be placed on either piece, but, assuming for the moment that
the intended size of the hole is the nominal size, the allowance
for the shaft is added to the nominal diameter for a press fit
and subtracted from it for a running fit. The allowance being
thus added to or subtracted from the nominal size, the result
is the intended size of the shaft. From the intended size the
actual size of each piece, when made, will differ, because of the
fact that the exact production of any intended size is an impos-
sibility. Moreover, not only will the pieces differ from the
intended sizes but they will differ among themselves and, recog-
nizing that some variation is inevitable, it becomes necessary
to decide how much variation is permissible, this variation
being small in high-class work and larger in more common work.
The variation between the largest and smallest sizes which is
thus decided upon as permissible is called the tolerance.
The allowance is an intentional difference between the sizes of
the two mating pieces, while the tolerance is an unavoidable
variation from the intended size. The allowance applies to
one piece, the tolerance to both.
FITS AND LIMITS 137
Finally the two extreme sizes are the limits, the tolerance
being the difference between the high and the low limits. The
actual sizes as made may fall anywhere between the limits.
Of the above terms, allowance is very commonly used as
defined. The words tolerance and limit are, however, used
somewhat loosely and even interchangeably. One will often
hear the expression that the limit on a certain piece is one or
more thousandths, the meaning being that the tolerance is one
or more thousandths. This usage, however, is not often the
cause of confusion.
VARIATIONS IN PRACTICE
In some cases the tolerance is all placed on one side of the
intended size, the intended size being one of the limits a
practice that is illustrated in the diagrams, Figs. 121 and 122.
In other, and probably more numerous, cases, the limits are
placed each side the intended size, the variation from the
intended size being one-half the total variation between the
largest and the smallest pieces. When this practice is followed
the variation from the intended size is sometimes called the
tolerance although but one-half the total range which is toler-
ated. It is from this that the usage of the word tolerance was
derived, and the use of the word for the total variation between
the largest and smallest sizes tolerated seems to the author the
more logical. For this reason the word has been thus used
throughout the accompanying text.
These considerations point out a serious limitation of any
system of gages which give the true sizes only. Whether we
have to deal with a running or a press fit, four sizes must be
considered the two limits of the shaft and the two of the hole.
Of these four sizes such a system of gages can give but one, the
allowance remaining a matter of judgment and skill as when
graduated scales are used, while no provision for the tolerance
of either piece is made.
THE SHAFT AND THE HOLE BASES OF FITS
Since in both running and press fits the intended size of
either part may be equal to the nominal size while the intended
138 METHODS OF MACHINE SHOP WORK
size of the other must differ from the nominal, there is liberty
of choice between the pieces as relates to the one of which the
intended size shall be the true size and to the one on which the
allowance shall be placed, it being understood that the one of
which the intended size is the true size is still made between
limits, which is to say that while it does not have allowance
it does have tolerance. '
Growing out of this liberty of choice, two systems of con-
struction are in use. In the first, called the hole basis, the
hole is made, within limits, of the true size, the allowance being
placed on the shaft, while in the second, called the shaft
basis, the shaft is made, within limits, of the true size and the
allowance is placed on the hole. In work of which the sizes
of both pieces are determined by the adjustment of the tool, as
in engine-lathe or boring-mill work, there is little choice between
the systems, but in work made with tools which are set to a
given size which is repeated indefinitely in the work, there is a
large advantage in keeping the hole as nearly as possible to the
true size and throwing the allowance on the shaft. This is due
to the fact that in work of this character the holes are commonly
finished with reamers and, by adopting this practice, the same
reamer may be used for all classes of fits of the same nominal
size, the shaft being made slightly smaller for a running and
slightly larger for a press or shrink fit. Meanwhile, since this
practice is most desirable for work of this character, it is natural
and desirable for the sake of uniformity to adopt it for all kinds
of work.
In this respect there is a difference of practice between Ameri-
can and British work. In the United States the hole is com-
monly, though not universally, kept as nearly as possible to the
true size, while in Great Britain the opposite practice prevails. 1
These terms are illustrated diagrammatically and grossly
exaggerated in Figs. 121 and 122 for both hole and shaft bases,
the allowances and tolerances being divided by two because
in the diagram we deal with radii while the measurements are
1 This statement regarding the practice in Great Britain is based on the author-
ity of the report of the British Engineering Standards Committee, rendered in
1906.
FITS AND LIMITS
139
made across the diameters. The same terms apply to press fits,
understanding that in such fits the shaft is larger than the hole
instead of smaller as in running fits.
In this as in many other matters the growing use of the grind-
ing machine has had large influence, especially in reducing the
tolerance on the shafts. With the holes made with reamers and
the shafts in an engine lathe it is easier to keep down the toler-
ance on the holes than on the shafts and, consequently, in work
In tended. Size and
{L'ower Limit of
Bearing
'rL'imit
of Bearing
n tended Size. True
ze and Lower
'L imit of Bearing
FIG. 121. Hole basis. FIG. 122. Shaft basis.
Allowances, tolerances and limits.
so made, the tolerance on the shafts is commonly larger than
on the holes. With the grinding machine, however, the reverse
is true and this machine has thus brought about an improve-
ment not only in the character of the surfaces as respects their
roundness and straightness but also in their sizes as respects
the tolerance.
THE VALUE OF THE TOLERANCE IN PRACTICE
In an actual case the decision regarding the allowance and
tolerance is a matter of large importance and, as regards lathe
140
METHODS OF MACHINE SHOP WORK
work, the practice of several leading constructors is available
for general use. An exhaustive investigation of the practice
in Great Britain as relates to running fits was made by the
Engineering Standards Committee, the result being a chart in
which are given recommended allowances and tolerances for
running fits of three grades of workmanship and for shafts up
to twelve inches in diameter. The practice of the General
Electric Company for sliding, press and shrink fits, and of the
Brown and Sharpe Manufacturing Company in allowances
and tolerances for ground fits, may be found in the Transac-
tions of the American Society of Mechanical Engineers, Vols.
24 and 32. The practice of the C. W. Hunt Company for all
classes of fits was published in the American Machinist for
July 16, 1903, and of the Lane and Bidley Company for press
fits in the same periodical for July 30, 1899. 1
It is neither feasible nor necessary to give all these data here
but some idea of the magnitude of these variations should be
given, if only to correct the impression among beginners that
they are smaller than is the case. The accompanying table
gives representative values of tolerances for running fits from
the report of the British Engineering Standards Committee.
BRITISH STANDARD TOLERANCES FOR THREE GRADES OF RUNNING FITS
3 ir
13
is. diam.
6 ins. diam.
12 ins. diam.
13
|
1
|
13
a
13
13
cr
cr
cr
cr
cr
cr
cr
cr
cr
H
H
no
H
-0
<N
nd
en
M
"S
"S
Shaft ....
.0018
0035
0053
.0025
.005
.0075
.003
.006
.009
Tolerance, in.
Hole
.OOI7
0035
.007
.OO25
.005
.010
.003
.006
.012
Less comprehensive information is available for work of
other character, but in milling-machine work of small size the
tolerance is seldom less than one-thousandth of an inch, two-
thousandths being much more common, the tolerances increasing
1 These and other data relative to fits have been collected together in the
author's Handbook for Machine Designers and Draftsmen.
FITS AND LIMITS 141
with the sizes dealt with as the table shows them to do in the
case of lathe work.
In turret lathe work of moderate size the tolerances do not
differ much*" from those of milling-machine work, one-thousandth
tolerance being feasible for pieces which do not exceed about
one inch in diameter when such workmanship is necessary, but
two- thousandths being much more common. Such a reduction
of the tolerance is always accompanied by increased cost.
The Cleveland Automatic Machine Company find that when the
tolerance on small pieces is reduced from two-thousandths to
one, the output of their automatic turret lathes is reduced about
twenty-five per cent. This loss is due to several causes. The
cutting tools must be adjusted more carefully, be given a lighter
cut to save their edges and be ground more frequently.
The attempt to reduce the tolerance below about one-thou-
sandth increases the cost at a rapidly accelerated rate, a point
being soon reached at which the cost is prohibitive and another,
not far from it, which passes the ability of cutting tools and the
production of the work with such tools becomes mechanically
impossible. These points vary with the size of the work and
a comprehensive statement regarding them is a difficult one to
frame, but, for work not exceeding about one inch diameter,
a single thousandth may be regarded as about the smallest
feasible tolerance with cutting tools. On the other hand, a
good grinding-machine operator will maintain sizes within a
quarter of a thousandth without difficulty.
TAPER PRESS FITS
The most approved practice with press fits is to make them
taper, the taper being so slight as not to endanger the security
of the work but introducing decided advantages. One of these
advantages is that the two pieces may be compared by inserting
the plug within the hole when, the system being properly laid
out, it is apparent from the distance by which the plug does not
go home if the parts are of the intended sizes. In addition to
this the lubricant is not scraped off as in the straight fit method
but covers the entire surface when the pressing action begins.
There is also, partly by reason of this and partly by reason of
142
METHODS OF MACHINE SHOP WORK
the fact that the pressing action is through a lesser length, much
less tendency for the pieces to cut and score one another.
The customary taper, measured on the diameters, is one-
sixteenth inch per foot of length. This taper has, however,
been improved upon by the Westinghouse Machine Company
who make the taper .06 instead of .0625 = one-sixteenth inch
per foot. This modified taper is equivalent to .005 inch per inch
of length which gives even thousandths for the diameters at
each inch of length. The Westinghouse method of measuring
these tapers is shown, with the taper exaggerated, in Fig. 123.
FIG. 123. Measuring taper press fits.
A strip of steel having holes drilled through it at even inches of
its length is placed within the hole when, by the inside microm-
eter caliper shown, the hole is readily gaged at any part of
its length. The readings are not exactly equal to the diameters
because of the slight inclination of the caliper, but the larger
diameter as read is made equal to the diameter called for in
the drawing, the difference between the two being too small to
be of any importance.
CHAPTER VII
DRIVING SYSTEMS FOR MACHINE TOOLS
The three leading systems of driving and their proper fields of use
Defects of the old type of cone pulley and methods of overcoming them
Individual vs. group motor driving.
COMPARISON OF THE CONE PULLEY AND THE VARIABLE SPEED
INDIVIDUAL MOTOR DRIVE
Machine tools are driven by the following methods:
(a) The cone pulley and back gears, power being obtained
from a line shaft.
(b) The variable-speed individual electric motor and back
gears.
(c) The constant-speed pulley and a set of gears arranged in
a gear box and fitted with a system of hand levers whereby they
are quickly shifted, power being obtained from either a line shaft
or a constant-speed individual motor.
The variable-speed motor was introduced with numerous
claims of superiority over the cone pulley, many of which were
imaginary, but, nevertheless, when contrasted with the cone
pulley as then made, it was found to have advantages which,
while not inherent, were pronounced and they gave the motor
drive a great vogue. No attempt had then been made to
develop the possibilities of the cone pulley. To shift its belt
the operator had to get a pole, which might or might not be
within convenient reach, while with the motor there was sup-
plied a controller at the operator's elbow by which the speed
changes were made quickly and without effort. Consequently,
while with the cone pulley the changes were often neglected,
with the motor the reverse was true, the result being an in-
creased output. A fundamentally worse defect of the cone pul-
ley than this was the fact that the intervals between successive
speeds were much too large while the intervals between the
motor speeds were much smaller.
143
144 METHODS OF MACHINE SHOP WORK
The large intervals between the cone-pulley speeds led to
constant loss of output. It is not a matter of the average of
gains and losses but of average losses. The cutting speed is
limited by the properties of the cutting tool and, except in the
few cases when the cone speed is equal or nearly equal to the cor-
rect speed for the work, the next lower cone speed must always be
used, the result being in nearly all cases a loss from the possible
output. The smaller the interval between the speeds the smaller
is this loss and, since the intervals with the motor were smaller
than those with the cone pulley, the loss was smaller, the result
being another increase of output. 1
Coincident with the introduction of the motor drive came the
introduction of high-speed steel and the great movement for
intensive production, both of which directed attention to and
served to emphasize the increased output which, mistakenly,
was attributed to some inherent property of the motor drive.
IMPROVED PROPORTIONS OF THE CONE PULLEY
There is, however, another serious defect of the cone pulley as
commonly and, when the motor drive came in, universally made
which, before it was generally understood, acted to further dis-
credit the cone-pulley drive. Because of defective relative pro-
portions of the steps the belt speed was unnecessarily low and
the driving power inadequate.
As the belt is shifted to the large steps of the driven cone its
speed never very high is seriously reduced until, on the larger
steps, it is incapable of delivering the power required by modern
requirements and this failure is just at the point where power
is most needed by reason of the heavier cuts which naturally go
with large work. The correction of this deficiency of the cone
pulley is, however, a simple matter of its proportions.
The change required is illustrated in Figs. 124 and 125, the
former of which shows the older defective and the latter the
newer improved type. The change consists essentially in
1 The ratio between successive speeds with the older type of cone pulley is
seldom less than 1.5. It frequently reaches 1.75 and occasionally goes as high
as 2. According to Carl G. Barth, the ideal value for this ratio is the fourth
root of 2 or 1.189. It should not be more than 1.25.
DRIVING SYSTEMS FOR MACHINE TOOLS
145
reducing the ratio between the highest and lowest cone speeds
and then supplementing this reduced ratio with additional back
gears in order to get the required overall range of speed, thereby
increasing the belt speed on all the steps but most on the large
ones where most needed. The effect of this change is greater
than at first sight appears possible. The best method of demon-
strating the effect is to calculate the comparative powers with
the belt on the larger steps of the two pulleys shown, which are
from actual machines and which are, as nearly as may be, of the
same overall dimensions and are thus fairly comparable.
2z Belt
4 "Belt
FIG. 124. Conventional design of cone FIG. 125. Improved design of cone
pulley. pulley.
Calling the highest belt speed in Fig. 124 that obtained
with the belt on the four-inch step 100, the slowest that on
the twelve-inch step will be: 1
100 X T V = 33l
To maintain the same driven-cone speed the highest belt
speed in Fig. 125 will be:
loo 11 ** = 288 +
4
and the lowest will be:
288 X ^f = 25 5 +
o
1 The counter-shaft cone is assumed to be, as is usual, a duplicate of the machine
cone.
10
146 METHODS Of MACHINE SHOP WORK
The smallest step of Fig. 124 is too small for a double belt,
while the reverse is true of Fig. 125. To obtain the ratio of
power capacities we must multiply the belt speed ratio by a
suitable ratio for the double belt, say ~, and also by the ratio
A
of the belt widths, -^. Doing this we obtain:
2 2
Power capacity of Fig. 125, small step _ 288 10 ^
Power capacity of Fig. 124, small step 100 7 ' i\
Power capacity of Fig. 125, large step _ 255 K> _4_
Power capacity of Fig. 124, large step 33^ 7 ' i\ "
That is, the capacity of the cone shown in Fig. 1 2 5 on the small
step is 6| and on the large step, where most needed, 17 J times
that of the one shown in Fig. I24. 1 In the cases shown, there
is a slight increase in the diameter of the large step but, without
this increase, the gain would be nearly as large, although so
large a gain is seldom needed. The pulley shown in Fig. 125
gives a smaller overall range of speeds and a smaller number of
speeds than does the one shown in Fig. 124. Additional back
gears are needed to correct both deficiencies. It is the necessity
for these gears that makes feasible the reduced number of cone
steps and the increased width of belt.
There is no doubt also that the direct connection between the
cone pulley and the work or tool spindle has been retained in
many cases for which it should have been discarded. With
small, light power machines this construction is satisfactory
but, as the size of the work increases, it ultimately becomes
inadequate, since with it the belt speed is too low to carry the
power required. The remedy is to connect the cone pulley and
spindle through gearing and thus speed up the pulley and belt.
As sizes of machines increase this is always done ultimately,
but the change is commonly deferred too long. High belt
speed costs nothing and advantage should be taken of the in-
creased power that goes with it. Were the speeds of machine
belts two or three thousand feet per minute, instead of as many
hundred, there would be no deficiency of belt power.
1 The first publication of the possibilities of improved cone-pulley design was
by H. M. Norris.
DRIVING SYSTEMS FOR MACHINE TOOLS 147
DIFFICULTIES INTRODUCED BY THE INDIVIDUAL MOTOR
The variable-speed motor drive brought in its train many
difficulties to the machine-tool maker, these difficulties being
chiefly structural and due to lack of standardization of the
motors. Motors from different makers differed in the ratio
between their extreme speeds and, since the ratio of the sup-
plementary back gears should have a suitable relation to the
overall speed ratio of the motor, it follows that any change in the
latter involved a change in the former ratio. Less fundamental,
but scarcely less troublesome, was the fact that motors of
different makes but of the same power were unlike in their
leading dimensions. If they had the same speed ratio the
heights to the shaft centers frequently varied as did the sizes
of the bases and the positions of the holding-down bolt holes.
These considerations interfered with the production of standard
machines by requiring the adaptation of each machine to its
motor. The makers found it no longer possible to make and
to sell from stock standard machines, special adaptation to
the specified motor being required in each case.
THE CONSTANT-SPEED PULLEY DRIVE
This was an impossible condition as the whole industry was
based upon standardization, and the constant-speed pulley sys-
tem was devised to meet the difficulty. In this system the
first motion shaft of the machine is arranged to be driven at a
constant speed which is easily obtainable from any constant-
speed motor by a mere selection of pulley sizes and then, added
to this, is a set of gears arranged in a gear box and fitted with
a system of levers by which the change of speed is made as
easily and as quickly as by the controller of the motor. The
result was to again standardize the machines and to give them,
from the makers' standpoint, the enormous advantage of equal
adaptability to both line shaft and individual motor driving.
Examples of the constant-speed pulley drive are given in Figs.
136, 163, 181, 182, 183, 216, and 217.
THE CONE-PULLEY BELT SHIFTER
For the milling machine the constant speed drive, as explained
at length in the chapter on milling, has peculiar fitness and in
148
METHODS OF MACHINE SHOP WORK
all applications it provides a self-contained machine, whereas
the cone-pulley drive includes a detached countershaft for
which, in shops designed for individual motor driving, it is
frequently difficult to provide. Nevertheless, the cone pulley
FIG. 126. Mechanical belt shifter for cone pulley belts.
is too simple, cheap and adaptable a thing to be discarded and
manufacturers are beginning to turn their attention to it again.
When proportioned in the manner that has been explained
its most serious original defects too large speed intervals and
inadequate power disappear and it only remains to devise a
DRIVING SYSTEMS FOR MACHINE TOOLS 149
convenient mechanical belt shifter to give it all the operating
qualities of either the variable-speed motor or the constant-
speed pulley gear box drive, together with a lower cost than
either one.
Fig. 126 shows such a belt shifter applied to a well propor-
tioned cone pulley by the R. K. LeBlond Machine Tool
Company. 1 The author ventures to predict that, through
such means as this, the cone pulley will eventually be reha-
bilitated as a leading method of machine-tool driving.
THE FIELD OF THE INDIVIDUAL MOTOR DRIVE
All this is not to be understood as meaning that the individual
motor drive has no place, for it has a large one. For portable
floor plate tools it is the only practicable system. For isolated
tools and for others so located that line-shaft layouts for their
accommodation are inconvenient, it is the natural and proper
recourse. It permits the locating of large tools under travelling
cranes without interference with the runway by overhead
structures, and for such tools this is a commanding advantage.
In general, flexibility of location is often of large importance in
connection with large tools, while, with such tools, the cost of
individual motors is, relatively, a less serious item of additional
cost than with small ones. For the great majority of small and
medium sized tools, however, no inherent advantage has been
shown to attend its use. It has, moreover, unquestioned and
inherent disadvantages, chief of which is its increased cost, both
of installation and of operation.
The power capacity of an individual motor must be that due
to the maximum requirement of the machine to which it is
attached. Unlike the group system, in which, through a line
shaft, one motor drives several machines, there is no opportunity
to take advantage of the average load. Of any group of
machines but few work simultaneously under maximum duty,
while at all times a considerable percentage is normally idle.