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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

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)

A_p - Addendum of Pinion?Z_p - Number of Teeth on Pinion?T - Number of Teeth on Wheel?Φ_gear - Pressure Angle of Gear?

Addendum of Pinion Example

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With units

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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.

2291.9323 = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (32))}^{2}} - 1)

2291.9323mm = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (32°))}^{2}} - 1)

2291.9323 = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (32))}^{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

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)

Next Step Substitute values of Variables

∴

A p = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (32°))}^{2}} - 1)

Next Step Convert Units

∴

A p = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (0.5585rad))}^{2}} - 1)

Next Step Prepare to Evaluate

∴

A p = \frac{8}{2} \cdot (\sqrt{1 + \frac{12}{8} \cdot (\frac{12}{8} + 2) \cdot {(\sin (0.5585))}^{2}} - 1)

Next Step Evaluate

∴

A p = 2.29193228148959m

Next Step Convert to Output's Unit

∴

A p = 2291.93228148959mm

LAST Step Rounding Answer

∴

A p = 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: A_p

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Addendum of Pinion

Number of Teeth on Pinion

Number of teeth on pinion is the count of teeth on pinion.

Symbol: Z_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Pinion

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.

Formulas to find Number of Teeth on Wheel

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

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 = 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 Rack

A R = \frac{Z p \cdot {(\sin (Φ gear))}^{2}}{2}

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 A_p 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 (Z_p), Number of Teeth on Wheel (T) & Pressure Angle of Gear (Φ_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 (Z_p), Number of Teeth on Wheel (T) & Pressure Angle of Gear (Φ_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, Square Root Function 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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Addendum of Pinion Formula

Addendum of Pinion Example

Addendum of Pinion Solution

Addendum of Pinion Formula Elements

Other formulas in Toothed Gear Terminologies category

How to Evaluate Addendum of Pinion?

FAQs on Addendum of Pinion

Variable Name