Addendum of Wheel Calculator

✖Number of teeth on wheel is the count of teeths on the wheel.ⓘ Number of Teeth on Wheel [T]			+10% -10%
✖Number of teeth on pinion is the count of teeth on pinion.ⓘ Number of Teeth on Pinion [Z_p]			+10% -10%
✖The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle of Gear [Φ_gear]			+10% -10%

✖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.ⓘ Addendum of Wheel [A_w]

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Formula

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Addendum of Wheel

Formula

`"A"_{"w"} = "T"/2*(sqrt(1+"Z"_{"p"}/"T"*("Z"_{"p"}/"T"+2)*(sin("Φ"_{"gear"}))^2)-1)`

Example

`"1346.572mm"="12"/2*(sqrt(1+"8"/"12"*("8"/"12"+2)*(sin("32°"))^2)-1)`

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Addendum of Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
A_w = T/2*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^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 Wheel - (Measured in Meter) - 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.
Number of Teeth on Wheel - Number of teeth on wheel is the count of teeths on the wheel.
Number of Teeth on Pinion - Number of teeth on pinion is the count of teeth on pinion.
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 Wheel: 12 --> No Conversion Required
Number of Teeth on Pinion: 8 --> No Conversion Required
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_w = T/2*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^2)-1) --> 12/2*(sqrt(1+8/12*(8/12+2)*(sin(0.55850536063808))^2)-1)

Evaluating ... ...

A_w = 1.34657221449183

STEP 3: Convert Result to Output's Unit

1.34657221449183 Meter -->1346.57221449183 Millimeter (Check conversion here)

FINAL ANSWER

1346.57221449183 ≈ 1346.572 Millimeter <-- Addendum of Wheel

(Calculation completed in 00.004 seconds)

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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 Wheel Formula

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 Wheel?

Addendum of Wheel calculator 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 calculate the 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. Addendum of Wheel is denoted by A_w symbol.

How to calculate Addendum of Wheel using this online calculator? To use this online calculator 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. Here is how the Addendum of Wheel calculation can be explained with given input values -> 1.3E+6 = 12/2*(sqrt(1+8/12*(8/12+2)*(sin(0.55850536063808))^2)-1).

FAQ

What is 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 and is represented as A_w = T/2*(sqrt(1+Z_p/T*(Z_p/T+2)*(sin(Φ_gear))^2)-1) or 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). Number of teeth on wheel is the count of teeths on the wheel, Number of teeth on pinion is the count of teeth on pinion & 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 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 is calculated using 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 calculate Addendum of Wheel, you need Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear). With our tool, you need to enter the respective value for Number of Teeth on Wheel, Number of Teeth on Pinion & 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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