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Addendum of Rack Formula

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

A_R - Addendum of Rack?Z_p - Number of Teeth on Pinion?Φ_gear - Pressure Angle of Gear?

Addendum of Rack Example

With values

With units

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

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

Here is how the Addendum of Rack equation looks like.

1123.2577 = \frac{8 \cdot {(\sin (32))}^{2}}{2}

1123.2577mm = \frac{8 \cdot {(\sin (32°))}^{2}}{2}

1123.2577 = \frac{8 \cdot {(\sin (32))}^{2}}{2}

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Addendum of Rack Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A R = \frac{8 \cdot {(\sin (32°))}^{2}}{2}

Next Step Convert Units

∴

A R = \frac{8 \cdot {(\sin (0.5585rad))}^{2}}{2}

Next Step Prepare to Evaluate

∴

A R = \frac{8 \cdot {(\sin (0.5585))}^{2}}{2}

Next Step Evaluate

∴

A R = 1.12325770642147m

Next Step Convert to Output's Unit

∴

A R = 1123.25770642147mm

LAST Step Rounding Answer

∴

A R = 1123.2577mm

Addendum of Rack Formula Elements

Variables

Functions

Addendum of Rack

Addendum of rack 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_R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Addendum of Rack

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

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)

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 Addendum of Rack?

Addendum of Rack evaluator uses Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2 to evaluate the Addendum of Rack, Addendum of Rack 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 and manufacturing, as it affects the gear's strength, durability, and overall performance. Addendum of Rack is denoted by A_R symbol.

How to evaluate Addendum of Rack using this online evaluator? To use this online evaluator for Addendum of Rack, enter Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) and hit the calculate button.

FAQs on Addendum of Rack

What is the formula to find Addendum of Rack?

The formula of Addendum of Rack is expressed as Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2. Here is an example- 1.1E+6 = (8*(sin(0.55850536063808))^2)/2.

How to calculate Addendum of Rack?

With Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) we can find Addendum of Rack using the formula - Addendum of Rack = (Number of Teeth on Pinion*(sin(Pressure Angle of Gear))^2)/2. This formula also uses Sine function(s).

Can the Addendum of Rack be negative?

Yes, the Addendum of Rack, measured in Length can be negative.

Which unit is used to measure Addendum of Rack?

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

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Addendum of Rack Formula

Addendum of Rack Example

Addendum of Rack Solution

Addendum of Rack Formula Elements

Other formulas in Toothed Gear Terminologies category

How to Evaluate Addendum of Rack?

FAQs on Addendum of Rack

Variable Name