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Worm Gears Email your question—along with your name,
job title and company name (if you wish to
remain anonymous, no problem) to: jmcguinn@
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QUESTION #1
How does one determine the center of a worm and a worm wheel?
First response provided by Joe pattern is to be from the nominal cen- have generally been applied with few
Mihelick, Gear Technology Technical ter of the worm gear towards the leav- problems.
Editor: ing side of the worm gear as deter- While each manufacturer will tout
The center of the single enveloping mined by the direction of the worm their particular tooth design as hav-
worm is straightforward, as it is at a rotation. ing performance advantages, the key
plane passing through the axis of the factor in power capacity remains
worm at its outside diameter. The cen- Second response provided by the physical size of the parts and the
ter of a double enveloping worm gear Charles D. Schultz, PE, Chief mechanical properties of the materi-
is a bit more involved. It is nominal- Engineer for Beyta Gear Service, and als used to make them. Worm gears
ly located at a plane passing through Gear Technology Technical Editor have some unique capabilities that can
the worm gear at its root diameter. If (gearmanx52@gmail.com): be used to good advantage in machin-
the worm gear is throated, the loca- Short answer: It depends upon who is ery design. They are the only gear sys-
tion of the minimum diameter of the asking and what the intended applica- tem where gear ratio does not affect
throat will locate the nominal center of tion is. If you are specifying an off-the- the outside diameter of the rotating
the worm gear. This is more useful for shelf solution, you can rapidly deter- parts; this means a machine can eas-
the manufacturing process but is less mine the appropriate size from sup- ily be supplied with a wide range of
important in the successful operation plier catalogs. Commercially supplied ratios — say 5:1 to 70:1 — without a
or the worm – worm gear pair. The worm gear speed reducers are avail- center distance change or multi-
successful operation of worm gear- able in a wide range of sizes, ratios and ple reductions. Another capabili-
ing involves the actual contact pattern assembly configurations — from both ty — self-locking — can be a boon or
between them. The observed contact U.S.-based and off-shore companies. a bane, depending upon your goals.
Worm gearing is not as Understanding these aspects of worm
standardized as spur, heli- gearing can be a lifelong project, but
cal and bevel gearing. users should ask the suppliers about it
Several different ‘systems’ before ordering.
coexist in the marketplace, The long answer: Many ‘systems’
and each has its propo- have been developed for worm gear-
nents. In the smaller gear- ing over the past 100 years. Each of
box sizes (less than 4-inch them has its proponents and, oddly
center distance), exterior enough in the normally polite world
and mounting dimensions of gear engineering, opponents. If off-
have become ‘standard’ and the-shelf components won’t work for
users can easily interchange your applications, you have to pick one
between brands. Larger of these competing systems and wade
units have no such com- through the often confusing recom-
monality, and users are well mendations to develop your gear set.
advised to carefully consid- Custom-made tooling is expensive and
er all factors of supply (ini- takes critical lead time to obtain, so
tial cost, availability, service designers are encouraged to use exist-
factor and after-sales sup- ing hobs and fly cutters. I recommend
port) before selecting a ven- the design system found in Daryl
dor. Published ratings can Dudley’s Gear Handbook, along with
be based on AGMA, DIN, the worm hob charts on Ash Gear and
The study of worm gears has come a long way: 16th century ISO or other methods, and Supply’s web site. AGMA’s standards
worm gear illustration (courtesy Leonardo daVinci).
50 GEAR TECHNOLOGY | October 2013
[www.geartechnology.com]
QUESTION #2
A gear handbook in my possession states: The ZI worm is identical to
an involute helical gear whose tooth number is the number of worm
threads. Equations of tooth surfaces of an involute helical gear are the
same as for an involute worm. Knowing that a ZI hob cutter is identical
to a ZI worm, I conclude that the mesh of the ZI worm and involute
helical gear is identical to a cross involute helical gear mesh; and even
identical to the hobbing process of an involute helical gear with a ZI
hob cutter.
I would like to know whether I am correct and what is their difference.
Response provided by Hermann J. Stadtfeld, vice president - bevel gear
are the most reliable rating method for technology - R&D for Gleason Corporation.
the independent designer.
If your requirement is for instru- Worm Gear Generation and their Manufacturing Tools
ment gearing or plastic gearing, it is The question will be answered considering the different possibilities in profile form,
recommended that you work with a kind of mesh, and type of tools. Figure 1 contains the general nomenclature used to
supplier of such parts or an experi- define the geometry parameters.
enced design engineer. Tooling costs Worm gear drives can be separated in three categories:
can be very high, and the performance Case A. Crossed helical worm gear drives
of prototype sets can vary depending Case B. Cylindrical worm gear drives
upon manufacturing method. Molded Case C. Double-enveloping worm gear drives
plastic teeth do not have exactly the Cylindrical worm gear drives “B” are the most common form. Their tooth pro-
same topography as cut gears; veteran files of the worms depend on the manufacturing method. The different profile forms
suppliers of plastic gearing understand according to DIN 3975 are:
the changes needed to make sample ZI: Tooth profile in face section is an involute; manufactured, for example, by hobbing,
parts that will work reliably without like a cylindrical pinion. The hob for the worm gear manufacturing is a “dupli-
skewing test results. cate” of the worm (however serrated and considering clearance and backlash).
Worm gearing design is an itera- ZA: Profile is a trapezoid in an axial section; manufactured, for example, by turning.
tive process which can be frustrating ZN: Profile is a trapezoid in a normal section; manufactured, for example, by turning
the first few times you work through with cutting blade tilted to lead angle of worm.
it. Standard worm hobs may not con- ZK: Profile with crowning. Tool is disk cutter with trapezoidal profile, which is tilted
verge on the solution you would pre- to lead angle of worm. Profile crown generated depending on disk cutter diameter.
fer. Some suppliers can make worm ZH: Disk cutter with convex cutting edges, causing hollow flank profiles in axial
gears using ‘fly tools’ — a custom sin- section on worm teeth.
gle-point cutter that allows more flexi- Disk cutter axis is par-
bility in design than the standard hobs. allel to worm axis (not
The cutting process is, by necessity, tilted like ZK).
much slower than hobbing, but for A. Crossed helical worm
one-off or low-volume requirements gear drive. This is a spe-
it is often the best solution. Regardless cial case of crossed helical
of the tooling ultimately employed, gears, where the worm is a
custom worm gearing design requires helical gear with one to six
compromises on center distance, face teeth, and the worm gear
width and numbers of teeth/threads. has a high number of teeth
More than any other gear type, ‘your (e.g., above 30). The pitch
results may vary’ is an appropriate dis- elements of a crossed heli-
claimer. cal worm and worm gear
are cylinders (Fig. 2). Both
members—worm and worm
gear—are manufactured
like helical gears, with stan-
For Related Articles Search dard hobs, for example. The
worm gears profile of both members is
involute. The hobbing tool
at www.geartechnology.com
in Case A is not identical to Figure 1 Worm gear drive nomenclature, single-throat
example (graphics courtesy of Gleason)
October 2013 | GEAR TECHNOLOGY 51
ask the expert
the worm. The two members have line contact, which appear instead as
point or small contacting zones.
B. Cylindrical worm gear drives (single-throat worm gear drives). A
typical worm gear drive; here the worm also has one to six teeth (starts),
and the worm gear has a high number of teeth (e.g., 30 to 300). The pitch
elements of a single-throated worm and worm gear are shown in Figure
3. The worm is manufactured on a lathe or with a disk milling cutter. The
profile is not a generated involute but a straight line. The geometry of a
cylindrical worm therefore is similar to an ACME screw. The worm gear is
manufactured with a hob and the hob’s enveloping surface is identical to the
mating worm. This enveloping surface generates the same involute profile
on the worm teeth as seen in Case A. However, the tooth thickness of the
hob is thicker by the desired backlash amount. The difference in the gear in
Case A is the shape of the pitch element, which in Case B has a hyperbolic
form known as “throat.” The throat is formed merely by plunging the hob
cutter at the center of the face width. The two members have line contact
that appears on the worm gear member like slim ellipses with a major ori-
entation (if projected in an axial plane) parallel to the worm gear axis.
C. Double-enveloping worm gear drives (double-throated worm gear Figure 2 Pitch elements of crossed helical worm gear pair.
drives). These are special types of worm gear drives with a very high con-
tact ratio and high torque transmission abilities. Again, here the worm has
one to six teeth (starts) and the worm gear has a high number of teeth (e.g.
30 to 300). The pitch elements of worm gear and worm have a hyperbolic
appearance which is why Case C is called “double-throated” (Fig. 4). The
worm is manufactured on a lathe, where the cutting blade profile rotates
around a center point while it moves along the face width. The distance
between the cutting blade pitch point and the center of blade rotation is
identical to the pitch radius of the worm gear. The profile is not a gener-
ated involute, but in a straight line. The worm gear is manufactured with a
hob that has the pitch diameter of the worm at the center of the throat and
the same number of starts, unlike the number of worm teeth. Also, here the
worm gear is cut (as in Case B) by plunging with the hob cutter at the cen-
ter of the worm gear’s face width. The two members have line contact that
appears even under light load, as with large elliptical zones—even in single
angular positions.
It should be mentioned that in Case B, where the worm gear tool resem-
bles the mating member within the flank surfaces, there remain several
differences. The tool face is extended in order to machine sufficient top-
root clearance, and the top-land corners to the flanks are rounded with Figure 3 Pitch elements of single-throat worm gear pair.
the desired root fillet radius. The dedendum depth of the tool is equal to
the addendum of the worm, plus an excess amount to prevent any cutting
action at the worm gear top-lands.
The short answer to all conclusions the questioner has posed is “yes.”
Hermann J. Stadtfeld Figure 4 Pitch elements of double-throat worm gear pair.
52 GEAR TECHNOLOGY | October 2013
[www.geartechnology.com]
