- Email: [email protected]
The relationship between lubricant shear strength and chemical composition of the base oil
Wear, 130 (1989)
213 - 224
213
THE RELATIONSHIP BETWEEN LUBRICANT SHEAR STRENGTH AND CHEMICAL COMPOSITION OF THE BASE OIL* ERIK HdGLUND Division
of Machine Elements,
Lule8 University
of Technology,
S-951 87 Lule8 (Sweden)
Summary A new method for the experimental evaluation of the shear strength of lubricants at high pressures and temperatures is presented. The main parts of the experimental apparatus are a lubricated sintered-carbide surface and an impacting steel ball. A picture-processing system is used to examine the ball trajectory after impact and to calculate the limiting shear strengthpressure coefficient of the lubricant. Using this apparatus the influence of the chemical composition of the base oil on the limiting shear strengthpressure coefficient has been investigated. It was found that the chemical structure of the oil is of major importance in determining the shear strength. Additives have no significant effect on the shear strength.
1. Introduction Lubricant rheology is of great importance when oil film thickness or traction properties in an elastohydrodynamically lubricated (EHL) contact must be calculated. Simple relationships between viscosity, or density, and pressure and temperature are often accurate enough to calculate the minimum or central oil film thickness. Among expressions of this kind are Newton’s equation [l] du r=qdy or the Bar-us-type equation [ 21 rl = go exp{o@
--PO)
--PV
-
To))
For density, the expression 0.6~ 1+ 1.7p
1
given by Dowson and Higginson [3] is used. *Paper presented at the Nordic Symposium June 26 - 29,1988. 0043-1648/89/$3.50
on Trihology,
Trondheim,
@ Elsevier Sequoia/Printed
Norway,
in The Netherlands
1
shear
Fig. 1. Relationship
strain
rate
between
shear stress and shear strain rate at different
pressures.
The reason why these equations are accurate enough is that the film thickness is mainly determined by what happens in the inlet region, where the pressure is relatively low. The traction properties, in contrast, are mainly determined by what happens in the high pressure region, and therefore the lubricant properties must be known at the high pressures and temperatures that prevail there. Using the aforementioned equations will lead to traction forces, given by the shear stresses according to Newton’s equation, that are unrealistic. As an example, the shear stress given by Newton’s ,equation for a normal lubricating oil will exceed 2 X lOi Pa with q. = 0.01 Pa s, (Y= 2 X 10F8 Pa-‘, du/ dy = 1 m s-l and p -p. = 2 GPa, which are all quite realistic values. Clearly, the oil cannot withstand such a high shear stress, and so there will be slip between the oil and one of the surfaces or possibly slip inside the oil film. Which of these takes place is determined by surface tension and surface energy. New and more accurate equations must therefore be used to describe lubricants under rapid and large pressure variations, short transit times and high shear rates. A typical shear stress-shear strain-rate curve. for a lubricating oil is shown in Fig. 1. Several authors [4 - 71 have tried to describe this behaviour by equations using strain rates, fluid shear modulus, viscosity etc., thereby modelling the linear elastic, nonlinear viscous and plastic behaviour of the lubricant. A condensed version of the different theories can be found in the book by Hamrock and Dowson [8]. One important factor in these theories is the limiting shear stress rL that an oil can sustain. If this stress is exceeded in the contact, slippage will occur. The limiting shear stress depends on the applied pressure, thus 7L
=To+YP
(1)
y is a property of the lubricant in the same way as viscosity or density and has been measured by, for example, Bair and Winer [9] and Hoglund and Jacobson [lo]. The investigation by Bair and Winer covered the range -27 “C!to 40 “C and pressures up to 1.2 GPa. They found values of y in the range 0.05 - 0.1. Hoglund and Jacobson used a high-pressure quasistatic
215
Fig. 2. Test apparatus.
apparatus in the range 20 - 200 “C and pressures of 0 - 2.2 GPa. The experiments showed that the range of y could be extended to 0.02 - 0.15. r0 has been measured by Jacobson [ 111 and is of the order 1 - 5 MPa. Jacobson [ 111 later built an apparatus where the value of y could be measured at even higher pressures, up to 5 - 7 GPa. The principle of the apparatus can be seen in Fig. 2. A steel ball, with a hardness of 62 HRC and a surface roughness of 0.04 pm r.m.s., is dropped against a flat surface made of sintered carbide. The surface hardness of the sintered carbide is 1500 HV3 and the roughness 0.05 pm. A sample of the oil to be tested is placed on the flat surface. The impacting ball is guided by guide bars and the inclination of the impacting ball can be changed. The ball is painted black and white, except at the point of impact, to make it more visible for the picture-processing system. After impact the ball has a vertical, a horizontal and a rotational speed. In the Jacobson apparatus, the horizontal speed was measured by using a small trolley on which the ball was made to land. However, several problems arose from using this trolley, the main one being that it was very difficult to measure small differences in horizontal forces while the vertical force, from the impact, was very large. In this paper a new idea for measuring the speeds after impact is presented. The values can then be used to calculate y. The principle is picture-processing which is a non-contact method for measuring events. This way of determining y has been applied to different lubricants in order to determine how different additives and chemical structures affect the y-value. Since the limiting shear stress is directly proportional to y, low y-values will give low friction forces at the surfaces of the mating bodies, and thus reduce energy losses and subsurface stresses (see Hoglund [12]). 2. Theory The theory used to evaluate y has been described at length by Jacobson [ll]. However, he neglected the energy dissipation during impact, an assumption which is not made in this paper.
Fig. 3. Speeds and forces for the ball, from Jacobson
[ 111
The forces acting on the ball during impact are shown in Fig. 3. The pressure and shear stress distributions in the impact zone are replaced by forces since the contact point is very small. Equilibrium gives $pdA-mg=mj;
(2)
srdA=-mjt
(3)
RsrdA=J&
(4)
The following assumptions are made: To<< YP in eqn.
(l),
owing
to
the very high pressures that exist in an EHL contact
Equations (1) - (3) together with these assumptions then give Tj; = j; Integrating gives 7y+c,
=4
(5)
The initial conditions are .
x = V,,
before impact and z? = Vh before impact and j, = eV,,
j, = -V,,
after impact after impact
where e is the coefficient of restitution. Equation (5) and the starting conditions give v,, -
vh
(6)
Y= Vdl
+e)
If there is pure rolling at the end of impact w =0
before impact
9 = -V,,
217 vh
w = R
after impact
Together
j, = eV,,
with eqn. (4) and putting
2mR *
J=
-
5 this gives v h
= 5%,(1+ 2
e)
(7)
This means that the sliding motion of the ball on impact will turn into pure rolling at the end of impact because of the friction in the oil film, Equation (7) can be rewritten as ,2v, Y=
5V”,(l
2wRe + e) = 5eV,,(l
The vertical speed after impact eV,, eV,, = (2gh)“*
(8)
+ e) can be written
as (9)
Thus 2wRe ’ = 5{2gh(l
+ e)} “*
(10)
By determining the values of w, h and e, y can be calculated. The condition of pure rolling at the end of impact is tested by calCdating the difference vh - oR. If this is equal to zero pure rolling exists; if this is not the case, the attitude angle of the guide bars is changed until the difference is zero.
3. Measuring system The main parts of the system for monitoring the ball trajectory after impact are a CCD camera, a flash unit, a PC with a floating point processor, a digitizing card (framegrabber) and a TV monitor (see Fig. 4). After impact two or three pictures are taken using the flash unit and the CCD camera. The reason for using such a camera is the almost negligible geometrical distortion of the picture. However, there is still some optical distortion from the zoom-lens of the camera. The flash unit is used to “freeze” the event in different positions after impact. It is a quite common electronic flash, and can be used for multiple flashes by not using full power. The time between successive flashes is about l/10 s. The exact time is calculated by using the internal clock in the PC. The whole picture-processing unit is triggered by an optical gauge. As the sledge, on which the ball lies, passes the gauge, an electrical signal is created which initiates the PC program. The program then fires the flash at
218
OIGI7L’O i P'CTLIHEOF BALL ROTAT~ON4L WEE@ HEIGHT
~
Fig. 4. Picture-processing
system.
given times, and the picture is read into the memory of the framegrabbercard. Each picture is given a sign showing the time for identification. When all the pictures have been read into the frame-grabber-card, the picture analysis starts. A framegrabber-card must be used to digitize the pictures from the camera in order for the computer to analyse them. The card is especially made for picture-processing on a PC. The digitized picture is formed by a number of cells called pixels. Four separate pictures can be stored simultaneously in the memory of the framegrabber-card. The pictures can also be displayed on a monitor by using the video output on the card. A horizontal piece of string is used as a reference for the coordinatesystem of the framegrabber-card. The string has a 300 mm white part and the rest of it is black. The level of the string corresponds to the centre of the ball at impact. It is also used to compensate for any possible camera tilt and to calculate the length corresponding to each pixel in the digitized picture. The reference string, giving the zero-level of the impacting ball, is identified using the first picture. The coordinates of the string are determined, and a new line is fitted to the coordinates of the string using a leastsquares method. The tilt of the camera is determined by comparing the slope of the calculated line and the actual horizontal string. After this, the ball is identified and a suitable area around the ball is used in the calculations which follow. Only the white part of the ball is seen by the camera since the rest of it is black like the background. The contour of the white half-moon-shaped area is detected and the coordinates of the circular arc and the straight line are stored in the memory. Linear regression is used to calculate the angular displacement of the ball. A line is fitted to the straight part of the half-moon-shaped area, and the slope of this line is used to calculate the angle relative to the horizontal line.
219
In order to calculate the ball trajectory after impact, a parabola is fitted to the centre of the ball in the different positions. The centre of the ball is identified by fitting a circle to the coordinates of the circular part of the half-moon. The centre of this new circle is identified as the ball centre. Knowing the angular displacement and height of the ball in each picture and also the time between the pictures, the angular speed and maximum height of the ball can be calculated. Finally, the vertical speed after impact is calculated using eqn. (9), and by comparing this with the velocity before impact Vvo, the coefficient of restitution e is calculated. Equation (10) then gives the value of y.
4. Accuracy
of the method
By testing the whole equipment against known values of angular displacement and height, the accuracy was found to be within kO.5” for angular displacement and within &0.5% of the height. The accuracy depends on the resolution between the pixels in the digitized picture.
5. Oils tested 23 oils of different types have been tested (see Table 1). All the tests were performed at room temperature, i.e. 20 “C. Oils nos. 1 - 4 are polya-olefines which have a very uniform chemical composition and are best characterized by their viscosities. Oils nos. 5 - 7 are esters of different types: no. 5 is a triisotridecyladipate, which is a type of diester with a high viscosity index (VI) and good coldclimate characteristics but which is rather sensitive to pollution by water; no. 6 is a polyolic ester, which is very stable to water and high temperatures; no. 7 is a type of diester which is more branchy than no. 5, and which cannot be directly compared with nos. 5 and 6 by just looking at the viscosities. Nos. 8 - 10 are solvent-refined naphthenic oils, i.e. aromatic and polar compounds are removed. They have branched molecules of different sizes giving good low temperature behaviour, and can be directly compared using the viscosities. Nos. 11 - 13 are solvent-refined paraffinic oils, which are produced in the same kind of way as oils nos. 8 - 10 and which are about as heavily refined. The molecules are long, and so there is a risk of crystallisation at low temperatures. The results can be compared with those for the naphthenic oils nos. 8 - 10 of comparable viscosity. No. 14 is also a paraffinic oil, but is hydrocracked instead of solventrefined and the results are thus not comparable with those of nos. 11 - 13. Oils nos. 15 - 20 are made from one base oil, a synthetic base made from a poly-cr-olefine and polyolic ester like that in oil no. 6, with different
Type
Poly-o-olefine (PAO) Poly-CYolefine Polyaolefine PolyXrolefine Triisotridecyladipate ester Polyolic ester Diester Naphthenic/solvent-refined Naphthenic/solvent-refined Naphthenic/solvent-refined Paraffinic/solvent-refined Paraffinic/solvent-refined Paraffiniclsolvent-refined Paraffinic hydrocracked PA0 with polyolic ester No. 15 with 1% antioxidant No. 15 with 0.5% antiwear No. 15 with 0.5% antiwear No. 15 with 0.1% corrosion inhibitor No. 15 with 0.01% passivator PA0 with different additives PA0 with seal-swell and borate additives PA0 with polyolic ester borate antiwear and anticorrosion additives
Lubricant
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Test lubricant types and corresponding values of ‘y
TABLE I
28.2 17.8 425.2 1170.7 26.0 22.6 14.8 100.8 24.7 7.6 464.4 89.8 30.3 24.4 162.7 161.5 160.5 162.6 162.2 161.8 140.4 146.4 155.6
880.7
40°C
Viscosity (mm* s-l )
825.8 820.8 819.6 852.0 913.8 991.5 906.4 911.9 895.1 877.2 900.3 884.3 870.8 841.0 854.3 856.6 856.7 855.0 855.6 855.3 847.0 869.7
Density
20.0
5.46 3.93 41.0 100.1 5.17 4.79 3.76 8.6 3.95 2.04 30.4 10.3 5.22 5.07 20.9 20.8 20.7 20.8 21.0 20.9 18.8 19.1
100°C
0.0434/0.00084 0.0439/0.00060 0.0328/0.00082 0.0315/0.0012 0.0541/0.00023 0.0459/0.00074 0.0452/0.00055 0.0497/0.00061 0.0610/0.00069 0.0628/0.0011 0.0374/0.00038 0.0462/0.00073 0.0532/0.00054 0.0460/0.00084 0.0375/0.00061 0.0372/0.00023 0.0372/0.00041 0.0369/0.00086 0.0371/0.00089 0.0377/0.00066 0.0378/0.00030 0.0388/0.00060 0.0380/0.00090 149
y mean value/ standard deviation
133 116 147 175 132 137 150 28 1 41 95 95 102 140 151 151 151 150 153 152 151 148
VI
,” 0
221
additives. No. 15 is the pure base oil; no. 16 contains 1% ~tioxidant; no. 17, 0.5% antiwear additive; no. 18, 0.5% of an antiwear additive different from that in no. 17; no. 19, 0.1% anti-corrosion additive and finally no. 20 contains 0.01% passivator. Oil no. 21 is based on poly-cll-olefine and contains antioxidant, metal passivator, EP-additives, antifoam and seal-swell additives. The seal-swell additive is of a non-ester type. This oil can be regarded as fully formulated. Oil no. 22 is also based on polyaolefine but here only seal-swell and 12% borate additives are present. The seal-swell additive is the same as that in oil no. 21. Oil no. 23, finally, is a blend of polya-olefine with a polyolic ester like oil no. 6. 12% borate, 1% antioxidant and 0.1% corrosion inhibitor additives are added. The ball and flat sintered carbide surfaces were thoroughly cleaned with toluene and acetone between each test and the next. 6. Results The tests were performed at room temperature and a nominal pressure of 5.0 GPa, i.e. well above the solidification limit at room temperature (see also Hoglund and Jacobson [lo]). The impact time was about 60 ps. The thickness of the oil film was less than 0.5 mm before impact. It was also checked that the metal surfaces did not come into contact, by measuring the electrical resistance between the ball and the sintered carbide surface. Each oil was tested at least 7 times in order to obtain a representative mean value. The mean values of 7 can be found in Table 1, together with the corresponding values of the standard deviation. In Figs. 5 and 6 the y-values are plotted as a function of viscosity for the different types of oil. From this the following conclusions can be drawn. Poly-o-olefines, nos. 1 - 4, have relatively low y-values, and the higher the viscosity, the lower the r-value. The ester-type oils, nos. 5 - 7, have higher y-values than poly-o-olefines. The ester based on ~i~o~idecy~dipate has a s~ificantly higher r-value than the two other esters. It must be remembered that the esters are quite different and cannot be compared using their viscosity values. Oils nos. 8 - 10, naphthenic-based, have higher r-values than poly-CColefines and esters, except for oil no. 8. They can be compared relative to each other by looking at the viscosity, and the same result is found as for oils no. 1 - 4, i.e. the higher the viscosity, the lower the r-value. The paraffinic oils nos. 11 - 14 cover the range 0.0375 - 0.053 in y. Oil no. 14 is different from the rest since it is produced in a different way, namely by hydrocracking. Nos. 11 - 13 can be compared with the naphthenic oils, nos. 8 - 10, of the same viscosity. Thus it can be concluded that paraffinic oils have somewhat lower y-values than naphthenic oils. Higher viscosities also give lower y-values.
222
I___..r__
0.065
,
~_ _ ~~_/_,_~~_~~~~~r~
rlo
i
naphtenic-base esters 0: paraffinic-base x: polyalphaolefines
+:
+---_.9
*:
+\
0 OF ;
'.\
I 0.055
5.
‘\,
\
13
L
\
ICY
0 05
0.045
0 01
u.035
!
6'i 7*-'614 1---x 2 l',
\
\
12 O\
t /
as a function
\ '1.
-1
'\ \
.
15-23
.<
'..:'
.\ ‘\
0 see
‘x-_
Fig. 6 1
_
3
-_
,
4
~~~~~__1..~.
10’
103
102
Fig. 5. y-value
a
+
'\
__.i_LI
0.03 10’
0.0384
‘1
l\
viscosity [mmz/sl
of viscosity
and type of oil.
\
/'
0.0382 '2' 0.0380 -
1.23 \ \ \
\ \ \
0.0378 0.0376 -
20
\
i /I \ ;I \ \/'l;
'4 lr/19 ; 17 16 ,
0.0374-
\
0.0372 400
15 ,;;
118 410
420
430
440
450
460
470
/ 480
viscosity [mm2/sl
Fig. 6. y-value as a function
of viscosity
for oils nos. 15 - 23.
Finally, oils nos. 15 - 23 all give about the same r-value despite the different additives. The value is about the same as for poly-cr-olefines, nos. 1 - 4, of the corresponding viscosity. The properties of the base oil are obviously the most important in determining 7, and the different additives do not affect this value in any significant way.
223
7. Conclusions The shear strength of a lubricating oil, represented by the y-value, is mainly determined by the chemical structure of the base oil. Additives have only a slight influence on the -y-value. Of the five types of oils tested, polycr-olefines have the lowest y-value. Paraffinic oils, esters and naphthenic oils have gradually increasing values of y. It is however also important to know the specific type of, say, ester since they are individually different, giving different y-values. Molecular size is also important. It is obvious that for all the types of oils tested, a high viscosity, i.e. large molecules, will give low y-values.
Acknowledgments The author would like to thank Mr Sten-Ivar Bergstrom of the Lule% University of Technology for great help with the experiments and Mr Per Redelius and Mr Bertil Eriksson, Nynas Industri AB, for helpful discussions and for supplying the oils.
References 1 I. Newton, Philosophiae Natumlis Principia Mathematics, Imprimatur S. Pepys, Regiae Societatis Praeses, 5 Julii 1686, 4to Londini 1687. 2 C. Barus, Isotherms, isopiestics and isometrics relative to viscosity, Am. J. Sci., 45 (1893) 87 - 96. 3 D. Dowson and G. R. Higginson, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication, Pergamon, Oxford, 1966. 4 E. G. Trachman and H. S. Cheng, Thermal and non-newtonian effects on traction in elastohydrodynamic contacts, Proc. 2nd Symp. on Elastohydrodynamic Lubrication, Institution of Mechanical Engineers, London, 1972, pp. 142 - 148. 5 W. Hirst and A. J. Moore, Non-newtonian behavior in elastohydrodynamic lubrication,Proc. R. Sot. London, Ser. A, 337 (1974) 101 - 121. 6 K. L. Johnson and J. L. Tevaarwerk, Shear behaviour of elastohydrodynamic oil films, Proc. R. Sot. London, Ser. A, 356 (1977) 215 - 236. 7 S. Bair and W. 0. Winer, A rheological model of elastohydrodynamic contacts based on primary laboratory data, Trans. ASME, 101 (1979) 258 - 265. 8 B. J. Hamrock and D. Dowson, Ball Bearing Lubrication, Wiley, New York, 1981, pp. 269 - 275. 9 S. Bair and W. 0. Winer, Shear strength measurements of lubricants at high pressure, J. Lubr. Technol., 101 (1979) 251 - 257. 10 E. Hoglund and B. Jacobson, Experimental investigation of the shear strength of lubricants subjected to high pressure and temperature, J. Tribol., 108 (1986) 571 - 578. 11 B. Jacobson, A high pressure-short time shear strength analyzer for lubricants, J. Tribol., 107 (1985) 221 - 223. 12 E. Hbglund, Subsurface stresses in a lubricated rolling/sliding elastohydrodynamic line contact considering limited shear strength of the lubricant, Proc. 12th Leeds-Lyon Symp. on Tribology, 1985, pp. 163 - 170.
224
Appendix A: Nomenclature coefficient of restitution
FI maximum height of ball after impact (m) J
m P R T u V
moment of inertia (kg m2) mass of ball (kg) pressure (Pa) ball radius, 0.050 m temperature (“C!) velocity (m s-l) velocity (m s-l)
Greek symbols pressure-viscosity coefficient (Pa-‘) F temperature-viscosity coefficient (“C’) limiting shear stress-pressure coefficient Y 17 dynamic viscosity (Pa s) density (kg mw3) P 7 shear stress (Pa) 0 rotational speed (s-l) Subscripts 0 reference value h horizontal L limiting value V vertical
213 - 224
213
THE RELATIONSHIP BETWEEN LUBRICANT SHEAR STRENGTH AND CHEMICAL COMPOSITION OF THE BASE OIL* ERIK HdGLUND Division
of Machine Elements,
Lule8 University
of Technology,
S-951 87 Lule8 (Sweden)
Summary A new method for the experimental evaluation of the shear strength of lubricants at high pressures and temperatures is presented. The main parts of the experimental apparatus are a lubricated sintered-carbide surface and an impacting steel ball. A picture-processing system is used to examine the ball trajectory after impact and to calculate the limiting shear strengthpressure coefficient of the lubricant. Using this apparatus the influence of the chemical composition of the base oil on the limiting shear strengthpressure coefficient has been investigated. It was found that the chemical structure of the oil is of major importance in determining the shear strength. Additives have no significant effect on the shear strength.
1. Introduction Lubricant rheology is of great importance when oil film thickness or traction properties in an elastohydrodynamically lubricated (EHL) contact must be calculated. Simple relationships between viscosity, or density, and pressure and temperature are often accurate enough to calculate the minimum or central oil film thickness. Among expressions of this kind are Newton’s equation [l] du r=qdy or the Bar-us-type equation [ 21 rl = go exp{o@
--PO)
--PV
-
To))
For density, the expression 0.6~ 1+ 1.7p
1
given by Dowson and Higginson [3] is used. *Paper presented at the Nordic Symposium June 26 - 29,1988. 0043-1648/89/$3.50
on Trihology,
Trondheim,
@ Elsevier Sequoia/Printed
Norway,
in The Netherlands
1
shear
Fig. 1. Relationship
strain
rate
between
shear stress and shear strain rate at different
pressures.
The reason why these equations are accurate enough is that the film thickness is mainly determined by what happens in the inlet region, where the pressure is relatively low. The traction properties, in contrast, are mainly determined by what happens in the high pressure region, and therefore the lubricant properties must be known at the high pressures and temperatures that prevail there. Using the aforementioned equations will lead to traction forces, given by the shear stresses according to Newton’s equation, that are unrealistic. As an example, the shear stress given by Newton’s ,equation for a normal lubricating oil will exceed 2 X lOi Pa with q. = 0.01 Pa s, (Y= 2 X 10F8 Pa-‘, du/ dy = 1 m s-l and p -p. = 2 GPa, which are all quite realistic values. Clearly, the oil cannot withstand such a high shear stress, and so there will be slip between the oil and one of the surfaces or possibly slip inside the oil film. Which of these takes place is determined by surface tension and surface energy. New and more accurate equations must therefore be used to describe lubricants under rapid and large pressure variations, short transit times and high shear rates. A typical shear stress-shear strain-rate curve. for a lubricating oil is shown in Fig. 1. Several authors [4 - 71 have tried to describe this behaviour by equations using strain rates, fluid shear modulus, viscosity etc., thereby modelling the linear elastic, nonlinear viscous and plastic behaviour of the lubricant. A condensed version of the different theories can be found in the book by Hamrock and Dowson [8]. One important factor in these theories is the limiting shear stress rL that an oil can sustain. If this stress is exceeded in the contact, slippage will occur. The limiting shear stress depends on the applied pressure, thus 7L
=To+YP
(1)
y is a property of the lubricant in the same way as viscosity or density and has been measured by, for example, Bair and Winer [9] and Hoglund and Jacobson [lo]. The investigation by Bair and Winer covered the range -27 “C!to 40 “C and pressures up to 1.2 GPa. They found values of y in the range 0.05 - 0.1. Hoglund and Jacobson used a high-pressure quasistatic
215
Fig. 2. Test apparatus.
apparatus in the range 20 - 200 “C and pressures of 0 - 2.2 GPa. The experiments showed that the range of y could be extended to 0.02 - 0.15. r0 has been measured by Jacobson [ 111 and is of the order 1 - 5 MPa. Jacobson [ 111 later built an apparatus where the value of y could be measured at even higher pressures, up to 5 - 7 GPa. The principle of the apparatus can be seen in Fig. 2. A steel ball, with a hardness of 62 HRC and a surface roughness of 0.04 pm r.m.s., is dropped against a flat surface made of sintered carbide. The surface hardness of the sintered carbide is 1500 HV3 and the roughness 0.05 pm. A sample of the oil to be tested is placed on the flat surface. The impacting ball is guided by guide bars and the inclination of the impacting ball can be changed. The ball is painted black and white, except at the point of impact, to make it more visible for the picture-processing system. After impact the ball has a vertical, a horizontal and a rotational speed. In the Jacobson apparatus, the horizontal speed was measured by using a small trolley on which the ball was made to land. However, several problems arose from using this trolley, the main one being that it was very difficult to measure small differences in horizontal forces while the vertical force, from the impact, was very large. In this paper a new idea for measuring the speeds after impact is presented. The values can then be used to calculate y. The principle is picture-processing which is a non-contact method for measuring events. This way of determining y has been applied to different lubricants in order to determine how different additives and chemical structures affect the y-value. Since the limiting shear stress is directly proportional to y, low y-values will give low friction forces at the surfaces of the mating bodies, and thus reduce energy losses and subsurface stresses (see Hoglund [12]). 2. Theory The theory used to evaluate y has been described at length by Jacobson [ll]. However, he neglected the energy dissipation during impact, an assumption which is not made in this paper.
Fig. 3. Speeds and forces for the ball, from Jacobson
[ 111
The forces acting on the ball during impact are shown in Fig. 3. The pressure and shear stress distributions in the impact zone are replaced by forces since the contact point is very small. Equilibrium gives $pdA-mg=mj;
(2)
srdA=-mjt
(3)
RsrdA=J&
(4)
The following assumptions are made: To<< YP in eqn.
(l),
owing
to
the very high pressures that exist in an EHL contact
Equations (1) - (3) together with these assumptions then give Tj; = j; Integrating gives 7y+c,
=4
(5)
The initial conditions are .
x = V,,
before impact and z? = Vh before impact and j, = eV,,
j, = -V,,
after impact after impact
where e is the coefficient of restitution. Equation (5) and the starting conditions give v,, -
vh
(6)
Y= Vdl
+e)
If there is pure rolling at the end of impact w =0
before impact
9 = -V,,
217 vh
w = R
after impact
Together
j, = eV,,
with eqn. (4) and putting
2mR *
J=
-
5 this gives v h
= 5%,(1+ 2
e)
(7)
This means that the sliding motion of the ball on impact will turn into pure rolling at the end of impact because of the friction in the oil film, Equation (7) can be rewritten as ,2v, Y=
5V”,(l
2wRe + e) = 5eV,,(l
The vertical speed after impact eV,, eV,, = (2gh)“*
(8)
+ e) can be written
as (9)
Thus 2wRe ’ = 5{2gh(l
+ e)} “*
(10)
By determining the values of w, h and e, y can be calculated. The condition of pure rolling at the end of impact is tested by calCdating the difference vh - oR. If this is equal to zero pure rolling exists; if this is not the case, the attitude angle of the guide bars is changed until the difference is zero.
3. Measuring system The main parts of the system for monitoring the ball trajectory after impact are a CCD camera, a flash unit, a PC with a floating point processor, a digitizing card (framegrabber) and a TV monitor (see Fig. 4). After impact two or three pictures are taken using the flash unit and the CCD camera. The reason for using such a camera is the almost negligible geometrical distortion of the picture. However, there is still some optical distortion from the zoom-lens of the camera. The flash unit is used to “freeze” the event in different positions after impact. It is a quite common electronic flash, and can be used for multiple flashes by not using full power. The time between successive flashes is about l/10 s. The exact time is calculated by using the internal clock in the PC. The whole picture-processing unit is triggered by an optical gauge. As the sledge, on which the ball lies, passes the gauge, an electrical signal is created which initiates the PC program. The program then fires the flash at
218
OIGI7L’O i P'CTLIHEOF BALL ROTAT~ON4L WEE@ HEIGHT
~
Fig. 4. Picture-processing
system.
given times, and the picture is read into the memory of the framegrabbercard. Each picture is given a sign showing the time for identification. When all the pictures have been read into the frame-grabber-card, the picture analysis starts. A framegrabber-card must be used to digitize the pictures from the camera in order for the computer to analyse them. The card is especially made for picture-processing on a PC. The digitized picture is formed by a number of cells called pixels. Four separate pictures can be stored simultaneously in the memory of the framegrabber-card. The pictures can also be displayed on a monitor by using the video output on the card. A horizontal piece of string is used as a reference for the coordinatesystem of the framegrabber-card. The string has a 300 mm white part and the rest of it is black. The level of the string corresponds to the centre of the ball at impact. It is also used to compensate for any possible camera tilt and to calculate the length corresponding to each pixel in the digitized picture. The reference string, giving the zero-level of the impacting ball, is identified using the first picture. The coordinates of the string are determined, and a new line is fitted to the coordinates of the string using a leastsquares method. The tilt of the camera is determined by comparing the slope of the calculated line and the actual horizontal string. After this, the ball is identified and a suitable area around the ball is used in the calculations which follow. Only the white part of the ball is seen by the camera since the rest of it is black like the background. The contour of the white half-moon-shaped area is detected and the coordinates of the circular arc and the straight line are stored in the memory. Linear regression is used to calculate the angular displacement of the ball. A line is fitted to the straight part of the half-moon-shaped area, and the slope of this line is used to calculate the angle relative to the horizontal line.
219
In order to calculate the ball trajectory after impact, a parabola is fitted to the centre of the ball in the different positions. The centre of the ball is identified by fitting a circle to the coordinates of the circular part of the half-moon. The centre of this new circle is identified as the ball centre. Knowing the angular displacement and height of the ball in each picture and also the time between the pictures, the angular speed and maximum height of the ball can be calculated. Finally, the vertical speed after impact is calculated using eqn. (9), and by comparing this with the velocity before impact Vvo, the coefficient of restitution e is calculated. Equation (10) then gives the value of y.
4. Accuracy
of the method
By testing the whole equipment against known values of angular displacement and height, the accuracy was found to be within kO.5” for angular displacement and within &0.5% of the height. The accuracy depends on the resolution between the pixels in the digitized picture.
5. Oils tested 23 oils of different types have been tested (see Table 1). All the tests were performed at room temperature, i.e. 20 “C. Oils nos. 1 - 4 are polya-olefines which have a very uniform chemical composition and are best characterized by their viscosities. Oils nos. 5 - 7 are esters of different types: no. 5 is a triisotridecyladipate, which is a type of diester with a high viscosity index (VI) and good coldclimate characteristics but which is rather sensitive to pollution by water; no. 6 is a polyolic ester, which is very stable to water and high temperatures; no. 7 is a type of diester which is more branchy than no. 5, and which cannot be directly compared with nos. 5 and 6 by just looking at the viscosities. Nos. 8 - 10 are solvent-refined naphthenic oils, i.e. aromatic and polar compounds are removed. They have branched molecules of different sizes giving good low temperature behaviour, and can be directly compared using the viscosities. Nos. 11 - 13 are solvent-refined paraffinic oils, which are produced in the same kind of way as oils nos. 8 - 10 and which are about as heavily refined. The molecules are long, and so there is a risk of crystallisation at low temperatures. The results can be compared with those for the naphthenic oils nos. 8 - 10 of comparable viscosity. No. 14 is also a paraffinic oil, but is hydrocracked instead of solventrefined and the results are thus not comparable with those of nos. 11 - 13. Oils nos. 15 - 20 are made from one base oil, a synthetic base made from a poly-cr-olefine and polyolic ester like that in oil no. 6, with different
Type
Poly-o-olefine (PAO) Poly-CYolefine Polyaolefine PolyXrolefine Triisotridecyladipate ester Polyolic ester Diester Naphthenic/solvent-refined Naphthenic/solvent-refined Naphthenic/solvent-refined Paraffinic/solvent-refined Paraffinic/solvent-refined Paraffiniclsolvent-refined Paraffinic hydrocracked PA0 with polyolic ester No. 15 with 1% antioxidant No. 15 with 0.5% antiwear No. 15 with 0.5% antiwear No. 15 with 0.1% corrosion inhibitor No. 15 with 0.01% passivator PA0 with different additives PA0 with seal-swell and borate additives PA0 with polyolic ester borate antiwear and anticorrosion additives
Lubricant
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Test lubricant types and corresponding values of ‘y
TABLE I
28.2 17.8 425.2 1170.7 26.0 22.6 14.8 100.8 24.7 7.6 464.4 89.8 30.3 24.4 162.7 161.5 160.5 162.6 162.2 161.8 140.4 146.4 155.6
880.7
40°C
Viscosity (mm* s-l )
825.8 820.8 819.6 852.0 913.8 991.5 906.4 911.9 895.1 877.2 900.3 884.3 870.8 841.0 854.3 856.6 856.7 855.0 855.6 855.3 847.0 869.7
Density
20.0
5.46 3.93 41.0 100.1 5.17 4.79 3.76 8.6 3.95 2.04 30.4 10.3 5.22 5.07 20.9 20.8 20.7 20.8 21.0 20.9 18.8 19.1
100°C
0.0434/0.00084 0.0439/0.00060 0.0328/0.00082 0.0315/0.0012 0.0541/0.00023 0.0459/0.00074 0.0452/0.00055 0.0497/0.00061 0.0610/0.00069 0.0628/0.0011 0.0374/0.00038 0.0462/0.00073 0.0532/0.00054 0.0460/0.00084 0.0375/0.00061 0.0372/0.00023 0.0372/0.00041 0.0369/0.00086 0.0371/0.00089 0.0377/0.00066 0.0378/0.00030 0.0388/0.00060 0.0380/0.00090 149
y mean value/ standard deviation
133 116 147 175 132 137 150 28 1 41 95 95 102 140 151 151 151 150 153 152 151 148
VI
,” 0
221
additives. No. 15 is the pure base oil; no. 16 contains 1% ~tioxidant; no. 17, 0.5% antiwear additive; no. 18, 0.5% of an antiwear additive different from that in no. 17; no. 19, 0.1% anti-corrosion additive and finally no. 20 contains 0.01% passivator. Oil no. 21 is based on poly-cll-olefine and contains antioxidant, metal passivator, EP-additives, antifoam and seal-swell additives. The seal-swell additive is of a non-ester type. This oil can be regarded as fully formulated. Oil no. 22 is also based on polyaolefine but here only seal-swell and 12% borate additives are present. The seal-swell additive is the same as that in oil no. 21. Oil no. 23, finally, is a blend of polya-olefine with a polyolic ester like oil no. 6. 12% borate, 1% antioxidant and 0.1% corrosion inhibitor additives are added. The ball and flat sintered carbide surfaces were thoroughly cleaned with toluene and acetone between each test and the next. 6. Results The tests were performed at room temperature and a nominal pressure of 5.0 GPa, i.e. well above the solidification limit at room temperature (see also Hoglund and Jacobson [lo]). The impact time was about 60 ps. The thickness of the oil film was less than 0.5 mm before impact. It was also checked that the metal surfaces did not come into contact, by measuring the electrical resistance between the ball and the sintered carbide surface. Each oil was tested at least 7 times in order to obtain a representative mean value. The mean values of 7 can be found in Table 1, together with the corresponding values of the standard deviation. In Figs. 5 and 6 the y-values are plotted as a function of viscosity for the different types of oil. From this the following conclusions can be drawn. Poly-o-olefines, nos. 1 - 4, have relatively low y-values, and the higher the viscosity, the lower the r-value. The ester-type oils, nos. 5 - 7, have higher y-values than poly-o-olefines. The ester based on ~i~o~idecy~dipate has a s~ificantly higher r-value than the two other esters. It must be remembered that the esters are quite different and cannot be compared using their viscosity values. Oils nos. 8 - 10, naphthenic-based, have higher r-values than poly-CColefines and esters, except for oil no. 8. They can be compared relative to each other by looking at the viscosity, and the same result is found as for oils no. 1 - 4, i.e. the higher the viscosity, the lower the r-value. The paraffinic oils nos. 11 - 14 cover the range 0.0375 - 0.053 in y. Oil no. 14 is different from the rest since it is produced in a different way, namely by hydrocracking. Nos. 11 - 13 can be compared with the naphthenic oils, nos. 8 - 10, of the same viscosity. Thus it can be concluded that paraffinic oils have somewhat lower y-values than naphthenic oils. Higher viscosities also give lower y-values.
222
I___..r__
0.065
,
~_ _ ~~_/_,_~~_~~~~~r~
rlo
i
naphtenic-base esters 0: paraffinic-base x: polyalphaolefines
+:
+---_.9
*:
+\
0 OF ;
'.\
I 0.055
5.
‘\,
\
13
L
\
ICY
0 05
0.045
0 01
u.035
!
6'i 7*-'614 1---x 2 l',
\
\
12 O\
t /
as a function
\ '1.
-1
'\ \
.
15-23
.<
'..:'
.\ ‘\
0 see
‘x-_
Fig. 6 1
_
3
-_
,
4
~~~~~__1..~.
10’
103
102
Fig. 5. y-value
a
+
'\
__.i_LI
0.03 10’
0.0384
‘1
l\
viscosity [mmz/sl
of viscosity
and type of oil.
\
/'
0.0382 '2' 0.0380 -
1.23 \ \ \
\ \ \
0.0378 0.0376 -
20
\
i /I \ ;I \ \/'l;
'4 lr/19 ; 17 16 ,
0.0374-
\
0.0372 400
15 ,;;
118 410
420
430
440
450
460
470
/ 480
viscosity [mm2/sl
Fig. 6. y-value as a function
of viscosity
for oils nos. 15 - 23.
Finally, oils nos. 15 - 23 all give about the same r-value despite the different additives. The value is about the same as for poly-cr-olefines, nos. 1 - 4, of the corresponding viscosity. The properties of the base oil are obviously the most important in determining 7, and the different additives do not affect this value in any significant way.
223
7. Conclusions The shear strength of a lubricating oil, represented by the y-value, is mainly determined by the chemical structure of the base oil. Additives have only a slight influence on the -y-value. Of the five types of oils tested, polycr-olefines have the lowest y-value. Paraffinic oils, esters and naphthenic oils have gradually increasing values of y. It is however also important to know the specific type of, say, ester since they are individually different, giving different y-values. Molecular size is also important. It is obvious that for all the types of oils tested, a high viscosity, i.e. large molecules, will give low y-values.
Acknowledgments The author would like to thank Mr Sten-Ivar Bergstrom of the Lule% University of Technology for great help with the experiments and Mr Per Redelius and Mr Bertil Eriksson, Nynas Industri AB, for helpful discussions and for supplying the oils.
References 1 I. Newton, Philosophiae Natumlis Principia Mathematics, Imprimatur S. Pepys, Regiae Societatis Praeses, 5 Julii 1686, 4to Londini 1687. 2 C. Barus, Isotherms, isopiestics and isometrics relative to viscosity, Am. J. Sci., 45 (1893) 87 - 96. 3 D. Dowson and G. R. Higginson, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication, Pergamon, Oxford, 1966. 4 E. G. Trachman and H. S. Cheng, Thermal and non-newtonian effects on traction in elastohydrodynamic contacts, Proc. 2nd Symp. on Elastohydrodynamic Lubrication, Institution of Mechanical Engineers, London, 1972, pp. 142 - 148. 5 W. Hirst and A. J. Moore, Non-newtonian behavior in elastohydrodynamic lubrication,Proc. R. Sot. London, Ser. A, 337 (1974) 101 - 121. 6 K. L. Johnson and J. L. Tevaarwerk, Shear behaviour of elastohydrodynamic oil films, Proc. R. Sot. London, Ser. A, 356 (1977) 215 - 236. 7 S. Bair and W. 0. Winer, A rheological model of elastohydrodynamic contacts based on primary laboratory data, Trans. ASME, 101 (1979) 258 - 265. 8 B. J. Hamrock and D. Dowson, Ball Bearing Lubrication, Wiley, New York, 1981, pp. 269 - 275. 9 S. Bair and W. 0. Winer, Shear strength measurements of lubricants at high pressure, J. Lubr. Technol., 101 (1979) 251 - 257. 10 E. Hoglund and B. Jacobson, Experimental investigation of the shear strength of lubricants subjected to high pressure and temperature, J. Tribol., 108 (1986) 571 - 578. 11 B. Jacobson, A high pressure-short time shear strength analyzer for lubricants, J. Tribol., 107 (1985) 221 - 223. 12 E. Hbglund, Subsurface stresses in a lubricated rolling/sliding elastohydrodynamic line contact considering limited shear strength of the lubricant, Proc. 12th Leeds-Lyon Symp. on Tribology, 1985, pp. 163 - 170.
224
Appendix A: Nomenclature coefficient of restitution
FI maximum height of ball after impact (m) J
m P R T u V
moment of inertia (kg m2) mass of ball (kg) pressure (Pa) ball radius, 0.050 m temperature (“C!) velocity (m s-l) velocity (m s-l)
Greek symbols pressure-viscosity coefficient (Pa-‘) F temperature-viscosity coefficient (“C’) limiting shear stress-pressure coefficient Y 17 dynamic viscosity (Pa s) density (kg mw3) P 7 shear stress (Pa) 0 rotational speed (s-l) Subscripts 0 reference value h horizontal L limiting value V vertical