Length of Path of Recess Calculator

✖Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle.ⓘ Radius of Addendum Circle of Pinion [r_a]			+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%

✖Path of recess is the portion of the path of contact from the pitch point to the end of contact.ⓘ Length of Path of Recess [P₂]

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Length of Path of Recess Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
P₂ = sqrt(r_a^2-r^2*(cos(Φ_g))^2)-r*sin(Φ_g)
This formula uses 3 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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

Path of Recess - (Measured in Meter) - Path of recess is the portion of the path of contact from the pitch point to the end of contact.
Radius of Addendum Circle of Pinion - (Measured in Meter) - Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle.
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 Addendum Circle of Pinion: 15.954 Millimeter --> 0.015954 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

P₂ = sqrt(r_a^2-r^2*(cos(Φ_g))^2)-r*sin(Φ_g) --> sqrt(0.015954^2-0.0102^2*(cos(0.55850536063808))^2)-0.0102*sin(0.55850536063808)

Evaluating ... ...

P₂ = 0.00800027198460171

STEP 3: Convert Result to Output's Unit

0.00800027198460171 Meter -->8.00027198460171 Millimeter (Check conversion here)

FINAL ANSWER

8.00027198460171 ≈ 8.000272 Millimeter <-- Path of Recess

(Calculation completed in 00.004 seconds)

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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)

Length of Path of Recess Formula

LaTeX Go

Why does interference occur in gears?

When two gears are in mesh at one instant there is a chance to mate an involute portion with a non-involute portion of the mating gear. This phenomenon is known as "interference" and occurs when the number of teeth on the smaller of the two meshing gears is less than a required minimum.

What are the advantages of smaller pressure angles?

Earlier gears with pressure angle 14.5 were commonly used because the cosine is larger for a smaller angle, providing more power transmission and less pressure on the bearing; however, teeth with smaller pressure angles are weaker. To run gears together properly their pressure angles must be matched.

How to Calculate Length of Path of Recess?

Length of Path of Recess calculator uses 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) to calculate the Path of Recess, Length of Path of Recess formula is defined as the distance along the path of recess of a gear tooth, which is a critical parameter in gear design, influencing the gear's strength, durability, and overall performance, and is used to determine the optimal gear tooth shape and size. Path of Recess is denoted by P₂ symbol.

How to calculate Length of Path of Recess using this online calculator? To use this online calculator for Length of Path of Recess, enter Radius of Addendum Circle of Pinion (r_a), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear (Φ_g) and hit the calculate button. Here is how the Length of Path of Recess calculation can be explained with given input values -> 12627.46 = sqrt(0.015954^2-0.0102^2*(cos(0.55850536063808))^2)-0.0102*sin(0.55850536063808).

FAQ

What is Length of Path of Recess?

Length of Path of Recess formula is defined as the distance along the path of recess of a gear tooth, which is a critical parameter in gear design, influencing the gear's strength, durability, and overall performance, and is used to determine the optimal gear tooth shape and size and is represented as P₂ = sqrt(r_a^2-r^2*(cos(Φ_g))^2)-r*sin(Φ_g) or 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). Radius of Addendum Circle of Pinion is radial distance between the pitch circle and the root circle, 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 Length of Path of Recess?

Length of Path of Recess formula is defined as the distance along the path of recess of a gear tooth, which is a critical parameter in gear design, influencing the gear's strength, durability, and overall performance, and is used to determine the optimal gear tooth shape and size is calculated using 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). To calculate Length of Path of Recess, you need Radius of Addendum Circle of Pinion (r_a), 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 Addendum Circle of Pinion, 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 Path of Recess?

In this formula, Path of Recess uses Radius of Addendum Circle of Pinion, Radius of Pitch Circle of Pinion & Pressure Angle of Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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