The formula to calculate the Minimum Number of Teeth on Pinion to Avoid Interference is:
\[ Z_{\text{min}} = \frac{2 \cdot A_w}{\sqrt{1 + \frac{Z_p}{T} \left( \frac{Z_p}{T} + 2 \right) \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1} \]
Where:
The minimum number of teeth on pinion is the count of teeth on pinion required to avoid interference.
Let's assume the following values:
Using the formula:
\[ Z_{\text{min}} = \frac{2 \cdot A_w}{\sqrt{1 + \frac{Z_p}{T} \left( \frac{Z_p}{T} + 2 \right) \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1} \]
Evaluating:
\[ Z_{\text{min}} = \frac{2 \cdot 0.0245}{\sqrt{1 + \frac{8}{12} \left( \frac{8}{12} + 2 \right) \left( \sin(0.55850536063808) \right)^2} - 1} \]
The Minimum Number of Teeth on Pinion is 0.218332145009355.
| Addendum of Wheel (m) | Number of Teeth on Pinion | Number of Teeth on Wheel | Pressure Angle (rad) | Minimum Number of Teeth on Pinion |
|---|---|---|---|---|
| 0.02 | 8 | 12 | 0.55850536063808 | 0.178230322457 |
| 0.022 | 8 | 12 | 0.55850536063808 | 0.196053354702 |
| 0.024 | 8 | 12 | 0.55850536063808 | 0.213876386948 |
| 0.026 | 8 | 12 | 0.55850536063808 | 0.231699419194 |
| 0.028 | 8 | 12 | 0.55850536063808 | 0.249522451439 |