Minimum Number of Teeth on Pinion to Avoid Interference Calculator

Calculate Minimum Number of Teeth on Pinion to Avoid Interference









Formula

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:

Definition

The minimum number of teeth on pinion is the count of teeth on pinion required to avoid interference.

Example Calculation

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.

Conversion Chart

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