*sin(γ)))/2 --> (0.0765-(0.035*sin(1.0471975511964)))/2

Evaluating ... ...

r_m = 0.0230945554337741

STEP 3: Convert Result to Output's Unit

0.0230945554337741 Meter -->23.0945554337741 Millimeter (Check conversion here)

FINAL ANSWER

23.0945554337741 ≈ 23.09456 Millimeter <-- Radius of Pinion at Midpoint

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Gears » Design of Bevel Gears » Mechanical » Geometric Properties » Radius of Pinion at Midpoint along Face Width for Bevel Gear

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Created by Akshay Talbar

Vishwakarma University (VU), Pune

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< Geometric Properties Calculators

Radius of Pinion at Midpoint along Face Width for Bevel Gear

Go Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2

Actual Number of Teeth on Bevel Gear

Go Number of Teeth on Bevel Gear = Virtual Number of Teeth for Bevel Gear*cos(Pitch Angle for Bevel Gear)

Cone Distance of Bevel Gear

Go Cone Distance = sqrt((Pitch Circle Diameter of Bevel Pinion/2)^2+(Pitch Circle Diameter of Gear/2)^2)

Virtual or Formative Number of Teeth of Bevel Gear

Go Virtual Number of Teeth for Bevel Gear = (2*Back Cone Radius)/Module of Bevel Gear

Radius of Pinion at Midpoint along Face Width for Bevel Gear Formula

Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2
r_m = (D_p-(b*sin(γ)))/2

Why midpoint radius is required ?

Midpoint radius is required to calculate parameters like pitch circle diameter of pinion and pitch angle or vice versa. to calculate tangential force also.

How to Calculate Radius of Pinion at Midpoint along Face Width for Bevel Gear?

Radius of Pinion at Midpoint along Face Width for Bevel Gear calculator uses Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2 to calculate the Radius of Pinion at Midpoint, Radius of Pinion at Midpoint along face width for Bevel Gear is used to calculate the parameters like tangential force. it is the radius of the smaller of the pair of bevel gears. Radius of Pinion at Midpoint is denoted by r_m symbol.

How to calculate Radius of Pinion at Midpoint along Face Width for Bevel Gear using this online calculator? To use this online calculator for Radius of Pinion at Midpoint along Face Width for Bevel Gear, enter Pitch Circle Diameter of Bevel Pinion (D_p), Face Width of Bevel Gear Tooth (b) & Pitch Angle for Bevel Gear (γ) and hit the calculate button. Here is how the Radius of Pinion at Midpoint along Face Width for Bevel Gear calculation can be explained with given input values -> 23094.56 = (0.0765-(0.035*sin(1.0471975511964)))/2.

FAQ

What is Radius of Pinion at Midpoint along Face Width for Bevel Gear?

Radius of Pinion at Midpoint along face width for Bevel Gear is used to calculate the parameters like tangential force. it is the radius of the smaller of the pair of bevel gears and is represented as r_m = (D_p-(b*sin(γ)))/2 or Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2. Pitch circle diameter of bevel pinion is twice the distance from the center of the gear to the pitch point. This is where the gear's speed is measured, Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis & Pitch Angle for Bevel Gear is the angle that the pitch line makes with the axis of the gear. The pitch angle is also known as center angle.

How to calculate Radius of Pinion at Midpoint along Face Width for Bevel Gear?

Radius of Pinion at Midpoint along face width for Bevel Gear is used to calculate the parameters like tangential force. it is the radius of the smaller of the pair of bevel gears is calculated using Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2. To calculate Radius of Pinion at Midpoint along Face Width for Bevel Gear, you need Pitch Circle Diameter of Bevel Pinion (D_p), Face Width of Bevel Gear Tooth (b) & Pitch Angle for Bevel Gear (γ). With our tool, you need to enter the respective value for Pitch Circle Diameter of Bevel Pinion, Face Width of Bevel Gear Tooth & Pitch Angle for Bevel 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 Radius of Pinion at Midpoint?

In this formula, Radius of Pinion at Midpoint uses Pitch Circle Diameter of Bevel Pinion, Face Width of Bevel Gear Tooth & Pitch Angle for Bevel Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radius of Pinion at Midpoint = Torque Transmitted by Bevel Pinion/Tangential Force Transmitted by Bevel Gear

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