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

GoRadius of Pinion at Midpoint given Torque and Tangential Force for Bevel Gear Formula

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The Radius of Pinion at Midpoint is the radius of the pinion at the midpoint along the face width. Check FAQs

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

r_m - Radius of Pinion at Midpoint?D_p - Pitch Circle Diameter of Bevel Pinion?b - Face Width of Bevel Gear Tooth?γ - Pitch Angle for Bevel Gear?

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

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Here is how the Radius of Pinion at Midpoint along Face Width for Bevel Gear equation looks like with Values.

Here is how the Radius of Pinion at Midpoint along Face Width for Bevel Gear equation looks like with Units.

Here is how the Radius of Pinion at Midpoint along Face Width for Bevel Gear equation looks like.

23.0946 = \frac{76.5 - (35 \cdot \sin (60))}{2}

23.0946mm = \frac{76.5mm - (35mm \cdot \sin (60°))}{2}

23.0946 = \frac{76.5 - (35 \cdot \sin (60))}{2}

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

Follow our step by step solution on how to calculate Radius of Pinion at Midpoint along Face Width for Bevel Gear?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

r m = \frac{0.0765m - (0.035m \cdot \sin (1.0472rad))}{2}

Next Step Prepare to Evaluate

∴

r m = \frac{0.0765 - (0.035 \cdot \sin (1.0472))}{2}

Next Step Evaluate

∴

r m = 0.0230945554337741m

Next Step Convert to Output's Unit

∴

r m = 23.0945554337741mm

LAST Step Rounding Answer

∴

r m = 23.0946mm

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

Variables

Functions

Radius of Pinion at Midpoint

The Radius of Pinion at Midpoint is the radius of the pinion at the midpoint along the face width.

Symbol: r_m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pinion at Midpoint

Pitch Circle Diameter of Bevel Pinion

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.

Symbol: D_p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Pitch Circle Diameter of Bevel Pinion

Face Width of Bevel Gear Tooth

Face Width of Bevel Gear Tooth is the length of the tooth parallel to the bevel gear axis.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Face Width of Bevel Gear Tooth

Pitch Angle for Bevel Gear

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.

Symbol: γ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pitch Angle for Bevel Gear

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.

Syntax: sin(Angle)

Other Formulas to find Radius of Pinion at Midpoint

Go Radius of Pinion at Midpoint given Torque and Tangential Force for Bevel Gear

r m = \frac{M t}{P t}

Other formulas in Geometric Properties category

Go Virtual or Formative Number of Teeth of Bevel Gear

z' = \frac{2 \cdot r b}{m}

Go Actual Number of Teeth on Bevel Gear

z g = z' \cdot \cos (γ)

Go Cone Distance of Bevel Gear

A 0 = \sqrt{{(\frac{D p}{2})}^{2} + {(\frac{D g}{2})}^{2}}

Go Back Cone Radius of Bevel Gear

r b = \frac{m \cdot z'}{2}

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

Radius of Pinion at Midpoint along Face Width for Bevel Gear evaluator 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 evaluate 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 evaluate Radius of Pinion at Midpoint along Face Width for Bevel Gear using this online evaluator? To use this online evaluator 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.

FAQs on Radius of Pinion at Midpoint along Face Width for Bevel Gear

What is the formula to find Radius of Pinion at Midpoint along Face Width for Bevel Gear?

The formula of Radius of Pinion at Midpoint along Face Width for Bevel Gear is expressed as Radius of Pinion at Midpoint = (Pitch Circle Diameter of Bevel Pinion-(Face Width of Bevel Gear Tooth*sin(Pitch Angle for Bevel Gear)))/2. Here is an example- 23094.56 = (0.0765-(0.035*sin(1.0471975511964)))/2.

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

With Pitch Circle Diameter of Bevel Pinion (D_p), Face Width of Bevel Gear Tooth (b) & Pitch Angle for Bevel Gear (γ) we can find Radius of Pinion at Midpoint along Face Width for Bevel Gear using the 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. This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Radius of Pinion at Midpoint?

Here are the different ways to Calculate Radius of Pinion at Midpoint-

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

Can the Radius of Pinion at Midpoint along Face Width for Bevel Gear be negative?

No, the Radius of Pinion at Midpoint along Face Width for Bevel Gear, measured in Length cannot be negative.

Which unit is used to measure Radius of Pinion at Midpoint along Face Width for Bevel Gear?

Radius of Pinion at Midpoint along Face Width for Bevel Gear is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Pinion at Midpoint along Face Width for Bevel Gear can be measured.

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

​GoRadius of Pinion at Midpoint given Torque and Tangential Force for Bevel Gear Formula

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

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

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

Other Formulas to find Radius of Pinion at Midpoint

Other formulas in Geometric Properties category

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

FAQs on Radius of Pinion at Midpoint along Face Width for Bevel Gear

Variable Name

GoRadius of Pinion at Midpoint given Torque and Tangential Force for Bevel Gear Formula