Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Calculator

Calculate Minimum Teeth on Pinion to Avoid Interference









Formula

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:

Definition

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

Example Calculation

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.

Conversion Chart

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