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Worm Gear Drives With Adjustable Backlash
Article in Journal of Mechanisms and Robotics · August 2015
DOI: 10.1115/1.4030164
3 authors:
Wojciech Kacalak
Maciej Majewski
Koszalin University of Technology
Koszalin University of Technology
Zbigniew Budniak
Koszalin University of Technology
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Worm Gear Drives With Adjustable
Wojciech Kacalak
Faculty of Mechanical Engineering,
Koszalin University of Technology,
Koszalin 75-620, Poland
e-mail: [email protected]
Maciej Majewski1
Associate Professor
Faculty of Mechanical Engineering,
Koszalin University of Technology,
Koszalin 75-620, Poland
e-mail: [email protected]
2 The Known Constructional Ways of Backlash
Even the most accurate conventional gear-based drives do not
provide nonbacklash operation, due to manufacturing imperfections of its elements [10], installation inaccuracy [2,9], operating
conditions, or degradation over time. Drive’s elements’ geometrical imperfection comprises dimensional inaccuracy and shape distortions. Backlash, which is a defect of precise machinery and
devices systems increases along with abrasion of interacting
Zbigniew Budniak
Assistant Professor
Faculty of Mechanical Engineering,
Koszalin University of Technology,
Koszalin 75-620, Poland
e-mail: [email protected]
This article presents the design of patented worm gear drives,
which allow backlash adjustment or elimination by using specially
designed worms and worm wheels. Many of the presented solutions allow backlash adjustment without disassembling the drive.
The proposed solutions allow reduction of both backlash and its
standard deviation to as little as 7.5% and 5% of their initial values, respectively. The presented solutions are a good alternative
to harmonic drives and conventional precise drives, which are
currently in use. The presented drives can successfully find their
application in mechanisms for precise positioning of test benches,
as well as in precise technological equipment, technological
instrumentation, and in the case of miniaturization—in mechanisms resistant to severe working conditions.
[DOI: 10.1115/1.4030164]
When it comes to linear or angular alignment systems, the automotive and machine-tool industries, robotics, automation systems,
and other applications, it is demanded that their mechanisms are
nonbacklash [1–6]. The carried out research shows that backlash
is nonlinear and is present in every mechanical system [7,8].
There are many factors impacting meshing and circumferential
backlash of a worm gear drive. These can be divided into two
groups. The first one are factors related to the spatial, mutual position of interacting components [2,9]. These factors have the most
substantial impact on meshing and, for the most part, on circumferential backlash. The other group are factors related to a worm
gear drive components’ manufacturing accuracy [2,10]. These
have impact on the pressure values [11], the condition of surfaces,
the directions and values of the friction forces between the worm
and the worm wheel [1]. Understanding of the impact of some of
the factors on meshing [1,7,10], e.g., the line of action [9], the
teeth contact line [12], the teeth surface’s topography, the estimated durability of a worm gear drive [13] may lead to aware
Corresponding author.
Manuscript received November 18, 2014; final manuscript received March 15,
2015; published online August 18, 2015. Assoc. Editor: James Schmiedeler.
Journal of Mechanisms and Robotics
modification and optimization of worm gear drives [1] in order to
improve their operating parameters.
Backlash adjustment mechanisms for conventional drives are
quite complex, and therefore expensive. Such complex backlash
adjustment mechanisms are also present in worm gear drives;
however, simpler solutions for backlash elimination are available
as well. The solution most commonly discussed in publications is
a drive with a double-lead worm [1]. Some other solutions are
also mentioned: worm gear drive with a split worm wheel [14] or
with a conical worm or a nonbacklash double-roller enveloping
hourglass worm gear [8]. Scientific publications are usually
descriptions of phenomena connected with the typical worm gear
drives or the technological ways of backlash adjustment.
This article presents new types of worm gear drives, the construction of which allows reduction or elimination of backlash.
Their advantages and disadvantages related to operation and durability have been identified.
2.1 Worm Gear Drive With a Double-Lead Worm. One of
the most common design approaches—aiming at worm gear drive
backlash reduction—is to substitute the conventional worm with a
double-lead worm. Drives with double-lead worms are used in
indexing tables and also as dividing heads in lathes. As a result of
implementation of two different pitch values of both sides of the
thread, the worm’s teeth thickness is variable. The difference
between thicknesses of teeth is linear and depends on the pitch
difference of both helical surfaces [1].
Another result of using two different pitch values in doublelead worms is that each tooth’s profile differs between its sides.
For this reason, in the case of double-lead worms it is advised to
use different profile angles, so that teeth’s working surface is not
limited on one side, which also helps avoid shortening of worm
wheel’s teeth [15].
A disadvantage of such drives is the necessity for the worm to
have considerable axial travel in order to reduce small backlash.
This can result in drive’s increased size. Such a worm gear drive
has a decreased contact area, which reduces its load ability or
causes quick degradation under high load [1]. In addition, for each
full turn of the worm wheel, there is only one nonbacklash position. Other positions have backlash, the amount of which depends
on the pitch difference between both sides of the worm’s thread.
2.2 Worm Gear Drive With a Split Worm Wheel. It is a
solution comprising a worm wheel split with a symmetry plane
perpendicular to the shaft’s axis. As a result, it consists of two
symmetrical parts mounted on one hub. The width of teeth can be
increased with angular displacement of the parts [14]. The width
increase causes reduction of backlash of the meshing teeth. Backlash elimination may be carried out automatically, periodically, or
by using elastic elements. Periodical adjustment is the most
difficult one to carry out and, moreover, it requires the drive to be
partially disassembled or to use removable covers facilitating
adjustment components access.
Unfortunately, the disadvantages of this solution are low load
ability and poor durability of the drive, which are caused by discontinuity of the worm wheel teeth’s profile. It means that the
worm wheel rim’s width is meshed only half-width, which is the
fundamental constraint in application of such drives. It is
C 2016 by ASME
Copyright V
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Fig. 1 The designed adaptive worm wheel solutions: (a) with
cut-outs and (b) with a joining wall
Fig. 2 The design of a worm wheel with its rim split with a circumferential cut-out: (a) bare worm wheel and (b) fully
assembled worm wheel
technologically quite difficult to manufacture such a worm wheel,
due to the necessity of maintaining high accuracy of that process
for both of its halves. The advantages of this solution are compactness and its ability to bear varying loads. The angle of a worm
wheel’s teeth profile can be slightly decreased in order to lower
the disadvantageous impact of the aforementioned discontinuity.
New Worm Gear Drive Design Ideas
3.1 Worm Gear Drive With an Adaptive Worm
Wheel. One of the solutions, which uses a modified worm wheel
is a drive described in the patent [16]. Its distinctive feature is a
worm wheel with deep, concentric to the hub hole, annular cutouts in its side areas (Fig. 1(a)). Their depth is greater than half of
the wheel’s width, and so their diameters are different and when
looked at in a cross section, they look like two oppositely situated
cut-outs. The aim of such a modification is to introduce a diametrical and axial adaptivity of the worm wheel’s rim.
Such an adaptivity can be also achieved by using two components to make a worm wheel—a rim and a hub—and joining them
together with a thin wall (Fig. 1(b)). The wall should have at least
one wavy bending, concentric to the wheel’s rim [16]. One of the
difficulties related to this solution is achieving concentricity of the
rim and hub during the process of manufacturing such a worm
3.2 Worm Gear Drive With a Worm Wheel’s Rim Split
With a Circumferential Cut-Out. In a nonbacklash worm gear
drive [17], worm wheel’s rim is split symmetrically with a circumferential cut-out, deep enough to reach the narrowing’s
smaller diameter. As a result, the width of the rim is split into two
equal parts, which can be brought closer together by applying
pressure onto the rim with an annular pressing element. One of
the solutions—described in the aforementioned patent—is that the
pressing element has the shape of an annular screw plug, and it is
mounted on the threaded surface of the worm wheel’s hub (Fig.
2(a)). The advantages of this solution are easy both manufacturing
and backlash adjustment. Figure 2 presents a solid model of this
Bringing the worm wheel’s halves closer together leads to a
decrease of backlash and also causes the meshing zone to move
toward the vertices of the worm wheel’s teeth. This can be taken
into account during the design stage, by decreasing tilt angle of
the teeth by the value appropriate to the chosen range of adjustment. However, this solution entails a disadvantage being the
result of the worm wheel adaptive tooth’s discontinuity [18].
The authors have designed a more effective solution, where one
part of the worm wheel has an adaptive rim (Fig. 3). Its deformation (adaptation) is achieved with a pressure disk, which has a
conical pressure surface with advantageously adaptive working
Fig. 3 The design of a worm wheel, one part of which has an adaptive rim: 1—rim, 2—worm
wheel’s circumferential cut-out, 3—circumferential narrowing of the worm wheel’s cross
section, 4—narrowing concentric to the worm wheel’s shaft hole, 5—pressure element,
6—worm wheel’s hub, 7—a screw, 8—a nut, 9—pressure ring’s circumferential cut-out,
10—conical pressure area, and 11—a washer
014504-2 / Vol. 8, FEBRUARY 2016
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Fig. 4 The design of a worm gear drive with worm wheel’s teeth situated on a thin-walled
sleeve: 1—teeth, 2—shaft, 3—thin-walled sleeve, 4—bearing, 5—worm, 6—thin-walled
sleeve’s bottom wall, 7—collar, 8—case, 9—eccentric pressure mechanism, 10—screw,
11—circumferentially prolonged holes, and 12—hook spanner hole [18]
3.3 Worm Gear Drive With Its Worm Wheel’s Rim
Situated on a Thin-Walled Sleeve. Another solution of backlash
reduction is to situate the worm wheel’s teeth on a thin-walled
sleeve. This can be done in a variety of ways [19–22].
Figures 4 and 5 show a worm gear drive with adjustable backlash characterized by a worm wheel—with an elastic thin-walled
sleeve—joined to a driven shaft. It is equipped with an adjustable
eccentric pressure mechanism, which allows to displace the driven
shaft’s axis along with the thin-walled sleeve and the wormwheel’s teeth perpendicularly to the worm’s axis. As a result of
the adjustable displacement of the entire unit along with the worm
wheel’s teeth, the worm wheel comes closer to the worm’s axis
and circumferential backlash is continuously reduced until the
worm wheel teeth’s surface circumferentially rests on the worm’s
teeth [18,19].
Continuously bringing the interacting elements closer causes
elastic deformation of the thin-walled sleeve and an increase of
surface pressure of teeth proportional to the stress of the sleeve,
Fig. 5 A photorealistic rendering of the worm gear drive with
worm wheel’s teeth situated on a thin-walled sleeve [18]
Journal of Mechanisms and Robotics
which allow to fully reduce the backlash. One of the disadvantages of this type of drive is the requirement that the worm wheel
be of the shape of a thin-walled sleeve, which results in the drive’s
increased size.
3.4 Worm Gear Drive With a Locally Axially Adaptive
Worm. Another solution with a modified worm is a nonbacklash
worm gear drive [23] presented in Figs. 6 and 7. Worm with an
advantageous cone-derived helical surface can be abraded with an
abrasive disk characterized by a working surface consisting of
straight lines in an axial cross section. The worm has an axial hole
with the diameter equal to or slightly larger than the diameter of
the tooth space’s bottom. The most important element of this solution is the cut between the threads along the helical line present
only in the middle part of the worm. The helical cut can be produced using an end mill with the diameter smaller than the width
of the of the tooth space, or with an erosion-based metalworking,
such as using a laser. As a result, the worm—in its middle part—
becomes a type of a spring with fixed endings, and characterized
by high axial stiffness. The cut results in the worm being locally
adaptive in the axial direction and it can be compressed or
expanded. Such a worm is slidable, it is situated on an arbor, and
it has one of its ends axially fixed in place and it is secured against
rotation around the arbor. This allows the other (loose) end’s position to be altered with a shift adjustment mechanism.
This mechanism impacts the coreless part of the worm. Compressing the worm results in a change of pitch, thereby impacting
the amount of backlash. The length of the worm’s part with its
tooth space’s bottom cut along the helical line depends on the
length of the meshing area as well as the working conditions and
it has to be shorter than the length of the threaded part of the
worm [18].
The advantage of such a solution is the ease of backlash adjustment, which can be done even when the drive is in operation. It
has good lubricating conditions in the meshing area between the
sides of teeth being under load, regardless of the direction in
which the drive is working. The adaptivity of the coreless part of
the worm (Figs. 6 and 7) has positive impact on reduction of
dynamical excess and also helps suppress vibrations. The latter
can be also impacted by the introduction of an elastic material
into the cut between the threads.
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Fig. 6 The design of the worm gear drive with a locally axially adaptive worm: 1—worm, 2—
worm wheel’s rim, 3—arbor, 4—pressure nut, 5—housing, 6—fitted worm situation surface,
7—screw cuts, and 8—worm wheel
The disadvantage of this solution is the limited maximal torque
it can transfer for the chosen requirements regarding its kinematic
accuracy when under load. However, by choosing appropriate
structural parameters of the worm, a sufficiently high maximal
torque value can be made possible.
In order to improve the working properties of such a drive, a
modification to the worm teeth’s profile is introduced [18]. The
radius of the teeth side curvature is decreased, which causes them
to be more protruding (Fig. 8(a)). The worm tooth outline’s curvature can be increased using a grinding wheel of an appropriate
diameter or one with a modified outline. It performs rotary motion
at the peripheral speed of vs (Fig. 8(b)). The worm rotates at the
peripheral speed of vw, which is combined with the axial feed rate
fa. The worm outline’s curvature also depends on the angle, at
which the grinding wheel’s axis is set, which usually corresponds
to the angle of the helical line’s lift in the tooth reference cylinder.
Such a modification reduces local shifts of the actual area of
The initial compression of the worm, causing a decrease of its
axial pitch, does not increase pressure forces in the meshing zone
until backlash is reduced to zero (in one of the worm and worm
wheel’s possible positions). Further compression is not advised,
as it would lead to increased pressing forces, due to excessive
pitch decrease. Only during the initial breaking-in phase it is an
acceptable practice to use increased axial compression of the
In yet another solution [24], which aims at reducing the possibility of one of the worm’s ends excessive axial travel, which
would result in too great pitch shortening in the middle part, an
option of radial deformation in that area was introduced. It is the
result of situating the worm on an arbor, which in its middle part
has a slightly shorter diameter (Figs. 6 and 7).
4 Research on the Worm Gear Drive With a Locally
Axially Adaptive Worm
4.1 Analysis of Changes of Drive’s Teeth Meshing
Resulting From the Introduction of Pitch Adjustment. The
necessary quantities for the determination of a drive’s backlash
Fig. 7 A photorealistic rendering of the worm gear drive with a
locally axially adaptive worm
014504-4 / Vol. 8, FEBRUARY 2016
Fig. 8 The modified outline of the locally axially adaptive
worm’s tooth, where Rc—the tooth curvature’s radius, Rm—the
modified curvature radius, R 5 Rc or R 5 Rm, Rm < Rc, vs—
peripheral speed of the grinding wheel, vw—peripheral speed of
the workpiece (of the worm), and fa—axial feed rate of the worm
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Fig. 9 A diagram illustrating backlash reduction as a result of worm axial contraction in a
worm gear drive with a locally axially adaptive worm, where (a) state of drive defined as initial, (b) boundary contraction, and (c) full contraction
(Fig. 9) are worm’s thread thickness t1 and worm wheel teeth’s
thickness t2, as well as the worm wheel teeth’s transverse pitch’s
deviation and the worm thread’s axial pitch’s deviation measured
for both sides of the teeth.
When the worm wheel rotates counterclockwise, as another
tooth takes the load, backlash values for pairs of teeth with the (R)
index increase, and for the ones with the (L) index they decrease.
When the direction of rotation is changing, backlash values for
the (R) indexed teeth decrease, and for the (L) indexed ones they
increase. In order to determine the amount of a drive’s backlash
after the adjustment has been made DB, it is not necessary to measure the backlash for pairs on both sides of the worm’s teeth.
When the amount of backlash in a drive is being reduced, the
backlash amount of biR and bjL for pairs indexed iR, i < 0 and jL,
j 0 becomes smaller, however, for pairs indexed iR, i > 0 and jL,
j < 0 it becomes larger. This is the reason why backlash amount
for specific pairs of the worm’s thread and the worm wheel’s
tooth, which become larger during the adjustment process, can be
omitted. Thus, the quantities important for a drive’s backlash
determination are the following: b2R ; b1R ; b0L ; b1L ; b2L . Such a
practice is acceptable, because already during the design process
the engineer should ensure the minimal backlash of a drive, and,
moreover, after assembly, drives are broken in, which further
increases their initial backlash value. Thus, brand new drives are
already characterized by some amount of backlash, which is
aimed at to be reduced by means of adjustment.
The main assumption of the analysis of teeth meshing is that
the initial state of a drive is the one in which in the meshing zone
its worm and worm wheel’s teeth are in contact (Fig. 9(a)). These
are the teeth, which the measurements were started with, and were
used to reset the readings of the measuring device.
The outcome of the adjustment DB, which is worm axial compression, are changes in the meshing zone. First is backlash reduction until a drive reaches a nonbacklash state in only one angular
position. Depending on the position of the pairs remaining
meshed, the following phases can be observed:
(1) Worm compression phase until reaching nonbacklash state
for only one angular position of the worm (Fig. 9(a)).
(2) Range increase of the worm’s angle of turn, until the
boundary compression state is reached (Fig. 9(b)), where
backlash b0 ¼ 0 (for u ¼ u1 ), which is an acceptable phenomenon only during the breaking-in process.
Fig. 10 The decrease of axial pitch along the worm’s thread for
different amounts of compression DB [25]
Journal of Mechanisms and Robotics
This article talks about the state, in which a worm wheel’s tooth
in the meshing zone is in contact with a worm’s tooth. As backlash decreases, by means of worm axial compression, the axial
pitch also decreases. Worm’s thread is most adaptive in the meshing zone, and this is where backlash should decrease and reach
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Fig. 11 A chart presenting the dependency between backlash
and angular position of the worm wheel with different drive’s
adjustments (amounts of axial compression) [25]
zero value for a certain angular position of the worm (Fig. 9(b)). It
is due to the fact that the worm with a cut tooth space becomes a
spring with fixed endings. This makes it a specific type of spring,
characterized by a nonlinear adaptivity of threads along the cut.
The characteristics of its adaptivity are nonlinear and the maximal
pitch decrease is present in the middle of the worm’s adaptive part
(Fig. 10).
In the case of considerable deviations of geometrical parameters of meshing, it may occur that two distant teeth pairs mesh
together—away from the middle of the meshing zone (Figs. 9(b)
and 9(c)). Simultaneous contact of two pairs causes a change of
worm’s stiffness. Since that moment the worm can be described
as comprising at least two elastic systems, which are characterized
by increased stiffness [25]. Such a state of axial compression is a
boundary one for a drive’s proper operation. Further worm contraction would lead to increased surface pressure of the already
meshed tooth pairs.
4.2 Research Results. As for measurement of teeth’s profile,
precise coordinates measurement devices or the method described
in the [26] patent may be used. The backlash research results for
one of the drives [24] with an axially and radially adaptive worm
with different amounts of introduced adjustment are depicted in
Fig. 11. The amount of backlash for the adjustment number zero
was on average 40 lm, and for the biggest one DB ¼ 150 lm it
decreased to about 5 lm; however, the range of backlash values
decreased from 30 lm to 2 lm.
Difficulties connected with worm and worm wheel teeth profile
modification were the subject of the papers [1,8,12,27], their
application [7,13], also in tool manufacturing [2,10], and the technological process of installation [9]. The presented designs of
patented worm gear drives allow to adjust or eliminate backlash
by introducing innovative designs of worms and worm wheels.
These solutions present a worthwhile alternative for harmonic
drives or precise conventional drives. Simulations and research in
operational conditions have been carried out for many of the presented worm gear drives and improvement has been shown
Based on experimental research and numerical analyses the following conclusions have been formulated:
(1) Analysis of dimensions and shape deviations of interacting
components and deviations in their mutual positions allows
to predict drive’s backlash amount before installation.
014504-6 / Vol. 8, FEBRUARY 2016
(2) The new worm gear drive designs, including the one with a
locally axially and radially adaptive worm, allow effective
and considerable backlash reduction as well as dispersion
of its values. Axial adaptivity in this type of drives results
in reduction of average backlash amount and leads to dispersion of its values. Radial adaptivity facilitates automatic
reduction of local variations of backlash amount.
(3) The carried out research has shown it is possible for precise
drives with modules m ¼ 2 4 to have average backlash
amount reduced to 7.5% of its initial value (from 40 lm to
3 lm) and even achieve twenty times smaller standard deviation (from 13 lm to 0.6 lm).
(4) Local radial bending of the worm’s thread does not result
in disadvantageous impact on the drive’s kinematic precision. Also, increasing axial stiffness of a worm with locally
cut tooth space, by assuming a greater module value, allows
to achieve a sufficient load ability of the drive. Worm’s
boundary adaptivity may be determined with the knowledge of the drive’s load amount and by assuming the
drive’s required kinematic precision. Increased stiffness of
the worm requires usage of a pressure mechanism, which is
optimized for such a structural property of the worm.
(5) The designed drives may be successfully applied in mechanisms for precise test bench positioning, in precise technological devices, technological instrumentation, and in
miniaturization, also in mechanisms resistant to severe
working conditions.
This project has been funded by the National Science Center on
the basis of the decision No. DEC-2012/2005/B/ST8/02802.
biR ¼ backlash amount for specific pairs of the worm’s thread and
the worm wheel’s tooth with the (R) index—backlash on
the worm thread’s right side (lm)
bjL ¼ above-mentioned backlash amount with the (L)
index—backlash on the worm thread’s left side (lm)
t1 ¼ worm’s thread thickness (mm)
t2 ¼ worm wheel teeth’s thickness (mm)
DB ¼ worm axial compression—(pitch) adjustment (lm)
u ¼ angular position of the worm wheel (deg)
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