FRICTION AND LUBRICATION REGIMES

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FRICTION AND LUBRICATION REGIMES
Socrates 2004
E. Ciulli Dipartimento di Ingegneria Meccanica,
Nucleare e della Produzione University of
Pisa Pisa - Italy
Porto, Portugal, May 2004
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SUMMARY

• 1 STRIBECK AND LAMBDA CURVES
• 2 EXPERIMENTAL INVESTIGATION
• 3 FLUID FILM RESULTS
• 3.1 Nonconformal contacts
• 3.2 Conformal contacts
• 3.3 Comparison with theory
• MIXED AND BOUNDARY RESULTS
• 4.1 Experimental nonconformal data
• 4.2 Wear and other problems
• 4.3 Theoretical observations
• CONCLUSIONS

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1 STRIBECK AND LAMBDA CURVES
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General considerations
1 STRIBECK AND LAMBDA CURVES

• Friction related problems are very important for
  engineering systems, in particular for a good
  design as regards elements life and energy
  savings.
• Friction losses can be measured directly on real
  machines, but a preliminary tribological
  research, experimental and/or theoretical, can be
  very useful for time and costs reduction.
• One of the most required data for design is the
  friction coefficient, also employed in simulation
  programmes useful to reduce the number of
  experimental tests.
• Unfortunately it is not always easy to find a
  realistic friction coefficient because there is a
  large number of variables (such as lubricant,
  velocity, load, geometry, roughness and
  materials) influencing its value.

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Lubrication regimes
1 STRIBECK AND LAMBDA CURVES

• The evolution of the friction coefficient is
  especially influenced by the parts of load
  supported by the lubricant and by the surface
  asperities of the solids, essentially depending
  on load, speed and lubricant viscosity values.
• Three different lubrication regimes, ranging from
  fluid-film to boundary, are usually considered
• fluid-film (or full fluid) lubrication
• mixed lubrication
• boundary lubrication
• Useful ways to represent the evolutions of the
  friction coefficient f, evidencing the transition
  between the different lubrication regimes, are
  the so-called Stribeck curves and lambda (L)
  curves.

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Stribeck curve
1 STRIBECK AND LAMBDA CURVES
boundary lubrication
mixed lubrication
full fluid lubrication
fs friction coefficient in boundary
lubrication (Coulomb) fh friction coefficient
for full lubricated conditions F total
load Fs part of the total load carried by
the asperity contacts Fh part of the total load
carried by the full lubricated zones T
total friction force
Sommerfeld number
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Influence of some parameters under mixed
lubrication
1 STRIBECK AND LAMBDA CURVES
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Altezza adimensionale del meato
1 STRIBECK AND LAMBDA CURVES

• Per avere bassi attrito e usura è importante che
  la coppia funzioni in regime di lubrificazione
  completa. Questo si verifica per unaltezza del
  meato sufficientemente grande rispetto alla
  rugosità superficiale.
• Ai fini dellefficacia della lubrificazione è
  pertanto più significativa unaltezza
  adimensionale del meato, indicata spesso con L,
  funzione dello spessore del meato h e delle
  rugosità quadratiche medie delle superfici dei
  corpi a contatto, Rq1 e Rq2.

Il valore di L per cui si ha il cambio di
regime dipende dal tipo di accoppiamento
lubrificato. Valori indicativi sono comunque Llt
0.1 1 lubrificazione limite 1 L 2 5
lubrificazione mista L gt 5
lubrificazione completa
Lgt3 L1
Meati con stessa altezza nominale h ma diverse
rugosità e relativi valori di L (indicativi)
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Inclusion of the effects of different surface
roughness L curve
1 STRIBECK AND LAMBDA CURVES
s(Rq12 Rq22)0.5
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2 EXPERIMENTAL INVESTIGATION
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Experimental rig
2 EXPERIMENTAL WORKS
specimens
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discs
2 EXPERIMENTAL WORKS
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3 FLUID FILM RESULTS
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3.1 Nonconformal contacts
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Test conditions non conformal contacts
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
lubricant bis(2-ethylhexyl)phthalate
(pure diester) temperature T 30C
(10C) viscosity h0 0.042 Pa s
(0.138 Pa s) pressure-viscosity coefficient a
1.8? 10-8 Pa-1 load F 20
N rolling speed u (us ud)/2
0.01, 0.0125, 0.02, 0.025, 0.03, 0.04,
0.05, 0.06, 0.075, 0.08, 0.1, 0.2, 0.4,
0.6, 0.8, 1 m/s slide-to-roll ratio S
(us - ud)/u 0, 0.25, 0.5, 1
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Friction coefficient for a spherical specimen
against a glass disc for two lubricant
temperatures
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
L1
L3
L1
L3
(spherical specimens S4, with diameter F41.275
mm and roughness Rq0.03 mm)
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Friction coefficient for a spherical specimen
against steel discs for two lubricant temperatures
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
L1
L1
L3
(spherical specimens S4, with diameter F41.275
mm and roughness Rq0.03 mm)
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Friction coefficient for a cylindrical specimen
against a glass disc
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
L1
L3
(cylindrical specimens C4, with diameter F42 mm
and roughness Rq0.14 mm)
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Line contacts
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
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Different specimens same test conditions
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
Surface roughness of the cylindrical specimens
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Lambda diagram
3 FLUID FILM RESULTS - 3.1 Nonconformal
contacts
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3.2 Conformal contacts
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Test conditions conformal contacts
3 FLUID FILM RESULTS - 3.2 Conformal contacts
lubricant bis(2-ethylhexyl)phthalate
(pure diester) temperature T
20C viscosity h0 0.075 Pa s load
F 10, 20, 30 N speed
Du 0.05, 0.1, 0.15, 0.2, 0.3, 0.4 m/s
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Friction coefficient for a tilting pad tested
against a glass disc
3 FLUID FILM RESULTS - 3.2 Conformal contacts
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3.3 Comparison with theory
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Nonconformal contacts friction coefficient
formulas
3 FLUID FILM RESULTS - 3.3 Comparison with
theory

• isothermal conditions
• Newtonian behaviour of the lubricant
• mean viscosity calculated introducing the mean
  Hertzian contact pressure in the Barus formula
• mean velocity gradient Du/hc (with DuSu sliding
  speed and hc central film thickness)
• Hertzian contact area as a reference surface

By introducing one of the most used formulas for
hc
For Eyring fluids (Jacod-Venner-Lugt formula)
ASME Journal of Tribology, 123 (2001)
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Nonconformal contacts experimental friction
coefficient compared with numerical results
(Newtonian and Eyring behaviour of the lubricant)
3 FLUID FILM RESULTS - 3.3 Comparison with
theory
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Conformal contacts friction coefficient for a
tilting pad against glass and steel discs
compared with numerical results
3 FLUID FILM RESULTS - 3.3 Comparison with
theory
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4 MIXED AND BOUNDARY RESULTS
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4.1 Experimental nonconformal data
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Friction coefficient for the spherical specimen
S4 against a steel disc at 30C
4 MIXED AND BOUNDARY RESULTS - 4.1
Experimental nonconformal data
L1
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Comparison of friction trends for different
specimens (S0.5)
4 MIXED AND BOUNDARY RESULTS - 4.1
Experimental nonconformal data
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4.2 Wear and other problems
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Evolutions of friction coefficient for two
cylindrical specimens under mixed conditions in
presence of wear
4 MIXED AND BOUNDARY RESULTS - 4.2 Wear and
other problems
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5 CONCLUSIONS
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Considerations on the friction trends
5 CONCLUSIONS
Differences between values of f measured for the
different S decrease by decreasing u at low
speeds (when boundary lubrication
approaches)
and by increasing u at high speeds (when thermal
effects for the highest values of S become more
significant)
f increases by increasing S
Specimen S4 against disc A8 (Stribeck-like
curves)
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Generalized lambda (L) diagram with lubrication
regimes
5 CONCLUSIONS
destructive wear
predominant turbulence effects
conformal
predominant thermal effects
nonconformal
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Final remarks
5 CONCLUSIONS

• The evolutions of the friction coefficient, in
  particular for nonconformal contacts, can be very
  different from the one of the typical Stribeck or
  L diagram. Many variables such as shape and
  dimension of the lubricated contact, roughness,
  materials, characteristics of the lubricant and
  thermal effects influence the friction trends.

• Many lubricated pairs of the most common machines
  do not work under steady-state but under
  transient conditions. Stationary results can be
  extended to real conditions only with a certain
  degree of approximation.

• Investigation under transient conditions show the
  presence of a loop on the Stribeck diagram.

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Friction coefficient in variable speed conditions
5 CONCLUSIONS
cylindrical specimen
 

spherical specimen
f (multiplied by 10) as a function of time for
specimen C4 (top) and S4 (bottom) for three
values of the slide-to-roll ratio S (S0.25, 0.5,
1, left to right). Test frequency 0.1 Hz. The
trend of the rolling speed is also shown on each
diagram.
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Summary of results under variable speed conditions
5 CONCLUSIONS
cylindrical specimen
spherical specimen
Filtered values of the friction coefficient f as
a function of the rolling speed u for three
values of the slide-to-roll ratio S and three
values of the test frequency (0.1, 0.5 and 1 Hz,
from left to right).
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Formulas for Lambda ratio and minimum film
thickness
To limit the influence of the differences of
roughness that, even low, can play an important
role at the very low speeds, f can be plotted as
a function of the dimensionless film thickness L
instead of the speed u
h minimum film thickness, Rq root mean square
roughness
line contacts
point contacts
Umu/(ER), GaE , WF/(tER), WF/(E'R2), R
specimens radius m lubricant viscosity - u
rolling speed, (usud)/2 with ud and us surface
speeds of disc and specimen
E2(1-ns2)/Es(1-nd2)/Ed-1 compound elastic
modulus (E and n respectively Young and Poisson
moduli of the materials) - a pressure-viscosity
coefficient - F applied normal load - t axial
width of the cylindrical specimen
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Numerical data
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Main characteristics of some specimens
Suppliers
data
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Main characteristics of some discs
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Stribeck curves for specimen C3 for different
loads and temperatures
2 EXPERIMENTAL DETAILS
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Rotational speed of specimen and disc for S0 and
S1
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Some references

• R. Bassani, E. Ciulli, B. Piccigallo,
  "Theoretical and experimental results on friction
  for line contacts in mixed and elastohydrodynamics
  lubrication regimes", in Lubrication at the
  frontier The role of the interface and surface
  layers in the thin film and boundary regime,
  Proceedings of the 25th Leeds-Lyon Symposium on
  Tribology, Lyon, F, 8th-11th September 1998,
  Elsevier, Amsterdam, pp.215-222, 1999.
• R. Bassani, E. Ciulli, "Friction in boundary and
  mixed lubricated line contacts with different
  roughness", in Thinning films and tribological
  interfaces, Proceedings of the 26th Leeds-Lyon
  Symposium on Tribology, Leeds, UK, 14th-17th
  September 1999, Elsevier, Amsterdam, pp.759-768,
  2000.
• E. Ciulli, Friction in lubricated contacts
  from macro- to microscale effects, in
  Fundamentals of Tribology and Bridging the Gap
  Between the Macro-and Micro/Nanoscales, NATO
  Sciences Series, Kluwer Academic Publishers,
  Dordrecht, The Netherlands, ISBN 0-7923-6837-1,
  2001, pp. 725-734.
• R. Bassani, E. Ciulli, "Experimental evaluation
  of shape effects on friction in lubricated
  nonconformal contacts", in Tribology research
  from model experiment to industrial problem,
  Proceedings of the 27th Leeds-Lyon Symposium on
  Tribology, Lyon, France, 5th-8th September 2000,
  Elsevier, Amsterdam, pp.403-414, 2001.
• R. Bassani, E. Ciulli, Friction from fluid-film
  to boundary lubricated conditions, Invited paper
  al 29th Leeds-Lyon Symposium on Tribology, in
  Tribological research and design for engineering
  systems, Proceedings of the 29th Leeds-Lyon
  Symposium on Tribology, Leeds, UK, 3-6 September
  2002, Elsevier, Amsterdam, pp.821-834, 2003, ISBN
  0-444-51243-8.