Addendum of Pinion Formula

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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. Check FAQs
Ap=Zp2(1+TZp(TZp+2)(sin(Φgear))2-1)
Ap - Addendum of Pinion?Zp - Number of Teeth on Pinion?T - Number of Teeth on Wheel?Φgear - Pressure Angle of Gear?

Addendum of Pinion Example

With values
With units
Only example

Here is how the Addendum of Pinion equation looks like with Values.

Here is how the Addendum of Pinion equation looks like with Units.

Here is how the Addendum of Pinion equation looks like.

2291.9323Edit=8Edit2(1+12Edit8Edit(12Edit8Edit+2)(sin(32Edit))2-1)
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Addendum of Pinion Solution

Follow our step by step solution on how to calculate Addendum of Pinion?

FIRST Step Consider the formula
Ap=Zp2(1+TZp(TZp+2)(sin(Φgear))2-1)
Next Step Substitute values of Variables
Ap=82(1+128(128+2)(sin(32°))2-1)
Next Step Convert Units
Ap=82(1+128(128+2)(sin(0.5585rad))2-1)
Next Step Prepare to Evaluate
Ap=82(1+128(128+2)(sin(0.5585))2-1)
Next Step Evaluate
Ap=2.29193228148959m
Next Step Convert to Output's Unit
Ap=2291.93228148959mm
LAST Step Rounding Answer
Ap=2291.9323mm

Addendum of Pinion Formula Elements

Variables
Functions
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.
Symbol: Ap
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Number of Teeth on Pinion
Number of teeth on pinion is the count of teeth on pinion.
Symbol: Zp
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Number of Teeth on Wheel
Number of teeth on wheel is the count of teeths on the wheel.
Symbol: T
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
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: Φgear
Measurement: AngleUnit: °
Note: Value should be greater than 0.
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)
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.
Syntax: sqrt(Number)

Other formulas in Toothed Gear Terminologies category

​Go Torque Exerted on Gear Shaft
τ=Ptdpitch circle2
​Go Work Output on Driven
w=Rcos(α2+Φ)πd2N2
​Go Work Output on Driver
w=Rcos(α1-Φ)πd1N1
​Go Addendum of Rack
AR=Zp(sin(Φgear))22

How to Evaluate Addendum of Pinion?

Addendum of Pinion evaluator 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 evaluate the Addendum of Pinion, Addendum of Pinion formula is defined as the radial distance from the pitch circle to the top land of a tooth in a toothed gear, which is a critical parameter in gear design that affects the gear's performance and efficiency. Addendum of Pinion is denoted by Ap symbol.

How to evaluate Addendum of Pinion using this online evaluator? To use this online evaluator 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.

FAQs on Addendum of Pinion

What is the formula to find Addendum of Pinion?
The formula of Addendum of Pinion is expressed as 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). Here is an example- 2.3E+6 = 8/2*(sqrt(1+12/8*(12/8+2)*(sin(0.55850536063808))^2)-1).
How to calculate Addendum of Pinion?
With Number of Teeth on Pinion (Zp), Number of Teeth on Wheel (T) & Pressure Angle of Gear gear) we can find Addendum of Pinion using the 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). This formula also uses Sine (sin), Square Root (sqrt) function(s).
Can the Addendum of Pinion be negative?
Yes, the Addendum of Pinion, measured in Length can be negative.
Which unit is used to measure Addendum of Pinion?
Addendum of Pinion is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Addendum of Pinion can be measured.
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