Worm Gear – compact design

Worm gears are usually used when large speed reductions are needed. The reduction ratio is determined by the number of starts of the worm and number of teeth on the worm gear. But worm gears have sliding contact which is quiet but tends to produce heat and have relatively low transmission efficiency.

As for the materials for production, in general, worm is made of hard metal while the worm gear is made from relatively soft metal such as aluminum bronze. This is because the number of teeth on the worm gear is relatively high compared to worm with its number of starts being usually 1 to 4, by reducing the worm gear hardness, the friction on the worm teeth is reduced. Another characteristic of worm manufacturing is the need of specialized machine for gear cutting and tooth grinding of worms. The worm gear, on the other hand, may be made with the hobbing machine used for spur gears. But because of the different tooth shape, it is not possible to cut several gears at once by stacking the gear blanks as can be done with spur gears.

The applications for worm gears include gear boxes, fishing pole reels, guitar string tuning pegs, and where a delicate speed adjustment by utilizing a large speed reduction is needed. While you can rotate the worm gear by worm, it is usually not possible to rotate worm by using the worm gear. This is called the self locking feature. The self locking feature cannot always be assured and a separate method is recommended for true positive reverse prevention.

Also there exists duplex worm gear type. When using these, it is possible to adjust backlash, as when the teeth wear necessitates backlash adjustment, without requiring a change in the center distance. There are not too many manufacturers who can produce this type of worm.

The worm gear is more commonly called worm wheel in Japan.

Related links :
“Raw Material” and “Gear Precision Grade” Equivalent Tables
The ABC’s of Gears / Basic Guide – B
Introduction to Gears
Gear Technical Reference
蜗杆蜗轮 – 中文页

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Table of Worm and Worm Gear Combinations

Please click on the diagram below. You can confirm the combinations of the KHK’s standard worms and worm gears in an enlarged table.

worm gear selection 2

Number of Threads in Worms

The number of threads in a worm is the number of teeth in a worm.

The speed transmission ratio of a worm and worm gear set is obtained by dividing the number of teeth of the worm gear by the number of threads of the worm.

When the number of threads of a worm is one, as the worm shaft rotates once, the worm gear advances one tooth, while when the number of threads of a worm is 2, the worm gear moves just two teeth. This indicates that a set of worm-worm gear can achieve great speed reduction in one step. By the way, when there are more than two threads in a worm, it is called multi-thread worm.

The photo below on the left shows SW2-R1, KHK’s standard worm, while the right photo shows SW2-R2. The number of threads of SW2-R1 is one (red line) and that of SW2-R2 is two (red and blue lines). For the two, the advancing angle of the teeth are also different.

worm 1 start 3

worm 2 starts

When the number of threads of a worm changes, so does the mating worm gear. In the case of KHK standard gears, double threaded SW2-R2, for example, cannot be used with CG2-50R1 which should be matched to a single thread worm. Also, as a set of worm gears, there are right hand and left hand threads
so that, for example, right hand thread worm and left hand thread worm gear cannot be used together.

By the way, the single thread combination below yields a speed reduction ratio of 50, while the double thread combination produces a speed reduction ratio of 25.

worm gear speed reduction 1

worm gear speed reduction 2

Duplex Worm Gear to adjust backlash

The objectives, characteristics and how to use duplex worm gears is briefly listed below.

In order to adjust worm gear backlash or to reduce the increased backlash due to wear, it is very difficult to change the center distance between the worm gear and worm without a possible major design modification. The duplex worm gear was designed to address this problem and it is suitable in applications where a small backlash high precision is needed. In this system, the worm gear side has the same tooth thickness around the circumference as other cylindrical gears, but on the worm side, different leads are used for the opposite tooth face leading to continuously changing tooth thickness. After the center distance is fixed, the actual adjustment of backlash is done by moving the worm axially with shims or screws. KHK’s standard duplex worm gears are designed to change the backlash by 0.02mm when the worm is moved axially by 1mm. In all cases, we do not recommend zero backlash since it is necessary to maintain a certain level of backlash in order to prevent the disruption of oil film.

Principle of Self-Locking Feature of Worm Gears

Self-locking means it is not possible to drive the worm using the worm wheel, and this feature is used in such things as reversing prevention systems and roll-up mechanisms.

A worm gear’s self-locking tendency increases as the lead angle decreases (It becomes easier to self-lock).
As the lead angle gets larger, it becomes less self-locking.

lead angle of worm

Number of threads of worm

If worms’ modules and pitch diameters are the same, the lead angle becomes larger as the number of threads increases, that is, it is easier to self-lock when the number of threads is smaller.

3 kinds of worms

Pitch diameter of worm

If worms’ modules and numbers of threads are the same, the lead angle becomes smaller as the pitch diameter gets larger, that is, it is easier to self-lock when the pitch diameter is larger.

difference of pcd of worms

When the lead angle is amall

Because the force shown in the red arrow is small, the turning force < coefficient of friction, and self-locking occurs.

small lead angle of worm

When the  lead angle is large

Because the force shown in the red arrow is large, the turning force > coefficient of friction, there is no self-locking.

big lead angle of worm


Ball screws have small coefficient of friction due to the rolling contact at the screw.
Even though the force shown in the red arrow is small, the turning force > coefficient of friction, and there is no self-locking.

other example of worm

Problem areas of Self-Locking

Because it is relying on the coefficient of friction, self-locking lacks stability.

  • Even with the same lead angle, it is difficult to self-lock with materials which have small coefficients of friction (μ)
    Example :
    Material Combination / Coefficient of Friction
    iron and iron / about 0.3
    Material Combination / Coefficient of Friction
    iron and aluminum bronze / about 0.2
    Material Combination / Coefficient of Friction
    iron and phosphor bronze / about 0.15
  • Coefficient of friction changes with speed
    When stationary, the static friction is high, but as the speed increases, it becomes dynamic friction, and the coefficient of friction decreases. When there is vibration, it is possible to reverse rotate.
  • Coefficient of friction is smaller when the surface roughness is low
    It is difficult to self-lock with ground worms.