The formula to calculate the Length of Path of Approach is:
\[ P1 = \sqrt{RA^2 - R_{wheel}^2 \cdot (\cos(\Phi_{gear}))^2} - R_{wheel} \cdot \sin(\Phi_{gear}) \]
Where:
Path of approach is the portion of the path of contact from the beginning of contact to the pitch point.
Let's assume the following values:
Using the formula:
\[ P1 = \sqrt{0.022^2 - 0.0124^2 \cdot (\cos(0.55850536063808))^2} - 0.0124 \cdot \sin(0.55850536063808) \]
Evaluating:
\[ P1 = 0.0127530282978548 \text{ m} \]
The Length of Path of Approach is 0.0127530282978548 meters.
| Radius of Addendum Circle of Wheel (m) | Radius of Pitch Circle of Wheel (m) | Pressure Angle of Gear (rad) | Path of Approach (m) |
|---|---|---|---|
| 0.02 | 0.0124 | 0.55850536063808 | 0.010441291570 |
| 0.021 | 0.0124 | 0.55850536063808 | 0.011606405400 |
| 0.022 | 0.0124 | 0.55850536063808 | 0.012753028298 |
| 0.023 | 0.0124 | 0.55850536063808 | 0.013884270035 |
| 0.024 | 0.0124 | 0.55850536063808 | 0.015002550350 |
| 0.025 | 0.0124 | 0.55850536063808 | 0.016109786521 |
| 0.026 | 0.0124 | 0.55850536063808 | 0.017207521394 |
| 0.027 | 0.0124 | 0.55850536063808 | 0.018297013232 |
| 0.028 | 0.0124 | 0.55850536063808 | 0.019379300279 |
| 0.029 | 0.0124 | 0.55850536063808 | 0.020455248111 |