TOOL MACHINE DRIVES 7
IRLF
TJ
7
5
B
3
Dlfl
CENTS
753
MACHINE TOOL
DRIVES
SPEED
AND FEED CHANGES- CONE PULLEYS
AND GEAR RATIOS- SINGLE PULLEY DRIVES
THIRD REVISED AND ENLARGED EDITION
MACHINERY'S REFERENCE BOOR NO. 16
PUBLISHED BY MACHINERY, NEW YORK
MACHINERY'S REFERENCE SERIES
IS
ONE UNIT IN A COMPLETE LIBRARY OF
MACHINE DESIGN AND SHOP PRACTICE REVISED AND
REPUBLISHED FROM MACHINERY
EACH NUMBER
NUMBER
16
MACHINE TOOL DRIVES
THIRD REVISED AND ENLARGED EDITION
CONTENTS
.
Data for the Design of Driving and Feed Mechanisms,
by FORREST E. CARDULLO
3
Speeds and Feeds of Machine Tools, by C. C. STUTZ
-
11
Machine Tool Drives, by JOHN EDGAR
Geared or Single Pulley Drives, by
-
20
WM.
GROENE
-
J.
C.
STEEN and
-
28
Drives for High Speed Cutting Tools, by C. E. COOLIDGE
35
F.
-
Copyright, 1910, The Industrial Press, Publishers of
49-"> Lafayette Street, New York City
MACHINERY
CHAPTER
I
DATA FOR THE DESIGN OF DRIVING
AND FEED MECHANISMS
There is probably no branch of machine design in which greater
changes have taken place in recent years than that of the design ol
machine tools. The greater part of these changes are without doubt
due to the work of Mr. Fred W. Taylor, the discoverer of high-speed
steel, who has more thoroughly investigated the capabilities and posTTie
sible performances of metal cutting tools than any other man.
writer had occasion some time ago to study carefully Mr. Taylor's
paper "On the Art of Cutting Metals." His study of this paper, together
with his own experience in machine tool design and operation, has
brought him to certain conclusions in regard to some points in machine
tool design which will be of interest and value not only to those who
may themselves design and build such tools, but also to everyone who
has to purchase or use them.
Ratio of Speed Changes
The
first
point to
which the writer would
call attention is
the neces-
number of speed changes. Those who have read
Mr. Taylor's paper will remember that he shows that there is a definite
sity of a sufficient
relation between the cutting speed and the length of time which a tool
will last without regrinding.
Should the machine be run at too high
a speed, the tool will last but a short time before it will have to be
reground. Should it be run at too low a speed, less work, of course,
will be done, although the tool will last a comparatively long time.
Somewhere there is a golden mean at which the cost of machining plus
the cost of tool dressing is a minimum, and theoretically our machine
should always be run at that speed. Of course, in handling materials
of varying grades of hardness, and, in the case of lathes and boring
mills, of varying diameters, this would necessitate a very great number
of speed changes.
If the number of speed changes be limited, it is
apparent that the machine cannot always be working at the point of
maximum efficiency. The speed of cutting which gives the maximum
efficiency is shown in Mr. Taylor's paper to be that speed which will
destroy the tool in from 50 minutes in the case of a %-inch X 1-inch
roughing tool, to 1 hour and 50 minutes in the case of a 2-inch X 3-inch
roughing tool. These times are of course only approximations and
will vary somewhat with the cost of steel and labor and the value of
the machine in which the tool is used. If the machine be slowed down
from this proper speed, the cost of machining will slowly increase, but
if the machine be speeded up above this proper speed, the cost of
machining will increase very rapidly. In his paper Mr. Taylor gives
a diagram wherein it is shown that if the machine be slowed down so
that the duration of the cut is increased from 50 minutes to about 4
347526
A J.
*
it
MACHINE TOOL DRIVES
hours and 40 minutes, the machine is then working at about 90 per
its former efficiency.
If the machine be speeded up until the
duration of the cut is decreased to about 15 minutes, the machine will
again be working at about 90 per cent efficiency. This range of speed
is shown by Mr. Taylor's equations to be in the ratio of
j/T5 to y/ "280
or of 1 to 1.45. Consequently, if we have a machine having several
speeds with the constant ratio of 1.45 between the successive speeds,
we know that such a machine may always be made to operate within
90 per cent of its maximum efficiency, and that on the average it will
operate at more than 95 per cent of its best efficiency.
The following table, which is derived in the manner indicated from
the diagram given in Mr. Taylor's paper, shows the speed ratios corresponding to the given average and minimum efficiencies of working.
cent of
Ratio
Average Efficiency
99.6 per cent
98. 7 per cent
97.3 per cent
95.6 per cent
93.5 per cent
90.6 per cent
86.5 per cent
1.1
1.2
1.3
1.4
1.5
1.6
1.7
From
Minimum
99.2
97.3
94.5
91.2
87.0
81.2
73.0
Efficiency
per cent
per cent
per cent
per cent
per cent
per cent
per cent
it will appear that even in the case of very costly
no particular advantage to reduce the ratio between
successive speeds unduly.
For instance, by doubling the number of
speeds and reducing the speed ratio from 1.2 to 1.1, we will increase
the average efficiency of the machine only about 1 per cent. It is very
doubtful if the accidental variations in shop conditions would not be
so great that the gain in practical work would be nothing, since the
workman or the speed boss, as the case might be, would be unable to
decide which of two or three speeds would be the best. The writer is
therefore of the opinion that there is absolutely no practical advantage
in reducing the speed ratio below 1.2 and that in the case of machines
of ordinary type and cost, a ratio of 1.3 is as small as is advisable. In
the case of a speed ratio of 1.3, the machine can always be made to
operate at such a speed that the efficiency of working will be above 94.5
per cent and in the average case the efficiency will exceed 97.5 per cent.
The 2.5 per cent loss of efficiency so caused is inappreciable as compared with other sources of loss, and it is exceedingly doubtful if the
added cost of additional speed changes would not more than compensate for the possible 1 or 2 per cent of gain, entirely aside from the
question of whether the extra speed changes would permit this theoretical gain to be realized.
The writer is also of the opinion that a speed ratio of more than 1.5
in the case of expensive machinery operated by highly skilled help, or
of 1.7 in the case of cheap machinery operated by comparatively unIt will be seen that with a speed ratio of
skilled help is inadvisable.
1.5 the average efficiency of working is, in general, about 93.5 per cent,
the table
machines
it is
making the
cent.
of
loss of efficiency in the average case about 6.5, or say 6 per
be seen that when the rent of the tool plus the wages of a
It will
mechanic amounts to $4 a day or upward,
this 6 per cent of loss
means
DRIVING AND FEED MECHANISMS
5
a money loss of $0.25 or more per day, or upward of $75 a year. Of
course, an increase in the number of speed changes and reduction of
ratio would not save all this loss, but assuming that it would save half
of it, and further, that the machine is operating only half the time, it
is evident that we can afford to spend $150 or $200 for the extra speed
changes necessary in order to bring the speed ratio down to 1.3. In
the case of a ratio of 1.7, the loss is 12 or 13 per cenf instead of only 6
per cent, and these figures apply with greatly added force.
We are thus compelled to the conclusion that the useful range of the
speed ratio in machine tool work is very narrow, ranging from 1.3 to
1.5 in ordinary cases and that a range of from 1.2 to 1.7 includes the
very extremes of rational practice.
Need
of Speed
Changes
Being- Easily
Made
A
second point in connection with the matter of the speed changes
tools which is of great importance is that these changes
should be easily and quickly made so that the operator will have every
incentive to use the proper speed. This is a matter of less importance
in the case of planers than in the case of lathes and boring mills, since
a planer requires a change of speed only when the character of the
material which is being cut is changed, while the lathe requires a
change when any great change is made in the diameter of the work
of
machine
operated upon.
In this respect a motor-driven tool may have a distinct advantage
over a belt-driven tool. The controller furnishes a ready means for
varying the speed while the shifting of a belt from pulley to pulley
is not always readily accomplished, and most machinists would much
rather take two cuts of differing diameters on the back-gear than shift
the belt from the small to the large pulley and throw out the back-gear
in order to obtain the fa'ster speed from the open belt.
This is particularly the case when the cuts are of small duration, so that the
shifting would be frequent.
It will be evident to the thoughtful mechanic that it is of great advantage to have the speed-changing mechanism so constructed that the
change may be made without stopping the machine. In the case of
large machines it will be of great advantage to be able to effect the
speed change from the operating station, which for instance in the case
of a long lathe will be the carriage. To the writer's mind the particular advantage of these refinements which he suggests, and which will
be found embodied in many of the designs of our best tool makers, lies
not in the fact that the time required to make the necessary speed
changes is shortened, but in the fact that the workman finds it just as
easy to run his machine at the proper speed as at an improper one.
Ratio of Feed Changes
A
matter of even greater importance than a proper series of easily
made speed changes is a proper series of easily made feed changes. A
change of speed does not mean in general a correspondingly great
change in the efficiency of operation of a machine tool, but a change in
feed does. Mr. Taylor points out in his paper that in general the best
6
No. 16
MACHINE TOOL DRIVES
results in quantity of metal removed per hour are obtained when the
cross-section of the chip is a maximum, even though this entails a
comparatively low speed. Therefore it is of importance that the machinist be able to take the heaviest cut which the nature of his work
and the power and stiffness of his machine will permit. Just as the
best results in the matter of cutting speeds are obtained when the successive speeds run in geometric ratio, so the best results in the matter
of feed adjustment are obtained when the successive feeds run in geometric ratio, unless the number of obtainable feeds is so great that
the entire range is closely covered. For instance, a lathe equipped
with the following feeds, 0.05, 0.10, 0.15, 0.20, 0.25, is distinctly inferior
in productive capacity to a lathe having the same number of feeds
arranged geometrically as follows, 0.05, 0.074, 0.111, 0.166, 0.25, wherein
each feed is about 50 per cent greater than the preceding one.
In general the best work is obtained from a machine tool when the
depth of cut is made such that the total depth of metal to be cut away
is removed with one or two cuts.
Such being the case, the depth of cut
is practically fixed and not within the control of the operator, leaving
the feed and speed as the variables which he must adjust. It is important therefore that the operator be able to take a cut as heavy as
the nature of the work or of the tool will permit. Mr. Taylor's paper
shows that the speed of cutting
approximately inversely proportional
needs therefore only a very elementary knowledge of mathematics to see that if the feed must be reduced
to say 80 per cent of its maximum value, the output of the lathe will
be only about 90 per cent of its maximum value. Or in general, if the
feed be reduced from its maximum possible value by any given per
cent, then the output of the machine will be reduced from its corresponding maximum value by about one-half of that per cent. We may
by means of this principle compute the ratio between successive feeds
which will give iis any required average value for the efficiency of
operation of the machine. The values so found are tabulated below:
is
to the square root of the feed.
It
Efficiency
Ratio
Efficiency
Ratio
98 per cent
"
"
96
"
"
94
"
"
92
1.08
1.18
1.32
1.46
90 per cent
"
"
88
"
"
86
1.66
1.92
2.27
An inspection of the table shows that when the ratio between successive feeds is about 1.1, the average efficiency of operation of the
machine may be practically perfect, and that with any considerable
increase of this ratio the efficiency drops off. It is the opinion of the
writer that the ratio between successive feeds should always be less
than 1.3 and that, more especially in the case of expensive machinery,
a value of 1.2 or less
It
is
preferable.
Importance of Convenience of Feed- changing- Mechanism
has already been pointed out that the speed-changing mechanism
should be of such a character that the speed changes may be easily
and quickly made. In the same way it is of even greater importance
that the feed changes may be easily and quickly made. In most small
DRIVING AND FEED MECHANISMS
1
which are now on the market, quick-change gears are fitted to
the screw-cutting mechanism, which are equally available as quickchange gears for the feed mechanism. In most shops small lathes are
not used very much of the time for screw-cutting, and in fact nine
lathes
lathes out of ten are never used for that purpose, but a quick-change
gear mechanism is of much greater importance when used for the
purpose of obtaining feed changes than when used for the purpose of
obtaining thread changes. In the average case the operator will not
have to touch the thread-cutting gear once a week, while it may be
advisable to change the feed every five minutes. In the case of large
lathes it is advisable to have the feed changes, not in the head-stock
but in the apron, in order that the workman may be encouraged to use
a proper feed whenever possible.
Unlike lathes, planers are generally equipped with ratchet feeds. The
successive values of the feed changes in the case of a ratchet feed will
necessarily run in an arithmetic and not a geometric series, the
successive feeds differing by some constant decimal of an inch.
So
long as the amount by which the successive feeds differ is small, and
the range of feeds given by the mechanism is large, a ratchet feed is
perfectly satisfactory. Many boring mills are fitted with a feed mechanism driven by a friction wheel of the type generally known as a
brush wheel, the driving mechanism consisting of a steel disk of 12
to 16 inches in diameter geared to the table, and against the face of
which a much smaller wheel edged with leather is pressed.
It is
obvious that if the steel disk rotate at a constant speed, the speed of
the driven wheel and consequently the amount of the feed may be
varied by adjusting its position. When it presses the disk near its
center it will revolve slowly. When it presses the disk near its edge, it
This feed mechanism has
gives an infinite number of feed changes over a
wide range, but has the disadvantage that it is not positive in its
On the
action, and lacks sufficient power for certain kinds of work.
whole, the best feed driving mechanism is a nest of gears so arranged
that any feed within the entire range may be had by the simple shiftwill revolve at a comparatively high speed.
the advantage that
it
ing of one or two levers.
Strength of the Feed Mechanism
In that part of his paper discussing the force required to feed the
tool of a lathe or boring mill, Mr. Taylor makes the assertion that the
feed mechanism should have sufficient strength to "deliver at the nose
of the tool a feeding pressure equal to the entire driving pressure of
the chip upon the lip surface of the tool."
This would lead to the
designing of a lathe or boring mill having feed gearing of equal
In the case of planers and
strength with its driving mechanism.
other machines in which the tool is moved at a time when it is not
cutting, these statements do not apply. It is not generally the custom
among machine tool builders to design machines having such strong
feed works as Mr. Taylor's ideas call for, and the writer sees no
reason why such strength is necessary. The amount of force required
to traverse a tool in a lathe is not proportional to the width of feed,
No. 16
MACHINE TOOL DRIVES
and while
it may be true for fine feeds that in the case of dull tools
the traversing pressure may be equal to, or greater than the downward pressure upon the tool, this is not necessarily the case with
heavy feeds. As the width of the feed is increased, the downward
pressure will increase almost in proportion, while the traversing
pressure will increase comparatively little, so that when the lathe is
taking the maximum cut which the driving mechanism is capable of
handling, the pressure required to feed the tool into the work, even
though it be very dull, is much less than the downward pressure. It
is the writer's opinion that a feed mechanism designed to have onehalf the strength of the driving mechanism is ample for large tools,
while for small tools in which of course the feed will be finer, a
strength of two-thirds of the driving mechanism might be preferable.
"Breaking- Piece" of Feed
Mechanism
The feed mechanism should be provided with a breaking piece whose
strength will be less than that of the rest of the mechanism and
which may be cheaply and easily replaced. The office of this piece is to
prevent the breaking of the more costly and less easily replaced parts
of the mechanism, exactly as the fuse in an electric circuit prevents
the destruction of any other part of the circuit. Two forms of breaking piece sometimes used for such service are, first, a soft steel pin,
driven through a shaft and hub of harder steel, which shears off when
the strain becomes too great; and second, a short section of shaft
turned down at its center, which twists off under similar circumA breaking piece must be of such a character that it will
stances.
not spoil any of the rest of the mechanism when it breaks, and should
not cost more than a few cents, and should be as easily removed and
replaced as a common change gear.
.It must not be imagined that a feed gearing designed to have onehalf the strength of the driving gear will not be strong enough to
meet Mr. Taylor's requirements in all ordinary cases. If a tool be deinch by
signed to take a maximum cut of
inch, it is not likely
If both
that much of its work will be done with such a heavy cut.
%
%
driving and feed gearing be designed with a proper factor of safety,
there is ample margin of strength for all usual conditions, while a
breaking piece is the best provision against extraordinary stresses.
Pressure on Lip Surface of Tool and
The pressure upon the
Its
Relation to Design
surface of the tool is required in order
that the designer may know, first, the strength required of the driving
mechanism and frame of a machine; second, the power required by the
machine; and third, the strength required for the feed mechanism.
The two materials upon which the vast majority of machine tools are
called to operate are cast iron and steel. Taking first the case of cast
lip
iron, we find from Mr. Taylor's paper that the pressure upon the lip
surface of the tool varies from 75,000 to 150,000 pounds per square
inch of chip section in the case of soft iron, and from 120,000 to
225,000 pounds in the case of hard cast iron. The finer the feed, the
greater the pressure per square inch upon the lip surface of the tool.
DRIVING AND FEED MECHANISMS
of cut and 1/64-inch feed, the pressure on
about 289 pounds, or 146,000 pounds per square inch. With
the same depth of cut and %-inch feed, the pressure on the tool is
1,358 pounds, or only about 86,900 pounds per square inch of chip section.
Both these figures are given for soft cast iron. Mr. Taylor gives
formulas for the total pressure of the work upon the lip surface of
the tool, but the following table will be found more convenient for
obtaining the required values, although the figures given are of course
Thus with an %-inch depth
the tool
is
only approximations:
Pressure per Square Inch
Hard Cast Iron
Soft Cast Iron
*
Feed, Inches
1/64
1/32
1/16
1/8
140,000
120,000
100,000
85,000
220,000
190,000
160,000
135,000
In the case of soft and medium steels we find that the pressure in
pounds per square inch of chip section runs from 250,000 to 300,000
pounds, being greater in the case of the finer feeds. In the case of
which combine high tensile strength and great elongation, it is probable that these figures would be very much exceeded.
The amount of the feed and depth of cut will depend on the kind of
work which is to be machined. In the case of small castings, 3/16
inch is an ample allowance for depth of cut and
inch would be
much more usual. In the case of very large and heavy castings the
special steels
%
depth of cut required might run up to y2 inch, and in the case of large
"meaty" forgings, it may be even greater than this at some places. In
those cases where the area of chip section is not fixed by the work, as
in the case of stocky forgings and castings, the greatest width of feed
is limited by the strength of the machine itself, which in turn is
limited only by the length of the purchaser's purse.
Presumably it
would be possible to build a boring mill or a planer capable of taking
a cut an inch deep with an inch feed if anyone wished to pay for such
a machine, but whether it could do the average line of work as economically as a machine taking a %-inch cut with %-inch width of feed
is another matter.
While there is no settled rule either for the maximum depth of cut or width of feed for anj particular type of machine,
the matter of the size of tool used is generally definitely known. In
the case of forged roughing tools the maximum chip section will be
from 2 to 3 per cent of the area of the section of the tool shank. For
instance, the heaviest cut which a tool forged from 1-inch by 1 %-inch
stock will be called upon to take will be .% inch by V8 inch, or perhaps a trifle greater. In the case of tools ground from bar stock and
held in tool-holders, the section of the chip may run up as high as 5
per cent of the section of the bar. Knowing the size of tool for which
the tool-holders are designed, we may proportion our machine accordingly.
A matter which has great effect not only upon the quantity of work
which a machine is capable of doing, but also upon its accuracy and
length of useful life, is its stiffness. While it is true that if we know
the maximum pressure upon the lip-surface of the tool, we may design
10
No, 16
MACHINE TOOL DRIVES
a machine for strength and have one which will probably never break
in service, yet it is often better to add many times the quantity of
metal which mere strength would call for, in order to have a machine
with the maximum of stiffness. Stiffness in machine tool design has
to do with
two
metal of which
points,
the
first
being the actual deflection of the
composed under the stresses which come upon it
in operation; the second is the play which invariably exists at all
joints, more especially the slides of compound rests in lathes, and of
saddles in boring mills and planers.
The best remedy for actual
deflection of metal is to use plenty of it, and to distribute it in such
a way as to realize from it its maximum strength. The writer has
found that an excellent method of designing such machine parts as
require great stiffness is by comparison with existing tools, whose
operation is satisfactory. Let us assume for instance that we are to
design the cross-rail of a planer. The rail is to be 8 feet between the
housings and the overhang of the tool below the center of the rail
is to be 30 inches.
The cut is to be, let us say, % inch deep by y8
inch feed.
Let us assume further that we have at our disposal a
4-foot planer, the overhang of whose cutting tool is 15 inches, and
which will take in a satisfactory manner a cut % inch deep by 1/16
inch feed.
We now have sufficient data to satisfactorily design a
cross-rail for the larger planer.
If we assume that the deflection of
the tool produced in the two cases should be identical in order to
have the work equally satisfactory, we will find that the pressure
upon the tool of the larger planer will be 4 times that upon the tool
of the smaller; that both the bending and the twisting moments set
up in the cross-rail will be 8 times as large, and that the distance
over which these moments will operate to produce a deflection will
be twice as great. Therefore, if the two rails had the same crosssection, the deflection of the tool of the larger machine would be 16
times that of the tool of the smaller. The stiffness of two bodies of
similar section varies directly as the 4th power of the ratio of their
homologous dimensions. Therefore, if we make the section of the
rail of the larger machine similar in form to that of the rail of the
smaller machine, each dimension twice as great as the corresponding
dimension of' the smaller rail, it will be 16 times as stiff and the
In case the rail of the
deflections in the two cases will be identical.
smaller machine were not of the best form to resist the stresses which
it must sustain, the form might be changed, the designer using his
best judgment as to what effect such change might have upon its
stiffness.
it is
CHAPTER
II
SPEEDS AND FEEDS OP MACHINE TOOLS
In designing machine tools of any type, be it a lathe, milling
machine, grinding machine, etc., aside from the correct proportioning
of the -parts, and the introduction of convenient means for rapidly
producing certain motions, a very important factor is to be taken into
the correct proportioning of the speeds and feeds
Before entering into an explanation of the
method which is to be set forth later, we will explain some of the
preliminary considerations which are to be met by the designer. Supconsideration, that
is,
of these various machines.
posing a problem of designing a lathe be presented; it follows, at once,
These
that certain conditions limiting the problem are also given.
limiting conditions may be considered as the size and material of the
piece to be turned.
consider the material of a piece to be machined as a limiting
condition for the reason that a lathe turning wood must run at a
We
different speed from one turning brass, and the latter at a different
speed from a lathe turning iron or steel. Then, again, in turning a
small piece, our machine will revolve faster than in turning a large
piece. The speeds required for machining advantageously the different
materials, according to the different diameters, may be termed "surface
Roughly speaking, the surface speeds for the different
speeds."
materials vary within comparatively narrow limits. We may assume
the following speeds for the following materials (using carbon steel
cutting .tools)
:
Cast iron
,
.
Steel
Wrought
.
30 to 45 feet per minute.
20 to 25 feet per minute.
30 feet per minute.
40 to 60 feet per minute.
iron
Brass
For cast iron as found in Europe, we may assume 20 to 35 feet per
minute; this lower figure is due to the fact that European cast iron
is
considerably harder.
The surface speeds above given are,^ of course, approximate, and
is left to the judgment of the designer to modify them according
it
1
to
the special given conditions. These surface speeds for cutting metal
are the same whether the piece to be cut revolves, or the cutting tool
revolves around the piece, or, as in a planer, the cutting tool moves
in a straight line along or over the work.
Therefore, the surface
speeds in a general sense hold good for all types of machines, such as
milling
machines,
lathes,
gear-cutting
machines,
drilling
machines,
planers, etc.
Suppose that a problem
and
to turn both cast iron
is
given requiring that a lathe be designed
and to turn pieces from one-half inch
steel,
No
12
16
MACHINE TOOL DRIVES
to twelve inches in diameter.
Simple calculation will show us that
a piece of work one-half inch in diameter, and having a surface speed
of 30 feet per minute, as would be suitable for cast iron, must make
230 revolutions per minute.
piece of steel, which is 12 inches in
diameter, with a surface speed of 20 feet per minute, must make 6.5
A
revolutions per minute approximately. It follows that the lathe to conform to the conditions imposed,, must have speeds of the spindle varying from 6.5 to 230 revolutions per minute. These are the maximum
and minimum speeds required. To meet the varying conditions of
intermediate diameters, the lathe will be constructed to give a certain
of speeds. The lathe, probably, will be back-geared and have
a four-, five-, or six-step cone.
,In a correct design these various speeds must have a" fixed relation
For reasons explained in Chapter III these speeds must
to each other.
form a geometrical progression, and the problem briefly stated is this:
"The speeds (the slowest and fastest being given) are to be proportioned in such a manner that they will form a geometrical progression."
The ratio of the gearing is also to be found. A geometrical progression
in a series of numbers is a progressive increase or decrease in each
successive number by the same multiplier or divisor at each step, as
number
3, 9, 27, 81, etc.
To
treat the problem algebraically let there be
number of required speeds,
=
6 = fastest speed,
d = number of speeds of cone,
= number of stops or intervals in
speeds,
= ratio of geometrical progression,
n
a =3 slowest speed,
n
the progression of required
1
or factor wherewith to mul-
f
tiply
any speed
to get the next higher.
Algebraically expressed, the various speeds, therefore, form the
fol-
lowing series:
a, af,
The
a/
2
a/
,
last, or fastest speed, is
Therefore, a/"-
1
=
b,
3
2
a/~ a/,
11 - 1
expressed by a/
and. also
by the letter
b.
or
/ n-i
n
b
-
,.and
/
~
=
J
IT"
.
^i
ct
a
Suppose we
have, as an example, a lathe with a four-speed cone,
In this case we would have four speeds for the cone,
triple geared.
four more speeds for the cone with back-gears, and still four more
speeds with triple-gears; therefore, in all, twelve speeds. Assuming a
11
and the
as the" slowest speed in this case, 6 would be expressed by af
series, therefore, beginning with the fastest speed,, would run
,
af
The four
1
,
af, af
.af af, a.
which are obtainable by means
,
fastest speeds,
alone would be
11
af
,
of
,
af af
,
.
of the cone
SPEEDS AND FEEDS
members
Dividing each of the four
the following series:
13
of this series
by f, we obtain
4
af, af, af, a/
,
as the speeds of cpne with back-gears.
Again dividing the series of speeds of the cone of11 to a/8 by f*Xf*
f* we obtain the series
af, af a/, a,
,
as the series of speeds of cone with triple-gears.
We have, therefore, in this way accounted for all the twelve speeds
that the combination given is capable of, and it is now very evident
that the ratio of the back-gears must be f* or, in general, fd , If d
number of speeds of cone, and the ratio of triple-gears /* (or, In gen.
=
t
eral, /?*).
carrying this example still further, we would find that the ratio
would be f d
We can summarize the preceding statements, and put them in a more
convenient form for calculation by writing:
By
qf quadruple-gears
.
= dig
= 2d
Ig of ratio of back-gears
"
Ig of ratio of triple-gears
Iff
We
=3dlgf
of ratio of quadruple-gear^
The problem, with this consideration,
ple will be worked out below.
f
Ig f
therefore, is solved.
An exam-
now
consider a complication of the problem which very
Should the overhead work of the drive in consideration
have two speeds, then we will obtain double the number of available
speeds for the machine/ and this number of speeds may be expressed
by 2n, in order to conform to the nomenclature used above. This
modified problem is treated just as the problem above, and the series
of speeds is found as in the first case, and we have as a factor
will
often occurs.
We
must consider now that one-half the
obtained, speeds are due to
overhead speed, the other half to the second.
In writing the odd numbers of speeds found in one line, and the even
numbers of speeds in another, we obtain the following two series:
the
first
a,
a/ a/ 4
3
5
a/ a/
a/,
2
.a/
,
2
a/
,
"-4
,
2n ~3
,
a/ 2 "-2
2 "a/
1
In examining these two series, we will find that they are both
geometrical progressions, and furthermore, that both progressions have
the same factor, and calling this factor, flt we have
fc=rf,
and the ratio of the two counter-shaft speeds is equal to f, because to
obtain any speed in the second series we multiply the corresponding
speed in the first series by f. The two series in our case are due to
the two overhead speeds. We need to concern ourselves with only one
(either one of the two series), and without going again through the
14
No. 16
MACHINE TOOL DRIVES
explanation for the first case,
the following- conclusions
it is
very evident that
we
will arrive at
:
Ig of ratio of back-gears
Ig of ratio of triple-gears
Ig of ratio of quadruple-gears
= d ^
= 2d ^
= 3<Z70/
Ig
Ig
:
1
the desired speeds and the ratios of
way
Having
the gears, it is a simple matter for the designer to determine the
actual diameters of the various steps for the cone and for the gears.
To do so he has at his disposal various methods,* 'which need not be
explained here. The main thing for him to have is a geometrical
progression of speeds, as a foundation for his design.
in this
obtained
all
Problem 1. A Triple-Geared Lathe
Suppose the following example to be given: Proportion the speeds
and find the gear ratio of a six-step cone, triple-geared lathe; slowest
speed, 0.75 revolution per minute; fastest, 117 revolutions per minute.
This example of a six-step cone, triple-geared, will give us eighteen,
1
available speeds. Using our previous notation, ft
18, -n
17, a
0.75,
and
6
= 117;
=
=
=
therefore
17
_" 1 ""
/
slj^~
;
I"
The slowest speed being given, we multiply it by the factor / ta
obtain the next higher, and this one in turn is again multiplied by the
COMPLETE CALCULATION OP CONE PULLET SPEEDS
Ig
0.75
Iff
/
!
= 0.8750613
= 0.m0073
0.0040686
0.1290073
0.1330759
1.0361270
1
= Ig
1.009
1.1651343
0.1290073
= Ig
1.358
1.2941416
= lg
1.4231489
1.828
0.1290073
0,3910905
0.1290073
0.5200978
0.1290073
0.6491051
0.1290073
0.7781124
0.1290073
0.9071197
0.1290073
*
and
II.
10.867
= Ig
14.626
= Ig
19.685
=
26.494
Ig
0.1290073
=
70
1.5521562
21461
= Ig .35.658
0.1290073
= lg
3.312
1.6811635
0.1290073
= Ig
4.457
1.8101708
0.1290073
=
7^
5.999
1.9391781
0.1290073
= 70
8.074
2.0681854
See MACHINERY'S Reference Series, No.
ters I
Ig
0.1290073
0.1290073
0.2620832
=
0.1290073
14,
= 70
47.991
= 70
64.591
=
86.932
70
= 70 117.000
Details of Machine Tool Design, Chap-
SPEEDS AND FEEDS
15
factor f, and so on, until we have reached the highest speed
17th root of 156 is easiest found by the use of logarithms.
We
6.
The
have
lg f
Ig 156 = 2.1931246
= 1/17 Ig 156 = 0.1290073
=
1.3459
f
follow out the multiplication by finding the logarithm of
0.75, the slowest speed, adding to it the logarithm of the factor f to
obtain the logarithm of the next higher speed; and adding the logarithm
of factor f to the sum of these two logarithms will give us the log-
Now we
arithm of the next higher speed.
the numbers for these
By looking up
we
The complete
find these speeds to be 1.009 and 1.358.
is given in tabulated form on the previous page.
for example, the number of speeds of cone d equals 6, and
logarithms,
calculation
Now,
according to our formula, the logarithm of the ratio of the backd lg f, and the logarithm of the ratio of the triple-gears
gears
2d Iff f. Expressed in figures we have:
0.1290073 X 6
lgf
0.7740438, and the ratio of the back-gears
5.9435. Further, 12 70 f =1.5480876, and the ratio of the triple-gears
=
=
=
=
=
=
35.325.
Problem
Lathe with two Counter-shaft Speeds
2.
Suppose the following example is given: Proportion the speedf and
find the gear-ratio of a four-step cone, back-geared, two speeds to
counter-shaft; slowest speed, 25 revolutions per minute; fastest speed,
500 revolutions per minute.
In this case n
8; 2n =16; and, consequently,
=
15
=
~500
|~500
Nl
1B
=
|
20
In following out the calculation as
the following series of sixteen speeds:
1) 25.00
5)
55.58
2) 30.53
6)
67.86
3) 37.28
7)
82.86
4) 45.51
8)
101.18
- 1 221
'
NJ
shown
in
Problem
1,
we
obtain
13) 274.64
14) 335.35
9) 123.54
10) 150.85
11) 184.20
15) 409.48
12) 224.92
16) 500.00
Of these sixteen speeds, eight are due to one over-head work speed;
the other eight are due to the second over-head work speed.
write
We
the odd and even speeds in two series, as below:
First Series.
1)
25.00
Second
Series.
2)
30.53
3)
37.28
4)
45.51
5)
55.58
6)
67.86
7)
82.86
8) 101.18
9)
123.54
10) 150.85
12) 224.92
14) 335.35
11) 184.20
13) 274.64
15) 409.48
In order to find the ratio of the back-gears,
of these two series, and as explained above,
16) 500.00
we can use
A
= f.
We
either one
therefore
16
No. 16
MACHINE TOOL DRIVES
= ratio
1.221'=: A, and further 4 X ty A
this the ratio of the back-gears
4.9418.
of counter-shaft speeds
1.221.
f
have
= =
=
We
From
back-gears.
that the ratio
of
know
also
This method of geometrically proportioning speeds in machine drives,
which has been explained at length, will be found, after one or two
applications, a rather simple one. But its usefulness is not limited to
the proportioning, of speeds in machine drives, as
to the proportioning of feeds.
it
can also be applied
Feeds for Machine Tools
Before proceeding to apply this method to geometrically proportioning feeds in machines, a few remarks on feeds may not be out of
By feeds are understood the advances of table, carriage, or
place.
work, in relation to the revolutions of the machine spindle. Feeds
may be expressed in inches per minute or inches per revolution of
spindle. In a table given below, feeds for different machines are given
in inches for one revolution per spindle, where not otherwise specified.
This table is supposed to represent modern practice, with carbon steel
cutting tools, but the figures given, of course, represent general experi,
ence,
and special
no doubt,
cases,
will often
modify them considerably.
Feed, Inches.
Plain milling machine
.
0.005-0.2
- 0.3
- 0.2
0.003 - 0.25
0.005 - 0.1
Large plain milling machine
Universal milling machine
Large universal milling machine
Automatic gear cutter, small
0.010
Drills
0.004-0.02
0.003
(spindle-feed)
-
Planing machine (traverse feed)
0.005
Slotting machine (feed, of work)
Drilling long holes in spindles (per revolution
0.005 - 0.2
of drill)
0.003
;
-
0.7
0.01
56-80 turns per inch
Lathes, feed for roughing
Lathes, feed for finishing
112
turns per inch.
Universal Grinding Machine
Surface speed of emery-wheel, 4,000-7,000 feet per minute. Traverse
of platen or wheel, 2 to 32 inches per minute; the fast feeds are for
cast iron. Surface speed of work on centers, 130--160 feet per minute!
For internal work use the following surface speeds of emery-wheel
(highest nominal speeds), with no allowance for slip of belt; lowest
nominal speed about 40 per cent less. Any speed between should be
1
obtainable.
Diameter of Wheel.
1 5/8
Feet per Minute.
3,600
1
2,750
3/4
2,100
7/16
1,450
1,100
1/4
:
Surface Grinding Machine
Surface speed of emery wheel, 4,000-7,000 feet per minute.
Table
SPEEDS AND FEEDS
17
speed per minute, 8-15 feet. Cross feed to one traverse of platen, 0.0050.2 inch.
Cross fee to one revolution of hand-wheel, 0,25 inch.
Problem 3 The Feeds of a Milling Machine
The problem of proportioning the feeds of different machines varies
in each case, although always embodying similar principles.
It is,
therefore, proposed to take a typical case and apply the method to the
problem presented, and in this way explain the advantages of the
particular method referred to.
Machine ry,N.Y.
Fig.
In Fig. 1
General View of Milling Machine, having Cone Pulley Feed
1.
given an outline drawing of a milling machine. The
not one of the latest designs, because it is easier to
comprehend the principles involved in a type such as shown. The
is
type selected
is
application, of the principles, however, is, with few modifications, the
same for the most modern gear-feed types, as for the one shown. The
Given the fastest and
problem in this case will be the following:
slowest
feeds
per
one revolution
of
main
spindle,
proportion
the
18
MACHINE TOOL DRIVES
No. 16
manner that they
required feeds in such a
progression.
Cones
D
and
E
will,
as well as pulleys
X
form a geometrical
and Y can be trans-
posed.
The main data with which we have to concern ourselves about- this
machine may be assumed to be. as follows: lead screw, four threads
advance of screw per one revolution, 0.25 inch;
per inch, single
;
largest feed wanted, 0.25 (equal to one revolution of screw) ;. smallest
feed wanted, 0.005 inch (equal to 1/50 revolution of screw)
for one
;
revolution of screw, shaft P (see Fig. 1) makes thirty revolutions;
for 1/50 revolution of screw, shaft P makes 30 4- 50
0.6 revolutions.
The ratio of revolutions between the screw and shaft P is therefore
in our example as 1 to 30; that is, given the .revolutions of shaft P
=
we
divide this number by 30 to obtain the revolutions
The revolutions of the screw multiplied by the lead L
of the screw,
(in. this case
equal to 0.25) gives the advance for given revolutions of P.
Y ratio of train from P to screw,
L lead of screw,
Let
=
=
R = revolutions of shaft P per one revolution of spindle,
p = advance or feed of screw per one revolution of spindle,
p
ex-
pressed in inches.
We
have
RP L
(1)
RP
If
now n
Vp
=-
(2)
L
equals the numbers of feeds wanted,
we
obtain for
f,
the
factor wherewith to multiply each feed to get the next higher feed,
in
which
6 is the fastest,
and
a,
the slowest speed of shaft P.
That
is,
in the present case
R maximum = 30 =
Rp minimum =0.6
p
6.
a.
The problem in our case stated that cones D and E, as well as pul-X and Y could be transposed. The cones have four steps, and
transposing them gives us eight speeds. Pulleys X and Y being also
transposable gives, therefore, 2 X 8 == 16 speeds. The numerical value
leys
for f is therefore in our case,
The maximum and the minimum speeds
of shaft
P
per one revolu-
tion of spindle of machine, as well as the number of steps required,
being known, we now readily obtain a geometrical series with the mini'
mum
speed of shaft
P
as a beginning, and the
maximum
speed as the
SPEEDS AND FEEDS
19
in the
The numerical values that follow are found exactly
last step.
same way
as the values for the different speeds of a lathe drive ag
already shown. The required speeds of shaft P are then:
1)
0.6
5)
1.7.0
4.83
13) 13.72
2)
0.78
6)
2.21
10)
6.27
3-)
1.01
7)
2.87
11)
8.14
4)
1.31
8)
3.72
12) 10.57
14) 17.81.
15) 23.11
16) 30.00
The value
9)'
of p, in our case, becomes, according to
p=
J?p
X 0.25
__
=
formula
(1),
0.0083 jRp
30
which R p the number of revolutions of shaft P, has the different
values found above. By substituting these values of JR P we obtain the
following feeds, which are the feeds of the lead screw per one turn
in
,
,
of
machine spindle.
= 0.005 inches
= 0.0065 "
"
3)1.01X0.0083 = 0.0084
"
=
0.0109
4)1.31X0.0083
"
5) 1.70X0.0083 = 0.0141
"
=
0.0183
6)2.21X0.0083
"
7) 2.87X0.0083 =
=
0.0308
8)3.72X0.0083
1)0.6 X 0.0083
2)0.78X0.0083
0.02*38
"
= 0.0400 inches
= 0.0520 ""
= 0.0677
11)
"
12)10.57X0.0083 = 0.0877
"
13) 13,72 X 0.0083 = 0.1138
"
=
0.1513
14)17.81X0.0033
"
23.11X0.0083 = 0.1918
"
=
0.2500
16)36.00X0.0083
9)
4.83 X: 0.0083
10.)
6.27X0.0083
8.14X0.0083
15.)
We now write the speeds found for shaft P in two columns, one containing the .odd numbers and the other the even numbers, in this
manner:
The
1)
0.6
2)
0.78
3)
1.01
4)
1.31
5)
1.70
6)
2.21
7)
2.87
8)
3.72
9)
4.83
10)
6.27
11)
8.14
12) 10.57
13) 13.72
15) 23.11
14) 17.81
16) 30.00
column forms a geometrical progression,
and we assume that the speeds in the first column are due to the position of the pulleys X and Y as shown in the outline drawing, Fig. 1,
and that the speeds in the second column are due to a reversed position of X and Y.
That is to say, the speeds in the second column
above are obtained after having changed Y to X and X to Y. As these
speeds in the second column are equal to the speeds in the first column
multiplied by factor f, it follows that the two speeds of shaft R are
to each other as 1 is to f. Assuming these two speeds to be m and n,
series of speeds in each
the proportion exists,
m:n=l:f
(3)
Supposing x and y to represent the diameters of the respective
leys;
it
will be evident that
pul-
20
MACHINE TOOL DRIVES
No. 16
1
x x = my
;
m=
or,
x
(4)
y
1
X
y
= nx
;
n
or,
=
y
(5)
x
Substituting the values (4) and (5) in formula (3)
x y
- :-
=
!
y x
The value
each other.
erom
f
=y
=
y
x y
x
-
:
-=
-
y
x
-
=
x
we have
y*
(6)
x*
known, we have in formula (6) an expression
which the diameters of the pulleys X and Y must bear
Putting this formula into a more handy shape we find
of f being
of the relation
to
:f,orf
x
y
2
3-
or
y*
=
fx*,
ory
=
\/fx~*
2
X*
=
y
-, OYX
f
= \
(7)
IF
-
(8)
\/
In using either (7) or (8), and assuming one diameter, the other
one is easily found. The remaining part of the problem, that is, to find
the diameters of the cone, is now a simple matter.
CHAPTER
III
MACHINE TOOL DRIVES
The present chapter contains considerable matter already treated
II. In order to make the present chapter a complete whole
in Chapter
by itself, it has, however, been considered advisable to repeat such
statements and formulas as are necessary to fully comprehend the
somewhat different treatment of the subject presented in this chapter.
One of the first problems encountered in the design of a new machine
The importance of a properly
tool is that of laying out the drive.
proportioned drive is coming more and more to be recognized. The
use of high-speed steels, and the, extra high pressure under which
modern manufacturing is carried on, precludes the use of any but the
;
most modern and efficient .drive.
The drive selected may be one of the following different kinds,
depending on the conditions surrounding the case in hand: We may
:
the drive to consist of cone pulleys only; we may use cone pulleys in conjunction with one or more sets of gears; or we may make
our drive to consist of gears only, depending on one pulley, which
runs at a constant speed, for our power. If the conditions will allow,
make
use an electric motor, either independently or in connection
with suitable gearing.
we may
MACHINE TOOL DRIVES
21
After having selected the form which our drive is to take and the
of power to be delivered, which we will assume has been
decided upon, we may turn our energies to the problem of arranging
the successive speeds at which our machine is to be driven. As most
machines requiring the kind of drive with which we are here concerned have spindles which either revolve the work, or a cutting tool
that has to be worked at certain predetermined speeds dependent on
the peripheral speed of the work or cutter, a natural question to be
asked at this point is, "What is the law governing the progression
of these speeds?"
As an example to show what relation these speeds must bear to one
another, let us suppose that we have five pieces of work to turn in a
lathe, their diameters being 1, 2, 5, 10, and 20 inches respectively.
In order that the surface speed may be the same in each case we must
revolve the one-inch piece twice as fast as the two-inch piece, because
the circumference varies directly as the diameter, so that a two-inch
piece would be twice as great in circumference as the one-inch piece.
The five-inch piece would revolve only one-fifth as fast as the one-inch
We have
piece; the 10-inch piece l/10th, the 20-inch piece l/20th.
seen that the addition of one inch to the diameter of the one-inch
piece reduces the speed 100 per cent. If we add one inch to the twoinch piece we reduce the speed 50 per cent, and similarly one inch
added to the 5-, 10-, and 20-inch' pieces reduces the speed 20, 10, and 5
per cent respectively. From this we see that, the speed must vary
It also
inversely with the diameter for any given surface speed.
shows that the speeds differ by small increments at the slow speeds,
the increment gradually increasing as the speed increases.
Speeds
laid out in accordance with the rules of geometrical progression fulfill
the requirements of the above conditions.
If we multiply a number by a multiplier, then multiply the product
by the same multiplier, and continue the operation a definite number
of times, we have in the products obtained a series of numbers which,
are said to be in geometrical progression. Thus 1, 2, 4, 8, 16, 32, 64
are in geometrical progression, since each number is equal to the one
preceding, multiplied by 2, which is called the ratio. The above may
be expressed algebraically by the following formula:
amount
b
where
the
=
a
r*-- 1
term or number which is the nth term from a which i
term in the series. The term r is the ratio or constant mul-
6 is a
first
tiplier.
If we
we may
speeds
are given the maximum and minimum of a range of speed:
find the ratio by the following formula, when the number of
is
given:
a
As most
use of logarithms,
we
we would
use this formula would require the
will express the above as
cases in which
22
MACHINE TOOL DRIVES
No. 16
Log r
= Log
b
Log a
n
1
we
are designing a drive which is to give a range of
18 spindle speeds, from 10 to 223 revolutions per minute. Now the
first thing to be done is to find the ratio r, which, by the above formula
is found to be 1.20, and by continued multiplication, the series is
found to be 10, 12, 14.4, 17.25, 20.7, 24.85, 29.8, 35.8. 43, 51.6, 62, 74.4,
Let us suppose
89.4, 107, 129, 155, 186, 223.
Our drive can be made to consist of one of the many forms just
As the cone and back-gear is the most common form, and
mentioned.
fills
the conditions well,
we
will choose that style drive for the case
We may
have a cone of six steps, double back-gears and one
counter-shaft speed, such as would be used in lathe designs, or we may
use a cone with three steps, double back-gears and two counter-shaft
speeds as is used in milling machines. This latter plan will be followed
in hand.
in our present case.
There are two methods of arranging .the counter-shaft speeds. First,
by shifting the machine belt over the entire range of the cone before
changing the counter-shaft speed; and second, by changing the countershaft speed after each shift of the machine belt. The method used
will have a very important effect on the design of the cone. The cone
resulting from the former practice will be quite "flat," with very small
difference in the diameter of the steps, while the use of the second
method will produce a cone which will have a steep incline of diam-
Some favor one, some the other. The controlling point in
favor of the first method is the appearance of the cone obtained.
"We will first design our drive with the conditions of the first method
in view; that is, we will arrange our counter-shaft speeds so that the
full range of the cone is covered before changing *the counter-shatt
speed, thus obtaining the flat cone. Tabulating the speeds in respect
eters.
to the
way they
CONE.
are obtained,
we have
MACHINE TOOL DRIVES
23
The ratio of counter-shaft speeds is
spending term in column 4.
obtained by dividing a term in column 5 by a corresponding term in
column 6; and the ratio of speeds off each step of the cone, by dividing
the term corresponding to step 1 in any column by a term corresponding to step 2 or 3, as desired, from the same column. The results for
the present case are as follows:
Ratio
Ratio
Ratio
Ratio
Ratio
of large ratio gears is
of small ratio gears is
8.94
to 1
2.98
to 1
of counter-shaft speeds is
of speeds off step 1 to those off step 2.
1.725 to 1
1.2
to 1
of speeds off step 1 to those off step 3
1.44
to 1
The matter of designing the cone seems to cause trouble for a good
many, .if we are to judge by the results obtained, which are various in
LARGE GEAR RATIO =8.94
14.9'"
SMALL GEAR RATIO -2. 08
LOOSE ON SPINOLE,
LOCKED TO SPINDLE
WHEN GEARS ARE -THROWN OUT
'Fig. 2.
Two Methods
of Laying out the Cone for a Double Back-Geared Spindle.
collection of machine tools, even in those of modern design.
It
possible to design a cone so as to obtain speeds in strict accordance
with the, geometrical series. In most cases the counter-shaft cone and
any
is
the one on the machine are made from the same pattern, so that itjs
necessary that the -diameters be the same for both cones, and since
the belt is shifted from one step to. another, its length must be kept
24
No. 16
MACHINE TOOL DRIVES
constant.
This is accomplished by having the sum of diameters of
corresponding steps equal.
We will take as the large diameter of the cone, 15 inches. The ratio
of the speeds off step 1 and step 3 is 1.44 to 1. This ratio also equals
DXD
dXd
where
D
of smallest step.
is
the diameter of largest step and d
Making them opposite terms
1.44
DXD = D
=r
d
Xd
X d = D-
d
or 1.44
15
I
X
15
I
-\1.44~"
The sum
N
in
is
the diameter
an equation we
get,
2
2
2
= 12.5
inches, diameter of small step.
1.44
of the corresponding diameters on the cones is 15
+
12.5
=
27.5.
Since this
27.5
fore
is
a three-step cone the middle steps must be equal. There-
= 13.75 = diameter of middle step.
We
found that the ratio
2
of the speeds oft first and second step is 1.2. Let us examine the above
figures to see that the diameter of the middle step is correct. Thus,
13.75
15
"
'
12.5
13,75
is the correct ratio.
This cone is shown in full lines in Fig. 2.
Let us now figure the .diameter of the back-gears. We will assume
that the smallest diameter possible for the small gears in the set is
which
5 inches. In order to keep the gears down as small as possible we will
take this figure as the diameter of the small gear here. It is general
practice, though obviously not compulsory, to make the two trains in
a set of "back gears equal as to ratio and diameters. When double
back gears are used, -the large ratio set is made with two trains of
similar ratio. The small ratio set is then composed of two trains of
gears whose ratios are unlike. The ratio of each train in the large
ratio set, if taken as similar, is equal to the square root of the whole
2.98, and from this the large
ratio; thus, in our drive we have \/S~94
The ratio of the small
14.9 inches in diameter.
gear is 5 X 2.98
ratio set is equal to 2,98, and as one train of gears in the double back
gear arrangement is common to both sets, the remaining train in the
=
=
+
=
9.95
14.9. rf- 2
small ratio set must be of equal diameters, or 5
inches, as shown in Fig. 2. These figures will have to be slightly altered in order to adapt them to a standard pitch for the teeth, which
part of the subject we will not deal with here.
In order to be able to compare the results of the two different methods of selecting counter-shaft speeds mentioned above, let us figure out
the dimensions of a drive with counter-shaft speeds arranged according
to the second method.
Proceeding in. a manner similar to that pursued for the case treated
above, we may tabulate the speeds as shown in the table on next page.
MACHINE TOOL DRIVES
CONE.
No.
-'6
16
MACHINE TOOL DRIVES
speed range of the latter type motor, which would cause a slight bend
in the curve, making it convex toward the right.
Motors using the
multiple-voltage system, or the obsolete armature resistance control,
would show curves quite as irregular as those from the cone and backgear drive.
Another method of comparison is by charting the pull or torque at
the spindle for each spindle speed. This is done in Fig. 4, where the
230
220
210
200
<D
-
S
180
17fi
MACHINE TOOL DRIVES
27
second method. The only good point the first method has over
the second is in the appearance of the cone which has, apparently,
powerful lines,' which are, however, misleading, as has been shown.
of the
Another disadvantage of the
first
method
Pull at Spindle in Inch-
is
the wide ratio of tne
Pounds
Machinery,
Fig. 4.
Comparison of Torques
for
Various Methods of Driving
counter-shaft speeds, where, in order to get sufficient power out of
the slow speed counter-shaft belt, we must have the high-speed pulley
running at almost prohibitive speed, which soon tells, and as loose
pulleys are a source of annoyance when their speed is moderate, trouble
is
sure to appear
when
the limit of speed
is
approached.
CHAPTER
IV
GEARED OR SINGLE PULLEY DRIVES
\
Whether the geared
drive, so called in order to distinguish it
from
the belt drive used with stepped cone pulleys, originated with some machine tool builder who was desirous of improving a given machine, or
whether it was first suggested by a machine tool user in an endeavor
to secure better facilities for machine operation, would be interesting
to know, but difficult to determine.
Whatever the origin, the geared drive is a. response to a demand for
a better method of speed variation than could be obtained from
stepped pulleys and a movable belt. The gradually growing demand for
more powerful machine drives in the past has led to the widening of
belts to the maximum point consistent with a desirable number of
steps of the pulley, and the ease of belt shifting. The limiting point
for belt width may be said to be reached when a belt can no longer
be shifted easily by hand. For some machines, notably lathes, the
maximum diameters of the driving pulleys are generally limited by
conditions inherent in the machine themselves.
Back-gears were in. many instances increased in ratio to make up
for what could not be had by further increase of belt, widths or pulley
diameters, until in some cases the gap between speeds obtained directly by the belt and those obtained through the back gears became too
great. When such conditions were reached, obviously, the next suggestion involved the combination of a constant speed belt of such a width
and operated at such a speed as to give the requisite ..power, in connection with some combination of gears to be used for obtaining the
desired variation in speeds. Such a combination is, in fact, a reversion of type; a going back to a system of driving formerly much used
by foreign builders of machine tools.
Many foreign builders objected to the use of stepped pulleys, considering their use as a deviation from, or, as being contrary to, good mechanical practice, preferring in many cases to secure speed variation by means of separate
changeable gears. The objectionable feature of such a system did not
suit American ideas, hence the early adoption of stepped pulleys and a
movable belt as a means of quickly effecting changes even though the
device was and is still considered by some designers as anomalous or
paradoxical from the standpoint of pure mechanics. The substitution
of the variable speed geared drive for the stepped pulley drive is therefore not due to" any inherent defect in the stepped pulley so much
as to its limitations as previously mentioned, and to a desire, for im-
proved
facilities
for quickly obtaining speed variations.
For belt-driven machines that require a variable speed, the geared
drive will probably come more into use whenever its adoption will be
Whatever
justified from a productive or a commercial standpoint.
GEARED OR SINGLE PULLEY DRIVES
29
defects may be existent in any of its varied forms will be tolerated just
as long as it meets and fulfills required conditions.
As a device of utility the geared drive has passed the point where it
might by some have been considered as a
fad.
As
a*
matter of
fact,
new
device representing a radical departure from generally accepted design and practice has ever been brought out that
was not considered a fad by some one. The history of machine tool
scarcely any
progress has shown that the fad of yesterday has frequently become
the custom or necessity of to-day. Extreme conservatism will see a
fad where progress views an undeveloped success. One drawback to
the general adoption of any geared drive is its -cost, and this will deter-
mine in most cases whether it or a belt drive shall be used; it is a
matter requiring careful judgment to determine the point where the
results obtained justify the added expense.
It is,
however, with very few exceptions, the opinion among builders
and users
of
machine
persede the cone drive.
tools that the single pulley drive will largely suStill for certain conditions it is doubtful whether
we will find anything better than our old servant, the cone. The two principal advantages possessed by the single pulley drive are:
First, a
great increase in the power that can be delivered to the cutting tool
owing
to the
stant, the
high
initial belt speed.
The
belt speed always being con-
practically the same when running on high or low
cone acts inversely in this respect; that is, as the diameter
power
is
speeds. The
of the work increases, for a given cutting speed, the
power decreases.
As a second advantage, the speed changes being made with levers, any
speed can be quickly obtained.
To these might be added several other advantages. The tool can
be belted direct from the lineshaft; no counter-shaft is required;
floor space can be economized. It gives longer life to the driving belt;
cone belts are comparatively short-lived,, especially when working to
There are, however, some disadvantages to be
capacity.
encountered. Any device of this nature, where all the speed changes
are obtained through gears, is bound to be more or less complicated.
The first cost, as mentioned, is greater. There is also more waste of
power through friction losses. A geared drive requires more attention, break-downs are liable to occur, and for some classes of work
it cannot furnish the smooth drive obtained with the cone.
Most of
these objections, however, should be offset by the increased production
obtained.
their full
To the designer the problem presented is one of obtaining an ideal
variable speed device, something that mechanics have been seeking
for years with but poor success, and it is doubtful whether we w'ill
get anything as good for this purpose as the variable speed motor in
combination with double, friction back-gears anti a friction head.
There are, it is true, some very creditable all-gear drives on the market in which the problem has been attacked in various ways. Still
there is ample room for something better. The ideal single pulley
drive should embody the following conditions.
1. There should be sufficient speed changes to divide the total range
30
No. 16
MACHINE TOOL DRIVES
into increments of say between 10 and 15 per cent.
2. The entire range of speeds should be -obtained without stopping
the machine.
3. Any speed desired should be obtained without making all the
intermediate changes between the present and desired speed.
4. All the speeds should be obtained within the tool itself, and no
auxiliary counter-shaft or speed variators should be used.
5. Only the gears through which the speed is .actually being obtained
should be engaged at one time.
6.
The
least possible
number
of shafts, gears
and levers should be
used.
.There are few subjects in machine design which admit of so many
combinations, arrangements and devices. In Figs. 5 to 10, inclusive,
are shown some examples taken at random from a large collection. All
of these, except Fig. 10,. have the number of teeth and the speeds
marked. Each has some good points, but none of them possesses all the
The only reason for showing them is to
points referred to above.
show what a vast number of designs can be devised. One ,of them,
that shown in Fig. 5, has been built, a number of machines have been
running for over, a year, and they give very good results. In Fig. 11
is shown" the way the idea was worked
Blond lathe.
out, as applied to a 20-inch
Le
The design for the headstock shown in Fig. 11 needs little explanaThe friction
tion since the drawing shows the parts quite clearly.
and
clutch on the driving-shaft Z, which alternately engages pinions
J, is of the familiar type used in the Le Blond double back-geared
H
moves the
milling machine. Sliding collar D, operated by handle
double tapered key E either to the right or left as may be desired, raisor Y within
or W, which in turn expand rings
ing either wedge
the recess in either of the two cups, F and F'. Either of two rates of
,
W
speed
is
thus given to quill gear
X
K
and the two gedrs L and
M
keyed
On the spindle is a triple sliding gear which may be moved to
engage P with M,~O with L (as shown in the drawing) or N with K,
thus giving three changes of speed when operated by lever T. The six
speeds obtained by the manipulation of levers S and T are doubled by
to
it.
throwing in the back-gears, giving 12 speeds in all.
In comparing the merits of a series of gear drive arrangements
like those shown in Figs. 5 to 10, one might apply the "point" system
in determining the most suitable one. The number of points that are
to be assigned to a device for perfectly fulfilling any one of the various requirements would be a matter requiring nice discrimination.
So the- method outlined below is to be taken as being suggestive, rather
than authoritative. The first requirement is that there shall be sufficient speed changes to divide the total range into increments of between 10 and 15 per cent. The six schemes proposed do not all, unfortunately for our proposal, take in the same range of speed; considering, however, that they were each to be designed to give from 9 to 240
revolutions per minute to the spindle, as in case Fig. 5, and that a 15
per cent increment is to. be allowed, the number of changes required
GEARED OR SINGLE PULLEY DRIVES
31
No. 16
MACHINE TOOL DRIVES
can be found in the usual way by dividing the logarithm of 27
the
total speed ratio required (240 -~ 9
27)
by the logarithm of 1.15,
which is the ratio of the geometric .series desired. This gives 24 speeds,
about, as needed to meet the requirements.
Suppose we assign 15
points to a machine having 24 speeds. Let us set this down in its
For the second
proper place in the suggested table given below.
qualification, that the machine shall not have to be stopped, we
=
may
assign 20 points to the ideal machine. The principle of "selective"
control is assigned 10 points. The fourth consideration, requiring that
all speeds shall be obtained, within the tool itself is a positive requireIf it is not met, the mechanism is out of the contest, so this
question need not be considered in our table of points. Fifteen points
axe suggested for the requirement that the gears not in use shall not
be running in mesh. The sixth requirement reads "The least possible
number of shafts, gears and levers should be used." It is suggested
ment.
A SUGGESTED TABULATION OF THE MERITS OP THE VARIOUS DRIVES
PROPOSED
Requirements.
GEARED OR SINGLE PULLEY DRIVES
I
33
34
No. 16
MACHINE TOOL DRIVES
We may therefore assign the value 7 to each of these designs on this
account. As to the question whether the gears not in use are running
idly in mesh, all the designs are nearly perfect. The values set down
in this table are suggested by this consideration.
In considering the
number
movements required to effect the number of changes obthrowing in of the back-gear is credited with four motions,
the stopping of the machine, unlocking of the spindle from the gear,
the throwing in of the back-gears, and the starting of the machine.
The 20 points of the ideal machine are then multiplied by each of the
ratios obtained by dividing the number of changes by the number of
movements, and the number of points found are set down as shown.
For the last item, twice as many changes as there are gears employed
With this
is taken as a maximum which can probably .not be exceeded.
as a standard, the ratio obtained by dividing the number of changes
by the number of gears used is employed to calculate the number of
points. Adding the number of points obtained in each column we find
that No. 1 has 67, No. 2. 3, and 4 each have 66, while No. 5 has 74, and
No. 6, 81.
The comparison has been undertaken in this way with the understanding that all the arrangements are susceptible of being embodied
That arrangement No. 6 is practicable is
in a practicable design.
of
tained, the
strongly to be doubted.
used are not given, and
The number
it is ..far
of teeth in the various gears
from probable that one could obtain
with this arrangement a series of speeds in geometrical progression
by moving in regular order the three levers required, Nos. 4 and 5,
while otherwise well arranged, are open to the objection that sliding
gears rotating at high rates of speed are used. This, if valid, constituted a disqualifying objection similar to that mentioned in relation
The first three cases in which a friction
to the fourth requirement.
clutch instead of sliding gears is used on the driving shaft are therefore much to be preferred for this reason. Of these first three cases,
our tabulation shows that case No. 1 has a slight advantage, and Fig.
lathe
11, in which this arrangement has been applied to a 20-inch
headstock, shows that the scheme is a simple and satisfactory one, so
far, at least,
as one can judge from a drawing,
CHAPTER V
DRIVES FOR HIGH-SPEED CUTTING TOOLS
What has been considered in the past as marvelous in the perform-,
ance of high-duty cutting tools may now be compared with the proved
results of air-hardening cutting tools.
The metallurgist has proved
to us, and a great many machine tool builders have satisfied themselves
by practical experiment, that the high-speed cutting steels are at our
service, but they must be properly shod if they are to be used to the
best advantage. Some concerns who have experimented with the highspeed steels, and who anticipated much, have failed through lack of
a proper, analysis of the conditions which accompany the use of the
high-speed cutting steels. It takes but a moment's reflection to convince one of the absurdity of trying to get as effective a fire from a sixinch as from a thirteen-inch gun, even though the same explosive
charge is used in both.
Some viewed this unusual commotion about the high-speed cutting
steels as being somewhat fanatical or -a fad which would rage for a
time, and then die a natural death, as many others have done. True,
this was not the first high-duty cutting steel which had been advanced
with enormous claims of efficiency. Mushet steel had been on the market for several years, and the great things predicted for it did not
The chief reason for this was
fully meet everybody's expectations.
its far too limited use in a great many cases, on account of its being
expensive, difficult to forge, grind, and to get a satisfactorily finished
surface with it, and the failure of the machine to stand up to the
chip it could take. Then again, when Mushet steel was introduced,
competition among machine tool builders for increased product from
their machines did not begin to compare with that which now exists
'with firms which more than ever are on an intensely manufacturing
basis. Manufacturing plants of any considerable size using metal cutting tools are bidding nowadays for special machinery of the simplest
form to augment the output of a single product, and not comparatively
complicated combination tools, designed for many operations on many
pieces, and which save considerable room and first cost of installation,
but are of necessity inconvenient, and unsuitable for high-duty service.
The complaint which has been made by some that the new highspeed cutting steels are unfit for finishing surfaces cannot be consistThe modernly-designed manufacturing grinder has
ently sustained.
unquestionably proved to be the proper tool for finishing surfaces
v
from the rough; and undoubtedly, and beyond peradventure, the
grinder is the natural running mate for the high-duty turning lathe
and planer; and it seems probable that, instead of the grinder being
a rarity and a luxury in shops, as a sort of tool-room machine, it
'
36
No. 16
MACHINE TOOL DRIVES
much in evidence -for manufacturing purposes as the more
commonly-known machine tools of the present, or more so.
The innovations of the day in machine tool evolution are in most
remarkable harmony and synchronism. The electric motor, which is fast
developing the independent machine drive, demands a high speed for
maximum efficiency of the motor; and what do we find contemporanewill be as
ously developed but the high-speed cutting steels, the practicable commercial grinder, and the comparatively high-speed non-stroke milling
machine to supersede the comparatively slow multi-stroke planer?
Unquestionably, there never, has been in the whole history of the
machine tool business such an opportunity for the enterprising capitalist, the engineer, and the designer, to invest their money, brains and
skill in a type of machine tools that will be as different from the present type of machine tools as the nineteenth century lathe is from the
simple and crude Egyptian lathe of tradition.
The development of the cutting or producing end of the machine
appears to be further advanced than' the driving end. The direct
motor drive without inter-connecting belts, chains, and gears is undoubtedly the simplest, most convenient, and most effective. The motor
which is most desired has hot been designed, but it should be a comparatively slow-speed motor having high efficiency, whose speeds vary
by infinitesimal steps between its minimum and maximum limits,
fully -as simple as the ^commutatorless" type, and with far higher
pressures than are now used. In the meantime, during the process
of development, we shall have to be content with' the usual, compound-
ing elements between the motor and the driving spindle; but these
compounding elements, in order to keep up with the procession, will
naturally undergo revolutionary changes in design.
The silent chain drive and -the high-speed motor are mutual helpmates; geared variable speed devices and single-speed induction motors
are well wedded, but cone pulleys are practically just beginning to
receive that examination and attention which can fit them for the service of higher speeds.
.ln the case of a turning lathe, as would naturally be expected, we
k
are very much limited in the range of the sizes of pieces that can be
if we maintain an efficient range of speeds and sufficient diamand widths of pulleys for surface speeds of belts unless we use
an abnormally ponderous cone pulley, which is entirely out of the
turned
eters
To make
may
be well to analyze a spedesigned with a fourstepped cone and with "front-gears" (the speed ratios of front-gears are
figured the same as back-gears, but their thrust at the front box is
opposite in direction to that of -the back-gears and to the lifting effect
of the tool, as it properly should be), two countershaft speeds, and
for cutting 30-point carbon steel at a speed of 100 "feet, per minute with
a chip of 5/16 by 3/32 inch cross section. It is furthermore assumed
that the work and cutting tool are rigidly supported, and that the cutting tool has the proper amount of rake for least resistance and a
fair amount of endurance.
question.
cific
case.
We
will
this point clear,
it
assume that the lathe
is
DRIVES FOR HIGH SPEED CUTTING TOOLS
37
Calculation of Cutting Force of Tool, and Speed of Belt
In order to make absolute computations of the required diameters,
we should have reliable data on the amount of cutting force at the
cutting edge of the tool when cutting the various metals at high
speeds, reliable data for the best efficiency of the redesigned machine,
and the approximate distance between the centers of the driving spindle and counter-shaft. Several experiments were made by Hartig, and
subsequently by others, on the horse-power required at the cutting edge
of a tool when cutting various metals at slow speeds with the ordinary
tempered steels. The horse-power was determined by multiplying the
weight of chips turned off per hour by a constant whose value varied
with the degree of hardness of the metal cut and the conditions of
the cutting edge of the tool. The average of the several constants for
about 30-point carbon steel seems to be about 0.035.
Hartig's expression is given in the formula
H:P.
= cW = 0.035 XirX'DXnXdXfX
and the usual expression
for horse
0.28
X
60
(9)
given in the form,
is
=FXvXDXn
F8
H.P=
power
33000
33000
X
(10)
12
which
in
= horse power absorbed at the cutting edge of
= constant 0.035.
W = weight chips per hour.
D = mean diameter of the area turned
per hour.
n = revolutions per minute.
d = depth of chip.
= thickness of chip.
0.28 = assumed average weight per cubic inch of 30-point carbon
H. P.
tool.
c
.of
off
t
t
steel.
F= force at cutting edge of tool.
S = distance through which force
F
acts.
X
d
Equating (9) and (10),
F = 0.035 X
0.28
X
60
X
33000
Since the chip assumed to be cut
then the force at the cutting tool is
is
X
12
F = 232850 X
If
the cutting speed
is
X
*
= 232850
=
6820 pounds.
5/16 X 3/32 inch
100 feet per minute then the work at the tool
W = 6820
X
100
= 682000
foot-pounds.
machine is assumed at 85 per
the belt must be
If the efficiency of the
effective
work
of
W=
dt.
5/16 by 3/32 inch cross section,
682000
X
100
= 802500
cent, then the
foot-pounds.
85
We
assume that a 5-inch double belt is the practical limit for the
which can be conveniently used on the machine, and that the effective pull is 70 pounds per inch width when wrapped around a cast-
belt
will
38
No.
it-MACHINE TOOL DRIVES
iron pulley with a contact surface of 180 degrees.
pull is then
The
total effective
=
5 X 70
350 pounds.
Since our belt must deliver 802500 foot-pounds per minute, its velocity
will be
802500
V
2295 feet per minute, approximately,
350
which must be proportional to the diameters of the cone pulleys and
the counter-shaft speeds, which are obtained as follows.
It is customary to consider speeds in a series of geometrical progression -if the most efficient and convenient range of speeds is desired.
The constant multiplier will then be
=
=
i
r ''=
I
'in which
I
(in
= constant multiplier.
= maximum R. P. M. of spindle.
a = minimum R. P. M. of spindle.
r
I
n t =: number of speeds.
be assumed that the lathe is designed to turn sizes from 1 to 6
The corresponding maximum and minimum revolutions per
inches.
minute for the cutting speed" 100 feet per mmute are 382 and- 62, approximately. Then from (11)
Let
it
=
log
/382\
UJ
r=
log 6.16
15
r
= 1.128
series of speeds in geometrical progression and the diameters of stock, which, will approximately correspond, if a cutting speed
The whole
of 100 feet per minute be used, is given in the following table:
SPEEDS
IN R.P;M.
DRIVES FOR HIGH S
= fastest speed of spindle to correspond with slowest countershaft speed.
= slowest speed of spindle without back-gears to correspond,
with slowest countershaft speed.
.= r
Let
(12)
D*
-L
n'Xr = N
1
= N<
''X
(13)
D,~ T
Then
(14)
l
(15)
r
CONE
C.S.
PULLEY
N
_SPINDLE.CONE
PULLEY
nt
/>.,
A'.
K
Pig. 12
Combining (14) and (15),
(16)
Substituting in (16) the proper speeds taken from the table,
n'==<J 145X101
From
(14)
r
=
= 121
-=-=
tft
145
w'
121
,
=
z> 4
1.199
y
(17)
7T71'
Substituting in (17) the value of
2295
3.14
From
X
X
V and
12
=
n',
72i/2
inches.
121
(12)
(18)
Substituting in (18) the value of r and
D
x
D
4
= 1.199 X 72y = 87
2
inches.
N'G.-K>MACH>NE TOOL DRIVES
40
The
gear ratio from spindle cone speed to driving spindle speed
145
frofit
= 1.629.
will be
89
Since the values of the constants used in computing the force at the
cutting tool were taken from experiments made with slow cutting
speeds, and would be considered low in view of the fact, noted by some,
that the work, at the tool for high speeds increases in far greater proportion than the increased cutting speeds; and since the assumed 70
pounds per inch width for effective pull at the belt is quite liberal, it
is clear that the pulleys are practically at a minimum size under the
conditions assumed.
It is therefore convincingly apparent that for
the ordinary back-geared head, belts can be of no avail for high-speed
cutting except for extremely limited ranges of diameters of stock.
If the diameters of the pulleys are reduced by speeding up the beltV
and gearing down the spindle, nothing is availed in most cases. but an
added and useless expense, since every compounding element is a loan
for a mortgage whose interest rates sometimes increase pretty nearly
in a geometrical progression.
.jrgj.s
BOU^^^PED BJ^V,-
TO
DAY AND
OVERDUE-
-
^^^
====^======:
YC 53944
UNIVERSITY OF CALIFORNIA LIBRARY
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worth, Sharp V- and Britis'i Association Threads;
Oi
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j.ag Screw, and Carriage Bolt Threads, "tc.
H Nuts.
No. 2. Screws, Bolts
Fillister-head,
<>n-head Screws;
Headless, Collar- I.e.
Standard and Special >.
T-iuits, T-bolts and
i Nuts; Machine Screw"
Washers; Thumb Screws
Drills.
Heads; Wood Screws;
Screw Threads,
No. 3. Taps and Dies. Hand, Machine, Tapper
and Machine Screw Taps; Taper Die Taps; Sellers
Hobs- Screw Machine Taps; Straight and Taper
Boiler Taps; Stay-bolt, Washout, and Patch-bolt
Taps; Pipe Taps and Hobs; Threading Dies.
No. 4. Reamers, Sockets, Drills and Millingr
Hand Reamers; Shell Reamers and ArCutters.
bors; Pipe Reamers: Taper Pins and Reamers;
Brown & Sharpe, Morse and Jarno Taper Sockets
and Reamers; Drills; Wire Gages; Milling Cutters;
Setting Angles for Milling Teeth in End Mills and
Angular Cutters, etc.
No. 5. Spur Gearing. Diametral and Circular
Pitch; Dimensions of Spur Gears; Tables of Pitch
Diameters; Odoutograph Tables; Rolling Mill Gearing; Strength of Spur Gears: Horsepower Transmitted by Cast-iron and Ra-vhide Pinions; Design
of Spur Gears; Epicyclic tearing.
No. 6. Bevel, Spiral and Worm Gearing. Rules
arid Formulas for h.-vel Gears; Str.-ngth of Bevel
Gears; Design of I level Gears: Rules and Kf mlas
for Spiral Gears; Diagram for Cutters
Gears; Rules and Formulas for Worm Ge'
No. 7. Shafting, Keys and Keyways. Horsepower of Shafting; Strength of Shafting; Forcing,
Driving, Shrinking and Uurmi.g Fits; Woodruff
Keys; Standard Keys; Gib Keys: Milling Keyways; Duplex Keys.
No. 8. Bearings, Couplings, Clutches, Crane
Chain and Hooks. Pillow Blocks: Babbitted Bearings; Ball and Roller Bearings; Clamp Couplings;
Flange Couplings; Tooth Clutches; Crab Couplings;
Cone Clutches: rnivivsal Joints: Crane Chain;
Crane Hooks; Drum Scores.
No. 9. Springs, Slides and Machine Details.
Formulas and Tables for Spring Calculations; Madune Slides; Machine Handles and Levers; Collars;
Hand Wheels; Pins and Cotters; Turn-buckles.
No. 10. Motor Drive. Speeds and Feeds, Change
for
Gearing, and Boring Bars. Power required
Machine Tools: Cutting Speeds and Feeds for
Machine
Screw
Carbon and Highspeed Steel;
Speeds and Feeds, Heat Treatment of High speed
Steel Tools; Taper Burning: Change Gearing for
the Lathe; Boring Bars ana Tools.
Nc.
11.
Milling Machine Indexing, Clamping
Devices and Planer Ja> *s. Tables for y .ling Machine Indexing; Chan, e Gears lor Milling Spirals;
Angles for setti ; Jndi ing Head wh--n Milling
Clutches; Jig C'.uiupu.^
No. 12. Pipe and Pipe Fu ngs. Pipe Threads
and Gages; Cast-iron Kitting, Bronze
and
Pipe Ci
ends;
Pipe Flanges
Hangers.
No. 13. Boilers and Chimneys. Pb
Spacing
and Bracing for Boilers; Su.'iigth of Boi r Joints;
Riveting; Boiler Setting; Chimucys.
No. 14. Locomotive and Railway Data. Locomotive Boilers; Bearing Pressures for Ix>comotive
Journals; Locomotive Classifications; Rail Sections;
Frogs, Switches and Cross-overs; Tires; Tractive
Force; Inertia of Trains; Brake Levers.
No. 15. Steam and Gas Engines. Saturated
Steam; Steam Pipe Sizes; Steam Engine Design;
Volume of Cylinders; Stuffing Boxes; S; fting Corliss Engine Valve Gears: Condenser and Air Pump
Data: Horsepower of Gasoline Engines, >-jtomobile Engine Crankshafts, etc.
Sonares of
No.
16.
Mathematical Tahles.
Mixed Number-:; Functions of Fractions. Circumference and Diameters of Circles: Tables for Spacing off Circles; Solution of Triangles: ^onnulas
Profor Solving Regular Polygons; -Jeomet
.,
.
i
gression,
etc.
Mechaijs and Strength of Materials.
Work; Energy; (' atrifugal Force; Center of GravNo.
17.
Motion; Friction; Pendulum; Falling I'.odVs;
Strength of Material.-.; <--tt-ength of Fls-t Elates;
Strength of Thick C.j jimlers, etc.
No. 18. Beam Formi.ias and S f v.ictural Design.
1 tea m
Formulas; Sectional Moduli of Structural
Shapes; Beam Charts; Net Areas of Structural
Rivet
Spacing; Splices for Channels and IAngles;
ity;
beauis; Stresses in Roof Trusses, etc.
No. 19. Belt,
sions of Pulleys;
of Belting; Belt
Rope and Chain Drives. DimenWeights of Pulleys; Horsepower
Velocity; Angular Belt Drives;
Horsepower transmitted by Ropes; She:.
Rope Drive; Rending Stresses in Wire Ropes;
Sprockets for Link Chains; Formulas and Tables
for Driving
No. 20.
Chain.
Wiring Diagrams, Heating and Ventila-
and Miscellaneous Tables. Typical Motor
Wiring Diagram.-,; Resistance of Round Copper
Wire; Current Densities for Various Contacts and
Materials; Centrifugal Fan and Blowe.- Capacities; Hot Water Main Capacities; Decimal EquivaMetric Conversion Tables. Weights and
lents,
tion,
Specific Gravity
ventions, etc.
of
Metals,
Drafting-room
Con.
MACHINERY, the leading journal in the machine-building field, the originator of
the 25-cent Reference and Data Books. Published monthly. Subscription, $2.00
yearly.
Foreign subscription,
$3.00.
The Industrial Press, Publishers of MACHINERY,
New York City, U.
49-55 Lafayette Street,
S.
A.
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