Friction, Lubrication, and Wear Technology (1997) Part 8 pdf

The resulting tribometric characteristics--in particular the friction or wear data--must understood as tribological systems characteristics associated with the following group of paramet

For the most part, the dislocation density is high and in the 1011/cm2 range Dislocations are highly correlated, with Rc

close to the average diameter of the subgrain for metallic filings and ZrO2 debris

Table 1 Results for body-centered cubic materials, face-centered cubic aluminum, and partially stabilized cubic zirconia

The results given in Table 1 for body- and face-centered cubic material allow a simple explanation to be given for the

structure of cold-worked fragments Filings show a high degree of correlation (small Rc/<L>) and high dislocation

densities This is related to sample conditions, such as the temperature and local conditions at which a high-density dislocation structure is produced Fragments produced by filing or grinding at room temperature, or even at liquid nitrogen temperature, cannot be "cold." Instead, they are rapidly heated to a high temperature during fracture, and rapidly quenched, because of their high surface-to-volume ratio Dislocations are mobile for short periods of time over short distances and can cluster

Table 1 includes results from cubic debris particles obtained from a worn PSZ The substrate contains three phases, as already discussed It should be noted that the cubic phase is stable at high temperatures, making it reasonable that only the cubic form should be found in the debris The dislocation density for zirconia is the highest entry, whereas the correlation distance is close to the mean diameter One can present the same arguments for zirconia debris as for cold-worked metal filings Prior to breakaway, material at the asperity has a very high dislocation density A high separation temperature allows some dislocation movement to form subgrain clusters

The question of how much debris one must collect for an ideal line-shape analysis needs to be considered Typically, for quantitative work, one would like to be able to fill a cavity of at least 15 mm (0.6 in.) in diameter to a depth of 2 mm (0.08 in.) The sample thickness should be several times the penetration depths already discussed Quantitative diffractometer studies require much more sample than what is required for an x-ray powder camera, but also offer the opportunity for more extensive data analysis

Conclusions and Future Trends

Both the wear-modified phase distribution and the debris indicate that at least a fraction of the surface material has been subjected to high temperatures during wear testing Zirconia debris has an even higher dislocation density than metal filings, indicating severe deformation before breakaway from the surface High correlation between dislocations is likely

to result from a time-restricted, thermally activated process taking place at an elevated temperature immediately after fracture It was found that large residual compressive strains build up in the ground surface region of the zirconia substrate A state of dynamic equilibrium is likely to be present between the production of regions of high defect density-residual strain and relaxations produced by annealing The annealing processes within near-surface bulk substrate material

is likely to offer a spectrum of possibilities

Data from a ground PSZ sample revealed the formation of a place gradient extending over a distance of several microns This represents another form of conditioning that could influence subsequent wear testing Depths from a few tenths to the micron range are typical x-ray probe distances for many commercial materials

Future research will require a careful selection of samples and radiation Quantitative diffractometer data will give the greatest amount of information A part from local surface asperities, the mean surface should be flat Typically, it also should have surface dimensions ranging from 10 to 30 mm (0.4 to 1.2 in.) to fit into commercial systems XRD data should be inter-related with XRF or other near-surface analyses revealing chemical changes Variable penetration depths often allow the condition near a surface to be compared with deeper regions that are relatively unaffected by wear processes

A detailed analysis of diffraction patterns from concentrated industrial wear debris under different conditions may establish trends that predict malfunctions Similarities or differences between the wear from a given machine and testers, which are used to simulate machine conditions, could also be examined

Thin-film attachments are available for most commercial diffractometers, allowing low glancing angles to be attained This can greatly reduce the beam penetration These attachments should be considered for examinations of worn surfaces,

as well as for thin layers of debris

Perhaps the most severe restriction in an x-ray analysis using conventional x-ray sources is the limited area of disturbed surface available for examination using routine pin-on-disk testing One would rather examine square cross sections of at least 15 mm (0.6 in.) Although synchrotron radiation would allow one to examine a small fraction of this size, it is often not readily available A smaller-sized sample used with conventional sources would force compromises in the data analysis and lessen the opportunity to obtain quantitative results Any use of x-rays must begin with a consideration of sample size

References

1 G.H Vineyard, Phys Rev B: Condens Matter, Vol 26, 1982, p 416

2 W.C McMaster, N Kerr Del Grande, J.H Mallett, and J.H Hubbell, "Compilation of X-ray Cross Sections," Report UCRL-50174, Sec I, 1970; Sec II, Rev I, 1969; Sec III, 1969; Sec IV, Lawrence Radiation Laboratory (Livermore), 1969

3 R.J Harrison and A Paskin, Acta Cryst., Vol 17, 1964, p 325

4 B Hwang and C.R Houska, J Appl Phys., Vol 63, 1988, p 5346

5 C.J Sparks, Synchrotron Radiation Research, H Winick and S Doniach, Ed., Plenum Publishing, 1980

6 B.E Warren, X-Ray Diffraction, Addison-Wesley, 1969

7 L.H Schwartz and J.B Cohen, Diffraction from Materials, Springer-Verlag, 1987

8 B.D Cullity, Elements of X-Ray Diffraction, Addison-Wesley, 1978

9 B Hwang, "Near Surface Structure of Ceramic Components," Ph D thesis, Virginia Polytechnic Institute and State University, May 1987

10 T.R Thomas, Rough Surfaces, Longman, London, 1982

11 B Hwang, C.R Houska, G.E Ice, and A Habenschuss, Adv Ceram Mater., Vol 3, 1988, p 189 V

12 R.C Garvie, R.H.K Hannink, and N.V Swain, J Mater Sci Lett., Vol 1, 1982, p 437

13 C.R Houska, J Appl Phys., Vol 41, 1970, p 69

14 C.R Houska, Treatise on Materials Science, Vol 19A, H Herman, Ed., Academic Press Inc., 1980

15 B Hwang, C.R Houska, G.E Ice, and A Habenschuss, J Appl Phys., Vol 63, 1988, p 5351

16 C.R Houska, J Appl Phys., Vol 52, 1981, p 748

17 S Rao and C.R Houska, Acta Cryst., Vol A42, 1986, p 14

18 S Rao and C.R Houska, Matter Res Soc Symp Proc., Vol 138, 1989, p 93

19 S Rao and C.R Houska, Acta Cryst., Vol A44, 1988, p 1021

Basic Tribological Parameters

Horst Czichos, BAM (Germany)

Introduction

TRIBOLOGICAL PARAMETERS are characteristics of mechanical systems with "interacting surfaces in relative motion," including the initiation of motion The tribological processes of interacting surfaces have a dual character They are on one hand necessary for the functional performance of "tribosystems" or "tribocomponents" (see the "Glossary of Terms" in this Volume), but are on the other hand inevitably connected with friction and wear In engineering applications, the functional purpose of trobosystems can be broadly classified into the following categories (Ref 1):

• The guidance, transmission, coupling, control, stop, and annihilation of motion, force, mechanical energy, and power (bearings, joints, gears, clutches, cams and tappets, bolts and nuts, fasteners, and brakes)

• The transportation and control of flow of matter (pipelines, wheel/rail, tire/road, valves, and seals)

• The forming, machining, and tearing of materials (drawing, pressing, cutting, shaping, quarrying, and dredging)

• The generation and transmission of information (printing heads and magnetic recording interfaces)

The diagnosis of friction and wear data of such tribosystems or corresponding laboratory test configurations and test specimens requires special attention because numerous characteristics, parameters, and factors must be taken into consideration This is due to the fact that friction and wear are not intrinsic materials properties, but must be related to the entire system of interacting components, namely materials pairs and interfacial lubricants This is obvious from a comparison between the test conditions to obtain strength data or friction and wear data (Fig 1)

Fig 1 Characteristics and parameters of (a) strength tests and (b) friction and wear tests

In strength tests (Fig 1a), the deformation or fracture resistance of a material specimen in a given environment is determined under the action of a certain stress mode, such as tension, compression, shear, bending, or torsion The

resulting strength data (in terms of force per cross section, or energy) are considered as intrinsic materials properties depending basically on the following groups of parameters:

• Materials parameters, such as composition, microstructure, and specimen geometry

• Operational parameters, such as stress type, load, deformation velocity, and temperature

In a friction or wear test (Fig 1b), the resistance against motion (friction) or the resistance against surface damage (wear)

of a material/material pair (dry system) or a material/lubricant/material combination (lubricated system) in a given environment is determined under the action of a certain type of motion, such as sliding or rolling The resulting tribometric characteristics in particular the friction or wear data must understood as tribological systems characteristics associated with the following group of parameters:

• Structural parameters, which characterize the components (materials, lubricant, and environment)

involved in the friction and wear process and their physical, chemical, and technological properties

• Operational parameters, that is, the loading, kinematic, and temperature conditions and their functional

duration

• Interaction parameters, which characterize, in particular, the action of the operating parameters on the

structural components of the tribological system and define its contact and lubrication modes

Structural Parameters

The analysis of structural parameters must identify first the components involved in a given friction and wear problem Figure 2 shows typical examples of tribosystems subject to friction and wear together with corresponding simplified test configurations and their elementary structure This figure illustrates that in any friction and wear situation, four tribocomponents are involved (Ref 2):

• Triboelement (1)

• Triboelement (2)

• Interfacial element (3), for example, lubricant or dust particles

• Environmental medium (4), for example, air or corrosive atmosphere

Table 1 lists examples of the tribocomponents that make up various tribosystems

Table 1 Structural components of common tribosystems

Tribosystem Triboelement (1) Triboelement (2) Interfacial

Wheel/rail Wheel Rail Moisture Air Open

Sliding guide Slider Support Grease Air Closed

Bearing Bushing Shaft Lubricant Oil mist Closed

Milling system Milling wheel Milling jaw Minerals Air Open

Fig 2 Examples of engineering tribosystems, test configurations, and their elementary structure

In analyzing the structure of tribosystems, a distinction can be made between "closed systems," in which all components are continuously involved in the friction and wear process, and "open systems," in which a materials flow in and out of the system occurs

The friction and wear data of tribosystems depend on various properties of their structural components (tribocomponents) Structural parameters of closed tribosystems can be classified in most cases into two groups

Group A consists of triboelements (1) and (2) and involves:

• Chemical parameters such as volume composition and surface composition

• Physical parameters such as thermal conductivity

• Mechanical parameters such as elastic modulus, hardness, and fracture toughness

• Geometric parameters such as geometry dimensions, and surface topography

• Microstructural parameters such as grain size, dislocation density, and stacking fault energy

Group B consists of interfacial (fluid) element (3) and environmental (gaseous) medium (4) and involves:

• Chemical parameters such as composition, additive content, acidity, and humidity

• Physical parameters such as density, thermal conductivity, and flash and fire point

• Mechanical parameters such as viscosity, and viscosity-temperature and viscosity-pressure

characteristics

For open systems, for example, manufacturing systems such as machining and molding, or quarrying and dredging systems, the structural parameters characterizing the materials flow in and out of the system are often difficult to specify

In addition to the structural elements necessary to fulfill the functional purpose of the tribosystem, detrimental elements such as dirt, dust, and moisture may also be present and must be recognized in the analysis of structural parameters To assist in the compilation of the various parameters relevant to a given friction and wear problem, a data sheet of basic tribological parameters is described later in this article (see the section entitled "Data Sheet of Basic Tribological Parameters" )

Operational Parameters

Operational parameters characterize the functional conditions of a tribosystem They can be considered (with the exception of friction-induced temperatures) as independent variables that can be varied during tribological testing to obtain friction and wear data experimentally The basic operational parameters in tribology are:

• Type of motion, that is, the kinematics of triboelements (1) and (2), to be classified in terms of sliding,

rolling, spin, and impact and their possible superpositions (Fig 3) The kinematics can be continuous, intermittent, reverse, or oscillating

• Load (FN), defined as the total force (including weight) that acts perpendicular to the contact area between triboelement (1) and (2), as shown in Fig 3

• Velocity (v), to be specified with respect to the vector components and the absolute values of the

individual motions of triboelements (1) ad (2) According to the Table 2, distinctions must be made

among the relative velocity vr (relevant to friction-induced temperature rises), the sum velocity vs

(relevant, in lubricated tribosystems, to the formation of an elastohydrodynamic film), and the roll ratios

slide-to-• Temperature (T) of the structural components at stated location and time, that is, the initial

(steady-state) temperature and the friction-induced temperature rise (average temperature rise and flash temperatures) to be estimated on the basis of friction heating calculations (see the following article in this Section on "Design of Friction and Wear Experiments")

• Time dependence of the set of operational parameters (FN, v, T, for example, load cycles and heating or

cooling intervals

• Duration (t) of operation, performance, or test

In addition to these functional operational parameters, disturbances such as external vibrations or radiation might need to

be taken into consideration as well

Table 2 Type of motion and velocities of the components of a tribosystem for sliding and sliding and rolling

Fig 3 Kinematics of tribosystems

Interaction Parameters

Interaction parameters characterize the action of the operational parameters on the structural components of tribosystems These parameters define in particular the contact mode and the lubrication mode of a tribosystem with a given material/material or material/lubricant/material structure The contact mode of two touching solid bodies is characterized microscopically by materials interactions, which are described by contact stresses and stress distributions The materials and stress interactions cause a resistance against motion (friction) and may lead to surface damage (wear) Therefore, the materials and stress interactions in tribosystems are also called friction and wear mechanisms, or generally tribological processes, and specified in terms such as adhesion, abrasion, tribochemical reactions, surface fatigue, and so forth

Interface Forces and Energies Theoretically, the microscopic interaction forces between contacting solids include,

at least in principle, all those types of atomic and molecular interaction that contribute to the cohesion of solids, such as metallic, covalent, and ionic, that is, primary chemical bonds (short-range forces), as well as secondary van der Waals bonds (long-range forces) (Ref 3, 4) These surface forces depend in a complicated manner on the physicochemical nature

of the materials and the structure and composition of the outermost surface layers and contaminants It should also be noted that the chemical composition, the electronic nature, and the microstructure of surfaces may be quite different from that of the subsurface (volume) of a material

Experimentally, the only macroscopic way to characterize adhesive interactions between two solid bodies contacting

under a normal load, FN, is to destroy the bonding and to measure in the opposite direction to FN the force, FA, necessary for the separation of the surfaces The ratio a = FA/FN is termed the coefficient of adhesion On the microscopic level, it is

possible to determine with an atomic force microscope (noise level 2 × 10-11 N) the interface forces (including friction forces) between single atoms of contacting surface tips (Ref 5)

In energetic terms, the formation of a solid/solid contact results in a net release of surface energy resulting from the replacement of two surfaces by one solid/solid interface of lower surface energy The change in surface energy per unit area of contact, , can be written as:

= 1 + 2 - 12 (Eq 1)

where 1 is the surface energy of solid 1, 2 is the surface energy of solid 2, and 12 is the surface energy of the interface

Contact Deformation Modes. The surfaces of solid tribocomponents possess a certain roughness for which

cross-sectional topography descriptors such as the centerline average (CLA), or the peak-to-valley roughness, as well as stochastic parameters such as the variances of the height and slope of asperities and the curvature are used for characterization (Ref 6) In addition, fractal geometry approaches may also be applied (Ref 7)

If two nominally flat and dry solid materials (1) and (2) are brought into static contact under the action of a normal load (Fig 4), the touching asperities of this tribocontact deform elastically or plastically under the given load The dominating contact deformation mode is governed by a deformation criterion (the so-called plasticity index), which depends on the deformation properties and the parameters of the surface topography of the contacting bodies (1) and (2) defined in Fig 4

(Ref 6) The summation of individual contact spots gives the real area of contact, Aor, which usually is much smaller than the apparent geometrical area of contact The real area of contact depends in the elastic case primarily on the ratio of FN

to the composite elastic modulus E' (see the discussion of "Contact Stresses" below) and in the plastic case on the ratio of

FN to the yield pressure, py, or the hardness, H, of the softer of the contacting bodies If, in addition to the normal load, a

friction force FF is introduced, a junction growth of asperity contacts may occur, leading to a considerably larger area of

contact The basic parameters relevant to the contact mode of a materials/materials pair are summarized in Fig 4 In engineering applications, the contact deformation mode may be additionally influenced by disturbances such as misalignments or vibrations

Fig 4 Characteristics of a tribocontact between solid bodies

Contact stresses in a tribosystem depend on groups of parameters characterizing (1) the contact geometry, for

example, conformal or contraformal contact configurations, (2) the elasticity, viscoelasticity, plasticity, or hardness of the materials, and (3) the external static or dynamic load

For curved bodies, the macroscopic elastostatic contact situation is described by the Hertzian equations (Ref 8) To illustrate the basic parameters, consider the fundamental idealized case of the pure elastic contact of two spherical bodies

(1) and (2) of radii r1 and r2, elastic moduli E1 and E2, and Poisson's ratios v1 and v2 under a normal load, FN, as shown in Fig 5(a) The contact pressure, p, at a location 1 within the contact area and the radius of contact aH are given by:

Fig 5 Hertzian contact between spherical bodies under (a) normal forces and (b) combined normal and

tangential forces

If a tangential force FT < FN · f0 (where f0 is the static coefficient of friction) is additionally applied to a static Hertzian

contact, slip and no-slip regions within the Hertzian contact area result before a macroscopic horizontal relative motion

between body (1) and body (2) occurs If aH denotes the radius of the Hertzian contact circle, it follows, according to

Mindlin (Ref 9), that no slip occurs within a circle of radius:

(Eq 6)

whereas in the part of the Hertzian contact zone in which the radius is between ai and aH, slip occurs (Fig 5b)

In the case of macroscopic relative motion, the superposition of normal forces, FN, and frictional forces FF > FN · f0 (perpendicular to FN) in a tribocontact leads to complex stress distributions in the contacting bodies The multiaxis stress

condition may be converted into a uniaxial tensile stress in such a way that the uniaxial tensile load affects the material to the same extent as the multiaxial stress state The basic stress hypotheses described below are suggested for tribocontacts such as rolling-element bearings or gears (Ref 10)

Distortion Energy Hypothesis (DEH) The equivalent stress, E, DEH, is obtained by equating the distortion energies for uniaxial and multiaxial loading (Mises criterion):

E, DEH = 1/2 [( 1 - 2)2 + ( 2 - 3)2 +

where 1 > 2 > 3 are the principal normal stresses

The distortion energy hypothesis takes into account how all three differences between the principal stresses influence the initiation of plastic deformation of the material

Shear Stress Hypothesis (SH) The extent to which the material is stressed is represented by the maximum effective principal shear stresses, Tmax (Tresca criterion) Using the Mohr notation, the equivalent stresses are given by

E, SH = | 1 - 3| = |2 Tmax| (Eq 8)

where 1 and 2 are the principal normal stresses

According to this hypothesis, fatigue occurs due to flow processes in the plane of the maximum principal shear stresses Tmax, which is located at 45° to the principal stress system

In addition to the contact pressure distribution of spherical bodies with a circular contact area illustrated in Fig 5, Fig 6 shows the contact pressure distribution in an elliptical Hertzian contact of two bodies with curvature in two planes The resulting principal normal stresses 1, 2, 3 along the z-axis (directed into the material) for an axis ratio A/B = 6 are plotted on the left side The equivalent stresses formed in accordance with the DEH and SH stress hypotheses are shown

on the right

Fig 6 Material stress for curved surfaces and elliptical contact (A/B = 6)

Contact Area/Wear-Track Ratio The formation of a contact is a necessary condition for all friction and wear

processes that occur, by definition, in the momentary contact area Ac The kinematics and time-dependent variation of the contact area leads to wear tracks (Aw1, Aw2), which may be different for the tribocomponents (1) and (2) of a given

tribosystem As illustrated in Fig 7 for the example of a pin-on-disk testing system, a tribocontact parameter, , can be defined This tribocontact parameter is also called the contact area/wear-track ratio (Ref 11)

Characteristics of

tribocomponents for which

= 1

Characteristics of tribocomponents for which

< 1 Permanent contact Intermittent contact

No macroscopic cyclic stressing Cyclic stressing

Permanent friction heating Intermittent friction heating

Reduced material-atmosphere interactions Direct material-atmosphere interactions on Aw - Ac

Fig 7 The tribocontact parameter, , for a pin-on-disk configuration

If for a given tribosystem, the tribocontact parameters of tribocomponent (1) and tribocomponent (2) are unequal (that is,

1 2), then the two tribocomponents are subject to different tribological actions with respect to the kinematics, stresses, friction-induced heating, and material-atmosphere interactions as summarized in Fig 7 It follows that in investigations of tribosystems, the response of both tribocomponents to the interfacial tribological processes must be carefully analyzed Therefore, the tribocontact parameter plays an important role in the appropriate design of friction and wear test configurations to be used for simulative testing of the components of real triboengineering systems For example, a material for a certain triboengineering component should only be tested in a test configuration where the materials specimens have the same tribocontact parameter as in the real triboengineering system

The lubrication modes of tribosystems, consisting of triboelement (1), triboelement (2), and lubricant (3), are

determined by structural parameters (for example, elastic moduli, E1, and E2, radii of curvature r1 and r2, surface roughness Ra1 and Ra2, lubricant viscosity, , and the viscosity-pressure coefficient, ) and operational parameters (for

example, load, FN, velocity, v, and bulk oil temperature, T) Three main lubrication regimes can be distinguished by

Stribeck curves (Ref 12) Figure 8 shows how lubrication regimes and variations of friction and wear coefficients are

functions of the parameter combination · v · , or the film thickness-to-roughness ratio

Fig 8 Lubrication regimes and variations of friction and wear coefficients as functions of the ratio of film

Regime III: fluid film lubrication (hydrodynamic or EHD lubrication) ( > 3) In this regime, the tribological behavior is determined by the rheology of the lubricant and can be calculated by the methods of fluid mechanics, for example, the Reynolds equation

The different lubrication regimes are connected with different ranges of friction coefficient and wear coefficient values as illustrated schematically in Fig 8 Additional information can be found in the article "Lubrication Regimes" in this Volume

Tribometric Characteristics

Tribometric characteristics are measures of the results of interfacial interactions, that is, tribological processes in tribosystems Friction and wear can be described phenomenologically by force-related or energy-related parameters with respect to friction, and by geometry-related or matter-related parameters with respect to wear (Ref 13) In addition to the numeric friction and wear parameters defined below, other tribometric characteristics, such as friction-induced noise or vibrations, may also be of interest Further, the tribological processes as well as changes in the composition and microstructure of the triboelements and the resulting shape and composition of wear surfaces and wear particles must be characterized (see the Sections of this Handbook that deal with laboratory characterization techniques) It is important to

recognize, however, that friction and wear parameters are system-dependent characteristics that must be related to the pertinent tribosystem as described in the article "Presentation of Friction and Wear Data" in this Section

Friction Parameters Friction, usually classified as static or dynamic friction, is the resistance to initiate or sustain

relative motion of contacting bodies (Fig 1b) The diagnosis of the relevant parameters shows that depending on the

kinematics (Fig 3), friction can be measured as frictional force, FF, in sliding and frictional torques, TFR or TFSP, in rolling

or spinning, respectively (Ref 14) The static or dynamic sliding friction coefficient, f, is defined as the quotient between the friction force, FF, to initiate or sustain relative motion tangential to the normal load, FN, that is, f = FF/FN It follows

that a rolling friction coefficient and a spin friction coefficient can be defined as the quotient of the friction torque and the

normal load times a characteristic radius related to the contact geometry The frictional work or energy, EF, with respect

to the kinematics (Fig 3) for sliding, rolling, and spinning, respectively, is given by:

where SP is the spin angle

In these equations the time dependence of the operational parameters has to be recognized (see the earlier section of this article on "Operational Parameters" ) The average frictional power is defined as frictional work or energy divided by the

operating duration, t (that is, PF = EF/t) For sliding friction, PF = FF · v = f · FN · v

Wear Parameters Wear is the progressive loss of substance from the operating surfaces of the mechanically

interacting elements of tribo-systems As illustrated in a simplified manner in Fig 9, wear may be measured in terms of:

• Length, that is, one-dimensional changes in the geometry of interacting triboelements perpendicular to

their common contact area

• Area, that is, two-dimensional changes of cross sections of interacting triboelements perpendicular to

their common contact area

• Volume, that is, three-dimensional changes of geometric regions of interacting triboelements adjacent to

their common contact area Wear volumes are connected via density or specific gravity with wear masses or wear weights

In addition to these quantities, a wear-time ratio may be defined as wear velocity (Ref 15) Other common wear

parameters are the wear rate, which is the wear volume per unit of sliding distance, and the wear coefficient, k, which is

defined as:

(Eq 12)

where W is the wear volume (in mm3), FN is the applied load (in Newtons), and s is the sliding distance (in meters)

Fig 9 Wear quantities illustrated for a tribosystem consisting of two sliding cylinders

It should be emphasized that wear quantities must be determined for both components involved in a wear process, that is, triboelement (1) and triboelement (2) of a given (closed) tribosystem

Data Sheet of Basic Tribological Parameters

The foregoing analysis has shown that the diagnosis of the relevant parameters of tribosystems must recognize

• Structural parameters

• Operational parameters

• Interaction parameters

• Friction and wear parameters

A data sheet containing the main items of these parameter groups is given in Fig 10 The data sheet, designed primarily for the characterization of closed tribosystems, can serve as a general guide for the compilation of the parameters to be specified individually for a given tribosystem If necessary, the data sheet can be shortened or extended, but in any case at least the structural tribocomponents (1) to (4) must be identified and characterized and the set of the operational variables

(FN, v, T, t) determined

Fig 10 Data sheet for determining basic tribological parameters

In summary, the data sheet can support the following tasks:

• Systematic analysis of tribosystems and compilation of relevant parameters

• Guide for the planning and performance of tests or failure analyses

• Documentation of test results

• Input document for tribological databases

References

1 H Czichos, Tribology A Systems Approach to the Science and Technology of Friction, Lubrication and

Wear, Elsevier, Amsterdam, 1978, p 351-353

2 "Wear: Terms, Systems Analysis of Wear Processes, Classification of the Field of Wear," DIN Standard 50

320, Beuth-Verlag, Berlin, Dec 1979

3 N.P Suh, Tribophysics, Prentice-Hall, 1986, p 26-45

4 D.H Buckley, Surface Effects in Adhesion, Friction, Wear, and Lubrication, Elsevier, Amsterdam, 1981, p

7 A Majumdar and B Bushan, Role of Fractal Geometry in Roughness Characterization and Contact

Mechanics of Surfaces, J Tribol (Trans ASME), Paper 89-Trib-20

8 H Hertz, On the Contact of Solid Elastic Bodies, J für die reine und angew Mathem., Vol 92, 1881, p 156

(in German)

9 R.D Mindlin, Compliance of Elastic Bodies in Contact, J Appl Mech (Trans ASME), Vol 71, 1949, p 259

10 E Broszeit, T Preussler, M Wagner, and O Zwirlein, Stress Hypotheses and Material Stresses in Hertzian

Contact, Z Werkstofftech., Vol 17, 1986, p 238-246

11 H Czichos, Tribology A Systems Approach to the Science and Technology of Friction, Lubrication and

Wear, Elsevier, Amsterdam, 1978, p 265-267

12 R Stribeck, The Principal Properties of Sliding and Rolling Bearings, VDI Zeitschrift, Vol 46, 1902, p

1341, 1432, 1463 (in German)

13 P.J Blau, The Units of Wear Revisited, Lubr Eng., Vol 45, 1989, p 609-614

14 "Friction in Bearings Definitions, Types, Conditions, Physical Quantities," DIN Standard 50 281, Verlag, Berlin, Oct 1977 (in German)

Beuth-15 "Wear Measuring Quantities," DIN Standard 50 321, Beuth-Verlag, Berlin, Dec 1979 (in German)

Experiments

Horst Czichos, BAM (Germany)

Introduction

FRICTION AND WEAR EXPERIMENTS must be carefully designed in order to meet the objectives of the tribotesting

to be performed During the design process, the wide variety of (1) tribological phenomena in industrial applications, (2) mechanical engineering equipment, and (3) laboratory studies available for tribotesting must all be considered Generally speaking, the scope of tribotesting can be classified into the following primary areas:

• Evaluation of the function, performance, maintainability, reliability, life, or efficiency of engineering tribosystems or tribocomponents

• Quality control of tribocomponents

• Characterization of the tribological behavior of materials and lubricants

• Investigation of basic tribological processes and friction-induced energy losses or wear-induced

materials losses

The tribotesting equipment to be used, the test conditions to be specified, and the friction and wear data to be measured must be selected with respect to the aims of tribotesting

Categories and Conditions of Tribotests

Depending on the structure and function of the tribomachinery, tribosystem, tribocomponent, or specimen to be studied, tribotests can be grouped into six categories (Ref 1) These categories, which are listed in Fig 1, consist of:

• Category I: Machinery Field Tests Testing of actual tribomachinery under practical operating

conditions

• Category II: Machinery Bench Tests Testing of actual tribomachinery under practice-oriented

(simplified, simulated, or accelerated) operating conditions

• Category III: Systems Bench Tests Testing of specific tribosystems under practice-oriented operating

conditions

• Category IV: Components Bench Tests Testing of specific tribocomponents under practice-oriented

operating conditions

• Category V: Model Tests Testing of model test specimens under practice-oriented operating conditions

• Category VI: Laboratory Tests Testing of arbitrary test specimens under laboratory operating

conditions

Each tribotesting category has a different scope, and results obtained in one category cannot be simply transferred to another This is obvious in considering the specific characteristics of the tribotesting categories listed in Fig 1

Fig 1 Categories of tribotesting

Tests of category I are performed with actual tribomachinery under practical conditions Clearly, these tests represent

the real performance of the object under study However, full-scale field tests are usually very expensive The broad

spectrum of the practical operating conditions often cannot be adequately characterized, and considerable efforts are necessary to confirm test results in a statistical manner in repeated tests

In tests of category II to IV, in which actual tribomachinery, tribosystems, or tribocomponents are studied in

well-defined bench tests, test results can be related to the actual triboengineering structures An important consideration of these tests is the appropriate choice of operating conditions, which may be simplified, simulated, or accelerated as compared with the often unknown broad spectrum of the practical full-scale operating conditions Sometimes attempts are made to determine the actual operating conditions of the full-scale filed performance with sensors and to simulate these conditions in less expensive bench tests Because tribotests of categories I to IV differ in scope and testing conditions, the techniques and procedures to be applied for the determination of fraction and wear quantities must be related to the individual tests and cannot be generalized

In tests of category V, model test specimens are used rather than actual tribocomponents If an attempt is made to

simulate actual triboengineering conditions with these tests, a sufficient similarity in the basic tribological parameters must be realized These parameters, which were described in the previous article in this Section, include:

• The determination of the physicochemical nature of the model test specimens and the triboengineering system to be simulated (use of the same materials/lubricant/environment combination and connected materials properties)

• Similarity of the contact and lubrication mode (characterized, for example, by the tribocontact) parameter, , and the film thickness-to-roughness ratio, ) to be obtained through an appropriate

similarity in the kinematics, and the suitable choice of load, FN, velocity, v, temperature, T, and test duration, t, as described in the article "Basic Tribological Parameters"

To support the appropriate selection of the structural and operational parameters of simulative testing, the characteristics

of the actual tribosystem to be simulated should be compiled in a data sheet (see Fig 10 in the article "Basic Tribologicial Parameters" in this Section), and the test conditions for simulative tests of category V should be selected accordingly

Tests of category VI are used primarily in fundamental studies of friction and wear processes The conditions of these

tests are often selected to study specific tribological phenomena rather than to simulate real triboengineering behavior

Laboratory Friction and Wear Tests and Simulative Tribotesting

The basic characteristics and relevant parameters of laboratory and simulative tests are shown in Fig 2 The design of laboratory friction and wear tests should be carried out in the following steps:

• Choose a suitable test configuration for the test specimens of triboelement (1) and triboelement (2) and specify the geometry of the test configuration, materials characteristics and properties, and surface characteristics (clean surfaces before test)

• Characterize the interfacial element (3) (for example, the lubricant) and the environmental medium or atmosphere (4) in terms of their chemical nature, composition, and chemical and physical properties

• Choose a suitable set of the operational parameters, including type of motion, load (FN), velocity (v), temperature (T), and test duration (t)

• Perform the tests as functions of varied structural parameters of the triboelements (for example, hardness or roughness) and operational parameters (for example, load cycles or velocity variations) The conditions of the tests, such as the time dependence of operational parameters, should be controlled by appropriate detectors or sensors and supported by on-line computer techniques

• Measure interesting tribometric characteristics, such as friction quantities, wear quantities, tribo-induced acoustic quantities (for example, noise or vibrations), and tribo-induced thermal quantities (for example, friction-induced temperature rise)

• Characterize the worn surfaces of triboelement (1) and triboelement (2) with respect to surface roughness and surface composition and structure

Fig 2 Basic characteristics and parameters relevant to laboratory tribotesting

The results of laboratory tribotests, that is, the measured friction and wear quantities, can be symbolically represented by:

friction, wear = f (structural and

• Selection of test configuration and structural parameters of test specimens (Fig 3(a))

• Specification of operational parameters and specimen properties (Fig 3(b))

• Tribotesting under unlubricated conditions (Fig 3(c))

• Tribotesting under fluid-film lubrication (Fig 3(d))

• Tribotesting under mixed or boundary lubrication (Fig 3(e))

Fig 3(a) Tribotest flow chart for selection of test configuration and structural parameters

Fig 3(b) Tribotest flow chart for specification of operational parameters and specimen properties

Fig 3(c) Tribotest flow chart for testing under unlubricated conditions

Fig 3(d) Tribotest flow chart for testing under fluid-film lubrication

Fig 3(e) Tribotest flow chart for testing under mixed or boundary lubrication

Evaluation of Tribotests

One of the primary problems in the evaluation of friction and wear data is coping with variability Variability is inherent

in every tribological process because of the great number of influencing parameters, their potential fluctuations, and time dependencies Generally speaking, there are systematic deviations (bias) and random deviations to be considered in the evaluation of experimentally measured data The two statistics most commonly used to characterize measured friction and

wear data are the mean and the standard deviation (Ref 2) If y1, y2, ., yn, are denoted the n individual observations of a random sample from a tribotest, the mean ( ) and standard deviation (s) are defined as follows:

(Eq 1)

(Eq 2)

While the mean characterizes the location of the observed values on a corresponding scale, the standard deviation gives a

measure of how the n observations vary or spread about the average The square of the standard deviation is called

variance

Recall that and s can be computed for a sample of n observations Therefore, call and s sample parameters the sample

mean and sample standard deviation It is important to note that these parameters can be understood as estimates of

"ideal" parameters which are characteristics of an assumed population of observations or, in other words, a random

variable, n, realizations of which form the sample of observations under consideration Call the corresponding parameters

population parameters, or more precisely, population mean and population standard deviation, and, denote them and ,

respectively It is then well known that a sample parameter approximates the corresponding population parameter if n

increases

Let y be a sample mean and s a sample standard deviation obtained from n measurements of a tribological quantity

Assume that the distribution of the corresponding population is approximately normal One can then specify a confidence interval for the population parameter , that is, an interval that contains with a given confidence level 1 - , and a

certain probability, p (for example, = 0.05 and 1 - = p = 0.95) by:

(Eq 3)

The values of t (depending on the number of measurements n and the confidence level 1 - ) can be taken from Table 1

It follows that the evaluation of tribotests may lead to the following results:

(Eq 4)

where and s are the sample parameters of a sample of n individual measurements of a friction or wear quantity

Table 1 Chart of t values (n number of individual observations, 1 - confidence level)

where the values of 2 (depending on n - 1 and ) can be taken from the 2 distribution (Table 2)

Table 2 Chart of x2 values (n number of individual observations, 1 - confidence level)

One-at-a-Time Approach In the conventional approach to model or laboratory tribotesting, one quantity (y), for

example, a friction quantity or a wear quantity, is measured as a function of only one independent variable (x1) to be selected out of the following three categories: (1) test duration, t, (2) an operational variable (for example, load), or (3) a

structural variable (for example, material hardness), where all other parameters and conditions are kept constant In

varying the values of the independent variable (x1), a relationship of the form y = f(x1) is obtained In a second test, the dependence of the measured quantity (y) on another independent variable (x2) may be determined The results of both tests can be jointly represented as a three-dimensional y = f(x1,x2) graph

An advantage of such one-at-a-time experiments is that the influence of single independent variables on the measured quantity can be clearly understood However, a large number of experiments are necessary to determine the simultaneous influence of more than one variable on the measured quantity For example, 24 experiments were needed to show the

influence of the basic set of operating variables (pressure p, velocity v, temperature T) on the friction coefficient of a dry

sliding polytetrafluoroethylene (PTFE)/materials pair, as shown in Fig 4 (Ref 5)

Fig 4 Friction coefficient of PTFE/steel (AISI 52100, 800 HV, Ra = 0.02 m) as a function of pressure (p), sliding velocity, (v), and temperature (T)

Simple Complete Factorials Approach A complete factorial is a design of experiments in which a measured

quantity is determined under the full set of combinations of the levels of all factors, that is, the variables included (Ref 4)

It allows an assessment of the main effects of the single factors and the interaction effects of all factors Although this method is based on the assumption of a linear dependence between the measured quantity and each of the independent variables, it may also serve as an approximative technique for nonlinear conditions as in tribology (Ref 6) The approach

of the complete factorial design of experiments will be explained below by using data obtained in the example of tribotesting shown in Fig 4

The aim is to assess the main effects and the interaction effects of the three operational variables (pressure p, velocity v, and temperature T), each at two levels (denoted as high, h and low 1), on the measured friction coefficient f The design is

called a 23 factorial, and the eight operating variable combinations can be displayed graphically as a cube (Fig 5) The values of the friction coefficient measured in the eight tests are listed in Table 3 The average value of the friction coefficient is:

6 (hlh) 6.2 10 70 0.02

7 (lhh) 0.62 10 70 0.18

8 (hhh) 6.2 10 70 0.09

Fig 5 Geometrical representation of the operating conditions of a 23 factorial design

By using the eight treatment combinations, the corresponding measured values of f, and the main effects of pressure, velocity, and temperature T, the two-factor interactions pv, pT, vT and the three-factor interaction pvT can be estimated

using the data in Table 3

Effect of Pressure. The effect of p when v and T are at low levels is (2 - 1) as shown in Fig 5 Similarly, the effect of

p when v is at the high level and T is at the low level is (4 - 3)

The effect of p when T is at the high level and v is at the low level is (6 - 5) Finally, the effect of p when both v and T are

at the high level is (8 - 7)

Thus, the average effect of p is the average of these four combinations, or:

f(p) = (2 - 1 + 4 - 3 + 6 - 5 +

Equation 7 can be developed as a contrast between the four treatment combinations in the right face of the cube of Fig 5

(where p is at the high level) and the four in the left face (where p is at the low level) Combining these gives:

f(p) = (2 + 4 + 6 + 8 - 1 - 3 - 5 - 7)/4

which means that an increase of the contact pressure in this example lowers the average friction coefficient

The effect of velocity v is a contrast between the four treatment combinations in the front face of the cube in Fig 5 and the four in the back This yields:

f(v) = (3 + 4 + 7 + 8 - 1 - 2 - 5 - 6)/4

which means that an increase of the velocity increases the average friction coefficient considerably

The effect of temperature T is a contrast between the four treatment combinations in the top face of the cube in Fig

5 and the four in the bottom, that is:

f(T) = (5 + 6 + 7 + 8 - 1 - 2 - 3 - 4)/4

which means that an increase in the temperature lowers the average friction coefficient (similar to an increase of p)

Interaction Effects of Pressure, Velocity, and Temperature. When T is at the low level, the effect of the pv interaction is the average difference in the p effect at the two levels of v, that is, [(4 - 3) - (2 - 1)]/2 When T is at the high level, the pv interaction is [(8 - 7) - (6 - 5)]/2 The average pv effect is the average of these two combinations, or:

This combined effect can be neglected

Summarizing the steps illustrated in the above discussion, a 23 factorial design, with 8 experiments to be performed, can

be used to determine the effect of three independent variables (x1, x2, x3), each at two levels, on a measured quantity y in

tribotesting Table 4 summarizes the results of the example discussed above, allowing an assessment of the main effects

f(p), f(v), f(T), and of the interaction effects f(p,v), f(p,T), f(v,T), f(p,v,T) on the coefficient of friction

Extended tables for more than three independent variables, or variation of these variables at more than two levels, can be designed accordingly (Ref 7, 8)

Table 4 Scheme for calculating effects in the 2 design of experiments

Terminology The following qualitative terms (Ref 9) are of key relevance for the planning and evaluation of

round-robin tests More detailed information on the quantitative aspects of round-round-robin tests can be found in Ref 10, 11, 12

Precision is a general term for the closeness of agreement between randomly selected individual measurements or test results The standard deviation of the error of measurement may be used as a measure of "imprecision."

Repeatability is the closeness of agreement between mutually independent replicate test results obtained with the same test method on identical test materials, under the same conditions (that is, the same operator, laboratory, apparatus, and time)

Reproducibility is the closeness of agreement between replicate test results obtained with the same test method on identical test materials but under different conditions (that is, different operator, laboratory, apparatus, or time)

General Rules for Round-Robin Tests A standard practice for conducting an interlaboratory study to determine the

precision of a test method is given in ASTM E 691 (Ref 11) The general rules for the planning of round-robin tests are described in Ref 10 According to these standards, the aspects listed below are of key importance for the performance of round-robin tests

Scope of the Tests. The goals to be reached during the round-robin tests should be determined from the outset

Planning and Organization of the Tests. All participating partners should be informed of the scope of the test Personnel for the test should include a coordinator of the entire test, a statistician for the planning and evaluation, and operators for the performance of the tests

Guiding the Performance of the Tests. A clear description of the test method to be applied, the characterization of test materials, the test conditions, the variables to be varied, the quantities to be measured, and the number of repeated tests to be performed must be given In addition, the format of compiling and describing the obtained results is to be specified

Analyzing the Test Results. The specimens should be carefully selected, prepared, and characterized for the tests The quantities to be measured and the format of reporting the measured data must be specified For the analysis and evaluation of the test results as part of the standard round-robin test procedure, well-defined statistical techniques must be applied

Case Study: International Round-Robin Sliding Wear Tests An international round-robin comparison on the

comparability, repeatability, and reproducibility of friction and wear tests has been performed within the framework of the Versailles Project on Advanced Materials and Standards (VAMAS) (Ref 13) Under the guidance of an international

committee on wear test methods, round-robin studies with -Al2O3 ceramic and steel specimens were performed with 31 participating institutions from seven countries

For the sake of simplicity, a ball-on-disk specimen configuration was selected as the test system The test specimens were uniformly manufactured with respect to their geometry, dimensions, and surface finish The conditions outlined below were specified on the basis of a thorough systems analysis of the main relevant characteristics of the tribotesters

Test System. Conditions for the test system, which featured the ball-on-disk configuration shown in Fig 6, were as follows:

• Stationary ball (10 mm, or 0.4 in., in diameter) against rotating disk (40 mm, or 1.6 in., in outer diameter and 32 mm, or 1.3 in., in track diameter)

• Rotation in the horizontal plane

• Direction of rotation of disk to be indicated by each laboratory

• Ball, disk, and debris to be collected and protectively stored in plastic containers

• Holders for disk and ball are left to the discretion of each laboratory

• Participants were asked to report (if possible) vibrations (for example, vibration amplitudes and frequency distribution) of the test rig at the stated location

• Participants were asked to report (if available) the stiffness data of the test rig

Fig 6 Conditions of VAMAS round-robin sliding wear tests FN, normal load; v, sliding velocity; s, sliding distance; T, ambient temperature; RH, relative humidity of the atmosphere

Materials used during the tests included an -Al2O3 ceramic and AISI 52100 steel The composition, roughness, hardness, and microstructure data were provided to each test participant

Atmosphere. Laboratory air with a relative humidity (RH) of 50 ± 10% and a temperature of 23 ± 1 °C (73 ± 2 °F) was

to be used

Lubricant. No lubricant was to be used in the round-robin tests

Operating variables included:

• Motion, continuous unidirectional sliding

Surfaces were cleaned immediately prior to each test Washing in freon (Cl2FC-CF2Cl) was preferred to washing in ethyl alcohol since the water content in the alcohol could corrode the metallic surfaces Following washing, the specimens were dried in warm air, rinsed with hexane, and re-dried in a drying oven at 110 °C (230 °F) for 30 min

In addition, only chemicals of pure quality were to be used and samples had to be stored and transported in desiccators

Wear and Friction Measurements. For wear measurements, each participant was asked to indicate whether wear of ball, wear of disk, or total wear of both ball and disk were measured Participants were also required to continuously measure and record linear wear, to weigh specimens before and after each test, to measure the wear scar diameter on the ball with an optical microscope, and to provide profilogram results of both surfaces before and after the test

Similarly for friction measurements, each participant was asked to indicate whether the frictional force or the friction torque were measured They were also required to submit a simplified graph giving the fluctuations at the beginning and the end of the test, as well as minimum and maximum deviations during the test

For both wear and friction measurements, all debris was collected

Examination. Surfaces and debris were to be examined by optical color photography and scanning electron microscopy techniques All photomicrographs had to be supplied at the standard magnifications of 50×, 100×, 200×, 500×, and 1000×

A detailed instruction sheet containing the above points and specimen pairings ready to be tested were sent from a central source to all participants

Data Evaluation. For the evaluation of numeric friction and wear data, the results of the participating laboratories were treated in the following manner to obtain statistically sound data

Only the results of laboratories that performed more than one test run per specimen kit were considered If laboratories reported only average values (as estimated by themselves from repeated test runs) these values were treated as if obtained from three measurements

From the results obtained from the participating laboratories, the following four types of numeric data were determined:

• The friction coefficient was determined after a sliding distance of 1000 m (3300 ft)

• The wear rate of the system was measured under steady-state conditions, that is, the displacement of the test specimens perpendicular to the sliding interface between 300 and 1000 m (1000 and 3300 ft) sliding distance divided by the sliding distance It should be noted that this is a geometry-dependent quantity

that cannot be compared directly with the wear rates of other test systems

• The ball wear scar diameter

• The disk wear-track width From the numeric data of the four quantities (friction coefficient, wear rate, ball wear scar diameter, and disk wear-track width), the mean values and the standard deviations for the different material pairings were calculated (Table 5)

Table 5 Results of the VAMAS round-robin sliding wear tests.

See Fig 6 for test conditions

(a) At 1000 m sliding distance

(b) Determined from the wear curve (steady-state range between 300 and 1000 m

sliding distance)

(c) Material transfer from disk to ball

(d) Material transfer from ball to disk

A comparison of the reported data showed that all the laboratories were able to perform the tests under the specified operating conditions of load, velocity, and ambient temperature However, the values of the relative humidity of the ambient atmosphere varied between 13% and 78% and less than half of the participating laboratories were able to keep the operating conditions within the specified range of 50 ± 10% RH

The results of the VAMAS round-robin comparison show that good reproducibility for the numeric friction and wear data

was obtained These data can be summarized in terms of the relative standard deviations (sr and sR according to ASTM

Standard E 691 divided by the mean value) as follows (Ref 13):

• Reproducibility of friction data: within laboratories ±9% to ±13%; interlaboratory, ±18% to ±20%

• Reproducibility of specimen wear data: within laboratories, ±5% to ±7%; interlaboratory, ±15% to

±20%

• Reproducibility of systems wear data: within laboratories, ±14%; interlaboratory, ±29% to ±38%

These results indicate that the reproducibility of friction and wear measurements is comparable with that of other engineering quantities, provided that the tests are performed under well-controlled conditions, applying standard round-robin test procedures

Appendix: Calculations of Elastic Contact Dimensions and Stresses (Ref 14)

Peter J Blau, Oak Ridge National Laboratory

General parameters used to calculate the elastic contact dimension and the stress of nonconforming surfaces are given in Table 6 The relation of these variables to specific contact geometries (Fig 7) is given in Table 7

Table 6 Elastic contact and stress nomenclature

Symbol Definition

P Normal force (load)

p Normal force (load) per unit contact length

E1 Modulus of elasticity (Young's modulus) for body 1

E2 Modulus of elasticity (Young's modulus) for body 2

v1 Poisson's ratio for body 1

v2 Poisson's ratio for body 2

D Diameter when only one body in the contact is curved

D1 Diameter of body 1 (in the case of two curved bodies, by convention D1 > D2 )

Sc Maximum compressive stress (Hertzian stress)

a Radius of the elastic, circular contact

b Width of the contact (used for cylinders)

c Semimajor axis of an elliptical contact area (used for crossed-cylinders)

d Semiminor axis of an elliptical contact area (used for crossed-cylinders)

Geometric factor used in crossed-cylinders calculations

Geometric factor used in crossed-cylinders calculations

Table 7 Formulas for calculating elastic contact dimensions and stresses of contact geometries shown in Fig 7

Geometry of the contact Elastic contact dimension(a) Maximum compressive stress

(b) To determine the values of and , first divide the larger diameter by the smaller to obtain a diameter

ratio, then use Fig 8 to determine the appropriate values for the two constants

Fig 7 Typical contact geometry models showing relation of D, D1, and D2 in elastic contact and stress analysis (see Table 7)

To calculate the maximum stress level of crossed-cylinder geometry designs, an additional step is required Two elastic contact dimension constants, and , must be obtained from Fig 8 to calculate c and d, which are then substituted into

the required formula for maximum compressive stress

Fig 8 Value of parameter constants, and , as a function of the ratio of diameters (D1/D2, where D1 > D2) for crossed-cylinder contact geometries