The formula to calculate the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion is:
\[ Z_p = \frac{2 \cdot A_p}{\sqrt{1 + G \cdot (G + 2) \cdot \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1} \]
Where:
The minimum number of teeth on pinion is the count of teeth on pinion required to avoid interference given the addendum of pinion.
Let's assume the following values:
Using the formula:
\[ Z_p = \frac{2 \cdot A_p}{\sqrt{1 + G \cdot (G + 2) \cdot \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1} \]
Evaluating:
\[ Z_p = \frac{2 \cdot 0.0225}{\sqrt{1 + 3 \cdot (3 + 2) \cdot \left( \sin(0.55850536063808) \right)^2} - 1} \]
The Minimum Number of Teeth on Pinion is 0.0350732824648497.
| Addendum of Pinion (m) | Gear Ratio | Pressure Angle (rad) | Minimum Number of Teeth on Pinion |
|---|---|---|---|
| 0.02 | 3 | 0.55850536063808 | 0.031176251080 |
| 0.022 | 3 | 0.55850536063808 | 0.034293876188 |
| 0.024 | 3 | 0.55850536063808 | 0.037411501296 |
| 0.026 | 3 | 0.55850536063808 | 0.040529126404 |
| 0.028 | 3 | 0.55850536063808 | 0.043646751512 |