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Radius of Base Circle of Pinion Formula

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Radius of base circle of pinion is the radius of circle from which the involute portion of the tooth profile is generated. Check FAQs

r b = r \cdot \cos (Φ gear)

r_b - Radius of Base Circle of Pinion?r - Radius of Pitch Circle of Pinion?Φ_gear - Pressure Angle of Gear?

Radius of Base Circle of Pinion Example

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Here is how the Radius of Base Circle of Pinion equation looks like with Values.

Here is how the Radius of Base Circle of Pinion equation looks like with Units.

Here is how the Radius of Base Circle of Pinion equation looks like.

8.6501 = 10.2 \cdot \cos (32)

8.6501mm = 10.2mm \cdot \cos (32°)

8.6501 = 10.2 \cdot \cos (32)

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Radius of Base Circle of Pinion Solution

Follow our step by step solution on how to calculate Radius of Base Circle of Pinion?

FIRST Step Consider the formula

r b = r \cdot \cos (Φ gear)

Next Step Substitute values of Variables

∴

r b = 10.2mm \cdot \cos (32°)

Next Step Convert Units

∴

r b = 0.0102m \cdot \cos (0.5585rad)

Next Step Prepare to Evaluate

∴

r b = 0.0102 \cdot \cos (0.5585)

Next Step Evaluate

∴

r b = 0.00865009058079612m

Next Step Convert to Output's Unit

∴

r b = 8.65009058079612mm

LAST Step Rounding Answer

∴

r b = 8.6501mm

Radius of Base Circle of Pinion Formula Elements

Variables

Functions

Radius of Base Circle of Pinion

Radius of base circle of pinion is the radius of circle from which the involute portion of the tooth profile is generated.

Symbol: r_b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Base Circle of Pinion

Radius of Pitch Circle of Pinion

The Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Pitch Circle of Pinion

Pressure Angle of Gear

The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_gear

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Gear

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Toothed Gear Terminologies category

Go Torque Exerted on Gear Shaft

τ = P t \cdot \frac{d pitch circle}{2}

Go Work Output on Driven

w = R \cdot \cos (α 2 + Φ) \cdot π \cdot d 2 \cdot N 2

Go Work Output on Driver

w = R \cdot \cos (α 1 - Φ) \cdot π \cdot d 1 \cdot N 1

Go Addendum of Pinion

A p = \frac{Z p}{2} \cdot (\sqrt{1 + \frac{T}{Z p} \cdot (\frac{T}{Z p} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

How to Evaluate Radius of Base Circle of Pinion?

Radius of Base Circle of Pinion evaluator uses Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear) to evaluate the Radius of Base Circle of Pinion, Radius of Base Circle of Pinion formula is defined as the radius of the circle that forms the base of the toothed pinion gear, which is a critical parameter in designing and manufacturing gear systems, as it affects the gear's overall performance and efficiency. Radius of Base Circle of Pinion is denoted by r_b symbol.

How to evaluate Radius of Base Circle of Pinion using this online evaluator? To use this online evaluator for Radius of Base Circle of Pinion, enter Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_gear) and hit the calculate button.

FAQs on Radius of Base Circle of Pinion

What is the formula to find Radius of Base Circle of Pinion?

The formula of Radius of Base Circle of Pinion is expressed as Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear). Here is an example- 8650.091 = 0.0102*cos(0.55850536063808).

How to calculate Radius of Base Circle of Pinion?

With Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_gear) we can find Radius of Base Circle of Pinion using the formula - Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear). This formula also uses Cosine function(s).

Can the Radius of Base Circle of Pinion be negative?

No, the Radius of Base Circle of Pinion, measured in Length cannot be negative.

Which unit is used to measure Radius of Base Circle of Pinion?

Radius of Base Circle of Pinion is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Base Circle of Pinion can be measured.

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Radius of Base Circle of Pinion Formula

Radius of Base Circle of Pinion Example

Radius of Base Circle of Pinion Solution

Radius of Base Circle of Pinion Formula Elements

Other formulas in Toothed Gear Terminologies category

How to Evaluate Radius of Base Circle of Pinion?

FAQs on Radius of Base Circle of Pinion

Variable Name