Addendum of Pinion Calculator

Formula

The formula to calculate the Addendum of Pinion is:

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

Where:

\(A_p\) is the Addendum of Pinion (m)
\(Z_p\) is the Number of Teeth on Pinion
\(T\) is the Number of Teeth on Wheel
\(\Phi_{\text{gear}}\) is the Pressure Angle of Gear (rad)

Definition

Addendum of pinion is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line.

Example Calculation

Let's assume the following values:

Number of Teeth on Pinion (\(Z_p\)) = 8
Number of Teeth on Wheel (\(T\)) = 12
Pressure Angle of Gear (\(\Phi_{\text{gear}}\)) = 0.55850536063808 rad

Using the formula:

\[ A_p = \frac{8}{2} \left( \sqrt{1 + \frac{12}{8} \left( \frac{12}{8} + 2 \right) \left( \sin(0.55850536063808) \right)^2} - 1 \right) \]

Evaluating:

\[ A_p = 2.29193228148959 \text{ m} \]

The Addendum of Pinion is 2.29193228148959 m.

Conversion Chart

Number of Teeth on Pinion	Number of Teeth on Wheel	Pressure Angle of Gear (rad)	Addendum of Pinion (m)
6	12	0.55850536063808	2.405426783852
7	12	0.55850536063808	2.344101750930
8	12	0.55850536063808	2.291932281490
9	12	0.55850536063808	2.247095552494
10	12	0.55850536063808	2.208202616056