Maximum Length of Path of Recess 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%
✖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.ⓘ Maximum Length of Path of Recess [P₂]

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Formula

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Maximum Length of Path of Recess

Formula

P 2 = R w \cdot \sin (Φ g)

Example

6.570999 mm = 12.4 mm \cdot \sin (32 °)

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Maximum Length of Path of Recess Solution

STEP 0: Pre-Calculation Summary

Formula Used

Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)
P₂ = R_w*sin(Φ_g)
This formula uses 1 Functions, 3 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)

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 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 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)
Pressure Angle of Gear: 32 Degree --> 0.55850536063808 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P₂ = R_w*sin(Φ_g) --> 0.0124*sin(0.55850536063808)

Evaluating ... ...

P₂ = 0.00657099887649063

STEP 3: Convert Result to Output's Unit

0.00657099887649063 Meter -->6.57099887649063 Millimeter (Check conversion here)

FINAL ANSWER

6.57099887649063 ≈ 6.570999 Millimeter <-- Path of Recess

(Calculation completed in 00.004 seconds)

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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

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)

Length of Arc of Contact

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

Maximum Length of Path of Recess Formula

Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)
P₂ = R_w*sin(Φ_g)

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 Maximum Length of Path of Recess?

Maximum Length of Path of Recess calculator uses Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear) to calculate the Path of Recess, Maximum Length of Path of Recess formula is defined as the maximum distance a wheel can travel along a gear's recessed path, influenced by the wheel's radius and the gear's angular displacement, providing critical insights into mechanical systems and gear interactions. Path of Recess is denoted by P₂ symbol.

How to calculate Maximum Length of Path of Recess using this online calculator? To use this online calculator for Maximum Length of Path of Recess, enter Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g) and hit the calculate button. Here is how the Maximum Length of Path of Recess calculation can be explained with given input values -> 6570.999 = 0.0124*sin(0.55850536063808).

FAQ

What is Maximum Length of Path of Recess?

Maximum Length of Path of Recess formula is defined as the maximum distance a wheel can travel along a gear's recessed path, influenced by the wheel's radius and the gear's angular displacement, providing critical insights into mechanical systems and gear interactions and is represented as P₂ = R_w*sin(Φ_g) or Path of Recess = Radius of Pitch Circle of Wheel*sin(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 & 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 Path of Recess?

Maximum Length of Path of Recess formula is defined as the maximum distance a wheel can travel along a gear's recessed path, influenced by the wheel's radius and the gear's angular displacement, providing critical insights into mechanical systems and gear interactions is calculated using Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear). To calculate Maximum Length of Path of Recess, you need Radius of Pitch Circle of Wheel (R_w) & Pressure Angle of Gear (Φ_g). With our tool, you need to enter the respective value for Radius of Pitch Circle of Wheel & 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 Pitch Circle of Wheel & Pressure Angle of Gear. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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