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(rA^2-r^2*(cos(Φgear))^2)-r*sin(Φgear)
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) - 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.
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
Radius of addendum circle of pinion: 20 Millimeter --> 0.02 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(rA^2-r^2*(cos(Φgear))^2)-r*sin(Φgear) --> sqrt(0.02^2-0.0102^2*(cos(0.55850536063808))^2)-0.0102*sin(0.55850536063808)
Evaluating ... ...
P2 = 0.0126274587238916
STEP 3: Convert Result to Output's Unit
0.0126274587238916 Meter -->12.6274587238916 Millimeter (Check conversion here)
FINAL ANSWER
12.6274587238916 12.62746 Millimeter <-- Path of Recess
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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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)

Length of Path of Recess Formula

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(rA^2-r^2*(cos(Φgear))^2)-r*sin(Φgear)

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, The length of path of recess is the path of contact from the pitch point to the end of contact. 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 (rA), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear gear) 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(0.02^2-0.0102^2*(cos(0.55850536063808))^2)-0.0102*sin(0.55850536063808).

FAQ

What is Length of Path of Recess?
The length of path of recess is the path of contact from the pitch point to the end of contact and is represented as P2 = sqrt(rA^2-r^2*(cos(Φgear))^2)-r*sin(Φgear) 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, 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 & 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 Length of Path of Recess?
The length of path of recess is the path of contact from the pitch point to the end of contact 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 (rA), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear gear). 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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