Length of Arc of Contact Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear)
L = P/cos(Φgear)
This formula uses 1 Functions, 3 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Length of arc of contact - (Measured in Meter) - Length of arc of contact is the ratio of length of path of contact and the cosine of the pressure angle.
Path of Contact - (Measured in Meter) - The path of contact is the path traced by the contact point of a pair of tooth profiles.
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
Path of Contact: 18 Millimeter --> 0.018 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
L = P/cos(Φgear) --> 0.018/cos(0.55850536063808)
Evaluating ... ...
L = 0.0212252112605163
STEP 3: Convert Result to Output's Unit
0.0212252112605163 Meter -->21.2252112605163 Millimeter (Check conversion here)
FINAL ANSWER
21.2252112605163 21.22521 Millimeter <-- Length of arc of contact
(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 Arc of Contact Formula

Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear)
L = P/cos(Φgear)

What is length of path of contact?

Path of contact is the locus of the point of contact on two mating teeth from the beginning of engagement to the end of it. It is also called contact length. It is the tangent to both the base circles and passes through the pitch point.

How to Calculate Length of Arc of Contact?

Length of Arc of Contact calculator uses Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear) to calculate the Length of arc of contact, Length of arc of contact is the ratio of the length of the path of contact and the cosine of the pressure angle. Length of arc of contact is denoted by L symbol.

How to calculate Length of Arc of Contact using this online calculator? To use this online calculator for Length of Arc of Contact, enter Path of Contact (P) & Pressure Angle of Gear gear) and hit the calculate button. Here is how the Length of Arc of Contact calculation can be explained with given input values -> 21225.21 = 0.018/cos(0.55850536063808).

FAQ

What is Length of Arc of Contact?
Length of arc of contact is the ratio of the length of the path of contact and the cosine of the pressure angle and is represented as L = P/cos(Φgear) or Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear). The path of contact is the path traced by the contact point of a pair of tooth profiles & 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 Arc of Contact?
Length of arc of contact is the ratio of the length of the path of contact and the cosine of the pressure angle is calculated using Length of arc of contact = Path of Contact/cos(Pressure Angle of Gear). To calculate Length of Arc of Contact, you need Path of Contact (P) & Pressure Angle of Gear gear). With our tool, you need to enter the respective value for Path of Contact & 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 Length of arc of contact?
In this formula, Length of arc of contact uses Path of Contact & Pressure Angle of Gear. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
  • Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
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