_SHAFTS FOR TRANSMITTING POWER._
There is no use in entering upon detailed explanations of what
a learner has before him. Shafts are seen wherever there is
machinery; it is easy to see the extent to which they are employed
to transmit power, and the usual manner of arranging them. Various
text-books afford data for determining the amount of torsional
strain that shafts of a given diameter will bear; explain that
their capacity to resist torsional strain is as the cube of the
diameter, and that the deflection from transverse strains is so
many degrees; with many other matters that are highly useful and
proper to know. I will therefore not devote any space to these
things here, but notice some of the more obscure conditions that
pertain to shafts, such as are demonstrated by practical experience
rather than deduced from mathematical data. What is said will
apply especially to what is called line-shafting for conveying
and distributing power in machine-shops and other manufacturing
establishments. The following propositions in reference to shafts
will assist in understanding what is to follow:--
1. The strength of shafts is governed by their size and the
arrangement of their supports.
2. The capacity of shafts is governed by their strength and the
speed at which they run taken together.
3. The strains to which shafts are subjected are the torsional
strain of transmission, transverse strain from belts and wheels,
and strains from accidents, such as the winding of belts.
4. The speed at which shafts should run is governed by their size,
the nature of the machinery to be driven, and the kind of bearings
in which they are supported.
5. As the strength of shafts is determined by their size, and
their size fixed by the strains to which they are subjected,
strains are first to be considered.
There were three kinds of strain mentioned--torsional, deflective,
and accidental. To meet these several strains the same means have
to be provided, which is a sufficient size and strength to resist
them; hence it is useless to consider each of these different
strains separately. If we know which of the three is greatest, and
provide for that, the rest, of course, may be disregarded. This,
in practice, is found to be accidental strains to which shafts are
in ordinary use subjected, and they are usually made, in point
of strength, far in excess of any standard that would be fixed
by either torsional or transverse strain due to the regular duty
performed.
This brings us back to the old proposition, that for structures
which do not involve motion, mathematical data will furnish
dimensions; but the same rule will not apply in machinery. To
follow the proportions for shafts that would be furnished by
pure mathematical data would in nearly all cases lead to error.
Experience has demonstrated that for ordinary cases, where power is
transmitted and applied with tolerable regularity, a shaft three
inches in diameter, making one hundred and fifty revolutions a
minute, its bearings three to four diameters in length, and placed
ten feet apart, will safely transmit fifty horse-power.
By assuming this or any other well-proved example, and estimating
larger or smaller shafts by keeping their diameters as the cube
root of the power to be transmitted, the distance between bearings
as the diameter, and the speed inverse as the diameter, the reader
will find his calculations to agree approximately with the modern
practice of our best engineers. This is not mentioned to give
proportions for shafts, so much as to call attention to accidental
strains, such as winding belts, and to call attention to a marked
discrepancy between actual practice and such proportions as would
be given by what has been called the measured or determinable
strains to which shafts are subjected.
As a means for transmitting power, shafts afford the very
important advantage that power can be easily taken off at any
point throughout their length, by means of pulleys or gearing,
also in forming a positive connection between the motive-power
and machines, or between the different parts of machines. The
capacity of shafts in resisting torsional strain is as the cube of
their diameter, and the amount of torsional deflection in shafts
is as their length. The torsional capacity being based upon the
diameter, often leads to the construction of what may be termed
diminishing shafts, lines in which the diameter of the several
sections are diminished as the distance from the driving power
increases, and as the duty to be performed becomes less. This plan
of arranging line shafting has been and is yet quite common, but
certainly was never arrived at by careful observation. Almost every
plan of construction has both advantages and disadvantages, and
the best means of determining the excess of either, in any case,
is to first arrive at all the conditions as near as possible,
then form a "trial balance," putting the advantages on one side
and the disadvantages on the other, and footing up the sums for
comparison. Dealing with this matter of shafts of uniform diameter
and shafts of varying diameter in this way, there may be found in
favour of the latter plan a little saving of material and a slight
reduction of friction as advantages. The saving of material relates
only to first cost, because the expense of fitting is greater in
constructing shafts when the diameters of the different pieces
vary; the friction, considering that the same velocity throughout
must be assumed, is scarcely worth estimating.
For disadvantages there is, on the other hand, a want of uniformity
in fittings that prevents their interchange from one part of a line
shaft to the other--a matter of great importance, as such exchanges
are frequently required. A line shaft, when constructed with
pieces of varying diameter, is special machinery, adapted to some
particular place or duty, and not a standard product that can be
regularly manufactured as a staple article by machinists, and thus
afforded at a low price. Pulleys, wheels, bearings, and couplings
have all to be specially prepared; and in case of a change, or the
extension of lines of shafting, cause annoyance, and frequently
no little expense, which may all be avoided by having shafts of
uniform diameter. The bearings, besides being of varied strength
and proportions, are generally in such cases placed at irregular
intervals, and the lengths of the different sections of the shaft
are sometimes varied to suit their diameter. With line shafts of
uniform diameter, everything pertaining to the shaft--such as
hangers, couplings, pulleys, and bearings--is interchangeable; the
pulleys, wheels, bearings, or hangers can be placed at pleasure,
or changed from one part of the shaft to another, or from one part
of the works to another, as occasion may require. The first cost
of a line of shafting of uniform diameter, strong enough for a
particular duty, is generally less than that of a shaft consisting
of sections varying in size. This may at first seem strange, but a
computation of the number of supports required, with the expense of
special fitting, will in nearly all cases show a saving.
Attention has been called to this case as one wherein the
conditions of operation obviously furnish true data to govern the
arrangement of machinery, instead of the determinable strains
to which the parts are subjected, and as a good example of the
importance of studying mechanical conditions from a practical and
experimental point of view. If the general diameter of a shaft is
based upon the exact amount of power to be transmitted, or if the
diameter of a shaft at various parts is based upon the torsional
stress that would be sustained at these points, such a shaft would
not only fail to meet the conditions of practical use, but would
cost more by attempting such an adaptation. The regular working
strain to which shafts are subjected is inversely as the speed at
which they run. This becomes a strong reason in favour of arranging
shafts to run at a maximum speed, provided there was nothing more
than first cost to consider; but there are other and more important
conditions to be taken into account, principal among which are the
required rate of movement where power is taken off to machines, and
the endurance of bearings.
In the case of line shafting for manufactories, if the speed varies
so much from that of the first movers on machines as to require
one or more intermediate or countershafts, the expense would be
very great; on the contrary, if countershafts can be avoided, there
is a great saving of belts, bearings, machinery, and obstruction.
The practical limit of speed for line shafts is in a great measure
dependent upon the nature of the bearings, a subject that will be
treated of in another place.
(1.) What kind of strains are shafts subjected to?--(2.) What
determines the strength of shafts in resisting transverse
strain?--(3.) Why are shafts often more convenient than belts
for transmitting power?--(4.) What is the difference between the
strains to which shafts and belts are subjected?--(5.) What is
gained by constructing a line shaft of sections diminishing in
size from the first mover?--(6.) What is gained by constructing
line shafts of uniform diameter?