FRICTION--ITS NATURE AND THEORY.
~29. Friction.~ The relative motion of one particle or body in forced
contact with another is always retarded, or prevented, by a resisting
force called friction.
Friction manifests itself in three ways: Between solids it is called
_sliding_ and _rolling friction_; between the particles of liquids, or
of gasses, when they move in contact with each other, or with other
bodies, it is called _fluid friction_. Quite different laws govern these
three kinds of friction, as they are quite different in character.
Friction can never of itself produce or accelerate motion, being always
a resisting force, acting at the surfaces of contact of the two
particles, or masses, between which it occurs, and in the direction of
their common tangent, resisting relative motion in whichever direction
it may be attempted to produce it. The greatest loss of energy in a
timepiece in which all the parts are rigid enough to prevent permanent
distortion, is that occurring through friction. Another source of loss
of energy is the reduction in elasticity of springs caused by a rise of
temperature.
~30. The Cause of Sliding Friction~ is the interlocking of the asperities
of one surface with those of another; and only by the riding of one set
over the other, or by a rubbing down or tearing off of projecting parts,
can motion take place. It follows, then, that roughness is conducive to
friction; and that the smoother the surface the less the friction will
be.
~31. The Cause of Rolling Friction~ is the irregularity and lack of
symmetry of the surfaces between which it occurs. It acts as a
resisting, or retarding, force when a smoothly curved surface rolls upon
another surface, plane or curved.
Motion is prevented, or retarded, by the irregular variation of the
distance between the center of gravity and the line of motion in the
common tangent of the two bodies at the point of contact, caused by the
irregularity of form, or of surface, in the one or the other body.
Rolling friction is small where hard, smooth, symmetrical surfaces are
in contact, and increases as the surfaces are soft, rough or irregular.
In a knife edge support, seen in some forms of pendulums, is exhibited a
form of rolling friction.
~32. Solid Friction~, either sliding or rolling, could be overcome if it
were possible to produce _absolutely_ smooth surfaces. It is evident,
then, that the character of the material, as well as the form of their
surfaces, determines the amount of friction.
In all time-keeping mechanism both sliding and rolling friction manifest
themselves; the former principally between the surfaces of pivots and
bearings and in the escapements, the latter mainly between the surfaces
of the teeth of wheels, and to some extent in some of the pivots, and
sometimes in parts of escapements. It is not the intention of the author
to treat of the proper shape of the teeth of wheels, leaves of pinions,
or the proportions of the escapements, the nature and scope of this work
not permitting of it; but he will confine his remarks principally to the
parts that involve lubrication.
~33. The Laws of Sliding Friction~, as given by Thurston,[7] with solid,
unlubricated surfaces, are, up to the point of abrasion, as follows:
1. The direction of frictional resisting forces is in the common tangent
plane of the two surfaces, and directly opposed to their relative
motion.
2. The point, or surface, of application of this resistance is the
point, or the surface, on which contact occurs.
3. The greatest magnitude of this resisting force is dependent on the
character of the surfaces, and is directly proportional to the force
with which two surfaces are pressed together.
4. The maximum frictional resistance is independent of the area of
contact, the velocity of rubbing, or any other conditions than intensity
of pressure and condition of surfaces.
5. The friction of rest or quiescence, "statical friction," is greater
than that of motion, or "kinetic friction."
He further states that these "laws" are not absolutely exact, as here
stated, so far as they affect the magnitude of frictional resistance. It
is found that some evidence exists indicating the continuous nature of
the friction of rest and of motion.
When the pressure exceeds a certain amount, fixed for each pair of
surfaces, abrasion of the softer surface or other change of form takes
place, the resistance becomes greater and is no longer wholly
frictional.
When the pressure falls below a certain other and lower limit the
resistance may be principally due to adhesion, an entirely different
force, which may enter into the total resistance at all pressures, but
which does not always appreciably modify the law at high pressures.
This limitation is seldom observable with solid, unlubricated surfaces,
but may often be observed with lubricated surfaces, the friction of
which, as will presently be seen (41), follows different laws. The upper
limit should never be approached in machinery.
The coefficient of friction is that quantity which, being multiplied by
the total pressure acting normally to the surfaces in contact, will give
the measure of the maximum frictional resistance to motion.
~34. Sliding Friction is Proportional to Pressure~ according to the third
law quoted above. This is easily demonstrated by ascertaining what force
is necessary to produce, or continue, motion in a body lying on a plane
surface; double the weight of the body and the force required to
produce, or continue, motion, will have to be doubled. The converse is
also true (36).
~35. Sliding Friction is Independent of the Area Of Contact~, the pressure
remaining the same (law 4, 33).
This is accounted for by the fact that if, for example, the area of
contact be doubled, though twice the number of asperities will present
themselves, each individual retarding force is only half of what it was
previously, and the general effect is the same (36).
~36. The Intensity of Sliding Friction is Independent of Velocity.~ (Law
4, 33.) This is explained by the fact that the interlocking of the
asperities on each surface has a shorter time to take place in increased
speed, and consequently cannot be so effective as with slow speed. But
with high speed more asperities are presented than in low speed, so the
effect is the same in both cases.
_The above (33-36) are not exact, being the statement of experimental
laws, and admit of considerable modification when applied in horological
science, as will be shown (41-42.)_
[Illustration: Fig. 12.]
~37. The Effect of a Loose Bearing~ is an increase of friction, and
consequently a loss of energy, resulting in the wear of _one_ or _both_
surfaces in contact, according to conditions. In Fig. 12, A is a loose
bearing, B a journal at rest and C the point of contact. If the journal
be now turned in the direction of the arrow by the motive force, it will
have a tendency to roll over a short arc of the bearing to a new point
of contact, as at D, when it begins to slide; so long as the coefficient
of friction is unchanged it retains this position; but approaches or
retreats from the point C, as the coefficient of friction diminishes or
increases, continually finding new conditions of equilibrium. The arc of
contact is thus too small to withstand the pressure without abrasion of
one or both surfaces.
It will thus be seen that the journal, or pivot, should fit its bearing
closely; but it should be borne in mind that no tendency to "bind"
should be produced, the fitting being such that the wheel will turn
readily with a minimum pressure.
The film of oil which must be interposed between the bearing surfaces of
the journal, or pivot, and its bearing, will also occupy _some_ space;
and this must be remembered, particularly in the case of pivots in the
escapement.
~38. The Laws of Rolling Friction~ are not as yet definitely established,
because of the uncertainty of the results of experiments, as to the
amount of friction due to (1) roughness of surface, (2) irregularity of
form, (3) distortion under pressure.
The first and second of these quantities vary inversely as the radius;
and the third depends upon the character of the material composing the
two surfaces in contact.
It follows, then, that in such minute mechanical contrivances as are
used in horology, as the motive force is in some cases very light, the
horologist should endeavor to produce, where rolling friction takes
place, the maximum--smoothness of surface--regularity of
form--adaptation of surfaces (31.)
There are many other points on which the writer would like to dwell, as
engaging and disengaging friction, internal friction, etc., etc., but
the scope of this paper will not permit.
~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 retarding force in mechanism it converts
the mechanical energy required to produce it into its heat equivalent,
thus raising the temperature of the mass 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 masses 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 passed, 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, assuming 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 space,
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 circumference, 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
" | Brass | 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
constitute, 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 brass 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
brass 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 brass bearings. Hence, with anything
short of an approximately perfect oil, the brass is most serviceable.
4. "Brass pivot holes are much less affected by the drying of the oil
than agate holes would be; and, in the absence of experiment, we must
assume that this would be the case with ruby or other jewels.
5. "When the oil is perfectly fresh, agate and steel have a very low
coefficient of friction."
How much these results would be altered by the use of a disk of such
weight, and pivots of such proportionate size, as to meet the actual
requirements in horology, remains to be ascertained.
Certainly the experiments of Jenkin, are _not_ applicable to the pivots
of a watch, as stated by E. Rigg; especially are they not applicable to
the friction of pivots in the escapement, where the laws of fluid
friction are more nearly applicable; and when it is remembered that the
weight of the disk was 86 pounds, and the pivots .25 c. m. in diameter,
(or about the size of pivot of a large barrel arbor,) it is evident that
the solid friction produced was much in excess of that produced in even
the heavy part of the train of a watch.
Furthermore, even Jenkin and Ewing, in their paper, state "that, owing
to the very great intensity of the pressure on the small bearing
surfaces of the axle, the lubricants must have been to a great extent
forced out." In a properly made watch, with a good lubricant, this does
not occur.
But there can be no doubt that if the apparatus above described were so
constructed as to meet the actual conditions in time recording
instruments, very valuable data could be thereby secured. This could be
done by reducing the weight of the disk, so as to make the weight bear
the proper relation to the size of the pivots.
FOOTNOTES:
[7] Thurston. Friction and Lost Work in Machinery.
[8] Philosophical Transactions, 1877, Vol. CLXVII., p. 502.
[9] The Horological Journal, Apr., 1881. Vol. XXIII., page 98.
[10] The writer has italicised this phrase.