GEOM internal single.xls

Calculates the geometry of an internal gear.

Calculation Reference

Machine Design

Calculating the geometry of an internal gear involves determining various parameters such as the pitch diameter, base diameter, addendum, dedendum, and outside diameter. You'll need the following input parameters:

• Module (m): The module is the ratio of the pitch diameter to the number of teeth. It should be the same for both the internal gear and its mating pinion to ensure proper meshing. The module is typically measured in millimeters per tooth (mm/tooth).
• Number of teeth (N): The number of teeth on the internal gear.
• Pressure angle (φ): The pressure angle is the angle between the line of action and the line tangent to the pitch circle at the point of tooth engagement. The pressure angle is typically 20° or 14.5° for most gears, but it can vary based on the application.

With these input parameters, you can calculate the geometry of the internal gear using the following formulas:

1. Pitch diameter (D): D = m * N

2. Base diameter (Db): Db = D * cos(φ)

3. Addendum (ha) and dedendum (hf): Addendum (ha) is the radial distance between the pitch circle and the tooth root. Dedendum (hf) is the radial distance between the pitch circle and the tooth tip. For standard gears, the addendum and dedendum are typically:

ha = m hf = 1.25 * m

4. Outside diameter (Do): Outside diameter of the internal gear (Do) = D - 2 * ha

5. Root diameter (Dr): Root diameter of the internal gear (Dr) = D - 2 * hf

These formulas will help you calculate the geometry of an internal gear. Make sure to use consistent units (e.g., millimeters) when performing the calculations.