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The term mandrel is applied to that class of
tools upon which work that is to be machined between centers is
usually held. It is frequently called an arbor, although the
distinction between the two may be quite clearly define.
A mandrel is designed to carry work that is to
be operated upon by a cutting tool, while on the other hand the
arbor carries and drives a cutting tool, as with the milling
machine and saw arbors. Mandrels may be classed
under two heads, solid and expanding. The solid mandrel is made
slightly tapering, in order that it may be forced to a right fit
in the bore of the work. The amount of this taper varies with
the class of work the mandrel is to be used on, it being but
slight at the most. A bar common round iron or
steel centered and turned to the required diameter constitutes
the mandrel in its simplest form. Such a tool, as it is usually
found in the average jobbing shop, is shown is Fig. 185.

It is hardly worthy the name mandrel, although a solid one might
fairly come under the expanding, or rather shrinking class, as
it is brought down by turning and filing to fit the bore of
every new piece of work that comes along. It has one quality,
however, that can always be depended upon, and that is untruth.
With mandrels of this class accurate results cannot be expected.
Since a mandrel must be rigid, it should be as short as the
nature of the work will permit, and made of as stiff a material
as possible. Its centers should be carefully formed, and the
body finished cylindrically true upon them. The centers, at
least should be tempered or case hardened, to prevent their
wearing out of true.

In Fig. 186 is shown the correct construction for the end of a
mandrel. The end for a length about equal to the diameter of the
tool is reduced slightly in diameter and provided with a flat on
one side, against which the screw of the dog or driver is set.
As the dog is very apt to mutilate somewhat the ends, this
reduction in diameter is quite necessary. Since the accuracy of
the mandrel depends so much on its centers, it is necessary to
protect them as much as possible from injury while forcing the
mandrel into the bore of the work. This is best accomplished by
recessing the ends around the center bearing as shown in the
figure. The angel of the bearing should be 60 degrees, with a
small hole drilled at the bottom. The object of this drilled
hole is to prevent strain being thrown onto the delicate point
of the machine center, and to form a small oil reservoir to aid
in lubricating the bearing.
 In Fig.
187 is shown a hardened and ground steel mandrel. These tools
are made for general shop work, the length increasing with the
diameter from 3 ¼ inches for a ¼ inch mandrel to 17 inches for a
4-inch. These lengths are, of course, arbitrary and may for
special uses be materially increased or decreased. As
manufactured by the several makers, these mandrels differ but
little in length and details of design. They should be made of a
good grade of tool steel, carefully hardened with the centers
lapped true after the hardening, and the body ground
cylindrically true upon these centers, it being rotated upon
stationary or dead centers for this last operation.
When the greatest possible accuracy is required it is considered
best to make these mandrels of tough, un-annealed tool steel,
with the ends only hardened. This arises from the fact that the
steel if hardened throughout changes somewhat in form and
receives temper strains, which, although relieved in the
grinding, does not allow the tools to immediately take its
permanent set. For this reason a mandrel that has been hardened
throughout should be first rough ground, leaving a small amount
for final finishing. This finishing should not be done for some
time after the rough grinding, thus allowing the tool to season
and to acquire permanent set. The set will not be appreciably
altered if only a very small amount is left for the final
finish. Hardening makes the mandrel stiffer and
less liable to surface injury than in the case of the unhardened
one. It is not, however, for the purpose of allowing careless
workmen to run their cutting tools into its surface with the
idea that it will not be injured thereby. Cutting tools are
usually made of a higher grade steel than the mandrel, and often
tempered harder, in which case the mandrel suffers if the tools
comes in contact with it.
These mandrels are usually tapered about
one-hundredth of an inch to the foot, the diameter being exact
at the center. The size is stamped on the flat at the larger
end. They will fit holes reamed with standard reamers, although
the taper prevents uniform grip on the work at the two ends of
the bore. In forcing these mandrels into the bore, good judgment
must be exercised, as they constitute a wedge, which will
produce enormous pressure if forced too hard, resulting in
bursting the work if hard and brittle, or if soft in permanently
enlarging the bore and giving it a taper corresponding to that
of the mandrel. The use of the hardened and
ground mandrel does much toward the preserving of uniformity in
the size of holes, in the work of shops, where these tools are
used. A hole only a few thousandths of an inch under or over
size prevents, in the first case, the mandrel from entering and
in the latter allows it to fall through.
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