profile in the piece of work
THE CAM-CUTTING MACHINE
Another important modification of the milling machine is
found in the cam-cutting machine of which an example, by the
Garvin Machine Company, is shown in Figs. 245 and 246.
Cams are of two chief varieties, called respectively face and
drum cams. The face cam is a disc with an irregular shaped
groove in its face for the production of a movement radial to
itself. The drum cam, on the other hand, is a cylinder with a
groove in its periphery for producing a movement parallel
with its center line. The machine is shown as set up for the
production of both kinds of cams. As in the profiling machine,
the milling cutter which produces the groove in the cam is
guided by a former having the exact outlined desired but, unlike
the profiling machine, the feed is by power and not by hand.
Referring to Fig. 245, which shows the machine in the act
of producing a face cam, two worm-driven turntables will be
seen mounted on the work table. The turntables revolve
slowly and in unison, the one in the background carrying the
hand-made former 1 while the one in the foreground carries the
cam blank in process of being cut. A long ribbed head slides
upon the cross rail and carries, depending from it, a pin at its
farther and a milling cutter at its nearer end the pin and
cutter being of the same diameter. The pin is held in contact
with the former by a weight suspended from a chain which, pass-
ing over a sheave, is attached to the sliding head. As the cam
and former revolve under the action of the feed, the action
of the former is to reciprocate the sliding head in accordance
with its own profile, and this movement being transmitted to
Uie milling cutter, the latter reproduces in the cam blank the
outline of the former.
Fig. 246 shows the machine as arranged for the production
of drum cams. The cam-holding turntable of the previous
frustration has been removed and in its place is a suitable drum-
1 The methods by which cams are laid out, including the making of the formers,
may be found in the author's Handbook for Machine Designers and Draftsmen.
METHODS OF MACHINE SHOP WORK
cam fixture. As before, the former is at the left and the cam
blank at the right. The two being mounted on the same
arbor, the action as this arbor revolves is to reproduce the out-
line of the former in the cam blank essentially as in the previous
THE SCREW-THREAD MILLING MACHINE
Another modification of the milling machine is found in the
thread or screw milling machine, originally developed by the
Pratt and Whitney Company, one of whose machines is shown
in Fig. 247. This machine may be regarded as a combination
of the lathe and the milling machine. Combined with the
general form of a lathe, with the construction of a lathe
FIG. 247. Screw thread milling machine.
so far as the means for determining the pitch of the screw are
concerned, is a milling machine head carrying a milling cutter
in place of the usual lathe tool. The cutter head is provided
with the necessary adjustment for adapting the angle at which
the cutter lies to the helix angle of the thread to be cut.
Still another modification is the hobbing machine of which
an example, by the Newton Machine Tool Works, has already
been shown in Fig. 43.
Both hobbing and cam cutting are frequently done by extern-
porized apparatus, the former frequently mounted on a lathe
and the latter on a milling machine, but no examples of such
equipments are here shown.
THE MILLING CUTTER GRINDER
An essential adjunct of the milling machine is the cutter
grinder of which one, by the Brown and Sharpe Manufacturing
Company, is shown in Fig. 248. This particular machine is
also adapted to the doing of small tool-room work of the char-
acter done on the universal grinding machine, but the features
which here engage us are those by which milling cutters and
similar tools are sharpened. To accommodate the various types
of cutters, extreme flexibility of adjustment in a cutter grinder
is essential. Without the exception of even the universal milling
machine, the center grinder is capable of doing a greater variety
of work than any other machine tool and of these it is only
possible to show a few of the more representative examples.
Fig. 248 gives a comprehensive view of the working parts of
the machine and also shows it adjusted for sharpening an angle
cutter, the angle being obtained by the swivel of the work table.
The angle is read from the divided arc on the front of the table.
Fig. 249 shows the grinding of the most common of all milling
cutters the slabbing cutter. A cupped grinding wheel is
used, thereby grinding flat faces to the teeth instead of concave
faces which would be the result of grinding with a common disc
wheel. A feature of the machine which is less clearly shown in
some of the views than others, but which is always present, is
the spring tooth rest shown clearly in Fig. 249, which projects
up from below and against which the tooth being ground rests.
The cutter is slid endwise on its supporting arbor by the hand,
contact with the rest being maintained by gentle pressure and,
as each tooth is finished, the cutter is turned to present the
next one to the wheel, the spring of the rest enabling it to give
way and snap past the teeth.
Figs. 250 and 251 show the adjustments for grinding a face
cutter, in one case that for the periphery and in the other
for the side, the latter showing also an adjustment of the tool-
carrying head which is frequently required for other pieces of
METHODS OF MACHINE SHOP WORK
work. The tooth rest is also clearly shown in this view. Fig.
252 shows the grinding of a convex shape cutter to a circular
profile by means of a swivel attachment provided for that pur-
pose, and Fig. 253 shows the adjustment for grinding large
inserted tooth cutters.
Multiplicity of forms of gear-cutting machines The advantages of the
diametrical pitch system The three basic systems of gear cutting
Machines embodying these systems Bevel gear-cutting machines
The octoid system of bevel gear teeth Gear-molding machines.
VARIETY OF GEAR-CUTTING MACHINES
There is no feature of machine work of greater interest than
gear cutting, as there is none to which so great a degree of
attention has been directed and with correspondingy fruitful
results. There is no other example of a single purpose machine
that has been produced in such a bewilderng diversity of
forms. It is impossible to give here more than an outline of the
leading methods of attacking the gear-cutting problem with
sufficient illustrations to show how these methods are embodied
in commercial machines. For additional information the
reader is referred to the excellent treatise, Gear Cutting Machin-
ery, by Ralph E. Flanders, wherein will be found, with but
one or two exceptions, all the machines now made, both American
and European. 1
ADVANTAGES OF THE DIAMETRAL PITCH SYSTEM OF GEARS
The diametral pitch system is at the base of all modern
cut gears of moderate size. This system, as already stated, was
invented by Bodmer but introduced as a general commercial
system by the Brown and Sharpe Manufacturing Company.
Coincident, or nearly coincident with this introduction, the
Brown and Sharpe Company developed and published in their
catalogue a set of simple formulas for the calculation of gears,
singly and in pairs. These formulas, which have been copied
1 Figs. 254, 257, 259 and 267 are, by permission, reproduced from Mr. Flander's
GEAR CUTTING 251
into all American mechanical engineer's pocket books, have
influenced beyond measure the introduction of the diametral
The superior convenience of the diametral pitch system is
largely due to the simplicity of these formulas and of the resulting
calculations. A series of standard pitches is selected, analogous
to the series of pitches of standard screw threads, an indefinite
number of intermediate pitches which might be used being dis-
carded, thus making systematized cutter manufacture possible.
By thus giving up complete liberty of choice in the matter of
the pitch, corresponding liberty of choice of diameters is sacri-
ficed. So far as the pitches themselves are concerned, this gives
rise to just as little inconvenience in the case of the gears as in
that of screw threads. It does, however, lead to an occasional
slight inconvenience in connection with the diameters and center
distances. Since a gear must contain a whole number of teeth,
it follows that, for any given pitch, only such diameters are
possible as will contain an exact whole number of teeth, the
diameters for any one pitch varying by a series of steps precisely
as the pitches vary. This series of diameters differs, of course,
with the pitch.
Thus considering eight pitch that is a pitch such that the
gear contains eight teeth for each inch of its pitch diameter a
gear of sixteen teeth will be of two inches pitch diameter. Simi-
larly, a gear of seventeen teeth will be of two and one-eighth and
one of eighteen teeth of two and one-quarter inches pitch diam-
eter, no diameter between these values being possible if gears
of eight pitch are to be used. This feature requires attention
in the design by giving the gear centers such locations as will
provide for the necessary diameters.
Another essential and valuable feature of the diametral pitch
system is that the diameters of the gears and the distances be-
tween centers are always expressed in even fractions and are
never incommensurate. In the circumferential pitch system,
since the pitch is commensurate, the circumference is also
commensurate, while the diameters and center distances are in-
commensurate. With the diametral pitch system the reverse
is true. The circumferential pitch of gears made on this system
METHODS OF MACHINE SHOP WORK
is incommensurate as is the circumference, but the diameters
and center distances are always commensurate and, while com-
mensurate circumferences have no particular value, commen-
surate diameters and center distances are sources of many
THE SYSTEMS OF GEAR CUTTING
There are three basic systems of gear cutting: (a) the formed
tool system; (b) the generating system, of which the hobbing
system is a development and, (c) the templet system.
FIG. 254. Principle of the formed tool system of gear cutting.
Of these the oldest and most widely used is the formed-tool
system, of which the principle is illustrated in Fig. 254. The tool,
which might be, and sometimes is, a planing tool as shown at
the top of the illustration but which, in the vast majority of
cases, is a rotary milling cutter as shown at the bottom of the
illustration, is accurately formed to the desired profile which it
reproduces in the gear. It was for this purpose that the
formed cutter which may be sharpened by grinding without
changing its form was originally invented.
Machines embodying this principle were first made in England.
254 METHODS OF MACHINE SHOP WORK
The first to perform their functions automatically, requiring no
attention on the part of the operator except to remove a com-
pleted gear and supply its place with a fresh blank were made by
William Sellers and Company in 1866, some of the machines then
made being still in use at the Sellers works. The Sellers machine
was ahead of its time and, while some were sold, they were not
placed on the general market, the first commercial automatic
machine being produced by the Brown and Sharpe Manufactur-
ing Company in 1877. This machine, which has supplied the
model for many others, is shown, as now made, in Fig. 255,
and were the original machine placed beside it even fewer
changes would be found than in the universal milling machine.
It is not the author's purpose to go into detailed description of
the operation of this or other complex machines, the intention
being to point out the principles of the work and the general
methods by which the various problems are attacked.
The action is entirely automatic, the feed and return of the
cutter and the indexing of the blank from tooth to tooth requir-
ing no attention on the part of the operator who has but to
remove the completed gears and supply their place with fresh
blanks. For larger work convenience of handling leads to the
horizontal instead of the vertical position for the gear in process
of being cut. Automatic machines have been made for
cutting gears of large size but, usually, such machines are non-
automatic, an example, by the Newton Machine Tool Works,
being shown in Fig. 256.
For the largest work, gear-cutting machines operate more
frequently on the templet principle, an example of this con-
struction appearing on a later page.
THE GENERATING SYSTEM OF GEAR CUTTING
The generating system was invented by Hugo Bilgram who
produced his first machine in 1885. This machine was invented
for the production of bevel gears for which at that time no
satisfactory method of production was available. 1 The system
1 A machine for the production of correct bevel gears was exhibited at the
Centennial Exposition of 1876 by George H. Corliss. The machine was of large
size suitable for the production of mill gearing. It was constructed especially
has now been adapted to the production of spur and spiral
gears and the principle is best described in connection with
spur gears. At the top in Fig. 257 is a gear of metal while
below it is a blank of some plastic material. If the two shafts
be connected by gears having their speed ratio equal to that
between the pitch diameters of the forming gear and the plastic
blank and the two be revolved together, the forming gear will
impress into the plastic blank tooth forms which are conjugate
FIG. 257. Principle of the generating system of gear cutting.
to those of the forming gear and which, if in metal, would form
suitable teeth for a gear to mate with the forming gear.
If the forming gear be made of hardened steel with suitable
rake and clearance to the teeth, and if it be then reciprocated
on its center line as the rotation proceeds, the plastic blank
may be replaced by a metallic blank, the teeth of the forming
gear acting as cutting tools to generate correct mating gear
to cut the transmission gears of the monumental Corliss engine which supplied
power for Machinery Hall of the Exposition and, among engineers, it attracted
almost as much attention as the engine. It operated on the templet principle
which was subsequently made commercial by the Gleason works, who produced
a machine that came into large use.
256 METHODS OF MACHINE SHOP WORK
teeth. It is exactly upon this principle that the Fellows gear
In this system the forming gear cutter might be a rack which
would then produce in blanks of various sizes, teeth which are
conjugate to those of the rack and to each other. In the
involute system the sides of rack teeth are straight, whereas
the sides of all gear teeth are curved. A straight-sided tool is
an easy thing to originate with a high degree of accuracy and
hence, in all applications of the generating system, the straight-
sided rack tooth forms at least the starting point. In its orig-
inal appearance on the Bilgram bevel gear machine the straight-
sided rack tooth forms the cutting tool. This is not to be
understood as meaning that an actual rack is used in the
machine but a cutting tool which represents a single tooth of
the rack or, more properly, one side of that tooth because, the
spaces between bevel gear teeth being tapered, but one side
can be formed at a time.
THE BILGRAM BEVEL GEAR GENERATING MACHINE
Mr. Bilgram's original bevel gear-cutting machine, as it
appeared in the American Machinest for May 9, 1885, is shown
in Fig. 258. The machines now made are fully automatic in
their action which the machine shown was not. It is here used
in preference to the modern machines, partly because of its
historic interest and partly because its comparative simplicity
makes its principle of action more apparent.
The straight-sided tool which represents one side of a rack
tooth in the case of bevel gears more properly a crown gear
tooth is mounted upon a ram driven precisely like a shaping
machine ram. The gear blank is mounted below the tool upon a
suitable arbor supported at its rear end by a conical segment
which rolls upon a plane surface below it. The conical seg-
ment is a portion of the pitch surface of the gear to be cut,
extended to the opposite nappe of the cone, while the plane
surface is a portion of the pitch surface of the imaginary crown
gear of which the cutting tool represents one side of a tooth.
Integrity of the rolling motion without slip is. maintained by a
pair of steel ribbons, one end of each of which is clamped to
the end of the rolling segment and the other end to the oppo-
site end of the stationary plate.
If the segment be rolled upon the plate the gear blank will
roll past the cutting tool precisely as though the latter were a
crown gear and, with the tool in reciprocating motion, it will
cut upon the gear blank a suitably formed tooth side when, the
gear blank being indexed for the next tooth and the action
repeated, the side of that tooth is formed and so on indefinitely.
FIG. 258. The original Bilgram bevel gear cutter, generating system.
The action is, perhaps, more clearly shown in Fig. 259.
Were the gear being cut a spur, a complete rack tooth could
be used as at a, but when cutting a bevel gear the taper of the
space between the teeth makes it necessary to use a single-sided
tool as at b a second tool symmetrical with the first planing
the second side after the first is completed. The teeth are
roughed out in a preparatory machine before the generating
machine is brought into action.
METHODS OF MACHINE SHOP WORK
THE GLEASON BEVEL GEAR GENERATING MACHINE
Consideration of Fig. 259 will show two modifications of the
plan of attack. The imaginary rack may be fixed as regards
endwise motion, the blank rolling past it as a gear might be
rolled in a rack, this being the plan incorporated in the Bilgram
machine. On the other hand, the rack may travel endwise
with the feed, the gear blank turning upon its center which
does not change its position. This latter plan of attack is
incorporated in the Gleason machine shown in Figs. 260
The gear in process of being cut appears in both views
mounted on the horizontal main spindle. Both sides of the
ideal crown gear tooth are repre-
sented by tools of which there are
two, by which construction both sides
of a tooth are shaped simultaneously.
These tools are mounted and re-
ciprocate in guides on an arm which
oscillates about the cone center of the
gear blank being cut, this oscillation
being obtained by the horizontal yoke
and vertical connecting rod shown
in Fig. 261. The yoke is secured to
the main spindle as shown in Fig. 261
and carries a segment gear shown in the same view, the pitch
cone of this segment being identical with that of the gear blank
being cut. Mounted on the tool-carrying arm is a second seg-
ment gear in mesh with the first, also shown in Fig. 261. The
second segment is a segment of a crown gear, its pitch plane
(pitch cone having a cone angle of ninety degrees) being identical
with that of the ideal crown gear tooth represented by the
cutting tools. As the yoke oscillates it turns the gear blank
with it while the meshing of the segments compels the tool
arm to oscillate and to carry the cutting tools past the blank
in the same relation as a crown gear tooth in mesh with a
tooth on the blank. The action of the machine is fully
FIG. 259. Generating gear
teeth from a rack tooth.
Gleason bevel gear cutting machine, generating system.
METHODS OF MACHINE SHOP WORK
THE OCTOID SYSTEM OF BEVEL GEAR TEETH
When inventing his machine, Mr. Bilgram also invented,
incidentally, an entirely new tooth form system which is neither
involute nor epicycloidal. This system appears in all generated
bevel gears, there being no spur gear tooth form analogous to it.
The starting point of the system is the straight-sided crown
gear tooth which determines the outlines of all gears cut by it.
It so happens that while the crown gear among bevel gears is
analogous to the rack among spur gears its teeth do not have a
straight side as do rack teeth.
The involute rack tooth has a straight side because, as alimit-
FIG. 262. The octold crown gear
FIG. 263. The spherical involute
crown gear tooth.
ing construction, its center of curvature goes off to infinity. In a
crown gear, however, the center of curvature does not go off to
infinity, the curve being that described by a point a of Fig. 263
in the meridian circle be when rolling upon the base circle cd.
The center of curvature is always upon the surface of the sphere
and never at an infinite distance and the involute crown gear
tooth side has, in consequence, the curved form indicated. 1
The introduction of the straight-sided crown gear tooth as in
Fig. 262 produced, therefore, an entirely new set of curves in
1 The rack is a limiting case of the crown gear. As the diameter of the crown
gear increases, the base sphere also increases. When the diameter of the gear
becomes infinite the gear becomes a rack. Simultaneously the sphere becomes
of infinite diameter and with it the radius of curvature of the tooth profile.
FIG. 264. Fellows gear shaper, generating system.
FIG. 265. Action of the Fellows gear FIG. 266. Cutter of the Fellows gear
262 METHODS OF MACHINE SHOP WORK
the bevel gear teeth. To this system of tooth forms the name
octoid has been given by George B. Grant because the outline of
the path of contact between two complete gear tooth forms is a
curve having a shape somewhat like the figure eight as shown in
THE FELLOWS GEAR SHAPER
The leading representative of the generating process for
spur gears is the Fellows gear shaper shown in Figs. 264 and
265, the principle of the action having been shown in Fig. 257.
Fig. 264 shows the complete machine with the cutter in position.
The gear blank arbor is shown at the right, the action of the
cutter on the blank appearing more clearly in Fig. 265. Cutter
and blank revolve slowly as the cutter reciprocates vertically.
The appearance of the cutter is shown in Fig. 266. It also is
generated from an ideal or imaginary rack tooth represented
by the side of an abrasive grinding wheel, the final generation
being done after the cutter is hardened. The machine for do-
ing this which, of course, is found at the works of the makers
only, is of the highest degree of precision.
THE ROBBING PROCESS OF GEAR CUTTING
The hobbing process is a modification of the generating
process and was originally developed to a commercial basis
by the production of machines for sale in Germany. The prin-
ciple of this method of attack is shown in Fig. 267, in which
the hob is represented by a worm, the two differing from one
another by the fact that in the hob the threads are gashed to
form cutting teeth as already shown in Fig. 44. The dotted
outline indicates the imaginary rack which, in axial section,
is represented by the worm.
The pitch of a hob as used in Fig. 43 for cutting worms has
its pitch, measured parallel with its axis, equal to that of the
worm which it is to cut, but the hob for cutting spurs has its
axial pitch so modified that the pitch measured on the normal
to its helix is equal to that of the gear to be cut. In action, the
hob is adjusted at an angle, as shown in the plan view of Fig. 267,
such that the tangent to the helix is parallel with the teeth
to be cut. At the beginning of the cut the hob is presented to
the side of the blank. The feed is double that is, the gear
blank revolves and as it does so the hob is fed slowly across it.
The cut is continuous, the gear being completed as the hob
leaves its further edge. The axial section of the hob being
the Hob which cuts
FIG. 267. Principle of the nobbing process of gear cutting.
that of a rack, the result is to produce conjugate forms in the
gear just as the reciprocating tool of the same profile produces