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Several years ago, the idea arose to write a general book on tribology. Students often requested a suitable book for the study of tribology and there were. FRICTION, WEAR, LUBRICATION A TEXTBOOK IN TRIBOLOGY K.C Ludema Professor of Mechanical Engineering The University of Michigan Ann Arbor. Industrial Significance of Tribology. 3. Origins and Significance of Micro/ Nanotribology. 4. Organization of the Book. 6. References.


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WEAR ELSEVIER Wear () Book Review Engineering Tribology by soundofheaven.infoms Dr Williams has written a comprehensive book dealing with the eng. Handbook of Micro/Nano Tribology, Bharat Bhushan. Modern Tribology This book contains information obtained from authentic and highly regarded sources. Fundamentals of Physics Textbook Friction, Lubrication, and Wear Technology. pdf lubrication, and wear into a versatile book on tribology. This is done on.

They are not available yet. Copper nitride is not listed, so nitrogen very likely forms only a physically adsorbed layer. Atomic arrangement in the body-centered and face-centered cubic lattice arrays. Most theories of the friction of polymers are based on continuous contact of sliding surfaces. The tool burnishes the surface, pushing high regions downward, which causes valleys to rise by plastic flow.

Email or Customer ID. Forgot password? Old Password. New Password. Your password has been changed. Returning user. Request Username Can't sign in? Forgot your username? Rheology and tribology of engineering oils.

Tribology courses in a mechanical engineering curriculum. Tribology Series. Nuclear tribology. Tribology course. Tribology news. Williams Dr Williams has written a comprehensive book dealing with the engineering aspects of Tribology.

The book is essentially in four main parts. The first looks briefly at lubricant and bearing material properties. This stress state exists when sliding occurs and the coefficient of friction is 0.

For a ratio of shear force to normal force i.

FRICTION, WEAR, LUBRICATION

This seems to be inconsistent with the stress states in tensile tests. The reason is that the small volume of plastically deforming metal is constrained by the large surrounding elastic field. If adjacent asperities are very close, they no longer have independent elastic stress fields supporting them. See Problem Set question 5 a. If the load is removed, separation of the sphere from the plate begins from the outer edge of contact and moves inward.

If only elastic deformation has occurred, both bodies return to their original shapes. If, for example, the flat plate had plastically deformed locally, upon removal of the sphere a dent is left in the plate.

This indicates clearly that much of the stress field shown in Figure 5. Subsequent repeated loading and removal of the same load produces only elastic strain cycling in the flat plate.

Repeat loading causes plastic strain cycling. With each cycle the sphere sinks a little farther into the flat plate to some limit. Plastic strain progression by a succession of highly loaded wheels makes a layer of rail shear forward relative to the deeper substrate eventually resulting in fatigue failure.

See Problem Set question 5 b. The same would apply to the pressing of a soft rubber ball against a flat plate. The previous discussion applied to the case of no sensible adhesion between the two bodies. Releasing the load allows each body to deform out of conformity to each other, and separate. The driving force is supplied by relaxation of the strain energy in the two substrates which was imposed by applying the load.

When the two bodies stick together upon loading, a new stress state prevails upon unloading. Take the case of a sphere pressing into a flat plate and restrict ourselves to the elastic case.

Engineering Tribology, Third Edition - PDF Free Download

Now suppose the two surfaces adhere over the contact area. This analysis uses unrealistic material properties, but it shows clearly the source of the tearing force. In the usual case the high stress at the edge of contact is alleviated but not eliminated by plastic flow. Thus, if the asperities stretch plastically at the periphery, contact is maintained and more force will be necessary to separate the parts.

A practical illustration of this effect may be seen using a rubber ball on a plate. When viewing through the glass plate, the area of contact is seen to vary with applied load. Cover the glass plate with a thin layer of a very sticky substance. Now press the ball against the flat plate and suddenly release the load. The ball recovers its shape slowly. Strands of the sticky substance can be seen to bridge the gap where once the bodies were in contact.

After some time a small region of adhesion remains. Metals behave the same way, only much more quickly and on a microscopic scale. See the section titled Adhesion in Chapter 3. It was thought that the question could be resolved by knowing the amount of real contact area sum of the tiny asperity contact areas between contacting and sliding bodies. That there is a large difference between real and apparent area of contact had been known for some time, particularly by people who had no concern for theories of friction, however.

As a result, most people understand why the flow of heat and electricity through contacting surfaces is enhanced by increasing contact pressure. Apparent or nominal area of contact is that which is usually measured, such as between a tire and the road surface or calculated for the case of a large sphere on a rough flat plate, by equations of elasticity as in the previous section.

Real area of contact occurs between the asperities of surfaces in contact. If all contacting asperities were in the fully developed plastic state, the contact pressure in them all would be about 2.

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Note that all asperities are assumed to be fully plastic in the calculation above. Actually, some of them will be elastically deformed only, so that the real area of contact will be larger than calculated above. Five methods and limitations are listed: Two large model surfaces with asperities greater than 1 inch in radius, one covered with ink which transfers to the other at points of contact.

Acceptable simulation of microscopic asperities has not yet been achieved. Electrical resistance method. Adhesion and separation of sticky surfaces.

Engineering Tribology, Third Edition

In this method two clean metal surfaces in a vacuum are touched together with a small force and then pulled apart. Optical method, interference, phase contrast, total internal reflectance, etc. With these methods it is difficult to resolve the thickness of the wedge of air outside of real contact area down to atomic units, which is the separation required to prevent adhesion.

In the absence of good measurement methods, researchers have always inferred the area of contact from contact mechanics. To summarize the case of contact between a single pair of spheres: In real systems consisting of complex arrays of asperities, the following conclusions have been reached, largely through experiments: In metal systems, ranging from the annealed state to the fully hardened state, contact appears to produce large strain plastic flow.

This simplifies matters greatly. Recall that we have considered hemispherical asperities for convenience. In most nonmetal systems contact appears to be nearer to elastic. For rubber, plastic, wood, textiles, etc. Thus, these brittle materials appear to deform plastically. However, there may be another reason. Archard found mathematically that for: These are elastic calculations and can be in error if the influence of close proximity of asperities is ignored.

When plastic strain fields of closely spaced asperities overlap, several asperities act as one larger asperity. See Problem Set question 5 c. Holm reported the mathematical work of Maxwell which showed the need for a correction due to the constriction of the stream of current in the regions of r2 and r4.

In many cases, the oxide may be the chief cause of resistance. Electrical contact resistance has been used to measure A but the results have usually been ambiguous.

Calculation of heat transfer rates and temperature distribution is rather daunting because it involves so many dimensional units.

Friction Wear Lubrication A Textbook in Tribology

Most tribologists would prefer to leave the topic to those who work in the field as a career, but sometimes it is necessary to estimate surface temperatures of sliding bodies in engineering practice.

The major concern among tribologists is to choose a useful equation from among the many available in the literature. Several of the more widely discussed will now be presented, as will a perspective on methods and accuracy of equations. The case of greatest interest in sliding is the pin-on-disk geometry. Assume a pin made of conducting material, surrounded by perfect insulation, and held by an infinite mass of very much higher thermal conductivity than the pin, as shown in Figure 5.

The pin slides along a flat plate of a perfect insulator with zero heat capacity. That is, none of the frictional heat is conducted into the flat plate and no heat is required to heat the surface layers of the flat plate. Then all of the frictional energy is conducted along the length of the pin as shown in the sketch. Now assume the opposite case, i. The simplest assumption in this case is that the temperature across the end of the pin is uniform.

This is the assumption of the uniform heat flux or uniform heat input rate. If that heat source is stationary, then in the first instant the temperature distribution across the surface of the plate assume the twodimensional case is as shown as the rectangular curve 0 in Figure 5. After some time, heat will flow to the left and right and if the rate of heat input is just sufficient to maintain the same maximum temperature as for curve 0 in Figure 5.

However, if the heat source had been shut off after curve 0 then the temperature distribution would change as shown in curve 3. Rectangular distribution 0 exists for a very brief time after initiation of heating; distributions 1 and 2 exist after some time of heating; and distribution 3 exists after the heat source is removed.

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If the heat source moves to the right, the surface material to the left cools by conduction of heat into the substrate, and the material to the right begins to heat. If the rate of heat input is equal to the rate of exposure to new surface times the amount of heat required to heat the material to the same temperature as before, the temperature distribution will be skewed as shown in Figure 5. The maximum temperature will be near the rear edge of contact rather than at the edge because heat is transferred away from the heated region.

Further, it may be seen that the higher the velocity of movement of the heat source relative to the thermal conductivity of the plate material, the nearer the maximum temperature will be to the rear edge of contact. In practical sliding systems, neither the pin nor the plate are insulators, or are insulated, generally.

For analysis, the temperature distributions over the region of apparent contact in each body are assumed to be the same, though not uniform. In other words, the mathematical solutions to each of the above ideal cases are combined, taking the contact temperature distributions on both surfaces to be the same.

The complete solution of the pin-on-disk sliding problem is very complicated. Engineers have therefore found it convenient to present equations for average surface temperature over nominal contact areas for several special cases.

For these equations, the symbols are given first: He as most others do interposed a thin plate between asperities on two surfaces.

The quantity 4a is the Holm representation of contact area: From the above equations it would seem that the influence of speed and load can be expressed as: Three points emerge from this work: Visible red heat begins in this temperature range.

Recently other writers have suggested the need to account for thermal softening of the surface. Assuming the Tabor equations apply reasonably well to metals, what order of V causes melting?

Gallium Lead Constantan Copper f. Metal brake disks last 20 to 40 landings depending on the amount of reverse thrusting used to aid braking, or one aborted take-off. Carbon brakes are now more common and last much longer than metal brakes. See Problem Set question 5 d. These equations are plotted in Figure 5. Note that there is a blend region between the two equations, and note also that a single equation for the full range of sliding speed shown in Figure 5.

Equations 5 and 7 show nearly the same results for stainless steel, but Equations 8 and 9 show rather different results. Recall that Equations 5, 6, and 7 represent the average temperature rise in the nominal area of contact, whereas Equations 8 and 9 apply to the real areas of asperity contact and is the flash temperature that we read of in some papers. Thus there are few, but very hot, points of asperity contact. All equations are shown intersecting a vertical line at the arbitrarily selected sliding speed of 1.

This sliding speed is near that at which the transition occurs between Equations 5 and 6 for copper sliding on copper. Restriction to this area also yields the impracticably small values of temperature rise seen in Figure 5.

Further, it may be inferred that for other contacting pairs, completely different equations are required, such as for cams and followers, for gear teeth, and for shafts that whirl in the bearings.

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The results hardly ever agree. The embedded thermocouple cannot be placed closely enough to the surface to read real and instantaneous temperature, certainly not of asperities. The dynamic thermocouple measures the electromotive force emf from many points of microscopic contact simultaneously, and the final result will be a value probably below the average of the surface temperature of the points.

Surface temperatures are also measured by radiation detectors. Again these devices measure the average temperature over a finite spot diameter. Size depends on the detector.

For opaque materials the measurements may be made after the sliders have separated, with some loss of instantaneous data.

Where one of the surfaces is transparent, the radiation that passes through can provide a good approximation of the real temperature. All of these methods require extensive calibration. Johnson, K. Bowden, F. Greenwood J. Archard, J. Dorinson, A. Four categories within which high or low friction may be desirable are given below. Force transmitting components that are expected to operate without interface displacement.

Examples fall into the following two classes: Drive surfaces or traction surfaces such as power belts, shoes on the floor, and tires and wheels on roads or rails. Some provision is made for sliding, but excessive sliding compromises the function of the surfaces. Normal operation involves little or no macroscopic slip. Static friction is often higher than the dynamic friction. Clamped surfaces such as press-fitted pulleys on shafts, wedge-clamped pulleys on shafts, bolted joining surfaces in machines, automobiles, household appliances, hose clamps, etc.

To prevent movement, high normal forces must be used, and the system is designed to impose a high but safe, normal clamping force.

In some instances, pins, keys, surface steps, and other means are used to guarantee minimal motion. In the above examples, the application of a friction force frequently produces microscopic slip. Since contacting asperities are of varying heights on the original surfaces, contact pressures within clamped regions may vary.

Thus, the local resistance to sliding varies and some asperities will slip when low values of friction force are applied. Slip may be referred to as micro-sliding, as distinguished from macro-sliding where all asperities are sliding at once. The result of oscillatory sliding of asperities is a wearing mechanism, sometimes referred to as fretting.

The works of all named authors in this chapter are described in reference 1 unless specifically cited. Energy absorption-controlling components such as in brakes and clutches. Efficient design usually requires rejecting materials with low coefficient of friction because such materials require large values of normal force.

Large coefficients of friction would be desirable except that suitably durable materials with high friction have not been found.

Furthermore, high friction materials are more likely to cause vibration than are low friction materials. An important requirement of braking materials is constant friction, in order to prevent brake pulling and unexpected wheel lockup in vehicles. A secondary goal is to minimize the difference between the static and dynamic coefficient of friction for avoiding squeal or vibrations from brakes and clutches. Quality control components that require constant friction.

Two examples may be cited, but there are many more: In knitting and weaving of textile products, the tightness of weave must be controlled and reproducible to produce uniform fabric. Sheet-metal rolling mills require a well-controlled coefficient of friction in order to maintain uniformity of thickness, width, and surface finish of the sheet and, in some instances, minimize cracking of the edges of the sheet.

Low friction components that are expected to operate at maximum efficiency while a normal force is transmitted. Examples are gears in watches and other machines where limited driving power may be available or minimum power consumption is desired, bearings in motors, engines, and gyroscopes where minimum losses are desired, and precision guides in machinery in which high friction may produce distortion.

See Problem Set question 6 a. After the start of the industrial revolution came the specialty of building and operating engines steam engines, military catapults, etc. Amontons — , a French architect turned engineer, gave the subject of friction its first great publicity in when he presented a paper on the subject to the French Academy.

The specimens tested by Amontons were of copper, iron, lead, and wood in various combinations, and it is interesting to note that in each experiment the surfaces were coated with pork fat suet. The scale of these irregularities must have been macroscopic because little was known of microscopic irregularities at that time.

Euler , a Swiss theologian, physicist, and physiologist who followed Bernoulli as professor of physics at St. Petersburg formerly Leningrad , said friction was due to hypothetical surface ratchets. His conclusions are shown in Figure 6. Figure 6. Coulomb — , a French physicist-engineer, said friction was due to the interlocking of asperities. He was well aware of attractive forces between surfaces because of the discussions of that time on gravitation and electrostatics.

In fact, Coulomb measured electrostatic forces and found that they followed the inverse square law force is inversely related to the square of distance of separation that Newton had guessed applied to gravitation.

However, he discounted adhesion which he called cohesion as a source of friction because friction is usually found to be independent of apparent area of contact. Coulomb and others considered the actual surfaces to be frictionless. This, of course, is disproven by the fact that one monolayer of gas drastically affects friction without affecting the geometry of the surfaces. An anonymous writer then asks whether motion destroys adhesion.

Leslie, also English — , argued that adhesion can have no affect in a direction parallel to the surface since adhesion is a force perpendicular to the surface.

Rather, friction must be due to the sinking of asperities. Sir W. Hardy works: He came to this conclusion by experimentation. His primary work was to measure the size of molecules. He formed drops of fatty acid on the end of capillary tubes and measured the size of a drop just before it fell onto water.

He then measured the area of the floating island of fatty acid on the water, from which he could determine the film thickness. One of these films was transferred to a glass plate. He found that the coefficient of friction of clean glass was about 0. He knew that the film of fatty acid was about 2 nm thick and the glass was much rougher. The film therefore did not significantly alter the functioning surface roughness but greatly reduced the friction. Hardy was also aware that molecular attraction operates over short distances and therefore differentiates between real area of contact and apparent area of contact.

Tomlinson elaborated on the molecular adhesion approach. The basis of his theory is the partial irreversibility of the bonding force between atoms, which can be shown on figures of the type of Figure 3.

In retrospect, friction research was accelerated with the publishing of an extensive work by Beare and Bowden. The adhesion hypothesis was the best alternative in the s although it was not clear which surface or substrate chemical species were prominent in the adhesion process.

Several laboratories took up the task of finding the real cause of friction but none proceeded with the vigor and persistence of the Bowden school in Cambridge. The adhesion explanation of friction is most often attributed to Drs.

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Bowden and Tabor although there are conflicting claims to this honor. On the other hand, it is easy to be mistaken in the presence of immature ideas and in the interpretation of research results, so full credit should not go to one who does not adequately convince others of his ideas.

On the latter ground alone, Bowden and Tabor are worthy of the honor accorded them, Bowden for his prowess in acquiring funds for the laboratory and Tabor for the actual development of the concepts. The adhesion theory was formulated in papers which were mostly treatises on the inadequacy of interlocking.

Tabor advanced the idea that the force of friction is the product of the real area of contact and the shear strength of the bond in that region, i. The average pressure of contact was thought to be that for fully developed plastic flow such as under a hardness test indenter, thus the subscript in Pf.

However, it was the first model that suggested the importance of the mechanical properties of the sliding bodies in friction. Similar results have been found for wax on a hard surface, etc. This principle has been applied to the design of sleeve bearings such as those used in engines, electric motors, sliding electrical contacts, and many other applications. Engine bearings are often composed of lead-tin-coppersilver and lately aluminum combinations applied to a steel backing.

The result is low friction, provided the film of soft metal has a thickness of the order of 10—3 or 10—4 mm, as shown in Figure 6. The most vociferous was Dr. Bikerman who continued until his death in to hold the view that friction must be due to surface roughness. This view is based on the finding that sliding force is proportional to applied load. By itself this finding does not prove the interlocking theory.

Bikerman agreed that the real area of contact should increase as load increases but insisted that it does not decrease as load decreases if there is adhesion. Thus, he would expect that friction would not decrease as load decreases if the adhesion theory is correct. Bikerman, an authority in his own right on the chemistry of adhesive bonding, had published his position as late as in the face of a continuous stream of evidence contrary to his conviction.

Influence of soft-film thickness on friction. From to a series of papers appeared that provided the best arguments for the adhesion theory of friction.

In essence, they show that for ductile metals, at least, asperities deform plastically, producing a growth in real area of contact which is limited by the shear stress that can be sustained in surface films. In effect, the coefficient of friction is determined by the extent to which contaminant films on the surface prevent complete seizure of two rubbing surfaces to each other.

Bowden and Tabor showed, using electrical contact resistance, that plastic flow occurs in asperities even for small static loads. Further difficulties for the interlocking theory appeared in the findings of C.

Strang and C. Eisner measured the path of the center of mass of a slider as a pulling force increased from zero and found a significant downward displacement component, consistent with plastic flow of asperities. See the discussion on plasticity in Chapter 2. The model begins with a two-dimensional asperity of non-work-hardening metal pressed against a rigid plate as shown in Figure 6. The initial load, W, is sufficient to produce plastic flow in the asperity, which produces a normal stress equal to the tensile yield strength, Py, in the asperity, and a cross-sectional area of A0.

Now apply a finite F and the proper forces to prevent rotation of the element. Deformation does not respond to the simple addition of stresses in the element as if the material were elastic. Rather, deformation occurs in order to maintain the conditions for continued plastic flow. Tabor used the shear distortion energy flow criteria of von Mises in his work. No exact theoretical solution for this case has yet come to light.

However, approximations can be made. But since this result is derived from measurements of Py and Ss in plane stress, it doubtless does not apply directly to the actual complex stress state of Figure 6. One approach is through experimental results. To do this the above equation was revised as follows: This is shown in Figure 6. Now assume that the surface contact region is weaker than the bulk shear strength, perhaps due to some contaminating film.

Take the shear strength of the interface film to be Si so that when the shear stress on the surface due to F equals Si, sliding begins. Now since: Or a study of the prevention of junction growth. The adhesion theory does not explain the effect of surface roughness in friction.

The general impression in the technical world is that friction increases when surface roughness increases beyond about micro-inches, although there are little reliable data to support this impression. Instantaneous variations in friction do increase in magnitude with rougher surfaces sliding at low speeds.

Bikerman explains this, however, by pointing out that the fluid film on all surfaces becomes important as a viscous substance on smooth surfaces. The adhesion theory is so superior to the interlocking theory that it is easy to dismiss the influence of colliding asperities, particularly those composed of hard second phases in the micro structure.

Several authors have published equations of the form: These then become two-term equations with a plowing term added to the adhesion term.

Plowing was thought by some to cause up to one third the total friction force. Another difficulty that the early adhesion theories of friction share with the classical laws of friction is that they apply to lightly loaded contact. The elastic fields under closely spaced asperities merge, or are coalesced, and in the limit become homogeneous as in a tensile specimen.

This assumption is widely used in metal working research. The question is far more important than a matter of favoring or rejecting the classic alternate explanation, namely the interference of asperities. The evidence that favors the adhesion explanation is actually rather direct, namely, that perfectly clean metals in vacuum stick together upon contact as discussed in Chapter 3.

See Equation 1, Chapter 8. Adhesion is not often discussed as a cause of lubricated viscous friction though one could argue that wetting, surface tension, and even viscosity are manifestations of bonding forces as well.

Surely then, we are convinced that there is adhesion between any and every pair of contacting substances, though we do not know exactly how it functions. All mechanisms of friction and wear should thus be referred to as adhesive mechanisms.

The fact that only a few are may mean that no other prominent cause or mechanism has been found for most cases. Coulomb, and later Bikerman, argued that friction could not be due to adhesion because adhesion is a resistance to vertical normal separation of surfaces, whereas friction is resistance to parallel motion of surfaces.

Neither one denied that atomic bonding functions during sliding, but perhaps both should have coined a new term for this case. Energy is required to move an atom from its rest position to the midpoint between two rest positions. However, that energy is restored when the atom falls into the next rest position. This cycle is thought to require no energy, and thus atom motion as shown cannot be the cause of friction.

A more plausible explanation, for fairly brittle materials at least, involves atom A following atom B for some distance as atom B moves, as shown in Figure 6. This continues until the forces required to pull atom A, as atom B moves still further, exceeds that exerted upon atom A by its neighbors to keep it in position.

At that point, atoms A and B separate. Atom A snaps back into position, setting its neighbors into vibration. Atom B snaps into the next rest position, setting its new neighbors into vibration. These lattice vibrations dissipate, heating the surrounding material, just as macroscopic vibration strains dissipate and heat a solid.

In ductile materials atoms can be pulled even further out of position to produce slip, which, in macroscopic systems, is referred to as plastic flow. At this point it is helpful to make a comment for perspective. It would appear that ductile materials metals, for example would produce high friction, whereas brittle ceramic materials would produce low friction.

In practice the opposite is usually found. These findings do not contradict the discussion of atomic friction: Friction also varies with direction of sliding on crystalline surfaces. In Figure 6. The single atom could move in many directions, locating wells at various spacings, requiring a significant range of energy exchange.

This variation depends strongly on the bonding system for the material in question. There are four bonding systems: These bond systems are described in Chapter 3. The asperities of rubber, some plastics, wood, and some textiles appear to deform elastically. The consequence of the difference in behavior is as follows: For a soft metal covered by a brittle oxide it has been found that there are three regimes of friction over a range of load. Visco-elastic materials such as rubber and plastics, show interesting friction properties that may vary by a factor of 5 to 1, or even 10 to 1 over a range of sliding speed or over a range of temperature.

For example, Grosch slid four types of rubber on glass, yielding results of the type sketched in Figure 6.

This implies a surprisingly narrow spectrum of vibrations which seems unlikely. The vibrations of Grosch may correspond with the waves of detachment described by Schallamach7 and discussed later in this chapter. By the model of Schallamach there need be no actual sliding of rubber over glass to effect relative motion. Rather, the rubber progresses in the manner of an earthworm, and the coefficient of friction may be due to damping loss in the rubber and irreversibility of adhesion.

Adapted from Grosch, K. Most theories of the friction of polymers are based on continuous contact of sliding surfaces. However, some are based on concepts derived from chemical kinetics. The Arrhenius equation is useful but not precise over a very wide range of temperature. Each release of bond and formation of a new one is conditioned by an activation process. Data are available from which Ar and Ss can be inferred.

Data for the fracture strength of a styrene-butadiene rubber are sketched in Figure 6. This curve is also transformable by the WLF equation. Data for E for the same rubber are given with a corresponding curve for Ar in Figure 6. Ar and Ss can be multiplied graphically to get F.

But this produces a fairly straight line, as shown in Figure 6. A different conclusion can be reached, however, based on the mechanics of the friction process. The variation in Ar is controlled by the strain rate relatively deep in the substrate. The rate of strain in the substrate is therefore some low multiple of the sliding speed, whereas the rate of strain in the asperities must be some high multiple of the sliding speed.

For a given sliding speed, therefore, the transitions in the two curves are not coincident. The curve for Ss reaches a high value of Ss at a relatively low sliding speed, i. A fair estimate is that the shear rate in the surface layer would be 5 to 6 orders of 10 higher than the average shear strain rate in the substrate when a slider slides. This would support the suggested mechanics of friction.

Several experimental observations in the sliding of rubber are not yet explained. For example, it is sometimes observed that the coefficient of friction changes after a speed change, but not immediately. Interesting effects are also seen in the linear polymers or plastics below Tg. Above Tg most linear polymers are viscous liquids, and below Tg there are structural transitions not found in rubber, which requires some caution.

The friction data for plastics often show rather mild slopes and often only suggestions of peaks, even when the experimental variables cover a very wide range. The curves do not transform as readily to a master curve as was shown above with rubber.

In addition, as found by Bahadur,9 morphological changes that occur in the polymer due to temperature change necessitate a vertical shift in data curves in addition to the horizontal WLF type of shift to produce a master curve. Nonetheless, the data for several polymers are interesting to study. The most notable points are that the coefficients of friction do indeed vary considerably for linear polymers and that only in rare instances do the measured coefficients of friction compare with those given in handbooks.

For example, Figures 6. The handbook value for the coefficient of friction for PTFE is 0. The sliding friction probably also includes a damping loss component of the magnitude of the rolling friction. Thermosetting polymer is one of the several constituents in brake materials, and is often the binder for asbestos, metal chips, Kevlar fiber, and other additives.

For safe and comfortable operation of vehicles it is necessary that the coefficient of friction of brake materials be constant in each wheel, with time and over a production lot. In brake material the coefficient of friction is controlled largely by the nature of wear debris in the rubbing interface and the transfer film attached to the rotating metal member, which considerably broadens the scope of friction studies.

See Problem Set question 6 c. This was attributed to van der Waals forces attracting the rubber to the glass. Johnson, Kendall, and Roberts10 calculated the area of contact using both the Hertz conditions and van der Waals forces and came very close to experimental observations. Each solid may attract the same polarity ions, which produces a net repulsive force, reducing the measurable coefficient of friction.

Such melting apparently occurs between the ring on the bourtolet of shells and the barrels of big military guns. Melting doubtless occurs on the surface of polymers more readily than on metal surfaces because metals have much higher thermal conductivity than do polymers.

A widely known case of melting at the sliding interface is that between skates and ice.