Addendum of Pinion Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Ap = Zp/2*(sqrt(1+T/Zp*(T/Zp+2)*(sin(Φgear))^2)-1)
This formula uses 2 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Addendum of Pinion - (Measured in Meter) - Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line.
Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on pinion.
Number of Teeth on Wheel - Number of teeth on wheel is the count of teeths on the wheel.
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
Number of Teeth on Pinion: 8 --> No Conversion Required
Number of Teeth on Wheel: 12 --> No Conversion Required
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ap = Zp/2*(sqrt(1+T/Zp*(T/Zp+2)*(sin(Φgear))^2)-1) --> 8/2*(sqrt(1+12/8*(12/8+2)*(sin(0.55850536063808))^2)-1)
Evaluating ... ...
Ap = 2.29193228148959
STEP 3: Convert Result to Output's Unit
2.29193228148959 Meter -->2291.93228148959 Millimeter (Check conversion here)
FINAL ANSWER
2291.93228148959 2291.932 Millimeter <-- Addendum of Pinion
(Calculation completed in 00.004 seconds)

Credits

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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

Addendum of Pinion Formula

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)
Ap = Zp/2*(sqrt(1+T/Zp*(T/Zp+2)*(sin(Φgear))^2)-1)

What is addendum?

The addendum is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line; also, the radial distance between the pitch diameter and the outside diameter.

How to Calculate Addendum of Pinion?

Addendum of Pinion calculator uses 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) to calculate the Addendum of Pinion, Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line. Addendum of Pinion is denoted by Ap symbol.

How to calculate Addendum of Pinion using this online calculator? To use this online calculator for Addendum of Pinion, enter Number of Teeth on Pinion (Zp), Number of Teeth on Wheel (T) & Pressure Angle of Gear gear) and hit the calculate button. Here is how the Addendum of Pinion calculation can be explained with given input values -> 2.3E+6 = 8/2*(sqrt(1+12/8*(12/8+2)*(sin(0.55850536063808))^2)-1).

FAQ

What is Addendum of Pinion?
Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line and is represented as Ap = Zp/2*(sqrt(1+T/Zp*(T/Zp+2)*(sin(Φgear))^2)-1) or 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). Number of teeth on pinion is the count of teeth on pinion, Number of teeth on wheel is the count of teeths on the wheel & 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 Addendum of Pinion?
Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line is calculated using 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). To calculate Addendum of Pinion, you need Number of Teeth on Pinion (Zp), Number of Teeth on Wheel (T) & Pressure Angle of Gear gear). With our tool, you need to enter the respective value for Number of Teeth on Pinion, Number of Teeth on Wheel & 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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