30079_21d.pdf

(H min ) 0 = ^^ = 3.63£/°- 68 G°- 49 W-°- 07 3 (1 - e-°- 6 * k °)

R X ,o

= 3.63 X 2.087 X IQ- 7 X 65.29 X 1.785 X 0.9919

(21.156)

- 0.876 x 10~ 4

Thus

(h min ) 0 = 0.876 X 10- 4 R^ = 0.665 Aim

In this case, the lubrication factor A is given by

(2U57 )

A ° = [(0.175) 2 + (0.0625)*r x 10-' = 3 ' 5 8

Once again, it is evident that the smaller minimum film thickness occurs between the most heavily

loaded ball and the inner race. However, in this case the minimum elastohydrodynamic film thickness

is about three times the composite surface roughness, and the bearing lubrication can be deemed to

be entirely satisfactory. Indeed, it is clear from Fig. 21.97 that very little improvement in the lubri-

cation factor F and thus in the fatigue life of the bearing could be achieved by further improving the

minimum film thickness and hence A.

21.4 BOUNDARYLUBRICATION

If the pressures in fluid-film-lubricated machine elements are too high, the running speeds are too

low, or the surface roughness is too great, penetration of the lubricant film will occur. Contact will

take place between asperities, leading to a rise in friction and wear rate. Figure 21.99 (obtained from

Bowden and Tabor 56 ) shows the behavior of the coefficient of friction in the different lubrication

regimes. It is to be noted in this figure that in boundary lubrication, although the friction is much

higher than in the hydrodynamic regime, it is still much lower than for unlubricated surfaces. As the

running conditions are made more severe, the amount of lubricant breakdown increases, until the

system scores or seizes so badly that the machine element can no longer operate successfully.

Figure 21.100 shows the wear rate in the different lubrication regimes as determined by the

operating load. In the hydrodynamic and elastohydrodynamic lubrication regimes, since there is no

asperity contact, there is little or no wear. In the boundary lubrication regime the degree of asperity

interaction and wear rate increases as the load increases. The transition from boundary lubrication to

an unlubricated condition is marked by a drastic change in wear rate. Machine elements cannot

operate successfully in the unlubricated region. Together Figs. 21.99 and 21.100 show that both

friction and wear can be greatly decreased by providing a boundary lubricant to unlubricated surfaces.

Understanding boundary lubrication depends first on recognizing that bearing surfaces have as-

perities that are large compared with molecular dimensions. On the smoothest machined surfaces

these asperities may be 25 nm (0.025 /nn) high; on rougher surfaces they may be ten to several

hundred times higher. Figure 21.101 illustrates typical surface roughness as a random distribution of

Fig. 21.99 Schematic drawing showing how type of lubrication shifts from hydrodynamic to

elastohydrodynamic to boundary lubrication as the severity of running conditions is increased.

(From Ref. 56.)

Fig. 21.100 Chart for determining wear rate for various lubrication regimes. (From Ref. 57.)

hills and valleys with varying heights, spacing, and slopes. In the absence of hydrodynamic or

elastohydrodynamic pressures these hills or asperities must support all of the load between the bearing

surfaces. Understanding boundary lubrication also depends on recognizing that bearing surfaces are

often covered by boundary lubricant films such as are idealized in Fig. 21.101. These films separate

the bearing materials and, by shearing preferentially, provide some control of friction, wear, and

surface damage.

Many mechanism, such as door hinges, operate totally under conditions (high load, low speed)

of boundary lubrication. Others are designed to operate under full hydrodynamic or elastohydrody-

namic lubrication. However, as the oil film thickness is a function of speed, the film will be unable

to provide complete separation of the surfaces during startup and rundown, and the condition of

boundary lubrication will exist. The problem from the boundary lubrication standpoint is to provide

a boundary film with the proper physical characteristics to control friction and wear. The work of

Bowden and Tabor, 5 6 Godfrey, 5 9 and Jones 6 0 was relied upon in writing the sections that follow.

Fig. 21.101 Lubricated bearing surfaces. (From Ref. 58.)

21.4.1 Formation of Films

The most important aspect of boundary lubrication is the formation of surface films that will protect

the contacting surfaces. There are three ways of forming a boundary lubricant film; physical adsorp-

tion, chemisorption, and chemical reaction. The surface action that determines the behavior of bound-

ary lubricant films is the energy binding the film molecules to the surface, a measure of the film

strength. The formation of films is presented in the order of such a film strength, the weakest being

presented first.

Physical Adsorption

Physical adsorption involves intermolecular forces analogous to those involved in condensation of

vapors to liquids. A layer of lubricant one or more molecules thick becomes attached to the surfaces

of the solids, and this provides a modest protection against wear. Physical adsorption is usually rapid,

reversible, and nonspecific. Energies involved in physical adsorption are in the range of heats of

condensations. Physical adsorption may be monomolecular or multilayer. There is no electron transfer

in this process. An idealized example of physical adsorption of hexadecanol on an unreactive metal

is shown in Fig. 21.102. Because of the weak bonding energies involved, physically adsorbed species

are usually not very effective boundary lubricants.

Chemical Adsorption

Chemically adsorbed films are generally produced by adding animal and vegetable fats and oils to

the base oils. These additives contain long-chain fatty acid molecules, which exhibit great affinity

for metals at their active ends. The usual configuration of these polar molecules resembles that of a

carpet pile with the molecules standing perpendicular to the surface. Such fatty acid molecules form

metal soaps that are low-shear-strength materials with coefficients of friction in the range 0.10-0.15.

The soap film is dense because of the preferred orientation of the molecules. For example, on a steel

surface stearic acid will form a monomolecular layer of iron stearate, a soap containing 10 1 4

molecules/cm 2 of surface. The effectiveness of these layers is limited by the melting point of the

soap (18O 0 C for iron stearate). It is clearly essential to choose an additive that will react with the

bearing metals, so that less reactive, inert metals like gold and platinum are not effectively lubricated

by fatty acids.

Examples of fatty acid additives are stearic, oleic, and lauric acid. The soap films formed by these

acids might reduce the coefficient of friction to 50% of that obtained by a straight mineral oil. They

Fig. 21.102 Physical adsorption of hexadecanol. (From Ref. 59.)

provide satisfactory boundary lubrication at moderate loads, temperatures, and speeds and are often

successful in situations showing evidence of mild surface distress.

Chemisorption of a film on a surface is usually specific, may be rapid or slow, and is not always

reversible. Energies involved are large enough to imply that a chemical bond has formed (i.e., electron

transfer has taken place). In contrast to physical adsorption, chemisorption may require an activation

energy. A film may be physically adsorbed at low temperatures and chemisorbed at higher temper-

atures. In addition, physical adsorption may occur on top of a chemisorbed film. An example of a

film of stearic acid chemisorbed on an iron oxide surface to form iron stearate is shown in Fig.

21.103.

Chemical Reaction

Films formed by chemical reaction provide the greatest film strength and are used in the most severe

operating conditions. If the load and sliding speeds are high, significant contact temperatures will be

developed. It has already been noted that films formed by physical and chemical adsorption cease to

be effective above certain transition temperatures, but some additives start to react and form new

high-melting-point inorganic solids at high temperatures. For example, sulfur will start to react at

about 10O 0 C to form sulfides with melting points of over 100O 0 C. Lubricants containing additives

like sulfur, chlorine, phosphorous, and zinc are often referred to as extreme-pressure (EP) lubricants,

since they are effective in the most arduous conditions.

The formation of a chemical reaction film is specific; may be rapid or slow (depending on tem-

perature, reactivity, and other conditions); and is irreversible. An idealized example of a reacted film

of iron sulfide on an iron surface is shown in Fig. 21.104.

21.4.2 Physical Properties of Boundary Films

The two physical properties of boundary films that are most important in determining their effect-

iveness in protecting surfaces are melting point and shear strength. It is assumed that the film thick-

nesses involved are sufficient to allow these properties to be well defined.

Melting Point

The melting point of a surface film appears to be one discriminating physical property governing

failure temperature for a wide range of materials including inorganic salts. It is based on the obser-

vation that only a surface film that is solid can properly interfere with potentially damaging asperity

contacts. Conversely, a liquid film allows high friction and wear. Under practical conditions, physi-

cally adsorbed additives are known to be effective only at low temperatures, and chemisorbed addi-

Fig. 21.103 Chemisorption of stearic acid on iron surface to form iron stearate. (From Ref. 59.)

Fig. 21.104 Formation of inorganic film by reaction of sulfur with iron to form iron sulfide.

(From Ref. 59.)

tives at moderate temperatures. High-melting-point inorganic materials are used for high-temperature

lubricants.

The correlation of melting point with failure temperature has been established for a variety of

organic films. An illustration is given in Fig. 21.105 (obtained from Russell et al. 61 ) showing the

friction transition for copper lubricated with pure hydrocarbons. Friction data for two hydrocarbons

(mesitylene and dotriacontane) are given in Fig. 21.105 as a function of temperature. In this figure

the boundary film failure occurs at the melting point of each hydrocarbon.

In contrast, chemisorption of fatty acids on reactive metals yields failure temperature based on

the softening point of the soap rather than the melting point of the parent fatty acid.

Shear Strength

The shear strength of a boundary lubricating film should be directly reflected in the friction coeffi-

cient. In general, this is true with low-shear-strength soaps yielding low friction and high-shear-

Fig. 21.105 Chart for determining friction of copper lubricated with hydrocarbons in dry he-

lium. (From Ref. 61.)

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