Length of Path of Contact Calculator

Calculate Length of Path of Contact











Formula

The formula to calculate the Length of Path of Contact is:

\[ P = \sqrt{RA^2 - R_{wheel}^2 \cdot (\cos(\Phi_{gear}))^2} + \sqrt{rA^2 - r^2 \cdot (\cos(\Phi_{gear}))^2} - (R_{wheel} + r) \cdot \sin(\Phi_{gear}) \]

Where:

Definition

The path of contact is the path traced by the contact point of a pair of tooth profiles.

Example Calculation

Let's assume the following values:

Using the formula:

\[ P = \sqrt{0.022^2 - 0.0124^2 \cdot (\cos(0.55850536063808))^2} + \sqrt{0.02^2 - 0.0102^2 \cdot (\cos(0.55850536063808))^2} - (0.0124 + 0.0102) \cdot \sin(0.55850536063808) \]

Evaluating:

\[ P = 0.0253804870217464 \text{ m} \]

The Length of Path of Contact is 0.0253804870217464 meters.

Conversion Chart

Radius of Addendum Circle of Wheel (m) Radius of Pitch Circle of Wheel (m) Pressure Angle of Gear (rad) Radius of Addendum Circle of Pinion (m) Radius of Pitch Circle of Pinion (m) Path of Contact (m)
0.02 0.0124 0.55850536063808 0.02 0.0102 0.023068750294
0.021 0.0124 0.55850536063808 0.02 0.0102 0.024233864124
0.022 0.0124 0.55850536063808 0.02 0.0102 0.025380487022
0.023 0.0124 0.55850536063808 0.02 0.0102 0.026511728759
0.024 0.0124 0.55850536063808 0.02 0.0102 0.027630009074
0.025 0.0124 0.55850536063808 0.02 0.0102 0.028737245245
0.026 0.0124 0.55850536063808 0.02 0.0102 0.029834980117
0.027 0.0124 0.55850536063808 0.02 0.0102 0.030924471956
0.028 0.0124 0.55850536063808 0.02 0.0102 0.032006759002
0.029 0.0124 0.55850536063808 0.02 0.0102 0.033082706835