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Addendum of Wheel Formula

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Addendum of wheel 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 w = \frac{T}{2} \cdot (\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

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

Addendum of Wheel Example

With values

With units

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

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

Here is how the Addendum of Wheel equation looks like.

1346.5722 = \frac{12}{2} \cdot (\sqrt{1 + \frac{8}{12} \cdot (\frac{8}{12} + 2) \cdot {(\sin (32))}^{2}} - 1)

1346.5722mm = \frac{12}{2} \cdot (\sqrt{1 + \frac{8}{12} \cdot (\frac{8}{12} + 2) \cdot {(\sin (32°))}^{2}} - 1)

1346.5722 = \frac{12}{2} \cdot (\sqrt{1 + \frac{8}{12} \cdot (\frac{8}{12} + 2) \cdot {(\sin (32))}^{2}} - 1)

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Addendum of Wheel Solution

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

FIRST Step Consider the formula

A w = \frac{T}{2} \cdot (\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

A w = 1.34657221449183m

Next Step Convert to Output's Unit

∴

A w = 1346.57221449183mm

LAST Step Rounding Answer

∴

A w = 1346.5722mm

Addendum of Wheel Formula Elements

Variables

Functions

Addendum of Wheel

Addendum of wheel 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_w

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Addendum of Wheel

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

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)

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 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 Wheel?

Addendum of Wheel evaluator uses 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) to evaluate the Addendum of Wheel, Addendum of Wheel formula is defined as the radial distance from the pitch circle to the top of the tooth of a gear, which is a critical dimension in gear design that affects the gear's strength, durability, and overall performance in power transmission systems. Addendum of Wheel is denoted by A_w symbol.

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

FAQs on Addendum of Wheel

What is the formula to find Addendum of Wheel?

The formula of Addendum of Wheel is expressed as 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). Here is an example- 1.3E+6 = 12/2*(sqrt(1+8/12*(8/12+2)*(sin(0.55850536063808))^2)-1).

How to calculate Addendum of Wheel?

With Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) we can find Addendum of Wheel using the formula - 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). This formula also uses Sine (sin), Square Root (sqrt) function(s).

Can the Addendum of Wheel be negative?

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

Which unit is used to measure Addendum of Wheel?

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

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