CHAPTER IV.

EMPLOYMENT OF FRICTION WHEELS.

497. THE substitution of rolling contact for sliding by the wheels of carriages is a simple and direct application of the three laws of friction already investigated (vide Art. 484 above).

Let AB be the frame of a carriage supported on three wheels. Let R be the radius of the wheel and r of the axles.

The machine rests therefore upon three points, and the weight (W) may be assumed to be equally distributed upon them.

Suppose the wheels to be prevented from revolving on their axles, and let the machine be drawn along the ground through a distance equal to the circumference of the wheel =πR. The amount of friction =3 × ƒWπR.

If, however, the wheels are left free to revolve, the rubbing friction is transferred to the contact of the cylindrical axes with their boxes, and the amount of rubbing in each revolution is the length of the circumference of the axle, and ..=3fWar. Thus the ratio of friction of a sledge and a wheel carriage of equal

R

weight drawn through any given distance = and this is

r

increased by the fact that the friction of the sledge on the ground is greater than that of the axles, which admit of lubrication.

That the application of wheels to carriages is of great antiquity is shown by the mention of them in the first books of the Scriptures.

498. Another device to facilitate the conveyance of irregularlyshaped heavy bodies, such as cubical masses of stone intended for buildings, was to enclose the mass in a wooden case of a cylindrical form, so that it could be rolled along the ground by men, or if furnished with pivots at each end, could be drawn by horses. This method is described in the tenth book of Vitruvius, who attributes it to Ctesiphon, but it must in all probability have occurred much earlier.

A more direct and complete substitution of rolling for sliding is commonly employed when heavy packages have to be moved

from one place to another on flat or inclined ground, by placing long cylindrical rollers beneath the heavy case. As the load is pushed forward the cylinders travel in the same direction, but (as is easy to see) with a velocity of half that of the load, from under and behind which they therefore escape in turn, and are taken up by the assistants and transferred to the front in order.

Fig. 345.

499. The friction of the shafts or axes of machinery in their bearings may be diminished by the employment of friction wheels, or rather anti-friction wheels. These are arranged in the manner shown in the diagram (fig. 345), which represents the wheels of Atwoods' machine, invented about. 1780 for the purpose of making experiments on the rectilinear motion of bodies, which are performed by suspending unequal weights to the two ends of a string which is carried over a pully, and observing the times of their descent. As the friction of the axis of the pully might interfere with the results, each extremity of the axis is supported by a pair of wheels or rollers, mounted in a suitable frame, so

that their neighbouring surfaces overlap and nearly touch each other. Their axes are short and parallel to that of the principal wheel. Thus by the overlapping of the rollers an angular trough or notch is formed at each end of the machine, by which the long axis of the pully is supported as shown in the figure. When

the pully revolves, its axis, pressed into contact with the rollers by the weight of the great wheel and that of its suspended load, causes them to rotate, and thus the sliding friction of the principal axis is transferred to the axes of the friction rollers.

If the principal axis rested in bearings at each end the quantity of friction in each revolution would be measured by the length of the circumference of the axis. But each revolution of the principal axis produces a fraction of a revolution = where R R

and r are the radii of the friction rollers and their axes.

The ends of the principal axis terminate in points which rest against a part of the frame of the friction rollers at each end.

Friction wheels were about the beginning of this century applied to heavy machinery. But it was found that the axes of these wheels were liable to stick fast in their bearings from the accumulation of dust and thick oil. When this happens, the axis of the principal wheel rotating upon the fixed circumference of the friction wheel thus prevented from moving, begins to wear a notch at the point of the circumference upon which it rests, and thus prevents it from revolving. This, and the additional complication caused by the employment of these wheels drove them out of practice, and finally the introduction of cast-iron and machine tools into the construction of mechanism rendered the surfaces of the cylindrical axes so much more perfect in form as to reduce the friction to an amount that was no longer injurious.

500. Mr. Whitworth's chain-link for the treadle of lathes is a remarkable and thoroughly practical application of the principle of substituting rolling contact for sliding, to prevent the wearing out of the surfaces. In the ordinary lathe the axis of the flywheel is bent into the crank form, and the link which connects it with the treadle terminates upward in a hook, which is simply kept in its place by the weight of the treadle; but the crank has an angular groove sunk in its circumference to receive and steady the hook laterally. Without great care in oiling and cleaning, the friction of the hook is apt to grind itself and the crank groove, and eventually to break the hook or the axle, which necessitates an expensive repair.

But in Mr. Whitworth's treadle-link the crank AB is provided with a strong cylinder A to receive a broad endless chain of metal constructed on the principle of watch chains. The lower loop of the chain passes over a cylindrical pully roller D which turns on an axis carried by the treadle. Thus the crank-pin and the treadle-pully are connected like two pullies with an endless

band. The crank cylinder being in one piece with the axis of the fly-wheel, revolves with it, and the chain rolls upon its surface,

rising and falling with it and with the treadle, of which C is the axis and E the tread. The grinding friction which destroys the ordinary crank is therefore removed.

CHAPTER V.

EMPLOYMENT OF COIL FRICTION.

501. WHEN a cord is coiled about a cylinder, for example, in the manner of fig. 347, with weights attached to its extremity, the

Fig. 347.

friction of the cord upon the surface increases with great rapidity, and can be shown to be independent of the magnitude of the diameter of the cylinder, and to depend solely on that of the angle embraced. This is best shown by fixing the cylinder so as to prevent its rotation, and suspending unequal weights to the two pendent ends of the cord respectively. If the cord be simply passed over the upper surface of the fixed cylinder it will be in contact with the upper half of its circumference, and the tension produced in the cord by the weights will generate friction throughout that portion of its length. If the difference of the weights is greater than this frictional resistance the heavier weight will descend and draw up the smaller one. But if the difference be less than the frictional resistance, the weights will remain at rest. Taking the mean value of friction at one-third of the pressure which generates it, it can be shown that any weight tied to one end will support a weight about three times as great at the other end.

If an additional coil of the cord is taken over the cylinder the small weight will support one twenty-seven times as great, and every additional coil multiplies the friction about nine times (in