Maximum Length of Arc of Approach Calculator

✖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_w]			+10% -10%
✖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%
✖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_g]			+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 Approach [L]

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Maximum Length of Arc of Approach Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
L = (R_w+r)*tan(Φ_g)
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 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.
Radius of Pitch Circle of Pinion - (Measured in Meter) - 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.
Pressure Angle of Gear - (Measured in Radian) - 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

Radius of Pitch Circle of Wheel: 12.4 Millimeter --> 0.0124 Meter (Check conversion here)
Radius of Pitch Circle of Pinion: 10.2 Millimeter --> 0.0102 Meter (Check conversion here)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (R_w+r)*tan(Φ_g) --> (0.0124+0.0102)*tan(0.55850536063808)

Evaluating ... ...

L = 0.0141220473531475

STEP 3: Convert Result to Output's Unit

0.0141220473531475 Meter -->14.1220473531475 Millimeter (Check conversion here)

FINAL ANSWER

14.1220473531475 ≈ 14.12205 Millimeter <-- Length of Arc of Contact

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Toothed Gearing » Mechanical » Length » Maximum Length of Arc of Approach

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Length Calculators

Length of Path of Contact

LaTeX 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

LaTeX 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

LaTeX 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)

Length of Arc of Contact

LaTeX Go Length of Arc of Contact = Path of Contact/cos(Pressure Angle of Gear)

Maximum Length of Arc of Approach Formula

LaTeX Go

Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
L = (R_w+r)*tan(Φ_g)

What is length of path of contact?

Path of contact is the locus of the point of contact on two mating teeth from the beginning of engagement to the end of it. Thus CD is the path of contact. It is also called contact length. It is the tangent to both the base circles and passes through the pitch point.

How to Calculate Maximum Length of Arc of Approach?

Maximum Length of Arc of Approach calculator uses Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear) to calculate the Length of Arc of Contact, Maximum Length of Arc of Approach formula is defined as the distance measured along the curve of a gear tooth from the starting point of engagement to the point where the gear tooth reaches its highest point of single tooth contact. Length of Arc of Contact is denoted by L symbol.

How to calculate Maximum Length of Arc of Approach using this online calculator? To use this online calculator for Maximum Length of Arc of Approach, enter Radius of Pitch Circle of Wheel (R_w), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_g) and hit the calculate button. Here is how the Maximum Length of Arc of Approach calculation can be explained with given input values -> 14122.05 = (0.0124+0.0102)*tan(0.55850536063808).

FAQ

What is Maximum Length of Arc of Approach?

Maximum Length of Arc of Approach formula is defined as the distance measured along the curve of a gear tooth from the starting point of engagement to the point where the gear tooth reaches its highest point of single tooth contact and is represented as L = (R_w+r)*tan(Φ_g) or Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear). 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 Pinion is the radial distance of the tooth measuring from the pitch circle to the bottom of the tooth space & 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 Maximum Length of Arc of Approach?

Maximum Length of Arc of Approach formula is defined as the distance measured along the curve of a gear tooth from the starting point of engagement to the point where the gear tooth reaches its highest point of single tooth contact is calculated using Length of Arc of Contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear). To calculate Maximum Length of Arc of Approach, you need Radius of Pitch Circle of Wheel (R_w), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_g). With our tool, you need to enter the respective value for Radius of Pitch Circle of Wheel, Radius of Pitch Circle of 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.

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 Wheel, Radius of Pitch Circle of Pinion & Pressure Angle of Gear. 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 Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)

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