Radius of Base Circle of Pinion Calculator

✖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.ⓘ Radius of Pitch Circle of Pinion [r]			+10% -10%
✖The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle of Gear [Φ_gear]			+10% -10%

✖Radius of base circle of pinion is the radius of circle from which the involute portion of the tooth profile is generated.ⓘ Radius of Base Circle of Pinion [r_b]

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Formula

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Radius of Base Circle of Pinion

Formula

`"r"_{"b"} = "r"*cos("Φ"_{"gear"})`

Example

`"8.650091mm"="10.2mm"*cos("32°")`

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Radius of Base Circle of Pinion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)
r_b = r*cos(Φ_gear)
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Radius of Base Circle of Pinion - (Measured in Meter) - Radius of base circle of pinion is the radius of circle from which the involute portion of the tooth profile is generated.
Radius of Pitch Circle of Pinion - (Measured in Meter) - 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.
Pressure Angle of Gear - (Measured in Radian) - The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

STEP 1: Convert Input(s) to Base Unit

Radius of Pitch Circle of Pinion: 10.2 Millimeter --> 0.0102 Meter (Check conversion here)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_b = r*cos(Φ_gear) --> 0.0102*cos(0.55850536063808)

Evaluating ... ...

r_b = 0.00865009058079612

STEP 3: Convert Result to Output's Unit

0.00865009058079612 Meter -->8.65009058079612 Millimeter (Check conversion here)

FINAL ANSWER

8.65009058079612 ≈ 8.650091 Millimeter <-- Radius of Base Circle of Pinion

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 22 Toothed Gear Terminologies Calculators

Efficiency of Spiral Gears using Pitch Circle Diameter

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*Pitch Circle Diameter of Gear 2*Speed of Gear 2)/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*Pitch Circle Diameter of Gear 1*Speed of Gear 1)

Efficiency of Spiral Gears

Go Efficiency = (cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 1))/(cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*cos(Spiral Angle of Gear Teeth for Gear 2))

Addendum of Pinion

Go Addendum of Pinion = Number of Teeth on Pinion/2*(sqrt(1+Number of Teeth on Wheel/Number of Teeth on Pinion*(Number of Teeth on Wheel/Number of Teeth on Pinion+2)*(sin(Pressure Angle of Gear))^2)-1)

Addendum of Wheel

Go Addendum of Wheel = Number of Teeth on Wheel/2*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)

Work Output on Driven

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)*pi*Pitch Circle Diameter of Gear 2*Speed of Gear 2

Work Output on Driver

Go Work Output = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)*pi*Pitch Circle Diameter of Gear 1*Speed of Gear 1

Maximum Efficiency of Spiral Gears

Go Efficiency = (cos(Shaft Angle+Angle of Friction)+1)/(cos(Shaft Angle-Angle of Friction)+1)

Resisting Force Acting Tangentially on Driven

Go Resisting Force acting Tangentially on Driven = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 2+Angle of Friction)

Force Applied Tangentially on Driver

Go Force Applied Tangentially on Driver = Resultant Reaction at Point of Contact*cos(Spiral Angle of Gear Teeth for Gear 1-Angle of Friction)

Axial Thrust on Driven

Go Axial Thrust on Driven = Resisting Force acting Tangentially on Driven*tan(Spiral Angle of Gear Teeth for Gear 2)

Axial Thrust on Driver

Go Axial Thrust on Driver = Force Applied Tangentially on Driver*tan(Spiral Angle of Gear Teeth for Gear 1)

Radius of Base Circle of Pinion

Go Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)

Radius of Base Circle of Wheel

Go Radius of Base Circle of Wheel = Radius of Pitch Circle of Wheel*cos(Pressure Angle of Gear)

Addendum of Rack

Go Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2

Tangential Force on Gear Shaft

Go Tangential Force = Maximum Tooth Pressure*cos(Pressure Angle of Gear)

Normal Force on Gear Shaft

Go Normal Force = Maximum Tooth Pressure*sin(Pressure Angle of Gear)

Shaft Angle

Go Shaft Angle = Spiral Angle of Gear Teeth for Gear 1+Spiral Angle of Gear Teeth for Gear 2

Gear Ratio

Go Gear Ratio = Radius of Pitch Circle of Wheel/Radius of Pitch Circle of Pinion

Torque Exerted on Gear Shaft

Go Torque Exerted on Wheel = Tangential Force*Diameter of Pitch Circle/2

Gear Ratio given Number of Teeth on Wheel and Pinion

Go Gear Ratio = Number of Teeth on Wheel/Number of Teeth on Pinion

Module

Go Module = Diameter of Pitch Circle/Number of Teeth on Wheel

Contact Ratio

Go Contact Ratio = Path of Contact/Circular Pitch

Radius of Base Circle of Pinion Formula

Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear)
r_b = r*cos(Φ_gear)

What is the function of pinion?

Pinion converts the rotational motion of the steering wheel into the linear motion needed to turn the wheels. It provides a gear reduction, making it easier to turn the wheels.

Why is pinion weaker than gear?

When the different materials are used, the product decides the weaker between the pinion and gear. The Lewis form factor is always less for a pinion compared with gear. When the same material is used for the pinion and gear, the pinion is always weaker than the gear

How to Calculate Radius of Base Circle of Pinion?

Radius of Base Circle of Pinion calculator uses Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear) to calculate the Radius of Base Circle of Pinion, The radius of base circle of pinion is the radius of the circle from which the involute portion of the tooth profile is generated. Radius of Base Circle of Pinion is denoted by r_b symbol.

How to calculate Radius of Base Circle of Pinion using this online calculator? To use this online calculator 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. Here is how the Radius of Base Circle of Pinion calculation can be explained with given input values -> 8650.091 = 0.0102*cos(0.55850536063808).

FAQ

What is Radius of Base Circle of Pinion?

The radius of base circle of pinion is the radius of the circle from which the involute portion of the tooth profile is generated and is represented as r_b = r*cos(Φ_gear) or Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear). 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 & The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

How to calculate Radius of Base Circle of Pinion?

The radius of base circle of pinion is the radius of the circle from which the involute portion of the tooth profile is generated is calculated using Radius of Base Circle of Pinion = Radius of Pitch Circle of Pinion*cos(Pressure Angle of Gear). To calculate Radius of Base Circle of Pinion, you need Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Radius of Pitch Circle of Pinion & Pressure Angle of Gear and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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