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 = Rwheel*sin(Φgear)
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) - 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 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 = Rwheel*sin(Φgear) --> 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)

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)

Maximum Length of Path of Recess Formula

Path of Recess = Radius of Pitch Circle of Wheel*sin(Pressure Angle of Gear)
P2 = Rwheel*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 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, The maximum length of path of recess is the path of contact from the pitch point to the end of contact when interference is avoided. 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 (Rwheel) & Pressure Angle of Gear gear) 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?
The maximum length of path of recess is the path of contact from the pitch point to the end of contact when interference is avoided and is represented as P2 = Rwheel*sin(Φgear) 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 & 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 Maximum Length of Path of Recess?
The maximum length of path of recess is the path of contact from the pitch point to the end of contact when interference is avoided 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 (Rwheel) & Pressure Angle of Gear gear). 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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