Maximum Length of Arc of Contact Calculator

✖The Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.ⓘ Radius of Pitch Circle of Pinion [r]			+10% -10%
✖Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.ⓘ Radius of Pitch Circle of Wheel [R_wheel]			+10% -10%
✖The Pressure Angle of 2 Gears is defined as is the angle between the tooth face and the gear wheel tangent.ⓘ Pressure Angle Of 2 Gears [α]			+10% -10%

✖Length of arc of contact is the ratio of length of path of contact and the cosine of the pressure angle.ⓘ Maximum Length of Arc of Contact [L]

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Formula

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Maximum Length of Arc of Contact

Formula

`"L" = ("r"+"R"_{"wheel"})*tan("α")`

Example

`"1.184416mm"=("10.2mm"+"12.4mm")*tan("3°")`

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Maximum Length of Arc of Contact Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
L = (r+R_wheel)*tan(α)
This formula uses 1 Functions, 4 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Length of arc of contact - (Measured in Meter) - Length of arc of contact is the ratio of length of path of contact and the cosine of the pressure angle.
Radius of Pitch Circle of Pinion - (Measured in Meter) - The Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
Radius of Pitch Circle of Wheel - (Measured in Meter) - Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space.
Pressure Angle Of 2 Gears - (Measured in Radian) - The Pressure Angle of 2 Gears is defined as is the angle between the tooth face and the gear wheel tangent.

STEP 1: Convert Input(s) to Base Unit

Radius of Pitch Circle of Pinion: 10.2 Millimeter --> 0.0102 Meter (Check conversion here)
Radius of Pitch Circle of Wheel: 12.4 Millimeter --> 0.0124 Meter (Check conversion here)
Pressure Angle Of 2 Gears: 3 Degree --> 0.05235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (r+R_wheel)*tan(α) --> (0.0102+0.0124)*tan(0.05235987755982)

Evaluating ... ...

L = 0.00118441581179651

STEP 3: Convert Result to Output's Unit

0.00118441581179651 Meter -->1.18441581179651 Millimeter (Check conversion here)

FINAL ANSWER

1.18441581179651 ≈ 1.184416 Millimeter <-- Length of arc of contact

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Length » Maximum Length of Arc of Contact

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Sri sivasubramaniyanadar college of engineering (ssn college of engineering), Chennai

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< 9 Length Calculators

Length of Path of Contact

Go Path of Contact = sqrt(Radius of addendum circle of wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)+sqrt(Radius of addendum circle of pinion^2-Radius of Pitch Circle of Pinion^2*(cos(Pressure Angle of Gear))^2)-(Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)

Length of Path of Recess

Go Path of Recess = sqrt(Radius of addendum circle of pinion^2-Radius of Pitch Circle of Pinion^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)

Length of Path of Approach

Go Path of Approach = sqrt(Radius of addendum circle of wheel^2-Radius of Pitch Circle of Wheel^2*(cos(Pressure Angle of Gear))^2)-Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)

Maximum Length of Arc of Contact

Go Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)

Maximum Length of Arc of Approach

Go Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)

Maximum Length of Path of Contact

Go Path of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*sin(Pressure Angle of Gear)

Maximum Length of Path of Approach

Go Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)

Maximum Length of Path of Recess

Go Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)

Length of Arc of Contact

Go Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear)

Maximum Length of Arc of Contact Formula

Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
L = (r+R_wheel)*tan(α)

law of gearing

Law of gearing is satisfied if common normal at the point of contact passes through the pitch point on the line joining the centres of rotation.

How to Calculate Maximum Length of Arc of Contact?

Maximum Length of Arc of Contact calculator uses Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears) to calculate the Length of arc of contact, The Maximum length of arc of contact formula is defined as length of arc of contact for two mating gears, in order to avoid interference. Length of arc of contact is denoted by L symbol.

How to calculate Maximum Length of Arc of Contact using this online calculator? To use this online calculator for Maximum Length of Arc of Contact, enter Radius of Pitch Circle of Pinion (r), Radius of Pitch Circle of Wheel (R_wheel) & Pressure Angle Of 2 Gears (α) and hit the calculate button. Here is how the Maximum Length of Arc of Contact calculation can be explained with given input values -> 1184.416 = (0.0102+0.0124)*tan(0.05235987755982).

FAQ

What is Maximum Length of Arc of Contact?

The Maximum length of arc of contact formula is defined as length of arc of contact for two mating gears, in order to avoid interference and is represented as L = (r+R_wheel)*tan(α) or Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears). The Radius of Pitch Circle of Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space, Radius of pitch circle of wheel is radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space & The Pressure Angle of 2 Gears is defined as is the angle between the tooth face and the gear wheel tangent.

How to calculate Maximum Length of Arc of Contact?

The Maximum length of arc of contact formula is defined as length of arc of contact for two mating gears, in order to avoid interference is calculated using Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears). To calculate Maximum Length of Arc of Contact, you need Radius of Pitch Circle of Pinion (r), Radius of Pitch Circle of Wheel (R_wheel) & Pressure Angle Of 2 Gears (α). With our tool, you need to enter the respective value for Radius of Pitch Circle of Pinion, Radius of Pitch Circle of Wheel & Pressure Angle Of 2 Gears and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of arc of contact?

In this formula, Length of arc of contact uses Radius of Pitch Circle of Pinion, Radius of Pitch Circle of Wheel & Pressure Angle Of 2 Gears. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear)
Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)

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