~39. The Friction Of Fluids~ in horology is of grave importance. It is subject to quite different laws from those met with in the motion of solids in contact. When a fluid moves in contact with a solid the resistance to motion experienced is due to relative motion of layers of fluid moving in contact with each other. At surfaces of contact with a solid the fluid lies against the solid without appreciable relative motion; as the distance from the surface is increased by layer upon layer of the fluid, the relative velocity of the solid and the fluid becomes greater. _Fluid friction is, therefore, the friction of adjacent bodies of fluid in relative motion._

While fluid friction acts as a r.e.t.a.r.ding force in mechanism it converts the mechanical energy required to produce it into its heat equivalent, thus raising the temperature of the ma.s.s in a greater or lesser degree.

The resisting property which thus effects this conversion, and which is the cause of fluid friction, is called _viceosity_.

It is thus apparent that a _variation of the viceosity_ of the oil used on a watch would cause a variation of fluid friction and consequently a variation of the effort (11), _and would seriously interfere with the rate of the watch_. This will be discussed (84) more thoroughly in another paragraph.

~40. The Laws of Fluid Friction~ are:

1. Fluid friction is independent of the pressure between the ma.s.ses in contact.

2. Fluid friction is directly proportional to the surfaces between which it occurs.

3. This resistance is proportional to the square of the relative velocity at moderate and high speeds, and to the velocity nearly at very low speeds.

4. It is independent of the nature of the surfaces of the solid against which the stream may flow, but it is dependent to some extent upon the degree of roughness of those surfaces.

5. It is proportional to the density of the fluid and is related in some way to its viscosity.

~41. The Compound Friction of Lubricated Surfaces~, as Thurston terms it, or friction due to the action of surfaces of solids partly separated by a fluid, is observed in all cases in which the rubbing surfaces are lubricated. The solids, in such instances, though partly supported by the layer of lubricant which is retained in place by adhesion (21) and cohesion (20), usually rub on each other more or less, as they are usually not completely separated by the liquid film interposed between them.

Wear is produced by the rubbing together of the two solids; and the rate at which the lubricant becomes discolored and charged with abraded metal indicates the amount of wear.

The journal and bearing are forced into close contact in the case of heavy pressures and slow speeds, as is shown by their worn condition; while the journal floats on the film of fluid which is continually interposed between it and the bearing, in the case of very light pressures, and high velocities; in the latter instance _the friction occurs between two fluid layers_, one moving with each surface.

With heavy machinery, as the hardness and degree of polish of the surfaces cannot be increased in proportion to their weight, the solid friction is so great that while the interposition of a lubricant between the surfaces adds fluid friction, it also reduces the solid friction; and as the fluid friction is so insignificant as compared to the solid friction, the former is almost completely masked by the latter. In this case the laws of solid friction are more nearly applicable.

But in a delicate machine like a watch, especially in the escapement, where the power is so light, and where the rubbing surfaces are so hard, smooth and regular, the solid friction is so minute as compared to the fluid friction, that the former is relatively very slight, as compared with the latter. The laws of fluid friction are more nearly applicable in this instance.

There are thus, evidently, two limiting cases between which all examples of satisfactorily lubricated surfaces fall; the one limit is that of purely solid friction, which limit being pa.s.sed, and sometimes before, abrasion ensues; the other limit is that at which the resistance is entirely due to the friction of the film of fluid which separates the surfaces of the solids completely.

~42. The Laws of Friction of Lubricated Surfaces~ are evidently neither those of solid friction nor those of fluid friction, but will resemble more nearly the one or the other, as the limits described in the previous paragraph are approached. The value of the coefficient of friction varies with every change of velocity, of pressure, and of temperature, as well as with the change of character of the surfaces in contact.

For _perfectly_ lubricated surfaces, were such attainable, a.s.suming it practicable with complete separation of the surfaces, the laws of friction, according to Thurston, would become:

1. The coefficient is inversely as the intensity of the pressure, and the resistance is independent of the pressure.

2. The friction coefficient varies as the square of the speed.

3. The friction varies directly as the area of the journal bearing.

4. The friction varies as the temperature rises, and as the viscosity of the lubricant is thus decreased (80).

~43. The Methods of Reducing Waste of Energy Caused by Friction~ in time keeping mechanisms are based upon a few simple principles. It is evident that to make the work and power so lost a minimum, it is necessary to adopt the following precautions:

1. Proper choice of materials for rubbing surfaces (29-32).

2. Smooth finish and symmetrical shape of surfaces in contact (29-32 and 38).

3. The use of a lubricant the viscosity of which is adapted to the pressure between the bearing surfaces (80).

4. The best methods for retaining the lubricant at the places required, and for providing for a continual supply of the lubricant.

5. The bearing surfaces of such proportions that the lubricant will not be expelled at normal pressure.

6. The reducing of the diameters of all journals, shoulders and pivots, to the smallest size compatible with the foregoing conditions, and with the stresses they are expected to sustain, thus reducing the s.p.a.ce, through which the fluid friction acts, to a minimum (40); as well as reducing the distance from the axis of the arbor or pinion at which the friction, both solid and fluid, acts. The work done is independent of the length of the journal; except as it may modify pressure, and thus the coefficient of friction.

7. Proper fitting of bearing surfaces (37).

8. The reducing of the rubbing surfaces in escapements as much as the nature of the materials will allow without abrasion in the course of time (55).

~44. Friction Between Surfaces Moving at Very Slow Speed~, has been investigated by Fleming Jenkin and J. A. Ewing. A contrivance, which would be very excellent with some improvement, for the determination of the amount of friction under such conditions, is given in a paper[8]

read before the Royal Society of London.

The arrangement employed by them was composed of a cast iron disk two feet in diameter and weighing 86 pounds. This disk, being turned true on its circ.u.mference, was supported by a spindle terminating in pivots 0.25 C. M. in diameter, the pivots resting in small rectangular bearings composed of the material the friction of which with steel is to be determined.

A tracing of ink was produced on a strip of paper which surrounded the disk, the ink being supplied by a pen actuated electrically by a pendulum, as in the syphon recorder.

As the traces thus left on the paper were produced without in any way interfering with the freedom of motion of the disk, they afforded a means of determining the velocity of rotation.

The relative velocities of the pivot to the bearing surfaces varied from .006 C. M. to 0.3 C. M. per second, being the velocities met with in the various parts of time keeping devices.

Experiments were made with the bearing surfaces successively in three different conditions: viz. 1, dry; 2, wet with water; and 3, wet with oil; and gave the following results:

TABLE I.

--------------------------------------------------------- SURFACES. | COEFFICIENT OF FRICTION.

------------------------------|-------------------------- JOURNAL. | BEARING. | DRY. | WATER. | OIL.

-------------|----------------|--------|--------|-------- Steel | Steel | 0.351 | 0.208 | 0.118 " | Bra.s.s | 0.195 | 0.105 | 0.146 " | Polished Agate | 0.200 | 0.166 | 0.107 ---------------------------------------------------------

Several facts of great interest to the horologist are here shown.

[9]

Edward Rigg has this to say in regard to the apparatus of Jenkin and Ewing. "The friction, then, is true sliding friction without any rolling, and it will be evident that if the bearing were a circular hole just large enough to admit the pivot freely, the character of the friction would be in no way changed. In both a watch and clock the pivots are pressed against the sides of the pivot holes, either by the motive force or by gravity. There is no rolling round the pivot holes, so that the friction is all of the first kind. Jenkin"s experiments are, then, _strictly applicable to the case of pivots_,[10] and they const.i.tute, so far as I am aware, the first scientific determination of the friction that occurs in time-keepers, and even in these experiments, the pressure, due to the weight of 86 pounds, is evidently too great, and thus too little regard is paid to the influence of adhesion."

E. Rigg further states that, reverting to the preceding table, we notice the following points of interest:--

1. "When the oil has dried up, the friction of a steel pivot in bra.s.s is actually less than in agate.

2. "A greater diminution of friction, by the application of oil, is effected when steel is used with steel, than where steel is used with bra.s.s or agate; although the fluid friction is probably equal in the three cases, when oil is used.

3. "With a perfect, non-drying, non-oxidizing lubricant, steel bearings for pivots would be preferable to bra.s.s bearings. Hence, with anything short of an approximately perfect oil, the bra.s.s is most serviceable.