Spiral bevel, hypoid and crossed helical gears

(a) Spiral bevel gears

• Bevel gears with curved, oblique teeth; the spiral angle is about 35 degrees.
• Teeth engage gradually, so contact is smooth, quiet and the contact ratio is higher than straight bevel gears.
• Stronger and can run at high speeds.
• Produce axial thrust, whose direction depends on spiral hand and rotation.
• Shafts intersect. Application: final drive of rear-wheel drive vehicles (older cars), machine tool gearboxes.

(b) Hypoid gears

• Similar to spiral bevel gears but the shaft axes are offset (do not intersect); pitch surfaces are hyperboloids.
• The pinion is larger and stronger than in a spiral bevel set of the same ratio, and can be mounted with bearings on both sides.
• There is sliding along the tooth length, so a special hypoid (EP) lubricant is needed.
• Application: automobile differential (propeller shaft is lowered, giving a lower floor).

(c) Crossed helical gears

• Two helical gears of any helix angle (and hand) on non-parallel, non-intersecting shafts. Shaft angle $\Sigma = \psi_1 + \psi_2$ (for like hand).
• Theoretically point contact, so only light loads can be carried; sliding velocity along the teeth is high.
• Velocity ratio $\dfrac{N_1}{N_2} = \dfrac{z_2}{z_1} = \dfrac{d_2\cos\psi_2}{d_1\cos\psi_1}$, so it depends on the pitch diameters too.
• Application: oil pumps, distributor drives, light instrument drives.