The formula to calculate the Length of Arc of Contact is:
\[ L = (R_{\text{wheel}} + r) \cdot \tan(\Phi_{\text{gear}}) \]
Where:
Length of Arc of Contact is the ratio of the length of the path of contact and the cosine of the pressure angle.
Let's assume the following values:
Using the formula:
\[ L = (0.0124 + 0.0102) \cdot \tan(0.55850536063808) \]
Evaluating:
\[ L = 0.0141220473531475 \text{ m} \]
The Length of Arc of Contact is 0.0141220473531475 m.
| Radius of Pitch Circle of Wheel (m) | Radius of Pitch Circle of Pinion (m) | Pressure Angle of Gear (rad) | Length of Arc of Contact (m) |
|---|---|---|---|
| 0.01 | 0.0102 | 0.55850536063808 | 0.012622360909 |
| 0.011 | 0.0102 | 0.55850536063808 | 0.013247230260 |
| 0.012 | 0.0102 | 0.55850536063808 | 0.013872099612 |
| 0.013 | 0.0102 | 0.55850536063808 | 0.014496968964 |
| 0.014 | 0.0102 | 0.55850536063808 | 0.015121838316 |
| 0.015 | 0.0102 | 0.55850536063808 | 0.015746707668 |
| 0.016 | 0.0102 | 0.55850536063808 | 0.016371577020 |
| 0.017 | 0.0102 | 0.55850536063808 | 0.016996446372 |
| 0.018 | 0.0102 | 0.55850536063808 | 0.017621315724 |
| 0.019 | 0.0102 | 0.55850536063808 | 0.018246185076 |