In this regime, EHL is ineffective andone must rely heavily on surface film or boundary lubrication to protect surfaces againstscuffing and wear.. S., Calculation of Elastohydrodynamic F
Trang 2Micro-Elastohydrodynamic Lubrication
Micro-EHL69deals with local pressure and film fluctuations around asperities or furrowswithin a macro-EHL conjunction For pure rolling, local pressure and film thickness dis-tributions at asperities are governed mainly by the normal approach action As an ellipsoidalasperity approaches the opposing surface, the lubricant at the asperity center becomes highlypressurized and entrapped to form a central pocket as it travels through the Hertzianconjunction.69,70
For pure transverse ridges, the normal approach action in pure rolling causes the lubricant
in the Hertzian region ahead of the asperity to become extremely viscous Subsequently,the asperity becomes frozen together with the lubricant and is transported through the Hertzianconjunction as an integral unit.71
FIGURE 14 Typical contact area patterns for longitudinally oriented, isotropic, and transversely oriented rough surfaces.
Trang 3For sliding EHL contacts, micro-EHL film thickness is controlled largely by entrainment
of lubricant at the inlet of an asperity For tranverse asperities, a lower limit of film thicknesscan be estimated by applying the classical EHL film thickness formulas to a sliding asperity
in a low pressure ambient For longitudinal asperities, very little is available to estimateminimum film thickness
For a pair of transverse asperities colliding in a lubricant of low ambient pressure, EHL film thickness can be estimated with existing theories.72,73 If collision takes place in
micro-a high-pressure micro-ambient, micro-EHL film is expected to incremicro-ase considermicro-ably but cmicro-annot
be predicted quantitatively
COMPLIANT HYDRODYNAMIC JOURNAL AND THRUST BEARINGS
In hydrodynamic journal and thrust bearings, EHL effects can become significant ifdeformation of the bearing surfaces is of the same order as the film thickness This occurs
in heavily loaded journal bearings for large diesel engines, in high-pressure thrust bearingsfor hydroelectric turbines, and in elastomeric bearings used to tolerate dirt Reference 74gives a detailed review of compliant hydrodynamic bearings
In journal bearings, minimum film thickness is increased slightly and peak film pressure
is reduced when elastic effects are included Surface deformations caused by local
compres-Volume II 155
FIGURE 15 Effect of surface roughness on the average film thickness of EHL contacts: Po/E = 0.003, pure rolling, αE = 3333, and σ/R = 1.8 × 10 -5
Copyright © 1983 CRC Press LLC
Trang 4sion, bending of pads, and thermal distortion can significantly affect performance of large,high-speed thrust bearings.75,76 Because deformation effects are sensitive to detailed padgeometry, they can only be determined by elaborate computer codes.77
APPLICATION TO MACHINE COMPONENTSBased on EHL theories, effectiveness of lubrication in rolling element bearings,3,78-81gears,3,78 and cams82 can be calculated through the film parameter Λ, the ratio of filmthickness to the composite surface roughness In this section, formulas are taken mostlyfrom an EHL guide book.78
Rolling Element Bearings
Roller bearings usually have line contacts and Equation 9 should be used to calculate filmthickness For ball bearings, contacts are elliptical with semimajor axis normal to the direction
of rolling and Equations 10 through 13 should be used; to evaluate the speed and loadparameter, rolling speed and contact dimensions must be determined from the geometry andkinematics of the system Reference 78 gives formulas for all common commercial rollingbearings A simplified film thickness formula, which does not involve detailed bearinggeometry and yet gives an adequate prediction of film thickness, is given below:78
(23)
where ∧ = h/σ, D = bearing outside diameter, m or in., C = a constant given in Table
2, dimensionless, LP = µoα · 1011, sec, µo = viscosity, N-sec/m2 or lb-sec/in.2, α =pressure-viscosity coefficient, m2/N or in.2/lb, N = difference between the inner and outerrace speeds, rpm, h = film thickness in microns if D is in meters or in microinches if D
is in inches, and σ = composite roughness, µm or µin Typical values of α for bearingsare given in Table 3
An adequate ∧ for protecting bearing surfaces against early surface fatigue was shown
to be greater than 1.5 Typical values of lubricant parameter, LP, for motor oils can befound in Figure 16
Table 2 VALUES OF C FOR BEARING RACEWAYS
Spherical and cylindrical 8.37 × 10 –4 8.99 × 10 –4 Tapered and needle 8.01 × 10 −4 8.48 × 10 –4
Table 3 TYPICAL VALUES OFσ
FOR BEARINGS
Composite roughness
Spherical and cylindrical 0.356 14
Trang 5Note: Where:
⎟⎟ = Absolute (positive) value Ng = gear wheel speed, rpm Ts = sun gear torque
C = Center distance NR = ring gear speed, rpm TR = ring gear torque
ED = reduced modulus (equation 2) Ns = sun gear speed, rpm γG = gear cone angle
F = face width RGm = midface pitch radius γP = pinion cone angle
mG = gear ratio RR = ring gear radius φn = normal pressure angle
n = Number of planets Rs = sun gear radius ψ = helix angle
Nc = Carrier speed, rpm TG = gear wheel torque ψm = midface spiral angle
Table 5 TYPICAL VALUES OF COMPOSITE
ROUGHNESS,
158 CRC Handbook of Lubrication
Table 4 GEAR EQUATIONS
Copyright © 1983 CRC Press LLC
Trang 6The critical value of Λ at which a 5% probability of surface distress is expected is anempirical function of pitch line velocity V as shown in Figure 17 Equations for V fordifferent types of gears are given in Table 4.
Cam-Follower Systems
The film parameter Λ for a cam-flat follower Figure 18 system can be calculated byEquation 25:
(25)FIGURE 17 Adjusted specific film thickness vs pitch line velocity (5% probability of distress).
FIGURE 18 Geometry of a cam-follower contact.
Trang 7where N = cam shaft speed, rpm, LP = lubricant parameter, sec, fN = |2rn – |, where
is the distance from the nose tip to the shaft axis and rnis the nose radius (see Figure 18),
m or in., R = (1/rn + 1/rf)-1, m or in., rn = nose radius, m or in., rf = follower radius,
m or in., and σ = composite roughness, µm or µin
In general, Λ in cam systems is well below one In this regime, EHL is ineffective andone must rely heavily on surface film or boundary lubrication to protect surfaces againstscuffing and wear
REFERENCES
1 Martin, H M., Lubrication of gear teeth, Engineering (London), 102, 199, 1916.
2 Grubin, A N., Contact stresses in toothed gears and worm gears, Central Scientific Research Institute for
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337 As communicated by Prof M M Krushchov to Prof A Cameron, Grubin’s contribution was originally studied by A M Ertel and after his death was seen ihrough the press by his co-worker Grubin and is thus often known as Grubin’s name alone.)
3 Dowson, D and Higginson, G R., Elastohydrodynamic Lubrication, Pergamon Press, Oxford, 1977.
4 Cheng, H S., Isothermal EHD theory for the full range of pressure-viscosity coefficient, J Lubr Technol.
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5 Ford, R A J., The Lubrication of High Speed Gas Turbine Roller Bearings, Ph.D thesis, University of
London, March, 1975.
6 Greenwood, J and Kanzlarich, J., Inlet shear heating in elastohydrodynamic lubrication, J Lubr
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7 Cheng, H S., Calculation of Elastohydrodynamic Film Thickness in High-Speed Rolling and Sliding
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8 Murch, L E and Wilson, W R D., A thermal elastohydrodynamic inlet zone analysis, J Lubr Technol.,
Trans ASME, 97(2), 212, 1975.
9 Wolveridge, P E., Baglin, K P., and Archard, J F., The starved lubrication of cylinders in line contact,
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10 Dowson, D., Saman, W Y., and Toyoda, S., A study of starved elastohydrodynamic line contacts, Proc.
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11 Archard, J F., Experimental studies of elastohydrodynamic lubrication, Proc Inst Mech Eng., 180(38),
17, 1965.
12 Crook, A W., The lubrication of rollers II Film thickness with relation to viscosity and speed, R Soc.
London Philos Trans Ser A, 254, 223, 1961.
13 Sibley, L B and Orcutt, F K., Elastohydrodynamic lubrication of rolling contact surfaces, Am Soc.
Lubr Eng Trans., 4(2), 234, 1961.
14 Wymer, D G and Cameron, A., EHD lubrication of a line contact, Proc Inst Mech Eng., 188, 221,
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15 Dowson, D and Higginson, G R., A numerical solution to the elastohydrodynamic problem, J Mech.
Eng Sci., 1(1), 6, 1959.
16 Dowson, D., Higginson, G R., and Whitaker, A V., Elastohydrodynamic Lubrication — a survey of
isothermal solutions, J Mech Eng Sci., 4(2), 121, 1962.
17 Archard, G D., Gair, F C., and Hirst, W., The elastohydrodynamic lubrication of rollers, Proc R
Soc London Ser A, 262, 51, 1961.
18 Hamilton, G M and Moore, S L., Deformation and pressure in an EHD contact, Proc R Soc London
Ser A, 322, 313, 1971.
19 Rodkiewicz, C M and Srinivanasan, V., EHD lubrication in rolling and sliding contacts, J Lubr.
Technol Trans ASME, 94(4), 324, 1972.
20 Rohde, S M., A unified treatment of thick and thin film EHD problems by using high order element
methods, Proc R Soc London Ser A, 343, 315, 1975.
21 Dowson, D., Elastohydrodynamic Lubrication, Interdisciplinary Approach to the Lubrication of
Concen-trated Contacts, Spec Publ No NASA SP-237, National Aeronautics and Space Administration, ington, D.C., 1970, 34.
Wash-22 Kannel, J W et al., A Study of the Influence of Lubricants on High-Speed Rolling-Contact Bearing
Performance, Part IV, Tech Rep No ASD-TR-61-643, Air Force Aero Propulsion Laboratory, Dayton, Ohio 1964.
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Trang 823 Gohar, R and Cameron, A., The mapping of F.HD contacts, ASLE Trans., 10, 214, 1967.
24 Orcutt, F K., Experimental study of elastohydrodynamic lubrication, ASLE Trans., 8, 381, 1965.
25 Kannel, J W., The measurement of pressure in rolling contacts, Proc Inst Mech Eng., 180(3B), 135,
1965.
26 Moes, I H., Communications to EHL symposium held at Leeds University, Proc Inst Mech Eng.,
180(3B), 244, 1965.
27 Herrebrugh, K., Solving the incompressible and isothermal problem in elastohydrodynamic lubrication
through an integral equation, J Lubr Technol., Trans ASME, 90(1), 262, 1968.
28 Archard, J F and Cowking, E W., A simplified treatment of elastohydrodynamic lubrication theory
for a point contact, Proc inst Mech Eng., 180(3B), 47, 1965.
29 Cheng, H S., A numerical solution of the elastohydrodynamic film thickness in an elliptical contact, J.
Lubr Technol., Trans ASME, 92(1), 155, 1970.
30 Hamrock, B J and Dowson, D., Isothermal elastohydrodynamic lubrication of point contacts, J Lubr.
Technol., 98(2), 223, 1976; 98(3), 1976; 99(2), 264, 1977; 99(1), 15, 1977.
31 Chiu, Y P., An analysis and prediction of lubricant film starvation in rolling contact systems, ASLE Trans.,
17, 22, 1974.
32 Chiu, Y P et al., Exploratory Analysis of EHD Properties of Lubricants, Rep No AL72P10 SKF
Industries, King of Prussia, Pa., 1972.
33 Snidle, R W and Archard, J F., Experimental investigation of elastohydrodynamic lubrication at point
contacts, Proc 1972 Symp Elasiohydrodynamic Lubrication, Paper C2/72, Institute of Mechanical
Engi-neers, London, 1972, 5.
34 Wedevan, L D., Optical Measurements in EHD Rolling-Contact Bearings, Ph.D thesis University of
London, March 1970.
35 Westlake, F J and Cameron, A., Interferomatric study of point contact lubrication, Proc 1972 Symp.
Elastohydrodynamic Lubrication, Paper C39/72, Institute of Mechanical Engineers, London, 1972, 153.
36 Sanborn, D M and Winer, W O., Fluid rheological effects in sliding elastohydrodynamic point contacts
with transient loading I Film thickness, J Lubr Technol., Trans ASME, 93(2), 262, 1971.
37 Parker, R J and Kannel, J W., EHD Film Thickness Between Rolling Discs with a Synthetic Paraffinic
Oil to 589 K, NASA Tech Note D-6411, National Aeronautics and Space Administration, Washington,
DC, 1970.
38 Gentle, C R., Duckworth, R R., and Cameron, A., EHD Film thickness at extra pressures, J Lubr.
Technol., Trans ASME, 97, 383, 1975.
39 Hirst, W and Moore, A J., Elastohydrodynamic Lubrication at High Pressures, Tech Rep., University
of Reading, Reading, U.K., 1977.
40 Foord, C A et al., Optical elastohydrodynamics, Proc Inst Mech Eng., 184(1), 487, 1969.
41 Jacobson, B., On the lubrication of heavily loaded spherical surfaces considering surface deformations and
solidification of the lubricant, Acta Polytechn Scand Mech Eng Ser., 54, 1970.
42 Ranger, A P., Numerical Solutions to the EHD Problems, Ph.D thesis, University of London, March,
1974.
43 Cheng, H S and Sternlicht, B., A numerical solution for pressure, temperature and film thickness
between two infinitely long rolling and sliding cylinders under heavy load, J Basic Eng., Trans ASME.
87(3), 695, 1965.
44 Dowson, D and Whittaker, B A., A numerical procedure for the solution of the elastohydrodynamic
problem of rolling and sliding contacts lubricated by a newtonian fluid, Proc Inst Mech Eng., 180(3B),
57, 1965.
45 Kannel, J W and Bell, J C., A method for estimating of temperature in lubricated rolling-sliding gear
or bearing EHD contacts, Paper C24/72, Proc 1972 Symp Elastohydrodynamic Lubrication, Institute of
Mechanical Engineers, London, 1972, 118.
46 Kannel, J W., Zugaro, F F., and Dow, T A., A method for measuring surface temperature between
rolling/sliding steel cylinders, J Lubr Technoi Trans ASME, 100(1), 100, 1978.
47 Nagaraj, H S., Sanborn, D M., and Winer, W O., Direct surface temperature measurement by infrared
radiation in elastohydrodynamic contacts and the correlation with the Block temperature theory, Wear, 49,
1, 1978.
48 Jaeger, J C., Moving sources of heat and the temperature at sliding contacts, Proc R Soc N.S.W., 56,
203, 1942.
49 Johnson, K L and Cameron, R., Shear behavior of elastohydrodynamic oil film at high rolling contact
pressures, Proc Inst Mech Eng., 182, 307, 1967.
50 Harrison, G and Trachman, E G., The role of compressional viscoelasticity in the lubrication of rolling
contacts, J Lubr Technol., Trans ASME, 95, 306, 1972.
51 Dyson, A., Frictional traction and lubricant rheology in elastohydrodynamic lubrication, Philas Trans R.
Soc London, 266, 1170, 1970.
Trang 952 Johnson, K L and Tevaariverk, J L., Shear behavior of EHD oil films, Proc R Soc London, A356,
215, 1977.
53 Barlow, A J et al., The effect of pressure on the viscoelastic properties of liquids, R Soc London Proc.,
A327, 403, 1972.
54 Montrose, C J., Moynihan, C T., and Sasake, H., Dynamic Shear and Structural Viscoelasticity in
EHD Lubrication, Vitreous State Laboratory Tech Rep., July 1977.
55 Bell, J C., Lubrication of rolling surfaces by a Ree-Eyring fluid, ASLE Trans., 5, 160, 1962.
56 Trachman, E and Cheng, H S., Thermal and non-Newtonian effects on traction in elastohydrodynamic
lubrication, Paper C37/72, Proc 1972 Syrnp Elastohydrodynamic Lubrication, Insfitute of Mechanical
Engineers, London, 1972, 142.
57 Smith, F W., Rolling contact lubrication — the application of elastohydrodynamic theory, J Lubr.
Technol., Trans ASME Ser D, 87, 170, 1965.
58 Bair, S and Winer, W O., A theological model for EHD contacts based on primary laboratory data, J.
Lubr Technol., Trans ASME, 101(3), 258, 1979.
59 Tallian, T E., The theory of partial elastohydrodynamic contacts, Wear, 21, 49, 1972.
60 Williamson, J B P., Topography of solid surfaces, in Interdisciplinary Approach to Friction and Wear,
NASA SP-181 National Aeronautics and Space Administration, Washington, D.C., 1968, 143.
61 Whitehouse, D J and Archard, J F., The properties of random surfaces of significance in their contact,
Proc R Soc London, A316, 97, 1970.
62 Patir, N and Cheng, H S., An average flow model for determining effects of three dimensional roughness
on partial hydrodynamic lubrication, J Lubr Technol., Trans of ASME, 100(1), 12, 1978.
63 Feblenik, J., New developments in surface characterization and measurement by means of random process
analysis, Proc Inst Mech Eng., 182(3K), 108 1967.
64 Johnson, K L., Greenwood, J A., and Poon, S Y., A simple theory of asperity contact in
elastohy-drodynamic lubrication, Wear, 19, 1972, 91.
65 Christensen, H., Stochastic models for hydrodynamic lubrication of rough surfaces, Proc Inst Mech.
Eng Tribology Group, 184(1,55), 1013, 1969.
66 Berthè, D., Les Effects Hydrodynamiques Sur La Fatigue Des Surfaces Dans Les Contacts Hertziens,D.
Sc thesis, University of Lyon, France, 1974.
67 Chow, L S H and Cheng, H S., The effect of surface roughness on the average film thickness between
lubricated rollers, J Lubr Technol., Trans ASME, 98(1), 117, 1976.
68 Cheng, H S and Dyson, A., Elastohydrodynamic lubrication of circumferentially ground disks, ASLE
Trans., 21(1), 25, 1978.
69 Cheng, H S., On some aspects of micro-elastohydrodynamic lubrication, Proc 4th Leeds-Lyon Symp.
Lubr., April 1977.
70 Christensen, H., Elastohydrodynamic theory of spherical bodies in normal approach motion, J Lubr.
Tech., Trans ASME, 92, 145, 1970.
71 Lee, K M and Cheng, H S., The Effect of Surface Asperity on the Elastohydrodynamic Lubrication,
NASA CR-2195, National Aeronautics and Space Administration, Washington, D.C., 1973.
72 Fowles, P E., The application of elaslohydrodynamic theory to individual asperity-asperity collisions, J.
Lubr Tech., Trans ASME, 91, 464, 1969.
73 Fowles, P E., A thermal elastohydrodynamic theory for individual asperity-asperity collision, J Lubr.
Tech., Trans ASME, 93, 383, 1971.
74 Rohde, S., Thick film and transient elastohydrodynamic lubrication problems, Proceedings on
Fundamen-tals of Tribology MIT Press, Cambridge, Mass., 1979.
75 Castelli, V and Malanowski, S B., Method for solution of lubrication problems with temperature and
elasticity effects: Application to sector, tilting-pad bearings, J Lubr Technol Trans ASME, 91(4), 634,
78 Anon., EHL Guidebook, Mobile Oil Corporation New York, 1979.
79 McGrew, J M et al., Elastohydrodynamic Lubrication — Preliminary Design Manual, Tech Rep.
AFAPL-TR-70-27, Air Force Propulsion Laboratory, Dayton, Ohio, 1970.
80 Cheng, H S., Application of Elastohydrodynamics of Rolling Element Bearings, ASME Paper 74-DE-32,
American Society of Mechanical Engineers, New York, 1974.
81 Anon., SKE Engineering Data, SKF Industries, Inc., King of Prussia, Pa., 1968.
82 Dyson, A., Discussion of “Elastohydrodynamic Lubrication” by D Dowson, Spec Publ SP-237, National
Aeronautics and Space Administration, Washington, D.C., 1970.
83 Orcutt, F K and Cheng, H S., Lubrication of rolling contact instrument bearings, gyro spin-axis,
Hydrodynamic Bearing Symp., Vol 2, M.I.T Instrument Laboratory, Cambridge, Mass., 1966.
162 CRC Handbook of Lubrication
Copyright © 1983 CRC Press LLC
Trang 10METALLIC WEAR
F T Harwell
INTRODUCTION
Nature of Wear
Wear of material from machine elements may occur as the result of direct overstressing
of surface material, by fatigue of subsurface material, melting, evaporation, chemical attack,
or by electrical or electrolytic action Because various mechanisms may act either singly or
in combination, the rate of wear may sometimes be determined by competition and sometimes
by mutual reinforcement of two or more effects There are, therefore, no simple laws toenable wear rates to be calculated without reference to specific environmental and operationalconditions relating to the actual machine under consideration For example, the expression
Conformal and Counterformal Surfaces
The most important consideration governing tribological interaction of two solid objects
is their shape, because this determines both the nature of the stress system and the thermalregime Two broad categories are as follows:
1 Conformal surfaces wherein stress is distributed over a comparatively wide nominal
area
2 Counterformal surfaces which produce either “point” or “line” contact The surfaces
deform either elastically or plastically so as to provide an adequate area of contact.56Compressive stress at the surface of such a Hertzian contact is distributed in accordancewith a parabolic law with the highest stress being at the center Shear stress in theabsence of tangential loading reaches a maximum at a depth within the surface ofabout l/6th of the breadth of the contact zone While detailed methods enable cal-culating the stresses in bodies of various shapes,4,12,56the following simple cases willenable the nature of Hertzian stress to be appreciated
Spheres in Contact
Radius of circle of contact = a
(2)
where W = load, v1and v2 = Poisson’s ratio of material of spheres 1 and 2, respectively,
E1 and E2= Young’s modulus of elasticity of spheres 1 and 2, respectively, and r1 and r2
Trang 11where po, the maximum compressive stress, is 2/3 times the average value The maximumshearing stress is approximately at a depth of 1/2 a below the surface The maximum tensilestress occurs at the edge of the contact zone Its magnitude is given by
(5)
Parallel Cylinders in Contact
Breadth of contact strip = 2a
Temperature of Interacting Surfaces
The amount of heat liberated at contact will be determined by the product of the forceacting between the surfaces, the velocity of relative motion, and the coefficient of friction.The temperature of the contact will depend on the thermal diffusivity of the material andthe rate of supply of fresh material into the contact zone A good estimate of the “flashtemperature”, that is the excess of temperature caused by friction over the bulk temperature
of the machine elements, is given by Blok7as
(8)where P is the load per unit width (measured at right angles to direction of relative motion),2a is the width at the Hertzian contact band (measured in direction of relative motion), U1and U2 are the surface velocities, K1and K2are the thermal conductivities, ρ1and ρ2 arethe densities, and c1and c2are specific heats per unit mass relating to the two bodies Anappropriate value for µ, the coefficient of friction, may vary widely from about 0.15 to 1according to the effectiveness of any lubrication or any surface films Oxygen or watervapor, for example, may cause films to be generated, which either mitigate the effects ofmetal-to-metal contact or have harmful abrasive effects
CHARACTERISTIC MODES OF DAMAGE
Trang 12smooth sliding (mild), severe, adhesive, fatigue, fretting, impact, gouging, firecracking,corrosion, cavitation, and electrical effects.
When two ferrous materials are rubbed together under moderate load, a certain degree ofprotection may be offered by the generation of oxide films and the sliding will occur smoothlyand without gross damage This has been described as “mild wear” but the writer proposesthe substitution of “smooth sliding” because the rate of wear can in certain circumstances
be greater during “mild” than during “severe” conditions
Transition Between “Smooth Sliding” and “Severe” Wear
The transition between different modes of wear may be abrupt and may be reversed evenwhen the severity of the applied conditions is apparently increased The complexity of theinteraction is illustrated by two classical experiments
Kerridge22loaded a flat-ended pin of tool steel against the peripheral surface of a rotatingring within an enclosure which could be evacuated The pin was made radioactive and wassofter than the ring, the hardness values being 270 and 860 HD30, respectively Materialwas rapidly transferred from the pin to the ring which soon attained a constant value ofradioactivity and the wear rate was constant throughout the test When the radioactive pinwas replaced by an inactive pin the activity of the ring soon ceased These results showedthat metal was first transferred from the soft pin to the harder ring This metal rapidly formed
an oxide film which resisted further transfer and thus introduced a “rate limiting” action
As this oxide was gradually removed by rubbing or fatigue, further transfer of material couldtake place at a controlled rate
Kragelskii26 found that during some experiments on the sliding of Armco iron, the wearrate fell off by a factor of about 600 when the rate of sliding increased beyond a certainvalue When the interfacial region was cooled by liquid nitrogen there was a very high-wearrate When it was electrically heated, wear was reduced one-thousand fold Kragelskiiexplains the contrasting behavior by a hardness or strength gradient within the material.When the interface between rubbing surfaces is composed of weak material, sliding willtake place there with relatively little damage; when the bond between the surfaces is strongerthan the underlying layers, failure will occur within the bulk of the material causing con-siderable roughening and superficial damage
There are, therefore, two fundamentally different ways in which rubbing surfaces mayreact During “external” friction, contact between the surfaces is dispersed and the truearea of interaction depends on the applied load and the strength properties of the weakermaterial With “internal” friction the surface of action is continuous, is independent of loadand the zone undergoing deformation occupies a considerable volume
Effect of Environment
Clarification of the effect of environment is provided by Soda and Sasada50 who studiedthe wear of pure metals in air under pressure ranging from 10–6 to 760 torr For most metalcombinations the wear was “cohesive”, but for the transition metals (Ni, Fe, Pt, Mo, andW) “noncohesive” wear occurred except under high loads (Figure 1)
This transition was explained by the “mean free time” of a contact point A small surface
of bare metal would be formed every time a contact bridge was broken Gas moleculeswould attack the clean spot forming a chemisorbed layer which would be thereby protectedfrom welding When either the speed or the load was high, the time between events would
be too short for an effective protective layer to form and severe or cohesive wear wouldoccur When air is replaced by nitrogen, Sasada and Kando43showed that the mean size ofparticles was increased by over one hundred times The powerful effect of oxygen preventedsurface adhesion and subsequent particle growth
Figure 2 shows the variation of wear rate with speed for Ni on Ni in air and vacuum
Volume II 165
Copyright © 1983 CRC Press LLC
Trang 13a Ultimate tensile strength.
From Clayton, P., in Tribology 1978 Materials Performance and Conservation, Institute of Mechanical Engineers
Conference Publication, Swansea, 1978, 83 With permission.
provide an example of the reaction of steel to intense Hertzian stresses Clayton9describes
a type of wear where intermittent high-stress dry-rubbing contact induces severe surfacedeformation which leads to the formation of small deformed metal wear platelets
Table 1 shows the relative wear resistance of different steels under operating conditions.Laboratory tests produced results which were consistent with track observations and Claytonconcluded that the wear-rate was a function of cumulative plastic strain If the equationfor a monotonic stress-strain curve is given by
where K and n are constants, then plastic strain is given by
(10)Hence, wear rate is a function of
He considers that wear is more likely to be stress-related than strain controlled and producesthe
(11)
For Hadfields steel with K taken as 2800 N/mm2and n as 0.31, a wear rate of 0.0332 mm3/
cm is predicted which corresponds to the relative value obtained
Jamieson18investigated mechanical wear of wheels and rails due to negotiation of curves.Two mechanisms differed in the rate of metal loss by factors of 10 to 100 Low-rate “flow-
Volume II 167 Table 1
RELATIVE WEAR RESISTANCE OF RAIL STEELS IN CURVED TRACK
163-184 4/10/06 12:36 PM Page 167
Copyright © 1983 CRC Press LLC
Trang 14where r1= wheel radius and r2= rail crown radius.
fatigue” wear occurred when normal forces between wheel and rail produced subsurfacestresses which exceeded 2.3 times the yield strength of the material High-rate “smearingwear” occurred when tractive forces were superimposed onto the normal force so that thesubsurface plastic flow boundary intercepted the surface Laboratory experiments indicatedthat high humidity could sufficiently lower traction forces so that the flow-fatigue type ofwear occurred, rather than smearing It is suggested that rail lubrication will produce thesame effect in practice
Analysis indicated that contact stresses between wheels and rail could exceed 350,000 lb/
in.2(2.4 GPa) sufficient for severe smearing wear Examination of wear debris from a highwear region of track in Canada confirmed that smearing wear predominated
Trang 15If M is taken as 800 kg the frequency will be 216 Hz Nayak32 has shown that randomsurface characteristics can excite oscillation at preferred frequencies.
Johnson and Gray20 demonstrated that such vibration can cause the interacting surfaces
to develop “corrugations” Some evidence of plastic flow has been found in the crests ofcorrugations but none in the troughs The position is so serious that a number of railwaysperiodically reprofile rail surface by grinding
Adhesion
When perfectly clean, flat metal surfaces are brought into close proximity (less than 1/5nm) they unite chemically When separation is wider, they are attracted to each other byvan der Waals’ forces At small separations (less than 10–8 m) these are governed by asquare law and at greater separations (greater than 10 –7m) by a cube law Practical surfacesare usually covered by oxide films and are so rough on the atomic scale that when bodiesare brought together, only a tiny fraction of the contacting area (about 1/1000) at the peaks
of asperities is subjected to powerful adhesive forces Experimental measurements of hesive forces are available with soft materials which conform when pressed together,19withmica which has been cleaved to produce an exceptionally smooth surface,17 and with hardspheres of very small diameters.25,36 Adhesive forces were sometimes two to three orders
ad-of magnitude higher than those applied initially to force the spheres together.25
Buckley8measured the force to rupture junctions made within a vacuum system evacuated
to 10–11 torr Crystals of copper, gold, silver, nickel, platinum, lead, tantalum, aluminum,and cobalt were cleaned by argon ion bombardment before being forced against a clean iron(011) surface by a force of 20 dyn When iron was pressed against iron, a separating forcegreater than the 400 dyn was required In the case of other metals this force varied from 50
to 250 dyn In every case the strength of the junction was greater than the force used topromote it Even in the case of lead (which is insoluble in iron), Auger analysis indicatedtransfer of lead to the iron surface Thus the adhesive bonds of lead to iron were strongerthan the cohesive bonds within the lead In general, the cohesively weaker metals adheredand transferred to the cohesively stronger
The adhesion theory of wear is based on the assumption that a similar welding actionoccurs between a limited number of asperities and that the welds are ruptured when thesolids slide one relative to the other.54
The actual process of formation of wear particles has been studied by Sasada and Kando43with a pin and disc machine They concluded that an initial metal-to-metal junction is sheared
by the frictional motion and a small fragment of either surface becomes attached to the othersurface As sliding continues this fragment constitutes a new asperity becoming attachedonce more to the original surface This “transfer element” is repeatedly transferred fromone surface to the other continually increasing in size and being flattened by the forcebetween the pin and the disc Once a flattened particle attached to the disc grows to such
a size that it supports the load, it becomes the only contact between pin and disc It thengrows quickly to a large size, absorbing many of the transfer elements dotted over the discsurface so as to form a flake-like particle from materials of both rubbing elements Unstablethermal and dynamic conditions brought about by rapid growth of this transfer elementfinally account for its removal as a wear particle These authors experimented with thefollowing materials: Mo, Fe, Mi, Cu, Ag, Zn, and Al
The combination of AI disc and pins of Mo, Fe, Ni, and Cu produced violent ploughing.The following combinations produced smooth sliding: Mo/Mo, Fe/Fe, Ni/Ni, Ni/Fe, Fe/Cu,Cu/Fe, Fe/Mo, Mo/Fe, Ni/Mo, and Mo/Ni Metal transfer was scarcely observed and thewear rate was very low in the case of Mo-Cu, Mo-Ag, Fe-Ag or Ni-Ag where the metalshave poor mutual solubility.44
Relative importance of adhesion and plastic flow is covered by Andarelli et al.1 who
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Trang 16observed the occurrence of dislocations by transmission electron-microscopy Glass fiberswere slid against aluminum specimens 10–5m thick, and normal and tangential forces weredetermined from the shape assumed by the loaded fiber Further tests31 employed a cold-rolled tungsten wire with a hemispherical tip of radius 2.5 10–6 m as the stylus The loadranged from 1 to 100 µN as compared with values of 1.2 to 2.4 µN calculated on the basis
of an interfacial energy of 100 to 200 mJ/m2 This indicates that van der Waals’ forcesbetween metals shielded by absorbed gases were responsible for the adhesion Load had toexceed a critical value before the stylus suddenly penetrated the surface Measurements offriction were consistent with this, nearly zero at low loads as long as deformation remainedelastic
These results emphasize that plastic deformation rather than adhesion was the importantagency determining friction and wear Comparison of the dislocation density based on tensiletests showed that 90% of the frictional energy was dissipated as heat with only a minorproportion being stored within the material
Fatigue
Sliding Wear
In all machinery there is a periodic variation of stress An element of metal at the surface
of a rotating shaft will be subject to reversal of bending stresses, the race of a rolling contactbearing will experience continual application and release of Hertzian stress, and the surface
of a conformal bearing will experience repeating stresses on a micro scale due to the passage
of asperities on the rotating surface All these repeating stresses can give rise to fatigueaction Tsuya et al.57 and Quinn and Sullivan39 have provided evidence of changes in thesubstrate of a wearing part due to relative motion
Because it provides a more direct account of the formation of a wear particle than theadhesion theory, the fatigue theory of wear warrants close attention Soda et al.51 reported
a series of experiments on the face-centered-cubic metals Ni, Cu, and Au When atmosphericpressure was reduced, wear of Ni and Cu decreased but that of Au remained unchanged.This was shown to affect the rate of wear fragment formation in contrast to mechanicalfactors which affected wear by changing the volume of fragments Mean thickness of thewear fragments was about one fourth of that of the plastically deformed substrate layer.Correlation with direct fatigue tests indicated that the number of wear fragments was governed
by the resistance of the materials to fatigue Environmental factors such as atmosphericpressure had similar effect on wear rate as on fatigue strength Kimura23produces additionalevidence of a correlation between the thickness of the deformed layer and that of the wearfragments
A particularly comprehensive test program was carried out by Tsuya58who used a variety
of test arrangements and ambient conditions Plastic working of the subsurface regions ofmaterials in contact led to the formation of micronized crystals and cracks which originated
in the boundary region between the micronized crystals and those nearer to the surface whichhad been simply distorted These cracks tend to develop in the direction of material flowuntil particles are released
The Delamination Theory of Wear
Koba and Cook24studied the wear of leaded bronze running against steel and demonstrated
by scanning electron electron micrographs that metal flowed freely at the surface, smoothingout hills and valleys Some metal transfer was observed but did not appear to be an essentialpart of the wear process
Suh52investigated a number of wearing systems and put forward the “ Delamination Theory
of Wear” which can be summarized as follows:
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