Maximum Length of Path of Approach Solution

STEP 0: Pre-Calculation Summary
Formula Used
Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)
P1 = r*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 Approach - (Measured in Meter) - Path of approach is the portion of the path of contact from the beginning of contact to the pitch point.
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 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
P1 = r*sin(Φgear) --> 0.0102*sin(0.55850536063808)
Evaluating ... ...
P1 = 0.00540517649517778
STEP 3: Convert Result to Output's Unit
0.00540517649517778 Meter -->5.40517649517778 Millimeter (Check conversion here)
FINAL ANSWER
5.40517649517778 5.405176 Millimeter <-- Path of Approach
(Calculation completed in 00.004 seconds)

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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 Approach Formula

Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear)
P1 = r*sin(Φgear)

What is meant by arc of approach in gears?

We have already defined that the arc of contact is the path traced by a point on the pitch circle from the beginning to the end of the engagement of a given pair of teeth.

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 Approach?

Maximum Length of Path of Approach calculator uses Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear) to calculate the Path of Approach, The maximum length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point when interference is avoided. Path of Approach is denoted by P1 symbol.

How to calculate Maximum Length of Path of Approach using this online calculator? To use this online calculator for Maximum Length of Path of Approach, enter Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear gear) and hit the calculate button. Here is how the Maximum Length of Path of Approach calculation can be explained with given input values -> 5405.176 = 0.0102*sin(0.55850536063808).

FAQ

What is Maximum Length of Path of Approach?
The maximum length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point when interference is avoided and is represented as P1 = r*sin(Φgear) or Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear). 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 Maximum Length of Path of Approach?
The maximum length of path of approach is the portion of the path of contact from the beginning of contact to the pitch point when interference is avoided is calculated using Path of Approach = Radius of Pitch Circle of Pinion*sin(Pressure Angle of Gear). To calculate Maximum Length of Path of Approach, you need 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 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 Approach?
In this formula, Path of Approach uses 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 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)
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