Maximum Length of Arc of Approach Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
L = (Rwheel+r)*tan(Φgear)
This formula uses 1 Functions, 4 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(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.
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.
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 Wheel: 12.4 Millimeter --> 0.0124 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
L = (Rwheel+r)*tan(Φgear) --> (0.0124+0.0102)*tan(0.55850536063808)
Evaluating ... ...
L = 0.0141220473531475
STEP 3: Convert Result to Output's Unit
0.0141220473531475 Meter -->14.1220473531475 Millimeter (Check conversion here)
FINAL ANSWER
14.1220473531475 14.12205 Millimeter <-- Length of arc of contact
(Calculation completed in 00.020 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 Arc of Approach Formula

Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear)
L = (Rwheel+r)*tan(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. Thus CD is the path of contact. It is also called contact length. It is the tangent to both the base circles and passes through the pitch point.

How to Calculate Maximum Length of Arc of Approach?

Maximum Length of Arc of Approach calculator uses Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear) to calculate the Length of arc of contact, The maximum length of arc of approach is the ratio of the length of the path of contact and the cosine of the pressure angle when interference is avoided. Length of arc of contact is denoted by L symbol.

How to calculate Maximum Length of Arc of Approach using this online calculator? To use this online calculator for Maximum Length of Arc of Approach, enter Radius of Pitch Circle of Wheel (Rwheel), Radius of Pitch Circle of Pinion (r) & Pressure Angle of Gear gear) and hit the calculate button. Here is how the Maximum Length of Arc of Approach calculation can be explained with given input values -> 14122.05 = (0.0124+0.0102)*tan(0.55850536063808).

FAQ

What is Maximum Length of Arc of Approach?
The maximum length of arc of approach is the ratio of the length of the path of contact and the cosine of the pressure angle when interference is avoided and is represented as L = (Rwheel+r)*tan(Φgear) or Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(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 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 Arc of Approach?
The maximum length of arc of approach is the ratio of the length of the path of contact and the cosine of the pressure angle when interference is avoided is calculated using Length of arc of contact = (Radius of Pitch Circle of Wheel+Radius of Pitch Circle of Pinion)*tan(Pressure Angle of Gear). To calculate Maximum Length of Arc of Approach, you need Radius of Pitch Circle of Wheel (Rwheel), 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 Wheel, 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 Length of arc of contact?
In this formula, Length of arc of contact uses Radius of Pitch Circle of Wheel, Radius of Pitch Circle of Pinion & 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 = Path of Contact/cos(Pressure Angle of Gear)
  • Length of arc of contact = (Radius of Pitch Circle of Pinion+Radius of Pitch Circle of Wheel)*tan(Pressure Angle Of 2 Gears)
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