The formula to calculate the Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Wheels is:
\[ Z_{\text{min}} = \frac{2 \cdot A_w}{\frac{T}{Z_p} \left( \sqrt{1 + \frac{Z_p}{T} \left( \frac{Z_p}{T} + 2 \right) \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1 \right)} \]
Where:
The minimum number of teeth on pinion is the count of teeth on pinion required to avoid interference given the addendum of wheels.
Let's assume the following values:
Using the formula:
\[ Z_{\text{min}} = \frac{2 \cdot A_w}{\frac{T}{Z_p} \left( \sqrt{1 + \frac{Z_p}{T} \left( \frac{Z_p}{T} + 2 \right) \left( \sin(\Phi_{\text{gear}}) \right)^2} - 1 \right)} \]
Evaluating:
\[ Z_{\text{min}} = \frac{2 \cdot 0.0245}{\frac{12}{8} \left( \sqrt{1 + \frac{8}{12} \left( \frac{8}{12} + 2 \right) \left( \sin(0.55850536063808) \right)^2} - 1 \right)} \]
The Minimum Number of Teeth on Pinion is 0.14555476333957.
| Addendum of Wheel (m) | Number of Teeth on Wheel | Number of Teeth on Pinion | Pressure Angle (rad) | Minimum Number of Teeth on Pinion |
|---|---|---|---|---|
| 0.02 | 12 | 8 | 0.55850536063808 | 0.118820214971 |
| 0.022 | 12 | 8 | 0.55850536063808 | 0.130702236468 |
| 0.024 | 12 | 8 | 0.55850536063808 | 0.142584257965 |
| 0.026 | 12 | 8 | 0.55850536063808 | 0.154466279462 |
| 0.028 | 12 | 8 | 0.55850536063808 | 0.166348300960 |