bevelgearparams-1754663655

Bevel Gear Parameters

Calculating bevel gear parameters for GearLab.

Nomenclature

• ${\theta }_p^g$ is the Gear pitch angle
• ${\theta }_p^p$ is the Pinion pitch angle
• ${\theta }_s$ is the Shaft angle
• $z$ is the Gear ratio
• $z^g$ is the Gear teeth
• $z^p$ is the Pinion teeth
• ${\theta }_f$ is the Face angle
• ${\theta }_r$ is the Root angle
• $d_f$ is the face cone offset
• $d_r$ is the root cone offset
• $a$ is the addendum
• $d$ is the dedendum
• $d_i$ is the inner pitch diameter
• $d_o$ is the outer pitch diameter
• $L$ is the pitch cone distance

Basic parameters

Pitch angles

$$\begin{gathered} z=z_p/z_g \\ {\theta }_p^g=\arctan (\sin ({\theta }_s)/z) \\ {\theta }_p^p={\theta }_s-{\theta }_p^g \end{gathered}$$

Pinion face and root angles

$$\begin{gathered} {\theta }_f^p={\theta }_s-{\theta }_r^g \\ {\theta }_r^p={\theta }_s-{\theta }_f^g \end{gathered}$$

Addendum and dedendum

By using the law of sines on the extensions of face, pitch and root angles, we can obtain the addendum and dedendum.

$$\begin{gathered} a^{g,p}=d_f^{g,p}\cdot \frac{\sin \left({\theta }_f^{g,p}\right)}{\cos \left({\theta }_f^{g,p}-{\theta }_p^{g,p}\right)}+L\tan \left({\theta }_f^{g,p}-{\theta }_p^{g,p}\right) \\ {d}^{g,p}=d_r^{g,p}\cdot \frac{\sin \left({\theta }_r^{g,p}\right)}{\cos \left({\theta }_p^{g,p}-{\theta }_r^{g,p}\right)}+L\tan \left({\theta }_p^{g,p}-{\theta }_r^{g,p}\right) \end{gathered}$$