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.

button of gear selector

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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

 What are Worm Gears ?

This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.

Worm gear is one type of gear device in which the two shafts are at a right angle or near right angle and non-intersecting. There are one or more teeth which are screw shaped, resulting in a gear that looks like a worm. The mating gear is called a worm wheel; together they are called worm and worm wheel or simply worm gear (worm gear device). As shown in Figure 6.1, a high ratio speed reduction in a small space can be obtained compared to spur gears. Therefore when a large speed reduction is desired in one quick stroke, it is common practice to use the worm as the prime mover. However, on rare occasions, the worm wheel is used as the prime mover in a speed increasing application.

Comparison of Sizes between Worm Gear and Spur Gear
Figure 6.1  Comparison of Sizes between Worm Gear and Spur Gear
1. Reduction ratio 1 : 126
2. 1512 teeth / 40’ diameter
3. 12 teeth / 4’ diameter

Origin of Worm Gears

In the case of when two axes are non-intersecting, consider a pair of screw gears in which the pinion gear teeth have been reduced to one or few teeth. Then the pinion becomes the shape of an ordinary screw and a large speed reduction can be obtained as shown in Figure 6.2(a). At this point, the meshing is point contact and can carry only a small load and tends to create friction. However, by using a hob cutter in the shape of the pinion and rotating the cutter equivalent to the motion of worm against the worm wheel, it is possible to obtain a gear set with a line contact. This is the usual worm gear shown in Figure 6.2(b) where the small gear is the worm and the larger gear is the worm wheel.

types of worm gears
Figure 6.2  Types of Worm Gears
(Left) Cylindrical Worm and Helical Gear
(Center) Cylindrical Worm and Worm Wheel
(Right) Hourglass Shape Worm and Worm Wheel

Since the two shafts are normally at a right angle, the rest of discussion will focus on this configuration. The tooth surface of the above worm gear is the worm’s enveloping surface. However, if we consider the cross section perpendicular to the worm wheel shaft, it becomes the rack and pinion mesh in which the tooth surface of the worm is the rack and the tooth surface of the worm wheel is the pinion. The cross section normal to the worm wheel shaft including the worm shaft is called the central cross section. This surface is the boundary between the worm’s advancing side and receding side. As shown in Figure 6.3, the contact situation between them is considerably different.

The common tangent at an arbitrary point on the contact line on both surfaces of the worm wheel always passes through the contact point (pitch point) of the two pitch cylinders and intersects the line parallel to the worm wheel shaft (pitch line, P1P2, in Figure 6.4).

There are many tooth forms for worms, but for the convenience of production, the line weave twist surface or approximation of the line weave twist surface is often used. It is normally the trapezoid based on the central cross section, cross section perpendicular to tooth or normal to the root cross section. However, there are others such as involute worms using involute helicoids and convolute worms using a straight line that intersects the involute worm generating line as its generating line.

Comparison of Meshing Conditions of Central Cross Section of Both Sides (Worm’s Advancing Side and Receding Side) (the Left Tooth Surface of the Worm is the Acting Surface)
1. Advancing Side
2. Receding Side
3. Advancing Side
4. Receding Side

Comparison of Meshing Conditions of Central Cross Section of Both Sides (Worm’s Advancing Side and Receding Side) (the Left Tooth Surface of the Worm is the Acting Surface)
1. Advancing Side

Comparison of Meshing Conditions of Central Cross Section of Both Sides (Worm’s Advancing Side and Receding Side) (the Left Tooth Surface of the Worm is the Acting Surface)
1. Receding Side

Figure 6.3  Comparison of Meshing Conditions of Central Cross Section of Both Sides (Worm’s Advancing Side and Receding Side) (the Left Tooth Surface of the Worm is the Acting Surface)

In order to increase the load carrying capacity, sometimes different tooth shape worms are used such as when the central cross section is a circular arc or various secondary curves. Consider each cross section parallel to the central cross section, and the pitch point as the boundary, the receding arc is a smoother mesh than the advancing arc, as in spur gear meshes. Therefore, there are times when the worm is negatively shifted (make worm’s addendum larger and dedendum smaller) so that the majority of the mesh is on the receding arc (Figure 6.5). In particular, if the worm is to be all addendum, it is desirable to have the sum of the number of teeth of both gears to be greater than 40.

The Shafts of Worm (I) and Worm Wheel (II) and the Pitch Line P1P2
Figure 6.4  The Shafts of Worm (I) and Worm Wheel (II) and the Pitch Line P1P2

Comparison of Non profile Shifted vs. Profile Shifted Worm Gear
Figure 6.5  Comparison of Non-profile Shifted vs. Profile Shifted Worm Gear
1. Pitch surface
2. Pitch surface
3. Central cross section
4. Pitch generating line
5. Pitch winding line
6. Receding side arc
7. Advancing side arc
8. Rotation of worm
9. Plan view of contact line on worm
10. Meshing area
11. Start
12. End

The lead on the right and left tooth surfaces of worms are normally the same. If it is varied as shown in Figure 6.6 so that the worm’s tooth thickness gradually changes in the shaft direction, then it is possible to adjust the backlash by moving the worm in the direction of its shaft. This is called the dual lead worm gear (duplex worm gear) and it is used to accurately eliminate the play in, for example, the hobbing machine’s main worm gear.

Figure 6.6   Dual Lead Worm Gear

Dual Lead Worm Gear
(a) Dual Lead Worm Gear
Central Cross Section of Dual Lead Worm Gear
(b) Central Cross Section of Dual Lead Worm Gear
1. Maximum adjustment amount ≈ ta
2. Direction of adjustment

Worm Manufacturing

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.

SW2-R1
worm 1 start 3

SW2-R2
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

Others

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.

 

Hourglass worm gear

This article is reproduced with the permission.
Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963.

There are special types of worm gear, whose pitch surface is gained by rotating arc which fits the part close to the worm of pitch circle around worm shaft in central section (see Pic 6.2(c)), providing teeth profile of worm gear in central section, making dedendum using the cutter appropriate for the teeth profile, then making teeth of worm gear with the hob whose teeth profile is same as the dedendum, or providing dedendum of worm gear and making worm using the cutter appropriate for the dedendum. Hindley worm and cone worm correspond to the former and have straight-line teeth profile in central section as in Pic 6.9, while plane worm gear corresponds to the latter and uses plain surface as the dedendum of worm gear. Some worm gears use involute helical gear. Such type of worm gear usually meshes near the central section (as for Hindley worm, all the teeth of the worm are constantly in line contact in central section) and has larger loading capability, but needs to be assembled precisely.

Hindley worm
Pic 6.9 Hindley worm