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An in situ mechanism for self-replenishing powdertransfer films: Experiments and modeling
C.F. Higgs III ∗, E.Y.A. WornyohCarnegie Mellon University, Mechanical Engineering Department, Pittsburgh, PA 15217-3890, USA
Received 9 August 2006; received in revised form 9 March 2007; accepted 26 March 2007
bstract
Pellets were formed by compacting MoS2 powder. A series of tests were conducted on a tribometer that consisted of simultaneous pellet-on disknd pad-on disk sliding contacts. The purpose of the tests was to intentionally transfer MoS2 third-body particles to a disk where its lubricationharacteristics could be studied. This work also showed that the MoS2 pellet actually acted as a self-repairing, self-replenishing, oil-free lubricationechanism. In the experiment, a pellet is sheared against the disk surface while the loaded slider rides on the lubricated surface and depletes the
eposited powder film. A control-volume fractional coverage modeling approach was employed to predict both (1) the friction coefficient at thead/disk interface and (2) the wear factor for the lubricated pellet/disk sliding contact. The fractional coverage varies with time and is a useful
D Podeling parameter for quantifying the amount of third body film covering the disk asperities. In the model, the wear rate of a pellet and pad
riction coefficient can be determined as a function of the pellet load, slider pad load, disk speed, and material properties. Results from the modelualitatively and quantitatively predict the tribological behavior of the experimental sliding contacts reasonably well.
2007 Published by Elsevier B.V.
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eywords: Powder lubrication; In situ solid lubrication; Transfer film; Fraction
. Introduction to powder lubrication
Advancements in engine technologies and the continuingepletion of the world’s petroleum oil supply have increasedhe need for oil-free lubrication. Additionally, conventional liq-id lubricants have proven inadequate in extreme-temperaturend load environments. Fortunately, lamellar powders orpowder lubricants” such as molybdenum disulfide (MoS2),itanium dioxide (TiO2) and tungsten disulphide (WS2) haveemonstrated excellent tribological capabilities [1]. In powderubrication, powders lubricate by forming transfer films fromompact, spray, or composite forms. In this paper, the lubricantource is obtained from powder compacts intentionally shearedgainst a rotating disk surface. Consequently, a thin transfer films formed on the surface on the order of the surface roughness.herefore, thick film powder lubrication theory, such as Hesh-
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Please cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
at’s quasi-hydrodynamic theory, does not apply to these thinsperity-covering transfer films.
∗ Corresponding author. Tel.: +1 412 268 2486; fax: +1 412 268 3348.E-mail address: [email protected] (C.F. Higgs III).
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043-1648/$ – see front matter © 2007 Published by Elsevier B.V.oi:10.1016/j.wear.2007.03.026
erage; Particulate lubrication
.1. Compacted powder transfer films
Powder lubricants, pelletized to serve as a deposition source,resent a novel approach to lubricating machine componentsn future applications. Research has shown that pellets can beuccessfully applied as transfer films to tribosurfaces [2–4].dditionally, Haltner compacted powder lubricants as a mecha-ism for transferring a thin lubricious film to a rotating disk [5].e studied MoS2 compacts in both vacuum and in room air (rel-
tive humidity of 50%), at a velocity of 0.84 m/s. In these tests,he steady-state friction coefficient was μ = 0.17. Compacted
oS2 powders have also exhibited transient frictional behav-or in tests done under both non-vacuum [1] and vacuum [6]onditions. Johnson and Vaughn, who did their tests in vacuum,oncluded that the “buildup” in initial friction values was due ton amorphous layer of sulfur generated at the initial point of slid-ng. Higgs and Heshmat, who conducted tests under non-vacuumi.e., atmospheric conditions at room temperature) introduced an
mechanism for self-replenishing powder transfer films: Experiments
lternate explanation to the build-up friction relating it to disor- 35
er as quantified by entropy [1]. The traction behavior of powder 36
raphite compacted at Hertzian pressure levels was studied to 37
haracterize the behavior of the powder particles in the contact 38
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egion [7]. In the disk-on-disk tribometer used in their experi-ents, the speed was U = 3.98 m/s (100 rpm) and the Hertzian
ressure Pc = 690 MPa. From their work, a method was devel-ped for predicting the film thickness of a powder film in aertzian contact, and the traction coefficient of a powder film in
olling element bearing configurations. Higgs et al. showed thatoS2 pelletized powder lubricants acted as a velocity accommo-
ating third-body in high-speed sliding contacts [1]. Extendingodet’s third-body approach [8], Fillot et al. [9] used a computa-
ional wear simulation to glean mass balance laws for describingear between tribosurfaces when a third-body is formed.The scope of this work presents experimental results from
competing transfer film deposition and lubricant depletionrocess. To predict this process, a control volume fractionaloverage (CVFC) model has been developed that extends theass-balance concepts of Fillot et al. [9] to analyze the com-
eting pellet transfer film (i.e., lubricant deposition) and padear (i.e., lubricant depletion) mechanisms on a pellet-on diskith slider pad tribometer configuration. Results from the pellet-n-disk with slider experiments are compared to the theoreticalesults from the CVFC model.
. Experimental details
.1. Pellet-on disk experiments
To analyze an in situ powder transfer film mechanism, a setuponsisting of in-line sliding of a MoS2 pellet and slider padFig. 1) was developed. Pellets fabricated from tap powder areear tested on the pellet-on-disk tribometer (Fig. 2), using the
n-line pellet and slider setup of Fig. 1. In the wear tests, MoS2ellets were sheared against the surface of the rigid rotatingisk. The thin-film interfacial third body particulates producedy the pellet were depleted by the loaded slider pad riding onhe lubricated surface.
.2. Fabricating pellets for wear testing
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Please cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
Preliminary work identified MoS2 powder as a suitable solidubricant material for this investigation [2]. A powder com-action system was designed for forming the cylindrical MoS2ellets, consisting of a top and bottom die, which housed the
ig. 1. Pellet-on-disk with slider apparatus enables the study of self-replenishingowder film transfer. The test parameters were as follows: Fp = 17.8 N;
c = 68.7–340.8 kPa; U = 4.5–45 m/s.
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PRig. 2. Pellet-on-disk with slider tribometer for measuring the pellet wear and
riction forces at pellet/disk and slider/disk.
owders during compaction. A thin sleeve of Inconel alloyncompassed the powders. A porous, split sleeve tube encasinghe powder and the Inconel was placed in the bore of the top die.his encasing was rested on top of a porous disk located at thease of the bore. The disk had a porosity of 0.5 �m and allowedhe air in the powders to escape during compaction. The pistonas less than 100 �m smaller than the porous encasing to avoidetal-to-metal contact. Once filled with powder, the fixture was
laced under a hydraulic press where it was compacted to theesired pressure. The resulting pellet had a diameter of 19 mmnd a length of 51 mm. The pellets were made by compactinghree different samples of MoS2 powder with varying averagearticle sizes; Sample A with 13.64 �m; Sample B with 7.4 �m;ample C with 1.56 �m. Similar to transfer films that are notelf-replenishing [10], Sample A was used in previous pellet-n-disk tests conducted without slider pads and was excludeds a self-replenishing solid lubricant candidate for this work, sonly Samples B and C are examined in this study. The mass,iameter, length, and density of the pellet were measured afterompaction.
.3. Pellet-on disk with slider experiments
After the pellets were fabricated and measured, they werelaced in the L-shaped pellet holder for wear testing. During theests, a pellet was loaded against the disk, as it rotates. A sliderad, located in-line with the pellet, was also loaded against theisk. In this project, the investigation of the film transfer process
mechanism for self-replenishing powder transfer films: Experiments
as studied using the pellet-on-disk wear test. Fig. 1 shows a dia- 102
ram of the pellet-on-disk with slider pad configuration. In the 103
xperiment, a powder transfer film from a pellet was deposited 104
n the disk and a slider pad depletes the film when its load 105
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at the pellet/disk interface μp and slider/disk interface μp were 185
also measured (from the frictional forces) to assess the fric- 186
tional behavior of the powder film at the two sliding contact 187
regions. The vertical wear �L of the pellet was also measured 188
Table 1Experimental parameters for pellet-on disk tests
Parameter Value
Ambient temperature (◦C) 23.3–24.4Relative humidity (%) 40–50Test speed, U (m/s) 4.5–45Compaction pressure, σyy (MPa) 34.5Pellet load, Fp (N) 17.8
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C.F. Higgs III, E.Y.A. Worn
xceeds the film’s load carrying capacity. Since the pellet isressed against the rotating disk by a weight Fp, the thin film isransferred to the disk by shearing. The transfer film supports theormal load on the slider, which is expressed as a contact pres-ure Pc. Lastly, the wear rate (i.e., transfer film delivery rate)f the pellet and the frictional behavior at the pellet-disk andad/disk interfaces were studied.
.4. Experimental setup
A schematic of the tribometer is shown in Fig. 2. The tribome-er from Mohawk Innovative Technology Inc. [1], consisted of aisk mounted on a spindle driven by a one HP variable-speed DCotor, which had a maximum speed of approximately 5000 rpm.he disk, made of Titanium Carbide cermet (TiC), had an aver-ge test track radius of 83.1 mm (3.27 in.) and a thickness of4 mm. A pellet lubricant holder for the test specimen main-ained the pellet in a vertical position. The holder, mounted atoplow friction slider, allowed the pellet to slide without constraintgainst the rotating disk. A load cell with a probe wire attachedo the base of the specimen holder measured the frictional forcexerted on the pellet. A linear variable differential transformerLVDT) with a resolution of 2.5 �m was placed on top of theellet to record its vertical displacement, which was convertedo the mass of material worn vertically. This calculated verticalass wear was verified against the total mass of wear measured
t the completion of the tests using a mass balance.The measurables in the experiments are shown in Fig. 2 as the
rictional (tangential) force FSt at the slider pad, the frictional
orce at the pellet FPt , and the wear displacement of the pellet
L (see Fig. 1).The high-speed pellet-on-disk tribometer was modified to
nclude a load arm capable of securing a slider pad on the diskuring wear tests. The slider pad supports the load on the filmnd was loaded by placing dead weights Fs on the load arm at aistance away from the pad’s center of mass. Since the point loadas not being applied at the pad, a moment balance was made
o determine the load actually realized at the pad, which wasransmitted by a pivot ball. At the pivot ball on the load arm,he contact pressure Pc on the bearing pad was computed byividing the normal load Fs by the pad area and multiplying thisuotient by a moment factor. This factor, 0.719, was determinedy taking the summation of moments about the load arm jointnd was used to determine the load actually experienced at theenter of the pad. The contact area of the pad was 6.45 cm2
1 in.2) and a photograph of the slider pads are shown in Fig. 3.A graphical user interface data acquisition software was
eveloped and used to record the relevant parameters of speed,riction forces, and pellet vertical displacement at acquisitionime intervals as small as a tenth of a second. Digital panel
eters also displayed the output values for manual verification,nd an alarm was designed to warn the user when the dry frictionoefficient was attained between the slider and disk.
UPlease cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
.5. Pellet-on disk with slider testing procedure
Testing was initiated when the disk reached the prescribedpeed. The data acquisition is started at the same time. To ensure
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ig. 3. Photographs of TiC slider pads: (a) pad was wear tested for 180 km andb) pad was untested pad.
eliability, data is also acquired manually by reading the digi-al panel meters, measuring the average wear depth and frictionorces. A special receptacle collects the wear debris emergingrom the interface. At the end of each run, the structural integrityf the pellet is visually examined, and the disk cleaned using hex-ne for the next run. The amount of wear for a particular run isxperimentally determined by computing the product of the pel-et cross sectional area, pellet density, and vertical displacementi.e., change in pellet length) as measured by the LVDT system.he mass wear of the pellet is also obtained using a mass balanceith a resolution of 0.05 g. The LVDT-based wear from exper-
ments is compared to the mass balance wear at the conclusionf the tests. The LVDT computed pellet mass loss was within% of the mass loss in wear tests. The in situ measurementsere vertical pellet wear �L and the pad and pellet coefficientf friction are μs and μp, respectively. Numerous pellet-on-diskith slider tests were conducted under normal room conditionsith the following experimental parameters shown in Table 1.
. Experimental results
The wear tests consist of a pellet-on-disk with a slider padepleting the film track deposited by the pellet. The series ofear tests show wear and friction trends of the pellet and pad
s a function of distance. The results depict the behavior of theellet as a function of disk speed U, load on pellet Fp, powderompaction pressure σyy, and pad load, Fs. Friction coefficients
mechanism for self-replenishing powder transfer films: Experiments
ad load, Fs (N) 56.8–307ange of test sliding distance (km) 6–8verage MoS2 powder particle sizes Samples B (7.4 �m)
and C (1.56 �m)
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F a TiCw Pa (2P
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ig. 4. Data from a single pellet-on-disk with slider test for pelletized MoS2 onear. (a and b) Test (#55) conditions for Sample B (σyy = 34.5 MPa), Pc = 137.8 k
c = 340.14 kPa (49.6 psi), U = 27 m/s.
nd converted into mass wear loss. While there were numerousests conducted on the tribometer, the authors exercise brevityy showing data friction and wear at one test condition in Fig. 4.ummary data are shown for both Samples B and C pellets at twodditional disk speeds U = 27 m/s and 45 m/s in Figs. 5 and 6,espectively. The friction and wear data at these speeds showrends that are representative of the other pellet-on disk withlider tests.
Fig. 4(a) and (b) shows data from a wear test with theoS2 pellet Sample B (Pd = 7.4 �m) at a compaction pressure
yy = 34.5 MPa, slider pad contact pressure Pc = 137.8 kPa, andisk speed U = 9 m/s. In Fig. 4a, the pellet friction coefficient μp
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Please cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
s shown as a function of wear distance LT. The friction coef-cient was determined by the quotient of the frictional forcePt measured at the base of the pellet and the normal load pro-uced on the disk by the pellet (see Fig. 2). It is not evident
dwTt
Fig. 5. (a) Slider pad friction and (b) pellet wear as a function of slider cont
disk. (a and c) Pellet and pad friction coefficient; (b and d) cumulative pellet
0 psi), U = 9 m/s; (c and d) Test (#80) conditions for Sample C (σyy = 34.5 MPa),
rom the μp versus distance graphs what the tribological effectn the pads would be. However, it seems that μp may be usefuln estimating the tangential force needed to detach the MoS2articles from the pellet [11]. Detachment forces, which relateo pellet wear, may be discernable by looking at the μp plot. Inig. 4a, the slider friction coefficient μs is shown as a functionf distance. The friction coefficient μs was determined by theuotient of the frictional force FS
t measured at the base of thelider pad and the normal load produced on the disk by the pad.uring run-in, the slider friction coefficient μs decreased below
he dry friction coefficient (μs = 0.2) until it reached the lowestriction coefficient for the test of μs = 0.08. Steady-state con-
mechanism for self-replenishing powder transfer films: Experiments
itions (i.e., when the wear rate becomes constant) for the test 217
ere reached at approximately 2 km at which point μs = 0.13. 218
his shows that the pad did not experience starvation during 219
he 5 km at steady state. Fig. 4b shows the mass loss of pel- 220
act pressure. Test conditions: U = 27 m/s, σyy = 34.5 MPa, Fp = 21.3 N.
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conta
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asperity height hmax. 289
(iii) The frictional response in the pellet/disk and slider/disk 290
interfaces is predominantly a function of the amount (i.e., 291
fraction) of transfer film covering the disk surface. 292
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Fig. 6. (a) Slider pad friction and (b) pellet wear as a function of slider
et wear as a function of distance LT. The corresponding wearactor φ, which is the steady state wear volume divided by theroduct of the mass-load on the pellet and the total wear dis-ance, is 1.07 × 10−8 cm3 cm−1 kg−1. The φ was approximatelyonstant for 5 km indicating that there was a continuous deliv-ry of powder lubricant being supplied to the pad/disk slidingontact. In another test, Fig. 4(c) and (d) shows data with theoS2 pellet Sample C (Pd = 1.56 �m) at a compaction pressure
yy = 34.5 MPa, slider pad contact pressure Pc = 340.14 kPa, andisk speed U = 27 m/s. In Fig. 4c, one can see that both thead and pellet friction coefficients approach steady-state val-es in the approximate range of 0.13–0.15. This corresponds tosteady-state wear rate which starts at approximately a wear
istance of 1 km as shown in Fig. 4d.The results from the pellet-on disk with slider wear tests for
oth MoS2 powder Samples B and C have been summarizedsing the bar charts in Figs. 5 and 6 which represent wear tests at= 27 m/s and 45 m/s, respectively. The normal load on the pad
reates a contact pressure Pc (in kPa) on the disk. In Figs. 5 and 6,he steady-state friction coefficient μs at the slider/disk inter-ace and the wear factor φ as a function of Pc are shown. At
= 27 m/s, Fig. 5a shows that the friction coefficient increasesith the pad load for both samples. In Fig. 5b, the wear fac-
or also increases with increasing slider load, except for Sampleat Pc = 137.8 kPa. At U = 45 m/s, Fig. 6a shows that the fric-
ion coefficient at the pad/disk interface increases with contactressure. However, Sample B slightly deviates from the globalrend at Pc = 137.8 kPa. In Figs. 5 and 6, Sample C consistentlyhows that the pad friction coefficient and pellet wear rate φ
oth increase with pad load. This likely suggests that increasinghe pad load increased the lubricant starvation which made theriction coefficient also increase. Consequently, the pellet wearate increased as the disk starvation (i.e., lubricant-depletion)romoted increased pellet wear. In Fig. 6b, the pellet’s wearncreases as the load on the pad increases for both MoS2 sam-les. It is likely that environmental fluctuations such as humidityay have caused the slight deviations from the expected trends
or Sample B in Figs. 5b and 6a. In Figs. 5b and 6b, one canee that the pellet with Sample C powder wears less than Sam-le B pellet for almost all contact pressures. This is attributedo the fact that for a prescribed compaction pressure, Sample C
UPlease cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
owder (i.e., the smaller particles) was more dense with higherohesion. Another telling feature of Figs. 5b and 6b is that aarger pad load increased pellet wear. As the film was depleted,he wear rate of the pellet increased to account for the lack of
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ct pressure. Test conditions: U = 45 m/s, σyy = 34.5 MPa, Fp = 21.3 N.
ubricant film present on the disk. This suggests the lubricationechanism appears to replenish the transfer film only as-needed.ne should note that Fig. 4c and b is the friction and wear evolu-
ion data for the test which is summarized in Fig. 5 (U = 27 m/s;ample C) when Pc = 340.14 kPa.
. Theory
Fig. 7 shows a simplified schematic of the pellet as it isheared against the disk whose surface asperities have been exag-erated. The third body particulates sheared from the pellet fillp the valleys on the disk surface en route to covering up thesperities.
.1. The control volume fractional coverage (CVFC) model
In order to develop a first principle tribology model of theubrication process, the third-body transfer film was made theontrol volume. Next, a wear and third body concept was adopted9]. As the pellet in Fig. 7 wears, it deposits a thin film of lubri-ant on the surface of the disk and covers the asperities on theisk surface. The control volume fractional coverage (CVFC)odeling assumptions are as follows:
(i) The slider/disk and pellet/disk interface topographies arerepresented by a nominally flat pellet or slider surface incontact with a rough disk with a composite roughness.
(ii) The disk topography varies little relative to the maximum
mechanism for self-replenishing powder transfer films: Experiments
Fig. 7. Schematic of pellet sheared against the disk.
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The fractional coverage, X, is dimensionless and is defineds the fraction of lubricant (third body particulates) that covershe asperities of the disk surface. That is:
= h
hmax(1)
here h is the local height of third body film. The film heighthen the disk asperities are completely covered is h = hmax and
n that case, X = 1. Similarly, X = 0 represents the case of noubricant coverage. Researchers have employed other forms ofractional coverage relations in modeling lubrication processes12–17]. Our model assumes that the slider pad can be treateds smooth and that the frictional response is primarily a functionf the change in the film height h of solid lubricant that covershe asperities. Referring to Fig. 7, consider the control volumehat encloses asperities and valleys as well as the third bodyarticulates transferred by the pellet as shown by the dotted lines.he third body has the pellet as its sources of supply, however, it
s being depleted from two sources: at the pellet’s leading edge,nd far away from the pellet, at the slider. From conservation ofass:
Third Body
Storage Rate
)=(
Third Body
Input Rate
)−(
Third Body
Output Rate
)(2)
To mathematically interpret Eq. (2), use is made of Archard’sear Law:
˙ = KFNU (3)
here V̇ is the volume wear rate, K the dimensional wear coeffi-ient, FN the normal load applied, and U is the sliding velocity.is an empirical constant that usually describes the probability
f wear occurring between two different materials such as TiCn MoS2, although in some instances, K could just be betweenhe same kind of material for instance MoS2 pellet riding on
oS2 third body. Using Archard’s wear law from Eq. (3), theonservation law of Eq. (2) becomes:
dh
dt= KpFpU
(1 − h
hmax
)− KepFpU
h
hmax
−KesFsUh
hmax(4)
here A is the cross-sectional area, and Fp and Fs are pellet andlider loads, respectively. Additionally, Kp is the wear coefficientor the pellet/disk interface, while the wear coefficients for thehird body wear due to shearing from the pellet and slider pad are
ep and Kes, respectively. Applying the definition of fractionaloverage from Eqs. (1)–(4) yields:
hmaxdX
dt= KpFpU(1 − X) − KepFpUX − KesFsUX (5)
Eq. (5) is the governing equation which together with thenitial condition X(0) = 0 completely defines the problem for the
UPlease cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
VFC model. The solution to Eq. (5) is given by:
(t) = FpKp
FsKes + Fp(Kep + Kp)
[1 − exp
(− t
τ
)](6)
fitTe
PR
OO
F
PRESSWear xxx (2007) xxx–xxx
here t is the time constant defined by:
= Ahmax
FsKes + Fp(Kep + Kp)U(7)
After a long time has elapsed, the steady state fractionaloverage is deduced from Eq. (6) as:
ss = FpKp
FsKes + Fp(Kep + Kp)(8)
Researchers have used other forms of fractional coverageo predict the friction coefficient. Adopting the linear-rule-of-
ixtures from Dickrell et al. [18,19], the pellet and slider frictionoefficients can be defined as:
p = Xμlub,p + (1 − X)μdry,p (9)
s = Xμlub,s + (1 − X)μdry,s (10)
here μp and μs are friction coefficients at the pellet/disk andlider/disk interfaces, respectively. The pellet and slider fric-ion coefficients for unlubricated conditions are μdry,p and μdry,shile those for lubricated conditions are indicated by μlub,p andlub,s.
To obtain the steady-state wear factor of the pellet, φ, Eq. (5)s first rewritten for the pellet alone:
˙p = dVp
dt= KpFpU(1 − X(t)) (11)
hus,
p,total =∫ ts
0KpFpU(1 − X(t)) dt (12)
here Vp is the pellet wear volume, Vp,total is the total pelletear volume over a total sliding time ts. Then, the result fromq. (12) is used in Archard’s wear law to give the steady-stateear factor as:
(cm3 cm−1 kg−1) = Vp,total
(Fp/g)tsU(13)
here g is gravitational acceleration.Table 2 has the numerical values that were used in the CVFC
odel. Based on Eq. (5), the wear coefficients Kp and Kes rep-esent the probability of the MoS2 pellet being worn by the TiCisk and the probability that the MoS2 film will be removedrom the disk by the trailing TiC slider pad, respectively. Thus,oth of these sliding contacts involve a TiC-on-MoS2 inter-ace configuration (Fig. 2), and it was assumed that Kp ∼= Kes =.5 × 10−8 m2/N, as shown in Table 2. The final wear coeffi-ient Kep represents the lower probability that the MoS2 pelletill become glazed and thus removes MoS2 transfer film from
he disk. Since this event happened less frequently in the tests,e assigned this wear coefficient with an order of magnitude
ower probability of Kep = 5.5 × 10−9 m2/N. These values rep-esent our best guess and can be improved through detailed curve
mechanism for self-replenishing powder transfer films: Experiments
tting. The authors chose not to curve-fit here to demonstrate 378
he reasonable effectiveness of the first-principle CVFC model. 379
he other values in Table 2 were taken to coincide with the 380
xperimental conditions. 381
DR
OO
F
ARTICLE IN PRESS+ModelWEA 98463 1–8
C.F. Higgs III, E.Y.A. Wornyoh / Wear xxx (2007) xxx–xxx 7
Table 2Parameter values for CVFC model
Pellet Slider
Friction coefficient μdry,p = 0.12, unlubricated μdry,s = 0.l5, unlubricatedμp = 0.05, good lubricant μs = 0.03, good lubricant
Wear coefficient (m2/N) Kp = 5.5 × 10−8; Kep = 5.5 × 10−9 Kes = 5.5 × 10−8
Normal load (N) Fp = 88.8 Fs = 0–225
Disk values—sliding speed: U = 27 and 45 m/s; roughness: hmax = 10−4 m.
382
f383
t384
4385
386
r387
t388
i389
t390
F391
4392
fi 393
a 394
o 395
c 396
s 397
t 398
t 399
t 400
t 401
CTE
Fig. 8. Fractional coverage vs. pellet load.
The results from Eqs. (8)–(10), and Eq. (13) form the basisor the comparison of the theoretical and experimental results inhe next section.
.2. Comparing experimental results with theory
The CVFC model qualitatively and quantitatively agrees withesults from the pellet-on-disk with slider tests. In Figs. 8 and 9,he model predicted the fractional coverage parameter to
UN
CO
RR
E
Please cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
ncrease with pellet load while decreasing with slider load, trendshat were irrespective of the sliding velocity at steady state.ig. 10a and b illustrate that at sliding speeds of 27 m/s and5 m/s, both the model and experiment show the friction coef-
bTmi
Fig. 10. Coefficient of fric
P Fig. 9. Fractional coverage vs. slider load.
cient at the slider/disk interface increase before levelling off,s slider load increases. Finally, for the same sliding speedsf 27 m/s and 45 m/s, Fig. 11a and b shows that the theoreti-al and experimental wear factors for the pellet increase withlider load. This actually demonstrates that the pellet repairshe transfer film and self-replenishes the depleted film. Sincehe frictional response of powder lubricants are dependent onhe environmental conditions, namely temperature and rela-ive humidity, one should note that the CVFC model could
mechanism for self-replenishing powder transfer films: Experiments
e improved by including thermal variables in the model. 402
his might certainly explain the deviations between experi- 403
ents and theory at higher loads where the frictional heat 404
ncreases. 405
tion vs. slider load.
ED
ARTICLE IN PRESS+ModelWEA 98463 1–8
8 C.F. Higgs III, E.Y.A. Wornyoh / Wear xxx (2007) xxx–xxx
r fact
5406
407
o408
u409
M410
d411
o412
p413
i414
w415
e416
p417
e418
c419
p420
s421
d422
A423
424
o425
i426
l427
v428
M429
n430
t431
r432
f433
R434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
[ 454
455
456
[ 457
458
459
[ 460
461
462
[ 463
464
465
[ 466
467
468
[ 469
470
471
[ 472
473
474
[ 475
476
[ 477
478
friction diamond-like carbon, J. Tribol. -Trans. ASME 126 (3) (2004) 615– 479
CO
RR
EC
TFig. 11. Pellet wea
. Conclusion
Experiments were conducted to test the feasibility of devel-ping a self-repairing, self-replenishing lubrication mechanismsing powder lubrication. The results indicate that compactedoS2 in a competing-process tribosystem is a suitable candi-
ate for providing continuous lubrication to sliding contacts. Inrder to predict the competing (deposition/depletion) lubricationrocess, a third-body control volume fractional coverage model-ng approach was developed to predict slider friction and pelletear on a pellet-on-disk with slider tribometer. The model is
ssentially based on first principle tribology with the only freearameters being the experimental wear coefficients. To thatnd, the model did an adequate job of predicting the frictionoefficient at the slider/disk interface and the wear factor for theellet. The experimental results also demonstrated that an in situelf-replenishing solid/powder lubrication mechanism could beeveloped using a pellet-on-disk with slider pad configuration.
cknowledgements
The authors would like to thank Hooshang Heshmat, Ph.D.f Mohawk Innovative Technology Incorporated for develop-ng the tribometer and introducing the authors to the powderubrication mechanism. We would also like to thank the Pennsyl-ania Infrastructure Technology Alliance (PITA), the Philip &arsha Dowd Foundation, and the Institute for Complex Engi-
eering Systems at Carnegie Mellon University for supportinghis work. The members of the Particle Flow & Tribology Labo-atory (PFTL) engaged us in scholarly discussions on the modelor which we are appreciative.
eferences
UN
Please cite this article in press as: C.F. Higgs III, E.Y.A. Wornyoh, An in situand modeling, Wear (2007), doi:10.1016/j.wear.2007.03.026
[1] C.F. Higgs III, H. Heshmat, Characterization of pelletized MoS2 powderparticle detachment process, J. Tribol. 123 (2001) 455–461.
[2] R. Kaur, H. Heshmat, 100 mm Diameter self-contained solid/powder lubri-cated auxiliary bearing operated at 30,000 rpm, Lubricat. Eng. 58 (6) (2003)13–20.
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13] P.L. Dickrell, et al., A gas-surface interaction model for spatial and time-dependent friction coefficient in reciprocating contacts: applications tonear-frictionless carbon, J. Tribol. 127 (1) (2005) 82.
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15] P.L. Dickrell, W.G. Sawyer, A. Erdemir, Fractional coverage model for theadsorption and removal of gas species and application to superlow frictiondiamond-like carbon, J. Tribol. 126 (3) (2004) 615.
16] E.Y.A. Wornyoh, C.F. Higgs III, Self-replenishing, Self-repairing solidlubrication: modeling and experimentation, in: Proceedings of the WorldTribology Conference III, 2005.
17] S. Jahanmir, M. Beltzer, An adsorption model for friction in boundarylubrication, ASLE Trans. 29 (3) (1986) 423–430.
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