Worm Gear Formula Table

Gear Engineering and Design Data

Worm gears are grouped into two general classes, fine-pitch worm gearing, and coarse-pitch worm gearing.
1) Fine-pitch worms and worm gears are generally used to transmit motion (linear or rotary) as opposed to power or torque. Tooth strength except at the coarser end of the fine-pitch range is seldom an important factor; durability and accuracy, as they affect the transmission of uniform angular motion, are of greater importance.
2) Housing constructions and lubricating methods are, in general, quite different for fine pitch worm gearing.
3) Because fine-pitch worms and wormgears are so small, profile deviations and tooth bearings cannot be measured with the same accuracy as can those of coarse pitches.
4) Equipment generally available for cutting fine-pitch wormgears has restrictions which limit the diameter, the lead range, the degree of accuracy attainable, and the kind of tooth bearing obtainable.
5) Special consideration must be given to top lands in fine-pitch hardened worms and wormgear-cutting tools.
6) Interchangeability and high production are important factors in fine-pitch worm gearing; individual matching of the worm to the gear, as often practiced with coarse-pitch precision worms, is impractical in the case of fine-pitch worm drives

Worm Gear Formulae (Based On Diametral Pitch)

To Find
Rule
Formula
Worm Gear Pitch Diameter
Divide Number of Teeth by Diametral Pitch
Pitch Diameter = Number of Teeth in Worm Gear Diametral Pitch
Worm Gear Throat Diameter
Add 2 Addenda to Pitch Diameter
Throat Diameter = (2 x Addendum) + Pitch Diameter
Worm Gear Outside Diameter
Add 3 Addenda to Pitch Diameter
Outside Diameter = (3 x Addendum) + Pitch Diameter
Worm Pitch Diameter
Subtract the Worm Gear Pitch Diameter from Twice the Center Distance
Worm Pitch Diameter = (2 x Center Distance) -Worm Gear Pitch Diameter
Worm Outside Diameter
Add 2 Addenda to Worm Pitch Diameter
Worm Outside = Worm Pitch Diameter + 2 x AddendumDiameter
Worm Lead
Divide 3.1416 by Diametral Pitch and Multiply by Number of Threads in Worm
Worm Lead = 3.1416 x Number of Threads in WormDiametral Pitch
Co-Tangent of Worm Helix Angle
Multiply Worm Pitch Diameter by Diametral Pitch and Divide by Number of Worm Threads
Co-Tangent Worm = Worm Pitch Diameter x Diametral Pitch Helix Angle Number Worm Threads
Center Distance
Add Worm Pitch Diameter to Worm Gear Pitch Diameter and Divide Sum by 2
Center = Worm Pitch Diameter + Worm Gear Pitch Diameter Distance 2
Ratio
Divide Number of Teeth in Worm Gear by Number of Worm Threads
Ratio = Number of Teeth in Worm Gear Number of Worm Threads

NOTE: Tooth data (Addendum, Full Depth, Etc.) is same as for Spur Gears.

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