CHAPTER XX.

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.