friction

FRICTION AND LUBRICATION REGIMES 1/40

FRICTION AND LUBRICATION REGIMESFRICTION AND LUBRICATION REGIMES

Socrates 2004

Porto, Portugal, May 2004

E. CiulliDipartimento di Ingegneria Meccanica, Nucleare e della

Produzione

University of PisaPisa - Italy


SUMMARYSUMMARY

1 STRIBECK AND LAMBDA CURVES1 STRIBECK AND LAMBDA CURVES

2 EXPERIMENTAL INVESTIGATION2 EXPERIMENTAL INVESTIGATION

3 FLUID FILM RESULTS3 FLUID FILM RESULTS

3.1 Nonconformal contacts 3.1 Nonconformal contacts

3.2 Conformal contacts3.2 Conformal contacts

3.3 Comparison with theory 3.3 Comparison with theory

44 MIXED AND BOUNDARY RESULTSMIXED AND BOUNDARY RESULTS

4.1 Experimental nonconformal data 4.1 Experimental nonconformal data

4.2 Wear and other problems4.2 Wear and other problems

4.3 Theoretical observations 4.3 Theoretical observations

55 CONCLUSIONSCONCLUSIONS


1 STRIBECK AND LAMBDA CURVES1 STRIBECK AND LAMBDA CURVES


1 STRIBECK AND LAMBDA CURVES

General considerations

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.



Lubrication regimes

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 () curves”.


Stribeck curve


Sommerfeld number

FF

fFF

fFT

f hh

ss

hs FFF

hhss FfFfT

fs friction coefficient in

boundary lubrication (Coulomb)

fh friction coefficient for full

lubricated conditionsF total load

Fs part of the total load carried

by the asperity contacts

Fh part of the total load carried

by the full lubricated zonesT total friction force

boundary lubrication

mixed lubrication

full fluid lubrication



Influence of some parameters under mixed lubrication


Altezza adimensionale del meato


Per avere bassi attrito e usura è importante che la coppia funzioni in regime di lubrificazione completa. Questo si verifica per un’altezza del meato sufficientemente grande rispetto alla rugosità superficiale.

Ai fini dell’efficacia della lubrificazione è pertanto più significativa un’altezza adimensionale del meato, indicata spesso con , funzione dello spessore del meato h e delle rugosità quadratiche medie delle superfici dei corpi a contatto, Rq1 e Rq2.

Il valore di per cui si ha il cambio di regime dipende dal tipo di accoppiamento lubrificato.

Valori indicativi sono comunque:

< 0.1 ÷ 1 lubrificazione limite

1 2 ÷ 5 lubrificazione mista

> 5 lubrificazione completa

22

21 qq RR

h

Meati con stessa altezza nominale h ma diverse rugosità e relativi valori di (indicativi)

>3 1



Inclusion of the effects of different surface roughness: curve

h

=(Rq12+ Rq2

2)0.5

1

F

uK

n

ml0


2 EXPERIMENTAL INVESTIGATION2 EXPERIMENTAL INVESTIGATION


2 EXPERIMENTAL WORKS

Experimental rig

specimens


2 EXPERIMENTAL WORKS

discs


3 FLUID FILM RESULTS3 FLUID FILM RESULTS


3.1 Nonconformal contacts 3.1 Nonconformal contacts


3 FLUID FILM RESULTS - 3.1 Nonconformal contacts

Test conditions – non conformal

contactslubricant: bis(2-ethylhexyl)phthalate (pure diester)

temperature: T = 30°C (10°C)

viscosity: 0 = 0.042 Pa s (0.138 Pa s)

pressure-viscosity coefficient: = 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



Friction coefficient for a spherical specimen against a glassglass disc for two lubricant

temperatures

glass disc D7Toil=10°C

0

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

f

S=0.25 S=0.5 S=1


0

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

f

S=0.25 S=0.5 S=1

(spherical specimens S4, with diameter =41.275 mm and roughness Rq=0.03 m)

=1 =3 =1 =3



Friction coefficient for a spherical specimen against steelsteel discs for two lubricant

temperatures

steel disc A10Toil=10°C

0

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

f

S=0.25 S=0.5 S=1


0

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

fS=0.25 S=0.5 S=1

(spherical specimens S4, with diameter =41.275 mm and roughness Rq=0.03 m)

=1 =1 =3



Friction coefficient for a cylindrical specimen against a glassglass disc

(cylindrical specimens C4, with diameter =42 mm and roughness Rq=0.14 m)


0

0,02

0,04

0,06

0,08

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

fS=0.25 S=0.5 S=1

glass disc D7

0

0,005

0,01

0,015

0,02

0,0 0,2 0,4 0,6 0,8 1,0u [m/s]

fS=0.5 - Toil=10°C

S=0.5 - Toil=30°C

=1 =3



Line contacts

Specimen Material E [N/m2] Rqa [m] Rqc [m]

C1 AISI 316 2.1·1011 0.30 0.045 0.015

C2 Aluminum 7.0·1010 0.33 0.330 0.030

C3 88 Mn V 8 2.1·1011 0.30 0.060 0.030

C5 K40 5.7·1011 0.22 0.035 0.015



Different specimens – same test conditions

Surface roughness of the cylindrical specimens



Lambda diagram


3.2 Conformal contacts 3.2 Conformal contacts


3 FLUID FILM RESULTS - 3.2 Conformal contacts

Test conditions – conformal contacts

lubricant: bis(2-ethylhexyl)phthalate (pure diester)

temperature: T = 20°C

viscosity: 0 = 0.075 Pa s

load: F = 10, 20, 30 N

speed: u = 0.05, 0.1, 0.15, 0.2, 0.3, 0.4 m/s


3 FLUID FILM RESULTS - 3.2 Conformal contacts

Friction coefficient for a tilting pad tested against a glass disc

0,00

0,01

0,02

0,03

0,04

0,0 0,1 0,2 0,3 0,4 0,5u [m/s]

f

20 N

30 N

10 N


3.3 Comparison with theory 3.3 Comparison with theory


3 FLUID FILM RESULTS - 3.3 Comparison with theory

Nonconformal contacts: friction coefficient formulas

Shu

p

ef

cm

pm0

SeE

R

F

u614.1f m

58.053.0

22.0

27.0

32.032.00 p

isothermal conditions Newtonian behaviour of the lubricant mean viscosity calculated introducing the

mean Hertzian contact pressure in the Barus formula

mean velocity gradient u/hc (with u=S·u sliding speed and hc central film thickness)

Hertzian contact area as a reference surface

Shue

52

arcsinhp

fc

p

0

00H

H

By introducing one of the most used formulas for hc

For Eyring fluids (Jacod-Venner-Lugt formula)

ASME Journal of Tribology, 123 (2001)


3 FLUID FILM RESULTS - 3.3 Comparison with theory Nonconformal contacts: experimental

friction coefficient compared with numerical results (Newtonian and Eyring

behaviour of the lubricant)

0,00

0,01

0,02

0,03

0,04

0 0,2 0,4 0,6 0,8 1u [m/s]

f

f exp (S=0.25) f New (S=0.25) f Eyr (S=0.25)

f exp (S=0.5) f New (S=0.5) f Eyr (S=0.5)

f exp (S=1) f New (S=1) f Eyr (S=1)


3 FLUID FILM RESULTS - 3.3 Comparison with theory

Conformal contacts: friction coefficient for a tilting pad against glass and steel discs

compared with numerical results

0,00

0,01

0,02

0,03

0,04

0,0E+00 2,0E-03 4,0E-03 6,0E-03 8,0E-03

(0 u L / F)0.5

fF=10N

F=20N

F=30N

numerical

5.05.0

5.05.00 L

F

uCf


4 MIXED AND BOUNDARY RESULTS4 MIXED AND BOUNDARY RESULTS


4.1 Experimental nonconformal 4.1 Experimental nonconformal data data


4 MIXED AND BOUNDARY RESULTS - 4.1 Experimental nonconformal data

Friction coefficient for the spherical specimen S4 against a steel disc at 30°C


0

0,04

0,08

0,12

0,16

0 0,2 0,4 0,6 0,8 1u [m/s]

fS=0.25 S=0.5 S=1

=1


4 MIXED AND BOUNDARY RESULTS - 4.1 Experimental nonconformal data

Comparison of friction trends for different specimens (S=0.5)

steel disc A9

0

0,04

0,08

0,12

0,16

0 1 2 3 4

f

S4 (spherical, 41.275 mm)

S3 (spherical, 24.606 mm)

R4 (cylindrical, 8 mm)

R2 (cylindrical, 4 mm)

steel disc A5

0

0,04

0,08

0,12

0,16

0,0 0,2 0,4 0,6 0,8 1,0

fS4

C4


4.2 Wear and other problems4.2 Wear and other problems


4 MIXED AND BOUNDARY RESULTS - 4.2 Wear and other problems

Evolutions of friction coefficient for two cylindrical specimens under mixed

conditions in presence of wear

steel disc A60

0,1

0,2

0,3

0,4

time

f

aluminium specimen C2

steel specimen C5

u=0.0125m/s u=0.025m/s u=0.05m/s u=0.075m/s u=0.1m/s u=0.2m/s

S =0,25 0,5 1

S =0,25 0,5 1

S =0,25 0,5 1

S =0,25 0,5 1

S =0,25 0,5 1

S =0,25 0,5 1


5 CONCLUSIONS5 CONCLUSIONS


Considerations on the friction trends

steel disc A8

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

u [m/s]

f

S=0.25 S=0.5 S=1

f increases by increasing S

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)

5 CONCLUSIONS

Specimen S4 against disc A8 (“Stribeck-like” curves)


5 CONCLUSIONS

Generalized lambda () diagram with lubrication regimes

destructive wear

predominantthermal effects

nonconformal

predominantturbulence effects

conformal


5 CONCLUSIONS

Final remarks

The evolutions of the friction coefficient, in particular for nonconformal contacts, can be very different from the one of the typical Stribeck or 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.


5 CONCLUSIONS

Friction coefficient in variable speed conditions

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 (S=0.25, 0.5, 1, left to right). Test frequency 0.1 Hz. The trend of the rolling speed is also shown on each diagram.

0 2 4 6 8 10

0

0.05

0.1

0.15

0.2

0.25

time [s]

S=0.25 - C4

u [m/s]

f * 10

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

u [m/s] f * 10

S=0.5 - C4

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3S=1 - C4

time [s]

u [m/s] f * 10

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

S=0.25 - S4

u [m/s]

f * 10

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3S=0.5 - S4

time [s]

u [m/s]

f * 10

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3

time [s]

f * 10

u [m/s]

S=1 - S4

spherical specimen

cylindrical specimen


5 CONCLUSIONSSummary of results under variable speed

conditions

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).

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle - 0.1 Hz - C4

u [m/s]

f

S=1

S=0.5S=0.25

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle - 0.5 Hz - C4

u [m/s]f

S=1

S=0.25 S=0.5

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle - 1 Hz - C4

u [m/s]

f

S=1

S=0.25 S=0.5

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle - 0.1 Hz -S4

u [m/s]

f

S=1

S=0.25

S=0.5

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle 0.5 Hz - S4

u [m/s]

f

S=0.5

S=1

S=0.25

0 0.05 0.1 0.15 0.2-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03mean cycle - 1 Hz - S4

u [m/s]

f

S=0.5

S=1

S=0.25

cylindrical specimen

spherical specimen



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 instead of the speed u

22

21 RqRq

h

U=u/(E’R), G=E’ , W=F/(tE’R), W=F/(E'R2), R specimen’s radius

lubricant viscosity - u rolling speed, (us+ud)/2 with ud and us surface speeds of disc and specimen E’=2[(1-s

2)/Es+(1-d2)/Ed]-1 compound elastic modulus (E and respectively Young and

Poisson moduli of the materials) - pressure-viscosity coefficient - F applied normal load - t axial width of the cylindrical specimen

RWGUh 13.054.07.065.2

h minimum film thickness, Rq root mean square roughness

line contacts

point contactsRWGUh 076.049.068.069.1


Numerical data

Specimen E' u [m/s] W U GHertzian half-width [mm]

Hertzian area

[mm^2]

Hertzian pressure [N/m 2̂] hmin [µm]

glass 1,21E+11 3,89E-07 1,68E-13 - 1,68E-11 2175 0,172 0,093 3,21E+08 0,01 - 0,22

steel 2,20E+11 2,14E+07 9,26E-14 - 9,26E-12 3955 0,141 0,063 4,79E+08 0,01 - 0,21

glass 1,21E+11 1,09E-06 2,83E-13 - 2,83E-11 2175 0,145 0,066 4,54E+08 0,01 - 0,17

steel 2,20E+11 6,01E-07 1,55E-13 - 1,55E-11 3955 0,119 0,044 6,76E+08 0,01 - 0,16

glass 1,21E+11 2,63E-06 1,65E-13 - 1,65E-11 2175 0,054 0,326 7,81E+07 0,02 - 0,53

steel 2,20E+11 1,44E-06 9,10E-14 - 9,10E-12 3955 0,04 0,242 1,05E+08 0,02 - 0,53

glass 1,21E+11 1,38E-05 8,69E-13 - 8,69E-11 2175 0,024 0,142 1,79E+08 0,01 - 0,26

steel 2,20E+11 7,58E-06 4,78E-13 - 4,78E-11 3955 0,018 0,105 2,42E+08 0,01 - 0,26

glass 1,21E+11 2,75833E-05 1,74E-12 - 6,95E-11 2175 0,017 0,101 2,53E+08 0,01 - 0,10

steel 2,20E+11 1,51667E-05 9,56E-13 - 3,82E-11 3955 0,012 0,075 3,41E+08 0,01 - 0,10

R2 0,01 - 0,4

0,01 - 1

0,01 - 1

0,01 - 1

0,01 - 1

S4

S3

C4

R4


Main characteristics of some specimens

S4 S3 C4 R4 R2

Material AISI 52100 AISI 52100 88MnV8 AISI 52100 AISI 52100

Diameter [mm]

41.275 24.606 42 8 4

Rq [m] 0.05 0.04 0.15 0.08 0.06

Hardness HRC

60-66* 60-66* 64 61 60

*Supplier’sdata


Main characteristics of some discs

D7 A8 A9 A5

Material Crown glass 38NCD4 38NCD4 AISI 316

Machining lapping fine grinding fine grinding grinding

Rq [m] 0.03 0.06 0.07 0.15

Hardness HV01 700 300 500 200


2 EXPERIMENTAL DETAILS

Stribeck curves for specimen C3 for different loads and temperatures


Rotational speed of specimen and disc for S=0 and S=1

S4 - frequenze provino e disco - S=0

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1 0,11 0,12 0,13 0,14 0,15 0,16 0,17 0,18 0,19 0,2

u [m/s]

f [1

/s]

wp [giri/s] - f

wd [giri/s] - f

S4 - frequenze provino e disco - S=1

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1 0,11 0,12 0,13 0,14 0,15 0,16 0,17 0,18 0,19 0,2

u [m/s]

f [1

/s]

wp [giri/s] - f

wd [giri/s] - f

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

t [s]

velo

city

[rp

m]

disc speed specimen speed

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

t [s]

velo

city

[rp

m]

disc speed specimen speed


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.

friction

Documents

mixed lubrication friction

different lubrication

lambda curves friction

friction coefficient

conclusions friction

qm friction

friction losses

fluid film results friction