Worm gears – geometry and nomenclature

a. The worm is similar geometry of power screw. Rotation of the worm simulates involute rack linear ones.

b. The geometry of worm gear similar to that of helical gear, except that the curved teeth to envelop the worm.

c. Enveloping the appliance provides more contact area but requires extremely precise mounting.

1. As a spur or helical gear, pitch diameter of the worm gear associated with circular pitch and number of teeth Z by the formula.


2. When the angle 90 between nonintersecting shafts, the lead angle a worm equal to the helix angle gear.   angles and have the same hand.

3. The pitch diameter of the worm a function of the number of threads, Z1.

4. This means that the velocity ratio worm gear set is determined by the ratio of worm gear teeth to threads; It is not equal to the ratio of the worm gear and diameters.


5. The worm gear is usually at least 24 teeth, and should the number of threads plus worm gear teeth to be more than 40:


6. worm can any pitch diameter with any number of threads and no axial pitch.

7. For maximum power transmission capability, should the pitch diameter of the worm usually associated with the middle distance shaft to the following equation


8. Integral worms can cut directly on the shaft, of course, have a diameter less than that of worms shell, made separately.

9. Shell worms bored to slip over the shaft and are driven by splines, key, or pin.

10. Strength considerations rarely allowed worm shell with a diameter smaller than


11 pitch width should not face the appliance more than half the worm outside diameter.


12. Lead angle λ, Lead L, and worm pitch diameter d1 is the following relationship with respect to the screw threads.


13. to avoid interference, pressure angles commonly associated with the worm lead angle as shown.

Maximum lead angle worm and worm gear Lewis form factor for various pressure angles:

worm gear Lewis

Frequently used standard values ​​of module and axial pitch of worm or circular pitch of pi gear mm:

axial pitch of worm