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Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and Vl-lmprovers
The Third Body Concept / D. Dowson et al. (Editors) 0 1996 Elsevier Science B.V. All rights reserved.
225
Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and Vl-Improvers B.-R. HOhn, K. Michaelis and U. Mann') Rchnical University of Munich Gear Research Centre (FZG), Arcisstrasse 21, 80333 Munich, Germany The objective of the research was the investigation of lubricant film formation in elastohydrodynamic contacts for oils of different origin (paraffinic, naphthenic, polyalphaolefin) and various types of VIimprovers (polymethacrylate, olefin copolymer, styrene butadiene copolymer). An essential part of the research was to find out whether VI-improvers maintain their thickening effect under contact conditions of high pressure (p > 8000 bar), temperature ( a > 100 "C), high shear rate (y > los s-l) and short time of contact, all these conditions occurring simultaneously. A twin disk machine was used to determine mean (integral) values of film thickness as well as film profile in the contact zone for line contact. For these measurements, two electrical capacitance methods were used. Important lubricant properties both for interpretation of the electrical data and for the corresponding EHL calculations were determined. In addition to a thermal viscosity loss, high shear rate y leads to considerably reduced film thicknesses due to non-Newtonian viscosity loss. 1
lntroductlon
Calculations of EHL film parameters depend very much on the assumptions and input values of lubricant properties into the calculation methods ([2], [l], [12]). Therefore thin film sensors were developed and applied to measure these values in disks and gear contacts ([15], [lOl). Foord, Hammann, and Cameron [5] mixed different base oils with polymethacrylates in different concentrations. An optical method (steel ball versus glass plate) was used to determine film thickness in point contacts. For cons-' and pm,=450 N/mm2 ditions of y,=4.1O7 they prove, that the thickening effect of polymers was lower than expected. 'I
Hirata and Cameron [7] showed that the viscosity loss of polymer containing oils under contact conditions is higher than for measurements in high pressure viscometers. Schrader [13] performed film thickness measurements with different oils under pure rolling conditions. He showed that already at low temperatures (Boj,=35"C) polymer containing oils build up lower film thickness than calculated. In the described investigations film thickness was measured under conditions as they occur in anti friction bearings and gear contacts of highly loaded transmissions.
Prof. Dr.-Ing. Bernd-Robert HOhn is head of the Institute of Machine Elements and the Gear Research Centre (FZG). Dr.-Ing. Klaus Michaelis is chief engineer at the FZG. Dr.-Ing. Ulrich Mann has written his thesis on the basis of the reported results.
226 2
rolling friction between the test disks, by the bearings or by any other elements.
Experlmental Procedures
2.1 Test Rlg .
The oil injection temperature Ooil and the oil volume flow rate Veil are controlled by an external oil pump and control unit. The oil is heated to a constant temperature using an oil heating unit with low thermal power density. The temperature is controlled to max. AOoi, k 0.5 K. The investigations run at constant oil temperature Ooi,, while the oil is directly injected between the test disks at a constant flow rate Voi,. The investigations were performed with constant rolling velocity vc
Fig. k
'Mn Disk Machine,
FZG.
The film thickness measurements were performed in a twin disk machine (Fig. 1). The test disks (1) and (2) are separately driven by two AC motors. For continuous variation of speed, friction drives are mounted between motors and driving shafts. The upper shaft is arranged in anti friction bearings in bench (3). The upper bench (3) is attached to the frame by two flat springs (4). These springs (4) allow only a horizontal translation of the upper bench which is restricted by a load cell (11) without an affection by hysteresis. The lower shaft is also arranged in anti friction bearings in the lower bench (6), which is fixed to link (7). The link (7)swivels around axis (8). The disks are loaded by the helical spring (9) and the load applier (10). For a velocity difference (vl + v2) between the two disks a frictional force FRis measured by the load cell (11). The measuring of a frictional force instead of a frictional torque allows the measurement of the tractional portion of the frictional force. The measured value FR does not contain any other losses e.g. caused by
vz = v l + v2
(1)
For measurements under sliding conditions the velocity of one disk is increased while the other is decreased simultaneously. The slide ratio s is defined as
2.2 Capacltance Fllm Thlckness Measure-
ments
W o electrical capacitance methods were used to determine film thickness.
The first method allows to measure a capacitance between the test disks (Fig. 2). The disks are electrically isolated from each other. Both disks are arranged in a RC-resonance circuit. Considering the elastic deformation of the contact zone it is possible to convert the capacitance to a mean (integral) film thickness. For details refer to [14].
227 contact conditions. The smaller the size of the sensor the better the resolution of the film profile. The bulk temperature is measured with a Pt-100 thermoresistor, near the surface of the disk. 2.3 Test Conditions
film profile integral measurements
Fig 2: Principle of Capacitance Oil Film Thickness Measurements.
'Ib measure a film profile the condenser area is reduced to a small stripe which is sputtered on the surface of the disk. The result is a variable capacitance signal C,(x) while the sensor passes through the contact zone. The thin film sensors are deposited by using a ion beam sputtering technique ([15], [lo]). insulating layer A1203 sensqr strip
The case-carburized steel disks are 80 mm in diameter. The relative radius of curvature is 20 mm and the reduced Young's modulus E' is assumed as 2.2740" N/m2. The contact length is 5 mm. The disks are ground and polished to a surface roughness of R, = 0.06 pm. The measurements were made for oil injection = 40, 60 and 90 "C. The temperatures aOi, Hertzian stress was varied in the range of pH = 800 to 1200 N/mm*. The measurements were performed for pure rolling conditions and f o r d i f f e r e n t values of s l i d e r a t i o s (s,,, = 30 %). Depending on rolling speed, the maximum sliding speed is vg = 3 m/s. The maximum rolling speed v, is 16 m/s.
/
2.4 Test 011s
'lbble 1 shows some characteristic parameters of the test oils. The viscosity pressure coefficient a is given for a pressure of 2000 bar.
Fig. 3: Sensor for Film Thickness Measurements (Film Profile).
Fig. 3 shows the geometry of a sensor for film thickness measurements. The sensor is electrically isolated from the steel test specimen. Both, insulating layer and sensor should be as thin as possible in order not to influence the
A paraffinic mineral oil (IS0 VG 100) was chosen as a reference oil for all measurements. First the nominal viscosity was varied (M32 and M460). Different chemical structure were tested using a naphthenic oil NlOO and a poly-alphaolefin PAO. Both oils have the some nominal viscosity (IS0 V G 100).
Four typical polymers were tested. The base oil MlOO was mixed with polymethacxylate (PMA),
228 olefin copolymer (OCP) and styrol butadiene copolymer (SBC)('l?ible 1). To verify the influence of shear stability on film formation, the polymethacrylate was used in two molecular weights.
For the evaluation of capacitance film thickness
measurements it is necessary to measure the dielectric constant of all test oils. For these measurements, a high pressure apparatus was used. A detailed description is given in [8]. 3
Measurements
3.1 Pure Rolllng
The next figures show some results of integral film thickness measurements. Table 1 Some Properties of Test Oils
rolling velocity vy
Fig. 4:
Influence of Rolling Velocity vn and Nominal Viscosity on Film Thickness.
Fig. 4 shows the measurements for the paraffinic oils under pure rolling conditions (s=O %). As expected, the measured film thickness increases with increasing rolling velocity vn. The oil M460 builds the highest oil films. For a better understanding the measured bulk temperature Voi, is also indicated in Fig. 4. It
229 can be seen, that the temperature rises with increasing rolling velocity va and increasing viscosity. A direct comparison of different oils is difficult because of the different bulk temperature. Under pure rolling conditions the bulk temperature UM is effected by shear and compression in the inlet zone of the contact. These effects were observed by Murch/Wilson [ll]. For practical applications they introduced a thermal correction factor C into isothermal EHL film thickness equation of Dowson/Higginson [2].
3.2 Sliding The next measurements were performed for sliding conditions.
0.0;
Fig. 6
rolling velocity vy
Fig. 5:
Influence of Rolling Velocity vn on Film Thickness (VI Improved Oils).
Fig. 5 shows the measurements for the polymer containing oils. Only for the oils PMAl and PMA2 a higher film thickness than for the reference oil MlOO can be observed. The increase of oil film thickness is lower than expected from the higher viscosity. Interesting is a comparison of the oils PMA2 and M460 (Fig. 4). In spite of the higher nominal viscosity of oil PMA2, the measured film thickness is lower than for the oil M460. This represents a certain viscosity loss because of high shear rate y in the inlet zone of the contact. Similar effects were investigated by Dyson/Wilson [3]. They derived an equation for the maximum shear rate y, in the inlet zone. Calculations show, that the shear rate is approx. lo6s-'. This shear rate is high enough to reduce the viscosity of polymer containing oils.
'
5:
10 :
'
15 :
' 20 : ' 25 : slide ratio s
'
30 :
'
X:
'
40 I
Influence of Slide Ratio s on Film Thickness (Chemical Structure).
Fig. 6 represents the measurements for oils with different chemical structure. It can be seen, that oil PA0 with a low pressure viscosity coefficient a, low coefficient of friction p and high VI for lower slide ratio s builds lower film thickness than the base oil M100. For higher slide ratio s the film thickness of the PA0 is higher. The measured bulk temperature fiM is lower than for the oil M100, the result is a higher film thickness. The oil NlOO is an oil with a higher viscosity pressure coefficient, higher coefficient of friction and low VI ("hble 1). The bulk temperature is higher and the film thickness is lower than for the reference oil M100. The measurements for the polymer containing oils are shown in Fig. 7. A significant higher film thickness can be observed for the oil PMA2. For higher values of slide ratio s the bulk temperature for all oils is on a similar level. The measurements of film profile were performed for control of integral film thickness measurements. Fig. 8 shows the measurements
230
slide ratio s
Flg. 7:
Influence of Slide Ratio s on Film Thickness (VIImprover). 1.0
Fig. 9
relative distance x/b,
Fig. 8
Measurement of Oil Film Profile for Oil M100.
1 3 pm 3.0
film thickness hprofile Comparison of Integral and Film Profile Measurements.
shear rate effected viscosity loss. The next step is to compare the viscosity of the oils at the same relevant temperature in the contact. 4
Results
4.1 Relatlve Film Thlckness
for oil M100. The minimum film thickness at the end of the parallel gap decreases with increasing slide ratio. This can be interpreted as a result of viscosity decrease while the oil is passing through the contact zone. Fig. 9 compares the two methods. For the film profile measurements the height of the parallel gap was evaluated. For the oil PMAl the measurements fit within a range of & 20 %. The film profile measurements for the other oils confirm the results. Considering the measurements, it is very important to distinguish between temperature and
The film thickness measurements were performed at different oil temperatures. If all other test parameters are kept constant, the film thickness can be described as a function of measured bulk temperature 6,. Fig. 10 shows the results for the oil M100. With a logarithmic scale for film thickness axis, the measured results can be interpolated with a straight line. This gives the possibility to compare film thickness for the tested oils at a constant chosen bulk temperature. Fig. 11 shows the comparison of relative film thickness for the polymer containing oils. The
23 1 polymer PMA2 is sensitive to shear rate because of its high molecular weight. The relative film thickness of oil SBC slightly increases with rising temperature. The polymer of this oil is shear stable, so the effect can be explained with a better viscosity-temperature behavior of oil SBC. 0
bulk temperature 4,
Fig. 10: Measured Film Thickness as a Function of Bulk Temperature.
O*O,L, C
s p
1.0
c
0.0
30
.
.
'
200 ! '
.
! . ' ' 400 ! . . 'mPos ! . -600 -I
' 300
nominal viscosity
Fig. 12: Thickening Effect of Polymers.
2.0
E
E
1I
40
50
60
70
bulk temperature
$
80
C
100
Fig. 11: Relative Film Thickness of Polymer Containing Oils.
relative film thickness is the ratio between tested oil and reference oil MlOO and can be interpreted as an effective viscosity related to the base oil. The oil PMAl builds higher film thickness as the reference oil M100. The film thickness is approx. 50 % higher for the whole temperature range. The film thickness of oil PMA2 is also higher than for the reference oil. The relative film thickness shows a dependence on rolling velocity v,,. First and foremost is this a result of different shear rates y in the inlet zone, which is a function of rolling velocity [ll]. The
The statements with respect to the thickening effect of VI-improvers are summarized in Fig. 12. The relative film thickness is shown as a function of the nominal viscosity. The oils are compared at a bulk temperature of 80 "C. It can be stated, that all polymer containing oils build up lower films than a straight mineral oil with the same nominal viscosity. The influence of rolling velocity v,, on relative film thickness for polymer containing oils is higher than for the straight mineral oils. In both cases this effect increases with increasing viscosity. This is mainly affected by a temperature rise in the inlet zone, which is higher for higher oil viscosities. High shear rate in the inlet zone reduces the effective viscosity of polymer containing oils. 4.2 EHL-Calculatlons
For the conditions of the measurements film thickness was calculated. The calculations were
232 performed with an EHL program of Oster [12]. Film thickness calculations in the parallel gap were made acc. to Ertl/Grubin ([4], [6]). The temperature for the calculations is the measured bulk temperature OM.For thermal correction the temperature measurements in disk contacts of Kagerer ([9], [16]) were evaluated. He measured a typical temperature rise AO,,, in the inlet zone of the contact. This temperature increase was added to the bulk temperature
The oil inlet temperature O(.l) is mainly influenced by oil viscosity and rolling velocity. Oil: MlOO
-
&-
p~ wL
60 ’C
1000 N/n
= 16 m/s
2
--
.
\ 3.0. 0
8
.
Calculation acc. Ostsr Correction of inlet temp.
I
I
I
Oil: M460
I
pH= 1000 N/mm’
s - o x
-
rolling velocity vE
Fig. 14: Comparison of Measured and Calculated Film Thickness for Oil M460.
Fig. 15 shows the results for the oil PMM. The calculation without thermal correction shows a considerable increase of calculated film thickness relative to measured film thickness with increasing rolling velocity. Considering the thermal correction, the calculated film thickness is two times higher than measured. A shear rate based viscosity loss is not taken into account in these calculations.
h
3d
\ 3.0 8 0
60.1 X
o.oJ
-2.0
!
-1.5
!
-1.0
1
!
-0.5
!
0.0
74.2 ‘C
!
0.5
relative distance x/bH
!
1.0
!
1.5
I
2.0
Fig. 13: Calculations of Film Profile. With the program system of Oster [12] it is possible to calculate a film profile (Fig. 13). For a comparison with the measurements, the calculations were evaluated in the parallel gap. Fig. 14 shows the results of film thickness calculation for oil M460. The ratio of measured to calculated film thickness is displayed. With increasing rolling velocity vp the calculated film thickness is always higher than the measured film thickness. Introducing the inlet temperature increase Atr(.l) the influence of rolling speed on calculated film thickness can be compensa ted.
0
.-u Y
r
2.5 2.0
c
E -
1.5
.-P
1.0
?
0.5
G
r
0
2
4
6
8
10
12
14
16
m/s
20
rolling velocity vL
Fig. 15: Comparison of Measured and Calculated Film Thickness for Oil PMA2. Film thickness calculations acc. Ertl [4] and Grubin [6] and a thermal correction according to MurchNilson [ l l ] led to comparable statements. From the measured film thickness using the Ertl/Grubin equation an effective viscosity in the contact can be calculated.
233
0 viscosity
calculated from film thickness
2
100 'C 160 50 oil temperature 29 Fig. 16 Recalculated Viscosity.
30
Fig. 16 displays the comparison of recalculated and measured viscosity of oil PMA2. The measurements of viscosity were performed for two shear rates. Viscosity measured at low shear rate (y = lo3 s-') and the recalculated viscosity do not correspond. Thinking of the comparison between measured and calculated film thickness, this result would have been expected. The recalculated viscosity corresponds better with the viscosity measurements at high shear rate (4 = lo6 s-*). For straight mineral oils and synthetic oils no difference is observed. This means, that the use of viscosity data from high shear measurements leads to better calculation results also for polymer containing oils. 5
Summary
The measurements prove that film thickness is influenced mainly by effects in the inlet zone of
the contact. For all oils, a temperature increase caused by compression and shear effects in the inlet zone leads to lower inlet viscosity and therefore to lower film thickness. In particular for high oil viscosities (> I S 0 VG 100) and high surface velocities, the measured values of film thickness are lower than expected. In case of polymer containing oils the high shear rate in the inlet zone (p i~ lo6 S') leads to an additional reduction of inlet viscosity. The result is that most of the polymer containing oils build up only marginally higher film thicknesses than their base oil. This tendency can be observed even more clearly from the measurements under sliding conditions. Measurements show that straight mineral oils, with a nominal viscosity equal to that of the polymer containing oils build up thicker films.
EHL calculations carried out in parallel with the experimental work show the limits of the isothermal film thickness calculation method. It is known, that the predicted film thickness is too high especially for high oil viscosities and high surface velocities. By introducing a thermal correction factor C [ 111 or an inlet oil temperature, the influence of self heating in the inlet zone can be taken into account. Because of that, calculations for the Newtonian oils show a good correspondence with the measurements. Even with these refinements, the calculations for VI-improved oils lead to results, which are up to 100 % higher than the measured values. Rmporary viscosity loss caused by high shear rate is not taken into account in the calculation method. Corresponding results for measurement and calculation can be obtained by considering the viscosity of polymer containing oils at high shear rates. Further, for VI-improved oils a permanent viscosity loss caused by continuous shear stress in practical applications must also be taken into account.
234 6
Acknowledgement
The authors would like to thank the German Society for Petroleum and Coal Science and Rchnology (DGMK) for their kind sponsorship of this project.
Oils. ASLE llans., Vol. 27 (1984), pp. 114-121.
HOhn, B.-R.; Mann, U.: Measurement of Oil Film Thickness in EHD Contacts, Influence of various Base Oils and VI Improvers. Final Report, DGMK Project 466 (1995).
References
Cheng, H.S.; Sternlicht, B.: A numerical solution for the pressure, temperature and filmthickness between two infinitely long lubricated rolling and sliding cylinders under heavy loads. 'Ifans. ASME, J. Basic Eng. (1965), vol. 3, pp. 695-705. Dowson, D.; Higginson, G.R.: Elastohydrodynamic Lubrication. Oxford: Pergamon Press (1966). Dyson, A; Wilson, AR.: Film Thickness in Elastohydrodynamic Lubrication by Silicone Fluids. Proc. Instn. Mech. Engrs., Vol. 180 Pt. 3K, (1965-1966), pp. 97-112. Ertl-Mohrenstein, A.: Die Berechnung der hydrodynamischen Schmierung gekrilmmter Oberfliichen unter hoher Belastung und Relativbewegung. VDI-Fortschrittsbericht Reihe 1, Nr. 115 (1984). Foord, C.A; Hammann, W.C.; Cameron, A: Evaluation of Lubricants Using Optical Elastohydrodynamics. ASLE ?fans. 11, (1968), pp. 31-43. Grubin, AN.; Vinogradova, J.E.: Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces. Symposium: Investigation of the contact machine components. Cent. Sci. Res. Inst. Rch. Mech. Eng. Moscow, Book No. 30 (1949). Hirata, M.; Cameron, A: The Use of Optical Elastohydrodynamics to Investigate Viscosity Loss in Polymer-thickened
Kagerer, E.: Messung von elastohydrodynamischen Parametern im hochbelasteten Scheiben- und Zahnkontakt. Thesis TU Munich (1991). Kagerer, E.; KOniger, M.: Ion Beam Sputter Deposition of Thin Film Sensors for Applications in Highly Loaded Contacts. Thin Solid Films, 182 (1989), pp. 333-344.
Murch, L.E.; Wilson, W.R.D.: A Thermal Elastohydrodynamic Inlet Zone Analysis. Pans. ASME F, J. Lubr. Rchn. 97 (1975) 2, pp. 212-216. Oster, R: Beanspruchung der Zahnflanken unter Bedingungen der Elastohydrodynamik. Thesis TU Munich (1982). Schrader, R.: EHD-61- und Fettschmierung und Mikro-EHD - AbschluObericht, FVA-Report 291 (1989). Simon, M.: Messung von elastohydrodynamischen Parametern und ihre Auswirkung auf die Griibchentragfahigkeit vergilteter Scheiben und Zahnriider. Thesis TU Munich (1984). Simon, M.; KOniger, M.E.; Reithmeier, G.:Ion Beam Sputter Deposition of Thin Insulating Layers for Applications in Highly Loaded Contacts. Thin Solid Films, 109 (1983), pp. 19-25. Winter, H.; HOhn, B.-R.; Michaelis, K.; Kagerer, E.: Measurement of Pressure, Rmperature and Film Thickness in Disk and Gear Contacts. JSME International Conference on Motion and Power 'Ifansmissions, pp. 474-479, Nov. 23-26 (1991) Hiroshima, Japan.
225
Measurement of Oil Film Thickness in Elastohydrodynamic Contacts Influence of Various Base Oils and Vl-Improvers B.-R. HOhn, K. Michaelis and U. Mann') Rchnical University of Munich Gear Research Centre (FZG), Arcisstrasse 21, 80333 Munich, Germany The objective of the research was the investigation of lubricant film formation in elastohydrodynamic contacts for oils of different origin (paraffinic, naphthenic, polyalphaolefin) and various types of VIimprovers (polymethacrylate, olefin copolymer, styrene butadiene copolymer). An essential part of the research was to find out whether VI-improvers maintain their thickening effect under contact conditions of high pressure (p > 8000 bar), temperature ( a > 100 "C), high shear rate (y > los s-l) and short time of contact, all these conditions occurring simultaneously. A twin disk machine was used to determine mean (integral) values of film thickness as well as film profile in the contact zone for line contact. For these measurements, two electrical capacitance methods were used. Important lubricant properties both for interpretation of the electrical data and for the corresponding EHL calculations were determined. In addition to a thermal viscosity loss, high shear rate y leads to considerably reduced film thicknesses due to non-Newtonian viscosity loss. 1
lntroductlon
Calculations of EHL film parameters depend very much on the assumptions and input values of lubricant properties into the calculation methods ([2], [l], [12]). Therefore thin film sensors were developed and applied to measure these values in disks and gear contacts ([15], [lOl). Foord, Hammann, and Cameron [5] mixed different base oils with polymethacrylates in different concentrations. An optical method (steel ball versus glass plate) was used to determine film thickness in point contacts. For cons-' and pm,=450 N/mm2 ditions of y,=4.1O7 they prove, that the thickening effect of polymers was lower than expected. 'I
Hirata and Cameron [7] showed that the viscosity loss of polymer containing oils under contact conditions is higher than for measurements in high pressure viscometers. Schrader [13] performed film thickness measurements with different oils under pure rolling conditions. He showed that already at low temperatures (Boj,=35"C) polymer containing oils build up lower film thickness than calculated. In the described investigations film thickness was measured under conditions as they occur in anti friction bearings and gear contacts of highly loaded transmissions.
Prof. Dr.-Ing. Bernd-Robert HOhn is head of the Institute of Machine Elements and the Gear Research Centre (FZG). Dr.-Ing. Klaus Michaelis is chief engineer at the FZG. Dr.-Ing. Ulrich Mann has written his thesis on the basis of the reported results.
226 2
rolling friction between the test disks, by the bearings or by any other elements.
Experlmental Procedures
2.1 Test Rlg .
The oil injection temperature Ooil and the oil volume flow rate Veil are controlled by an external oil pump and control unit. The oil is heated to a constant temperature using an oil heating unit with low thermal power density. The temperature is controlled to max. AOoi, k 0.5 K. The investigations run at constant oil temperature Ooi,, while the oil is directly injected between the test disks at a constant flow rate Voi,. The investigations were performed with constant rolling velocity vc
Fig. k
'Mn Disk Machine,
FZG.
The film thickness measurements were performed in a twin disk machine (Fig. 1). The test disks (1) and (2) are separately driven by two AC motors. For continuous variation of speed, friction drives are mounted between motors and driving shafts. The upper shaft is arranged in anti friction bearings in bench (3). The upper bench (3) is attached to the frame by two flat springs (4). These springs (4) allow only a horizontal translation of the upper bench which is restricted by a load cell (11) without an affection by hysteresis. The lower shaft is also arranged in anti friction bearings in the lower bench (6), which is fixed to link (7). The link (7)swivels around axis (8). The disks are loaded by the helical spring (9) and the load applier (10). For a velocity difference (vl + v2) between the two disks a frictional force FRis measured by the load cell (11). The measuring of a frictional force instead of a frictional torque allows the measurement of the tractional portion of the frictional force. The measured value FR does not contain any other losses e.g. caused by
vz = v l + v2
(1)
For measurements under sliding conditions the velocity of one disk is increased while the other is decreased simultaneously. The slide ratio s is defined as
2.2 Capacltance Fllm Thlckness Measure-
ments
W o electrical capacitance methods were used to determine film thickness.
The first method allows to measure a capacitance between the test disks (Fig. 2). The disks are electrically isolated from each other. Both disks are arranged in a RC-resonance circuit. Considering the elastic deformation of the contact zone it is possible to convert the capacitance to a mean (integral) film thickness. For details refer to [14].
227 contact conditions. The smaller the size of the sensor the better the resolution of the film profile. The bulk temperature is measured with a Pt-100 thermoresistor, near the surface of the disk. 2.3 Test Conditions
film profile integral measurements
Fig 2: Principle of Capacitance Oil Film Thickness Measurements.
'Ib measure a film profile the condenser area is reduced to a small stripe which is sputtered on the surface of the disk. The result is a variable capacitance signal C,(x) while the sensor passes through the contact zone. The thin film sensors are deposited by using a ion beam sputtering technique ([15], [lo]). insulating layer A1203 sensqr strip
The case-carburized steel disks are 80 mm in diameter. The relative radius of curvature is 20 mm and the reduced Young's modulus E' is assumed as 2.2740" N/m2. The contact length is 5 mm. The disks are ground and polished to a surface roughness of R, = 0.06 pm. The measurements were made for oil injection = 40, 60 and 90 "C. The temperatures aOi, Hertzian stress was varied in the range of pH = 800 to 1200 N/mm*. The measurements were performed for pure rolling conditions and f o r d i f f e r e n t values of s l i d e r a t i o s (s,,, = 30 %). Depending on rolling speed, the maximum sliding speed is vg = 3 m/s. The maximum rolling speed v, is 16 m/s.
/
2.4 Test 011s
'lbble 1 shows some characteristic parameters of the test oils. The viscosity pressure coefficient a is given for a pressure of 2000 bar.
Fig. 3: Sensor for Film Thickness Measurements (Film Profile).
Fig. 3 shows the geometry of a sensor for film thickness measurements. The sensor is electrically isolated from the steel test specimen. Both, insulating layer and sensor should be as thin as possible in order not to influence the
A paraffinic mineral oil (IS0 VG 100) was chosen as a reference oil for all measurements. First the nominal viscosity was varied (M32 and M460). Different chemical structure were tested using a naphthenic oil NlOO and a poly-alphaolefin PAO. Both oils have the some nominal viscosity (IS0 V G 100).
Four typical polymers were tested. The base oil MlOO was mixed with polymethacxylate (PMA),
228 olefin copolymer (OCP) and styrol butadiene copolymer (SBC)('l?ible 1). To verify the influence of shear stability on film formation, the polymethacrylate was used in two molecular weights.
For the evaluation of capacitance film thickness
measurements it is necessary to measure the dielectric constant of all test oils. For these measurements, a high pressure apparatus was used. A detailed description is given in [8]. 3
Measurements
3.1 Pure Rolllng
The next figures show some results of integral film thickness measurements. Table 1 Some Properties of Test Oils
rolling velocity vy
Fig. 4:
Influence of Rolling Velocity vn and Nominal Viscosity on Film Thickness.
Fig. 4 shows the measurements for the paraffinic oils under pure rolling conditions (s=O %). As expected, the measured film thickness increases with increasing rolling velocity vn. The oil M460 builds the highest oil films. For a better understanding the measured bulk temperature Voi, is also indicated in Fig. 4. It
229 can be seen, that the temperature rises with increasing rolling velocity va and increasing viscosity. A direct comparison of different oils is difficult because of the different bulk temperature. Under pure rolling conditions the bulk temperature UM is effected by shear and compression in the inlet zone of the contact. These effects were observed by Murch/Wilson [ll]. For practical applications they introduced a thermal correction factor C into isothermal EHL film thickness equation of Dowson/Higginson [2].
3.2 Sliding The next measurements were performed for sliding conditions.
0.0;
Fig. 6
rolling velocity vy
Fig. 5:
Influence of Rolling Velocity vn on Film Thickness (VI Improved Oils).
Fig. 5 shows the measurements for the polymer containing oils. Only for the oils PMAl and PMA2 a higher film thickness than for the reference oil MlOO can be observed. The increase of oil film thickness is lower than expected from the higher viscosity. Interesting is a comparison of the oils PMA2 and M460 (Fig. 4). In spite of the higher nominal viscosity of oil PMA2, the measured film thickness is lower than for the oil M460. This represents a certain viscosity loss because of high shear rate y in the inlet zone of the contact. Similar effects were investigated by Dyson/Wilson [3]. They derived an equation for the maximum shear rate y, in the inlet zone. Calculations show, that the shear rate is approx. lo6s-'. This shear rate is high enough to reduce the viscosity of polymer containing oils.
'
5:
10 :
'
15 :
' 20 : ' 25 : slide ratio s
'
30 :
'
X:
'
40 I
Influence of Slide Ratio s on Film Thickness (Chemical Structure).
Fig. 6 represents the measurements for oils with different chemical structure. It can be seen, that oil PA0 with a low pressure viscosity coefficient a, low coefficient of friction p and high VI for lower slide ratio s builds lower film thickness than the base oil M100. For higher slide ratio s the film thickness of the PA0 is higher. The measured bulk temperature fiM is lower than for the oil M100, the result is a higher film thickness. The oil NlOO is an oil with a higher viscosity pressure coefficient, higher coefficient of friction and low VI ("hble 1). The bulk temperature is higher and the film thickness is lower than for the reference oil M100. The measurements for the polymer containing oils are shown in Fig. 7. A significant higher film thickness can be observed for the oil PMA2. For higher values of slide ratio s the bulk temperature for all oils is on a similar level. The measurements of film profile were performed for control of integral film thickness measurements. Fig. 8 shows the measurements
230
slide ratio s
Flg. 7:
Influence of Slide Ratio s on Film Thickness (VIImprover). 1.0
Fig. 9
relative distance x/b,
Fig. 8
Measurement of Oil Film Profile for Oil M100.
1 3 pm 3.0
film thickness hprofile Comparison of Integral and Film Profile Measurements.
shear rate effected viscosity loss. The next step is to compare the viscosity of the oils at the same relevant temperature in the contact. 4
Results
4.1 Relatlve Film Thlckness
for oil M100. The minimum film thickness at the end of the parallel gap decreases with increasing slide ratio. This can be interpreted as a result of viscosity decrease while the oil is passing through the contact zone. Fig. 9 compares the two methods. For the film profile measurements the height of the parallel gap was evaluated. For the oil PMAl the measurements fit within a range of & 20 %. The film profile measurements for the other oils confirm the results. Considering the measurements, it is very important to distinguish between temperature and
The film thickness measurements were performed at different oil temperatures. If all other test parameters are kept constant, the film thickness can be described as a function of measured bulk temperature 6,. Fig. 10 shows the results for the oil M100. With a logarithmic scale for film thickness axis, the measured results can be interpolated with a straight line. This gives the possibility to compare film thickness for the tested oils at a constant chosen bulk temperature. Fig. 11 shows the comparison of relative film thickness for the polymer containing oils. The
23 1 polymer PMA2 is sensitive to shear rate because of its high molecular weight. The relative film thickness of oil SBC slightly increases with rising temperature. The polymer of this oil is shear stable, so the effect can be explained with a better viscosity-temperature behavior of oil SBC. 0
bulk temperature 4,
Fig. 10: Measured Film Thickness as a Function of Bulk Temperature.
O*O,L, C
s p
1.0
c
0.0
30
.
.
'
200 ! '
.
! . ' ' 400 ! . . 'mPos ! . -600 -I
' 300
nominal viscosity
Fig. 12: Thickening Effect of Polymers.
2.0
E
E
1I
40
50
60
70
bulk temperature
$
80
C
100
Fig. 11: Relative Film Thickness of Polymer Containing Oils.
relative film thickness is the ratio between tested oil and reference oil MlOO and can be interpreted as an effective viscosity related to the base oil. The oil PMAl builds higher film thickness as the reference oil M100. The film thickness is approx. 50 % higher for the whole temperature range. The film thickness of oil PMA2 is also higher than for the reference oil. The relative film thickness shows a dependence on rolling velocity v,,. First and foremost is this a result of different shear rates y in the inlet zone, which is a function of rolling velocity [ll]. The
The statements with respect to the thickening effect of VI-improvers are summarized in Fig. 12. The relative film thickness is shown as a function of the nominal viscosity. The oils are compared at a bulk temperature of 80 "C. It can be stated, that all polymer containing oils build up lower films than a straight mineral oil with the same nominal viscosity. The influence of rolling velocity v,, on relative film thickness for polymer containing oils is higher than for the straight mineral oils. In both cases this effect increases with increasing viscosity. This is mainly affected by a temperature rise in the inlet zone, which is higher for higher oil viscosities. High shear rate in the inlet zone reduces the effective viscosity of polymer containing oils. 4.2 EHL-Calculatlons
For the conditions of the measurements film thickness was calculated. The calculations were
232 performed with an EHL program of Oster [12]. Film thickness calculations in the parallel gap were made acc. to Ertl/Grubin ([4], [6]). The temperature for the calculations is the measured bulk temperature OM.For thermal correction the temperature measurements in disk contacts of Kagerer ([9], [16]) were evaluated. He measured a typical temperature rise AO,,, in the inlet zone of the contact. This temperature increase was added to the bulk temperature
The oil inlet temperature O(.l) is mainly influenced by oil viscosity and rolling velocity. Oil: MlOO
-
&-
p~ wL
60 ’C
1000 N/n
= 16 m/s
2
--
.
\ 3.0. 0
8
.
Calculation acc. Ostsr Correction of inlet temp.
I
I
I
Oil: M460
I
pH= 1000 N/mm’
s - o x
-
rolling velocity vE
Fig. 14: Comparison of Measured and Calculated Film Thickness for Oil M460.
Fig. 15 shows the results for the oil PMM. The calculation without thermal correction shows a considerable increase of calculated film thickness relative to measured film thickness with increasing rolling velocity. Considering the thermal correction, the calculated film thickness is two times higher than measured. A shear rate based viscosity loss is not taken into account in these calculations.
h
3d
\ 3.0 8 0
60.1 X
o.oJ
-2.0
!
-1.5
!
-1.0
1
!
-0.5
!
0.0
74.2 ‘C
!
0.5
relative distance x/bH
!
1.0
!
1.5
I
2.0
Fig. 13: Calculations of Film Profile. With the program system of Oster [12] it is possible to calculate a film profile (Fig. 13). For a comparison with the measurements, the calculations were evaluated in the parallel gap. Fig. 14 shows the results of film thickness calculation for oil M460. The ratio of measured to calculated film thickness is displayed. With increasing rolling velocity vp the calculated film thickness is always higher than the measured film thickness. Introducing the inlet temperature increase Atr(.l) the influence of rolling speed on calculated film thickness can be compensa ted.
0
.-u Y
r
2.5 2.0
c
E -
1.5
.-P
1.0
?
0.5
G
r
0
2
4
6
8
10
12
14
16
m/s
20
rolling velocity vL
Fig. 15: Comparison of Measured and Calculated Film Thickness for Oil PMA2. Film thickness calculations acc. Ertl [4] and Grubin [6] and a thermal correction according to MurchNilson [ l l ] led to comparable statements. From the measured film thickness using the Ertl/Grubin equation an effective viscosity in the contact can be calculated.
233
0 viscosity
calculated from film thickness
2
100 'C 160 50 oil temperature 29 Fig. 16 Recalculated Viscosity.
30
Fig. 16 displays the comparison of recalculated and measured viscosity of oil PMA2. The measurements of viscosity were performed for two shear rates. Viscosity measured at low shear rate (y = lo3 s-') and the recalculated viscosity do not correspond. Thinking of the comparison between measured and calculated film thickness, this result would have been expected. The recalculated viscosity corresponds better with the viscosity measurements at high shear rate (4 = lo6 s-*). For straight mineral oils and synthetic oils no difference is observed. This means, that the use of viscosity data from high shear measurements leads to better calculation results also for polymer containing oils. 5
Summary
The measurements prove that film thickness is influenced mainly by effects in the inlet zone of
the contact. For all oils, a temperature increase caused by compression and shear effects in the inlet zone leads to lower inlet viscosity and therefore to lower film thickness. In particular for high oil viscosities (> I S 0 VG 100) and high surface velocities, the measured values of film thickness are lower than expected. In case of polymer containing oils the high shear rate in the inlet zone (p i~ lo6 S') leads to an additional reduction of inlet viscosity. The result is that most of the polymer containing oils build up only marginally higher film thicknesses than their base oil. This tendency can be observed even more clearly from the measurements under sliding conditions. Measurements show that straight mineral oils, with a nominal viscosity equal to that of the polymer containing oils build up thicker films.
EHL calculations carried out in parallel with the experimental work show the limits of the isothermal film thickness calculation method. It is known, that the predicted film thickness is too high especially for high oil viscosities and high surface velocities. By introducing a thermal correction factor C [ 111 or an inlet oil temperature, the influence of self heating in the inlet zone can be taken into account. Because of that, calculations for the Newtonian oils show a good correspondence with the measurements. Even with these refinements, the calculations for VI-improved oils lead to results, which are up to 100 % higher than the measured values. Rmporary viscosity loss caused by high shear rate is not taken into account in the calculation method. Corresponding results for measurement and calculation can be obtained by considering the viscosity of polymer containing oils at high shear rates. Further, for VI-improved oils a permanent viscosity loss caused by continuous shear stress in practical applications must also be taken into account.
234 6
Acknowledgement
The authors would like to thank the German Society for Petroleum and Coal Science and Rchnology (DGMK) for their kind sponsorship of this project.
Oils. ASLE llans., Vol. 27 (1984), pp. 114-121.
HOhn, B.-R.; Mann, U.: Measurement of Oil Film Thickness in EHD Contacts, Influence of various Base Oils and VI Improvers. Final Report, DGMK Project 466 (1995).
References
Cheng, H.S.; Sternlicht, B.: A numerical solution for the pressure, temperature and filmthickness between two infinitely long lubricated rolling and sliding cylinders under heavy loads. 'Ifans. ASME, J. Basic Eng. (1965), vol. 3, pp. 695-705. Dowson, D.; Higginson, G.R.: Elastohydrodynamic Lubrication. Oxford: Pergamon Press (1966). Dyson, A; Wilson, AR.: Film Thickness in Elastohydrodynamic Lubrication by Silicone Fluids. Proc. Instn. Mech. Engrs., Vol. 180 Pt. 3K, (1965-1966), pp. 97-112. Ertl-Mohrenstein, A.: Die Berechnung der hydrodynamischen Schmierung gekrilmmter Oberfliichen unter hoher Belastung und Relativbewegung. VDI-Fortschrittsbericht Reihe 1, Nr. 115 (1984). Foord, C.A; Hammann, W.C.; Cameron, A: Evaluation of Lubricants Using Optical Elastohydrodynamics. ASLE ?fans. 11, (1968), pp. 31-43. Grubin, AN.; Vinogradova, J.E.: Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily Loaded Cylindrical Surfaces. Symposium: Investigation of the contact machine components. Cent. Sci. Res. Inst. Rch. Mech. Eng. Moscow, Book No. 30 (1949). Hirata, M.; Cameron, A: The Use of Optical Elastohydrodynamics to Investigate Viscosity Loss in Polymer-thickened
Kagerer, E.: Messung von elastohydrodynamischen Parametern im hochbelasteten Scheiben- und Zahnkontakt. Thesis TU Munich (1991). Kagerer, E.; KOniger, M.: Ion Beam Sputter Deposition of Thin Film Sensors for Applications in Highly Loaded Contacts. Thin Solid Films, 182 (1989), pp. 333-344.
Murch, L.E.; Wilson, W.R.D.: A Thermal Elastohydrodynamic Inlet Zone Analysis. Pans. ASME F, J. Lubr. Rchn. 97 (1975) 2, pp. 212-216. Oster, R: Beanspruchung der Zahnflanken unter Bedingungen der Elastohydrodynamik. Thesis TU Munich (1982). Schrader, R.: EHD-61- und Fettschmierung und Mikro-EHD - AbschluObericht, FVA-Report 291 (1989). Simon, M.: Messung von elastohydrodynamischen Parametern und ihre Auswirkung auf die Griibchentragfahigkeit vergilteter Scheiben und Zahnriider. Thesis TU Munich (1984). Simon, M.; KOniger, M.E.; Reithmeier, G.:Ion Beam Sputter Deposition of Thin Insulating Layers for Applications in Highly Loaded Contacts. Thin Solid Films, 109 (1983), pp. 19-25. Winter, H.; HOhn, B.-R.; Michaelis, K.; Kagerer, E.: Measurement of Pressure, Rmperature and Film Thickness in Disk and Gear Contacts. JSME International Conference on Motion and Power 'Ifansmissions, pp. 474-479, Nov. 23-26 (1991) Hiroshima, Japan.