Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth Calculator

Calculate Minimum Number of Teeth on Pinion





Formula

The formula to calculate the Minimum Number of Teeth on Pinion is:

\[ Z_p = \frac{2 \cdot A_p}{\sqrt{1 + 3 \cdot (\sin(\Phi_{\text{gear}}))^2} - 1} \]

Where:

Definition

Number of Teeth on Pinion is the count of teeth on the pinion gear to avoid interference when the pinion and wheel have equal teeth.

Example Calculation

Let's assume the following values:

Using the formula:

\[ Z_p = \frac{2 \cdot 0.0225}{\sqrt{1 + 3 \cdot (\sin(0.55850536063808))^2} - 1} \]

Evaluating:

\[ Z_p = 0.125921217683036 \]

The Minimum Number of Teeth on Pinion is 0.125921217683036.

Conversion Chart

Addendum of Pinion (m) Pressure Angle of Gear (rad) Number of Teeth on Pinion
0.02 0.55850536063808 0.111929971274
0.021 0.55850536063808 0.117526469838
0.022 0.55850536063808 0.123122968401
0.023 0.55850536063808 0.128719466965
0.024 0.55850536063808 0.134315965529
0.025 0.55850536063808 0.139912464092
0.026 0.55850536063808 0.145508962656
0.027 0.55850536063808 0.151105461220
0.028 0.55850536063808 0.156701959783
0.029 0.55850536063808 0.162298458347