ANTIFRICTION BEARINGS, BALL AND ROLLER.
The cycle art has developed the use of antifriction, or, we might say,
rolling-friction bearings, to an extent never before attained; these
bearings are in the form of balls and rollers; the former are made in
several styles and the latter in at least two, but all are more or less
old in the arts.
[Illustration: 1861. Ball-bearing patent.]
The first prominent patent in the American office, upon balls or
rollers, is dated June 18, 1861, No. 32,604. There are some three
hundred drawings of roller and ball-bearing patents on file at the
United States office; this, however, does not represent the entire
number issued. All of the more recent patents are substantially
modifications of former patterns, such as No. 29,570, 1860; 37,765,
1863; 58,739, 1866; 63,609, 1867; 82,665, 1868; 113,867, 1871; 202,271,
1878, and Peter’s, November 20, 1877, No. 197,289.
One of the most useful variations and the one best adapted to the
cycle art, is the lateral adjusting bearing of this style.
[Illustration: Rear-wheel bearing.]
Below find selected figure and claim from a prominent patent over which
there has been much contention.
+J. H. HUGHES, BEARING FOR WHEELS, NO. 227,632, PATENTED
MAY 18, 1880.+
[Illustration: Hughes’s Patent.]
“What I claim, and wish protected by Letters Patent is,—
“In bearings for bicycles, tricycles, or carriages, the combination
of hardened conical or curved surfaces, hardened spherical balls,
and the means, substantially as shown and described, of adjusting
or setting up the parts, for the purposes set forth.
“+Joseph Henry Hughes.+”
Other forms, such as the disk pattern with an annular groove upon its
face, have their special uses.
As to friction, ball-bearings may be said to reduce this to nothing,
since in mathematical calculations, rolling friction on hard surfaces
is usually neglected, as compared with sliding friction. In actual
practice this would not quite hold good, since oil and dirt will make
a difference. The balls, in the ordinary bearings in the market, roll
upon conical, spherical, or cylindrical surfaces. In either of the last
two cases the radius of curvature of the box is so much greater than
that of the ball that the effect is the same as upon the cone, and in
all cases where a bearing is well constructed the action is the same as
that of a ball rolling upon a flat surface. True, some friction results
from the contact of the balls with each other, but as there is no force
driving them together, it is very slight.
[Illustration: Annular, ball-bearing.]
So long as the bearings are new and properly made, each ball touches
and rolls along what may be considered a mathematical line, and there
is, in fact, no friction worthy of consideration. Nevertheless there
is some, and in time a small groove is worn, or rolled, into the
bearing, which groove just fits the ball. The friction is greater now
than before, and increases with the deepening groove until, finally,
when the depth of the groove equals the radius of the ball, the
friction reaches its maximum and would be at that time nearly equal to
one-fourth of the amount of friction engendered if the ball actually
slid in the groove. The ball would then roll on lines along the groove
through points _c_, _c_ thirty-eight and one-fourth degrees around from
_E_ towards _D_, as shown in the annexed diagram. (Fig. 1.)
[Illustration: Fig. 1.
Rolling Lines, ball-bearing.]
The reader can form a tolerably clear idea of the amount of friction
caused by the ball sliding without rolling; let this then be the unit.
Also let the radius of the ball be the unit depth of groove. The
following table gives roughly in these units the frictions for the
groove depths expressed in tenths.
+---------------+---+---+---+---+---+---+---+---+---+---+---+
|+Groove Depths+| 0 |.1 |.2 |.3 |.4 |.5 |.6 |.7 |.8 |.9 |1.0|
|+Frictions+ | 0 |.01|.02|.03|.05|.07|.09|.12|.15|.18|.21|
+---------------+---+---+---+---+---+---+---+---+---+---+---+
To what is this friction due? Look at this diagram (Fig. 2),
representing a transverse section of the groove and ball.
[Illustration: Fig. 2.
Transverse section groove and ball.]
Is it not evident that the ball really rolls on two parallel lines in
the groove somewhere between _D_ and _E_, say the lines through _cc_
perpendicular to the plane of the paper? This granted, it follows that
points on the ball-surface touching the groove above _c_ are going
faster, while those touching below _c_ are going slower than points
touching at _c_. Hence, no wonder there is friction. The position
of _cc_ is such that the sum of the moments of friction above _cc_
balances the sum of the moments of friction below _cc_. Take axes _OX_,
_OY_, as indicated; let the _x_ of _cc_ be _a_, and that of _D D_, _b_;
put _d s_ for an element of arc, and let _A_ be the angle between the
radius to _d s_ and _OY_. Then the friction on _ds_ is proportional to
_ds_ cos _A_ = _dy_, and its moment about _cc_ is proportional to _dy_
(_x − a_), or, _dy_ (_a − x_), according as _ds_ is above or below _cc_.
√(1 − _a_²) √(1 − _b_²)
Therefore, ∫(_x − a_) _dy_ = ∫(_a − x_) _dy_
0 √(1 − _a_²)
The ball’s radius being unity, the solution of the above equation is,—
arc cos _b_
_a_ = ½(——————————— + _b_ √(1 − _b_²)),
√(1 − _b_²)
which determines _a_ for all values of _b_; that is, determines the
points _c_, _c_. It was stated above that _d s_ was proportional to
the friction upon itself. Of course, we meant that it was proportional
so long as _a_ remained constant. In terms of the unit given at the
beginning of this discussion, the friction
_ds_
is ———————————————, and the total friction upon the ball is therefore
2_a_ √(1 − _a_²)
√(1 − _a_²)
4 ∫(_x − a_) _dy_
0 arc cos _a_
————————————————— = ——————————— = 1,
2_a_ √(1 − _a_²) √(1 − _a_²)
which is the formula used to calculate our table above.
As to the weight balls can safely carry in any bearing, below will
be found results of experiments and calculations made by Professor
Robinson, of the Ohio State University. This article is the result of
careful, exhaustive work, and I am under great obligations for the
privilege of introducing it here, as it has never before been in print.
“To find the load which a single hardened steel ball will safely
carry in any ball-bearing, either when running between two flat
surfaces or between two equally grooved surfaces of hardened steel,
in each case the following formula may be applied,—viz.: Load in
_d_
pounds = 190 _d_² √(1 + —————————), where _d_ equals the diameter
_d′_ − _d_
of the ball in inches and _d′_ equals the diameter of the groove
in which the ball runs, either top or bottom. For flat surfaces,
_d_
for top and bottom bearing of ball _d′_ = ∞ and ————————— = 0, so
_d′_ − _d_
that, for a ball between hardened flat plates, Load = 190 _d_². For
_n_ balls in a nest, all in equally fair bearings, the load equals
_d_
_n_ 190 _d_² √(1 + ——————————); for example, a one-inch ball between
_d′_ − _d_
flat surfaces will carry one hundred and ninety pounds safely.
190
“Again a one-half-inch ball will carry ——— = 47.5 pounds; and again
4
a one-inch ball in a groove of one and one-eighth-inch diameter top
1
and bottom will carry 190 √(1 + —————————) = 570 pounds. So that
1′ (8 − 1)
there is great advantage in supplying grooves for the balls to run
in. Again, suppose the ball be one inch and the grooves one and
one-eightieth inches in diameter; then the load equals seventeen
hundred and ten pounds. Again, if the ball is one-half-inch
diameter, and the groove nine-sixteenths-inch diameter, the load
equals 142.5 pounds, etc.
“Hundreds of experiments in all were made on this subject, and
the above formula deduced by theory was found to agree almost
exactly with the experimental results for hardened steel for balls
and track for same. When a much greater load than the above is
attempted to be carried, the balls will indent a groove of their
own until the necessary bearing surface is obtained.
“I am not aware that the coefficient of friction for ball-bearings
is definitely known. Experiments made with the Lick telescope, in
which the weights of some parts had to be guessed at, gives .00175
for the value of friction coefficient for one-inch balls; but
this, though the best I have, is not a reliable figure. It is for
hardened steel on hardened steel.”
Mr. Robinson here shows an advantage in the groove so far as capacity
for resisting strain is concerned, but he would hardly construct a
ball-bearing with grooves fitting the balls after a careful perusal of
our section on grooves and friction.
As to _ball-heads_ to bicycles, they have been highly recommended by
a few makers and much admired by some riders. As before said, the
balancing of the bicycle is accomplished by means of the steering
apparatus, and the easier the head swivels the less work the rider
has to do to effect his object. If simple steering—that is, changing
the general course of the rider’s progress—happened to be all for
which the head is swivelled, it would make little difference whether
it moved very easily or not; nay, it would be better to have it move
a little stiff, since it would then stay in place. But when it comes
to balancing, the head is constantly moving, and every resistance is
work to be overcome by the rider’s muscular exertion. To say that a
head cannot swivel too easily, would be a valid axiom in the art of
balancing; hence a ball-head could do no harm, and might do some good.
In the Rover or Safety pattern, ball-heads are quite common and are
rather a valuable acquisition, especially in the telescope. In the
Stanley head, however, it is very questionable whether the advantage
gained is sufficient to justify the extra complication and weight of
the parts. Conical heads can be, and are, made to work so smoothly
and the amount of motion is so small that the same question in regard
to friction does not apply as in the case of other bearings about the
machine. It is the opinion of the writer that every other part about a
wheel should be about perfect, and of the very highest grade, before
the question of ball-heads should be considered at all.
In regard to the patents on, and general use of, ball-bearings in
cycles, I think the necessity of using the prominent lateral adjusting
bearings is really not so absolute as many suppose; of course this is
the most artistic form and the most easily-made pattern of all, and is
in every way adapted to cycle use; but it would not be policy to throw
aside any other advantage in a wheel to gain the lateral adjustment
in the bearings. There are some other styles of ball-bearing boxes
which answer the purpose very well, the chief difficulty being that a
greater amount of work is necessary for their adjustment. If the boxes
are split in a plane through the geometric axis of the axle, they will
be slightly out of round after adjusting, but when it is taken into
consideration that the weight is all on one side or, as in a bicycle,
on the top, the fault will not be noticeable; it is more serious when
the boxes revolve than when they are stationary.
The patents now existing on lateral adjusting bearings have caused
many attempts at other methods of taking up the wear. The validity
of these patents is questioned by many, and considerable litigation
has been the result, though in many cases makers prefer to use other
devices to running the chance of a law suit. The happy medium adopted
by others is to pay the royalty demanded; this is, perhaps, the best
course to pursue if the said royalty is not made burdensome. Every
maker, however, should assure himself, by special examination, if his
particular bearing really infringes any patent before paying; the
fact of it being a ball-bearing with a lateral adjustment is not an
incontrovertible reason that it should infringe, since both of these
elements are, in themselves, old. It is only a special ball-bearing
with a special adjustment that is patented. Unhappily, however, the
special adjustment is a screw. How the patent will stand, time alone
can tell; its validity is certainly questionable.
A word here in regard to paying royalties in general. Makers are too
scrupulously averse to such payments, even when small, and buyers have
the idea that any one who pays a royalty is naturally working at a
disadvantage. This is not necessarily the case. Some would save more by
the use of an ingenious machine for making the parts than several times
the royalty often amounts to. In the manufacturing business there are
so many ways of saving and losing money, that unless a careful watch is
kept all round the little matter of royalty on some one part will fall
into insignificance as compared with other leaks.
The advertisement of a maker that he pays no royalty gives us but
little assurance that he can make a better machine for less money.
When a patent is evaded by slight changes, such, for instance, as the
increase or decrease of an inch in the diameter of a wheel, it shows
not so much a great shrewdness on the part of the pirate as a frailty
in the patent; this sort of evasion of royalties is considered to be
perfectly legitimate, however, and means that either the attorney who
took out the patent was incompetent, or that there was but little
invention to be claimed.
ROLLERS.
Theoretically there is less friction in roller- than in ball-bearings,
as there need be no sliding action whatever in the former if well
made. But in actual practice no bearing can be made in which there is
no tendency of the rollers to run together; and if we place them in a
frame to hold them apart we shall have about as much friction as when
they rub against one another. The most perfect plan is to place a small
roller between each of the larger; with this arrangement the friction
is practically nothing. The action of rollers upon the boxes is always
a pure rolling friction, which cannot be the case with balls after the
slightest groove is worn in the casing.
One reason for rollers being little used is that they tend to work out
of line with the axle and box, which causes some ends to get a little
in advance of the others, when they can no longer work perfectly. For
an oscillating bearing,—that is, one that goes backward and forward,
instead of continually around,—I have found rollers very good, since
they cannot get much out of line; even when the bearing is a little
imperfect, the rollers cannot multiply the imperfection, as they will
in one that keeps going on in the same direction. The other great fault
of the roller is its non-adjustability, although this can be rectified
in the following way:
[Illustration: Roller construction.]
The above cut shows a bearing and the construction lines that must be
followed in its manufacture. The taper of the axle, roller, and box
must all meet in a point, as at _a_; this arrangement is evident. The
roller must be kept in proper position and roll around the large end
in the same number of turns as the small end; hence the circumference
of the small end of the roller must bear the same relation to the
circumference of the larger as the relative ends of the axle and box
bear to each other. The geometrical conditions are as follows: π
being the relation of circumference to the diameter, referring to the
diagram, we have _bc_ : _fg_ :: _cd_ : _gh_ :: _be_ : _fi_; hence π_bc_
: π_fg_ :: π_cd_ : π_gh_ :: π_be_ : π_fi_. Now, by virtue of the last
formula, when the axle or box is revolved, each end of the roller will
travel through exactly the same number of degrees around the axle and
in the box, wherefore the axle rollers and box all keep straight.