This calculator determines bevel gear and pinion parameters for a 90-degree angle between the gears.
Formulas:
Pitch Diameter: \( D = \frac{N}{P} \)
Whole Depth: \( H_t = \frac{2.188}{P} + 0.002 \)
Addendum: \( a = \frac{1}{P} \)
Dedendum: \( b = H_t - a \)
Clearance: \( c = H_t - 2a \)
Circular Tooth Thickness: \( T = \frac{\pi}{2P} \)
Pitch Angle: \( L_p = \tan^{-1} \left( \frac{N_p}{N_g} \right) \), \( L_g = \tan^{-1} \left( \frac{N_g}{N_p} \right) \)
Pitch Cone Radius: \( R_{cp} = \frac{D}{2 \sin(L_p)} \), \( R_{cg} = \frac{D}{2 \sin(L_g)} \)
Face Width: \( F = \min \left( \frac{C}{3}, \frac{8}{P} \right) \)
Outside Diameter: \( D_{op} = D_p + 2a \cos(L_p) \), \( D_{og} = D_g + 2a \cos(L_g) \)
Back Cone Radius: \( R_{bp} = \frac{D_p}{\cos(L_p)} \), \( R_{bg} = \frac{D_g}{\cos(L_g)} \)
Virtual Number of Teeth: \( V_p = \frac{N}{\cos(L_p)} \), \( V_g = \frac{N}{\cos(L_g)} \)