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The film forming behavior at high speeds under oil−air lubrication
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The film forming behavior at high speeds under oil-air lubrication He Liang, Dan Guo, Liran Ma, Jianbin Luo
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PII: DOI: Reference:
S0301-679X(15)00248-0 http://dx.doi.org/10.1016/j.triboint.2015.06.010 JTRI3715
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Tribology International
Received date: 11 February 2015 Revised date: 1 June 2015 Accepted date: 2 June 2015 Cite this article as: He Liang, Dan Guo, Liran Ma, Jianbin Luo, The film forming behavior at high speeds under oil-air lubrication, Tribology International, http: //dx.doi.org/10.1016/j.triboint.2015.06.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The film forming behavior at high speeds under oil-air lubrication He Liang; Dan Guo*; Liran Ma, Jianbin Luo*
State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China. Corresponding authors: [email protected] (Dan Guo); [email protected] (Jianbin Luo)
Abstract The film forming behavior has been investigated under oil-air lubrication, compared with that under oil-jet lubrication in present work. Images of microscopic oil reservoir and interference were obtained up to 30 m/s. A parameter η describing the oil supply effects is 30 times higher and the film thickness reduces in starved regime much slower under oil-air lubrication compared with that under oil-jet lubrication. The contribution of micron-order oil droplets on film forming is discussed. More micron-order oil droplets can spread onto the disc while less of them are driven away by centrifugal effects. As a result, the oil supply efficiency of oil-air lubrication is improved. The high pressure compressed air can blow off the oil and intensify the film oscillation.
：High speeds, Elastohydrodynamic lubrication, Oil-air lubrication, Starvation
Keywords
Nomenclature h
Lubricant film thickness (m)
t0
Operating temperature (K)
η0
Ambient viscosity (Pa s)
u
Lubricant entrainment speed, u =(u1 + u2)/2
u1 , u2
Surface velocities of disc and ball (m/s)
E’
Reduced modulus (Pa)
pH
Maximum Herzian pressure (Pa)
b
Theoretical Hertz contact radius (m)
Re
Reynolds Number, ρud/η0
d
Diameter of oil droplets, m
1 Introduction The lubrication film thickness distribution in a point contact could be measured experimentally by optical interferometry introduced by Gohar and Cameron[1, 2] in the 1960s. Following this, different interferometry-based film thickness measurement techniques were developed [3-5]. These interferometry-based techniques made it easier to measure film thickness directly with high resolution up to a few nanometers under different conditions. For fully flooded lubrication, the film thicknesses under high speed [6, 7], high pressure [8-10] and high slide-roll-ratio [11, 12] were measured and showed deviations compared with those predicted by Hamorock and Dowson equations [13]. Many 1
new phenomena of lubrication films showed close relation to the speed, i.e. thin film lubrication phenomenon [4, 14, 15] and superlubricity phenomenon [16-19]. For starved lubrication, the characteristics and the judge of starvation degree were on the focus. The mechanism in point contact was investigated by Wedeven et al. [20] and Chiu [21] using a ball-on-disc test rig, indicating that the starvation was determined by the fluid replenishment ability into the track. Later, the inlet film was adopted to define the degree of starvation by Chevalier et al.[22] and Damiens et al.[23] in numerical models of starved elastohydrodynamic lubrication and Svoboda et al. [24] in ball-on-disc experiments. Criteria were proposed by Liu and Wen[25] to determine lubrication conditions between fully flooded, starved and parched lubrication. The influence of operational parameters conditions, including speed, viscosity, load and lubricant volume, on the onset of starvation in EHL contacts were performed experimentally [7, 26] later. However, roller bearings in high-speed spindles and aircraft engines are likely to run at much higher speeds. Numerical studies by van Zoelen et al.[27, 28] and experiments by Liang et al. [7, 29]suggested that centrifugal effects might drive the lubricant to flow vertically and the film thickness distribution was asymmetric under starved lubrication. Most of above works were under immersed or half immersed lubrication, which was proper for low speed conditions, but not for high-speed rolling ball-bearings in aircraft engine, high-speed spindles and other machine tools due to the high oil loss by splashing. Therefore, the oil-air lubrication, oil-mist lubrication and oil-jet lubrication were developed for improving the oil supply efficiency. Under the oil-air lubrication and oil–mist lubrication, the oil is broken down into micro-droplets and then make their way precisely into the friction point continually by high pressure compressed air flow. The difference is that under oil-air lubrication, the oil droplets are not atomized. Therefore, the oil-air lubrication system has the advantages of high lubricating efficiency and environmental benefits [30, 31]. Under oil-jet lubrication, the oil is jetted into the bearings. It needs to deliver much more oil into the bearings compared with the other two ways. As a result, the oil-jet lubrication obtains lower bearing temperature and higher power losses [32]. The researches on oil-air lubrication mainly focus on its thermal effects. Ramesh et al. [33] found that convection was the major component of heat transfer in this method. Materials, rotating speed, preload, oil supply rate and other factors [34-36] were optimized to reach the lowest temperature rise. Few efforts were made on the film thickness measurement under oil-air lubrication system. It was proved that thin film maintained in bearing up to 20 000 rpm using the capacity method under oil-air lubrication by Ramesh et al. [33] and under oil-jet lubrication by Gorse et al.[37]. However, the film distribution and the film forming characteristic are still invisible perhaps due to the difficulties in validating experimental measurements. In this article, the film forming behavior was investigated under the oil-air lubrication and compared with that under the oil-jet lubrication. Film thicknesses and temperature rises near the inlet zone were recorded on a ball-on-disc test rig for speeds up to 30 m/s using relative optical interference intensity (ROII) technology and compared with theories. The roles of high pressure compressed air and 2
micron-order oil droplets on film forming behavior were discussed under oil-air lubrication. 2 Experimental 2.1 Ball on disc test rig A homemade high-speed ball-on-disc test rig is used in the tests. The properties and functions are introduced in Ref.[7] . The material properties of the balls and discs were measured and are quoted in Table 1. Three 1-mm-diameter thermo couples (Omega, US) are located in the oil bath, near the inlet zone and near the outlet region of the contact on the disc separately, to record the temperature variations. The thermo couples are located close to the contact at macro level (about 5 mm away from the contact), however, it is still far away from the contact at micro level. What the thermo couples can detect is the temperature rise of the disc surface. If the thermo couples get closer to the contact, the temperature rise will increase. Therefore, during all tests, the positions of the thermo couples are fixed so that temperature rise of different tests can be compared. Interference images are taken by use of a high speed camera. Film thicknesses are determined by the relative optical interference intensity (ROII) technique [4, 38] and are given by the following expression[39]:
h=
λ nπ [( n + sin ) ⋅ π + arc cos( I ) ⋅ cos nπ − arc cos( I 0 )] 4π k 2
(1)
where λ represents wave length of the incident light, k is reflective index of lubricant, n is interference ¹
order, I is light intensity,
I max , I min is maximum or minimum interference light intensity, I is ¹
relative interference light intensity ( I
¹
= (2 I − I max − I min ) / ( I max − I min ) ) and I 0 is relative light
intensity when the lubricant film thickness is zero. 2.2 Lubrication systems The oil supply system is an autonomous system (Fig.1). In the tests, both the oil-air lubrication system and the oil-jet lubrication system are used and can be replaced. The basic structures of used oil-air lubrication device (SKF Vogel, Germany) are shown in Fig.2. It consists of an oil reservoir, an oil pump and mixing valves. The oil pump delivers the oil intermittently into the mixing valves, where the oil and the compressed air are mixed and distributed to oil-air supply pipes. Finally, oil-air stream is ejected by means of the nozzle and shoots onto the disc. The oil flow rate, oil supply position and air pressure can be controlled. The oil-jet lubrication is used as comparison. It contains an oil reservoir, a peristaltic pump and pipes. The oil is delivered from the oil reservoir via a pipe by the pump and then jets onto the disc through a nozzle near the inlet zone. The splashing oil is collected and flows back to the oil reservoir to form a supply circulation. 2.3 Test conditions In the present work, all tests are carried out at pure rolling. The operating conditions are shown in Table 1. One kind of polyalphaolefin oil (PAO8) is used in the tests. The viscosity and density of PAO8 is about 86.55 mPa s and 833 kg/m3 at 25 oC, as measured by a viscometer (Anton Paar, Austria) and the 3
surface tension is 29.4 mN/m as measured by a surface tension-meter (Dataphysics DCAT21, Germany). Three lubrication conditions are used as shown in Table 2 and Table 3. The changes of film thickness and temperature rise as a function of entrainment speed are studied at various speeds from 3 m/s to 30 m/s. 3. Results and discussions 3.1 The effects of high pressure compressed air on film forming The oil is supplied firstly near the inlet zone under oil-air lubrication, shown in Fig.3. (Labelled as Lub I in Table 2). The oil supply of 0.11 ml/s and the high pressure compressed air of 3 bar and 6 bar are utilized. Figure 4 shows the minimum film thickness as a function of entrainment speed. The film thickness seems to oscillate under 5 m/s and above 10 m/s under high pressure compressed air of 3 bar and 6 bar and the amplitude is larger for a stronger air pressure (6 bar). As the oil supply by the oil-air lubrication and oil-jet lubrication used in the tests is periodic. The oil reservoir and film thickness may oscillate. It is normally believed that there is a critical inlet distance where the film thickness starts to decrease[40]. The oscillation of oil reservoir starts to influence the film thickness onwards 10 m/s as the volume of oil reservoir shrinks with entrainment speed. The amplitude of film thickness oscillation is influenced by the oil supply, frequency and other factors. In such conditions, the amplitude of film thickness oscillation is about 50 nm and 80 nm under high pressure compressed air of 3 bar and 6 bar. The amplitude of film thickness under oil-air lubrication avoiding the impact of compressed air and under oil-jet lubrication is 15 nm and 30 nm separately (see Fig. 8). The comparison of oscillation amplitude of film thickness indicates that the high pressure compressed air intensifies the oscillation of film thickness. For speeds lower than 5 m/s, the oscillation amplitude of film thickness is quite large and the contact may experience parched starvation as the oil can be blown off the contact region directly (the images of oil reservoir is shown in Fig.5). The oil reservoir still exists but has been separated from the contact. It is of interest to find that the starvation degree is reduced when the speed is higher than 5 m/s. A comparison test is made to remove the oil on the disc by adding a wiper behind the contact. Figure 6 shows the images of oil reservoir changes about the whole process. First step [Fig.6 (a)], the contact achieves fully flooded lubrication under oil-air lubrication (Lub I, 5 m/s, 0.11 ml/s, 6 bar). Second step [Fig.6 (b)], a wiper is added to block the oil on the disc. The oil from oil-air lubrication is the only way to supply the contact. The oil reservoir immediately shrinks and the minimum film thickness decreases from 600 nm to about 120 nm although the oil supply is continuing. Third step [Fig.6 (c)], the wiper is removed. The oil reservoir slowly grows and recovers after 10 seconds. It indicates that only small part of oil from oil-air lubrication can reach near the contact directly, most of the other oil droplets will be blown off or spread on the disc. The spreading oil will rotate with the disc and accumulate. It can replenish the oil reservoir after one revolution or more. The oil reservoir should be a result of comparison between oil loss intensified by high pressure compressed air and the oil supply in the inlet zone. At lower speeds, it takes longer to go around one revolution, during this time, the oil loses more 4
by high pressure air than that can flow back. While at higher speeds, the interval between revolutions is reduced, the high pressure air still blow off the oil in the inlet zone at high speeds, however the spreading oil accumulates fast and replenishes the oil reservoir promptly to avoid the film from collapsing. The high pressure compressed air is commonly regarded to transport oil droplets and to help with heat dissipation. In this section, it shows that the high pressure compressed air blow off the oil in the inlet zone and intensify the oscillation of film thickness. 3.2 The effects of oil droplets on film forming 3.2.1 Film thickness measurement and oil supply effects There are two significant characteristics for oil-air lubrication: high pressure compressed air and homogenous oil droplets with diameter of tens of micrometers. The effects of the oil droplets on film forming are detected in this section. In order to avoid the impact of high pressure compressed air on lubricant flowing near the inlet zone, the oil is supplied far from the contact under oil-air lubrication, shown in Fig. 7 (labelled as Lub II in Table 2). Figure 8(a) shows the measured minimum film thicknesses for different oil supply against entrainment speed under oil-air lubrication far from the inlet zone (Lub II). For starved lubrication, the minimum film thicknesses decrease linearly against entrainment speed. The distribution of film thickness along y axis is asymmetric at high speeds because of centrifugal effects [7]. The film thicknesses (Fig. 8(b)) under oil-jet lubrication were measured as comparison. For fully flooded lubrication, the minimum film thicknesses under oil-air lubrication are little smaller than those under oil-jet lubrication with errors less than 10%. This may be mainly caused by the thermal effects which will be discussed in section 3.3. If compared with predicted ones by Hamrock-Dowson equations, the film thicknesses show increasing discrepancies at speeds higher than 4 m/s which may be mainly caused by the inlet shear heating [41]. For starved lubrication, the changes of film thickness under oil-jet lubrication show different patterns: the minimum film thicknesses collapse higher than a critical speed, decrease rapidly and finally maintain at about 30 nm. The film thickness under starved conditions are compared with Cann et al. [26] in which a parameter using the ratio speed/volume can superpose curves under different oil supply at lower speeds. However, it may not proper for high speed conditions. The film thickness descending is more impacted by speed due to the centrifugal effects [7]. Therefore, the ratio u2/S (S represents the oil supply, the unit is µL/s) is used and superposition of curves under a range of oil supply is obtained (see Fig. 9). There are two main differences between curves of oil-air lubrication and that of oil-jet lubrication. The first one is the starting point of starvation, where the relative film thickness starts to decrease. Both of them are larger than what Cann et al. found because the parameter u2 is used and the oil is supplied continuously instead of a limited volume used by Cann et al. [26]. Apparently, the starting point under oil-air lubrication is much larger than that under oil-jet lubrication. The second one is the curvature of film thickness against u2/S under starvation. The film thickness under oil-jet lubrication decreases faster than that of oil-air lubrication. It indicates that the film 5
thickness decreasing under oil-jet lubrication is more affected by speed. A parameter
η
is defined to describe the oil supply effects:
η=
V S
(2)
where V represents the volume of oil reservoir calculated by integration according to its shape, and S represents the oil supply per second. The oil supply S is fixed for a test while the volume of oil reservoir V reduces with entrainment speed. Therefore the parameter entrainment speed (Fig. 10). Under oil-air lubrication, the parameter
η
η
also decreases with
decreases from 10-6 s to 10-8 s
as the entrainment speed increases from 3 m/s to 30 m/s. It means that the oil needed to support the lubrication is quite minor compared with the large amount of oil supply and most of the oil is lost or spread on the disc though it is higher than that under oil-jet lubrication, which is almost 5 times higher at 3 m/s and 30 times higher at 30 m/s under such conditions. 3.2.2 The oil droplets effects The whole oil supply process can be divided into two steps both for oil-air lubrication far from the contact (Lub II) and oil-jet lubrication: Firstly, oil is ejected out from the nozzle with an initial speed and then impacts on the disc. Some oil may spread on the disc while some other may rebound or splash. Then, the oil spreading on the disc will rotate with the disc at high speeds and be driven outwards by the centrifugal force simultaneously. Only the oil on the track close to the radius of the contact can flow into the inlet zone. The difference between two kinds of lubrication systems in these two steps are discussed. 1.
Oil droplets impact on the disc
When the oil droplets impact on a disc at a certain speed, four cases of conditions may occur and a parameter Weber Number (We) is normally used to decide the conditions. This is achieved through the evaluation of the splashing parameter K (K=We0.5Re0.25, Re=Reynolds Number )[42]. The critical value Kc, above which the droplets will breakup and splash is determined experimentally by Cossali et al.[43]. If the droplet does not splash, it is further classified as sticking (We <5), rebounding (5
ρU 2 d σ K c = 649 + 3.76 / ( Ra / d )0.63 We =
Where
ρ , d , σ represents
(3) (4)
the density, diameter and surface tension of oil droplets separately, U
represents the vertical velocity (perpendicular to the disc) of oil droplets, Ra represents the roughness of the disc. To calculate the Weber Number, the mean diameter of oil droplets for oil-air lubrication is selected and the diameter of oil droplets by oil-jet lubrication is assumed to be the same with the diameter of jet nozzle (Table 3). For oil-air lubrication, the mean diameter of oil droplets is about 60 µm, and the jetting speed of oil is about 3~5 m/s, therefore the calculated Weber Number is 15~43, just locating in the spreading stage. For oil-jet lubrication, the mean diameter of oil droplets is about 2 mm. The jetting speed is proportional to the oil supply in this test. As the oil supply ranges from 0.57~1.13 6
ml/s, the jetting speed is 0.18~0.36 m/s and the Weber Number is 1.84~7.38. The comparison of Weber Number indicates that chances of oil spreading on the disc under oil-air lubrication are higher than that of oil-jet lubrication. 2.
Centrifugal effects on oil droplets
When the spreading oil droplets on the disc rotate with the disc at high speeds, they suffer from high centrifugal forces which will drive them to move along the direction of centrifugal forces and slowly get far away from the contact. The mass of a 2 mm-diameter oil droplet from oil-jet lubrication is 37 000 times larger than that of a 60 µm-diameter oil droplet from oil-air lubrication. Therefore, the oil droplets from oil-jet lubrication deposited on the disc are under stronger centrifugal forces due to their larger size. More of them are driven away faster from the track at higher speeds. As a result, the parameter
η
of oil-air lubrication decreases more slowly than that of oil-jet lubrication with
increasing speed as shown in Fig.10. In summary, under oil-air lubrication, more oil droplets can deposit on the disc while less of them are driven away by centrifugal effects. Therefore, the parameter η is much higher than that of oil-jet lubrication. 3.3 The thermal effects on film forming The temperature rise near the inlet zone is recorded under three different lubrication conditions (as described in Table 2). A dimensionless parameter R1 is used to represent the change of oil reservoir which is defined to be the ratio of inner side oil reservoir radius, r1 in Fig.2, to Hertz radius, b [7]. Under fully flooded lubrication (Fig. 11), the temperature rise increases linearly while R1 decreases as a power-law with entrainment speed under all lubrication conditions and the slopes of the exponent of the power-law are about -0.95 and -0.36 for oil-jet lubrication and oil-air lubrication (Lub II), respectively. Lub II (oil-air lubrication far from the inlet zone shown in Fig.7 and Table 2) results in smaller size of inner side oil reservoir, and the highest temperature rise while Lub III (Oil-jet lubrication) results in largest oil reservoir (When the R1 is larger than 14, it is out of the field of view) and lowest temperature rise. Lub I (oil-air lubrication near the inlet zone shown in Fig.3 and Table 2) gets almost the same size of oil reservoir as Lub II while the temperature rise is little lower which shows 1
℃ of decrease at 30m /s. The real temperature rise near the inlet zone should be much higher
than what can be detected 5 mm away from the inlet zone. Because of the temperature discrepancy, the film thicknesses under oil-air lubrication are little lower than those under oil-jet lubrication (as shown in Fig.8). As it is almost the same film forming conditions under pure rolling, the discrepancy of temperature rise should be based on the difference of heat loss mainly via heat conduction through ball and disc and heat convection through oil flowing. As only little part of oil supply can get to contact or go cross the contact successfully, it can be suggested that bigger oil reservoir may represent that more oil goes across the contact and thus intensifies the heat convection. The high pressure compressed air also help of heat convection to a limited extent. Under starved lubrication, the results are quite different from those of fully flooded lubrication [Fig.12 (b)]. Cases of similar turning point under three lubrication conditions are chosen so that the 7
thermal effects can be compared. The turning point of starvation is near 8 m/s under all lubrication. [Fig.12 (a)]. Under Lub III (Oil-jet lubrication) the temperature rise gets the highest as the film thickness and oil reservoir decreases the fastest. Lub I with high pressure compressed air still gets lower temperature rise which shows 1
℃ of decrease at 30 m/s compared with Lub II. Although the
oil-jet lubrication entails quite low temperature rise under fully flooded lubrication, the oil-air lubrication shows more stable thermal effects from fully flooded lubrication to starved lubrication. 4 Conclusion In present work, the film forming behavior was investigated under oil-air lubrication. Film thickness and temperature rise were recorded and compared with those under oil-jet lubrication. A parameter η is defined as the ratio of oil reservoir’s volume to the oil supply to describe the oil supply effects. The results show that the parameter η under oil-air lubrication is 5 times higher than that under oil-jet lubrication at 3 m/s and 30 times higher at 30 m/s. A parameter u2/S is used and superposition of curves under a range of oil supply is obtained The film thickness reduces in starved regime under oil-air lubrication is much slower than that under oil-jet lubrication and the temperature rise at 30 m/s is 2 oC lower than that under oil-jet lubrication in starved regime while it is 2 oC higher for fully flooded lubrication. The roles of micron-order oil droplets and high pressure compressed air were verified and discussed separately. The lubricating efficiency and stability are improved because more micron-order oil droplets can spread to the disc judged by Weber Number while less of them are driven away by centrifugal effects. The high pressure compressed air is used to transport the oil droplets. It can blow off the oil and cause oscillation of oil reservoir and film thickness, meanwhile, it helps to cool down the contact to a limited extent. Acknowledgments The work is financially supported by National Natural Science Foundation of China (51335005, 51375 255, 51321092), and National Key Basic Research Program of China (No.2014CB046404)
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Table 1 Operating conditions for measurements Material properties
Operating conditions
ball
disc
Load(N)
15
Material
Steel
Glass with Cr coating
E’(GPa)
117
Radius(mm)
11.1125
45
pH(GPa)
0.43
Roughness(nm)
5
3
b (µm)
128
t0(oC)
25
Table 2 Lubrication conditions (t0=25 oC) Label
Lub I
Lubrication System Oil-air
Oil supply position Near the inlet zone (Fig.3) 10
Air pressure 3/6 bar
Oil supply
0.036~0.22ml/s
Lub II
Oil-air
In the lower disc (Fig.7)
/
0.036~0.22ml/s
Lub III
Oil-jet
Near the inlet zone
/
0.57~2.83ml/s
Table 3 Lubrication conditions (t0=25 oC) Lubrication
Supply
Jetting speed
Mean diameter of oil
Weber
System
(ml/s)
(m/s)
droplet (m)
Number
Oil-air
0.036~0.22
3~5
60µm
15~43
Oil-jet
0.57~1.13
0.18~0.36
2mm
1.84~7.38
Fig.1 Diagram of oil supply system
Fig. 2 Diagram of oil-air lubrication system (a) Schematic of oil-air lubrication; (b) Homogenous oil droplets under oil-air lubrication; (c) Poor wetting under oil-jet lubrication
11
Fig. 3 Schematic of oil supply position under oil-air lubrication (Lub I in Table 2), the oil is supplied near the inlet zone.
Filmthickness (nm)
Oscillation region for 6 bar Oscillation region for 3 bar
Lub I (0.11ml/s, 3 bar) Lub I (0.11ml/s, 6 bar) Hmin (HD) 1
10
Entrainment speed (m/s)
Fig. 4 Measurements of minimum film thickness under oil-air lubrication which the oil is supplied near the inlet zone (Lub I in Table 2). The error bars indicates the oscillation of film thickness induced by high pressure compressed air.
12
Fig. 5 Images of oil reservoir blown off at u=1.4m/s under oil-air lubrication (Lub I in Table 2), the dashed lines show the edge of oil reservoirs, oil supply: 0.11ml/s, air pressure: 6 bar
Fig. 6 Images of oil reservoir of a comparison test under oil-air lubrication (Lub I in Table 2). The dashed lines represent the edge of oil reservoirs. (a) Start of the test, fully flooded (b) A wiper was added to block the oil on the disc (c) Oil reservoir recovered after the wiper was removed. u=5m/s, oil supply: 0.11ml/s, air pressure: 6 bar
Fig. 7 Schematic of oil supply position under oil-air lubrication (Lub II in Table 2), the oil is supplied on the lower disc, far from the contact.
13
(a) Oil-air lubrication (Lub II) 0.036ml/s 0.072ml/s 0.11ml/s 0.18ml/s 0.22ml/s Hmin(HD)
Film thickness (nm)
1000
1
10
Entainment speed (m/s)
(b) Oil-jet lubrication (Lub III) 0.57ml/s 0.85ml/s 1.13ml/s 2.83ml/s Hmin(HD)
Film thickness (nm)
1000
100 1
10
Entrainment speed (m/s)
Fig. 8 Minimum film thickness as a function of entrainment speed (a) under oil-air lubrication (Lub II in Table 2);
℃, PAO8
(b) under oil-jet lubrication (Lub III in Table 2), pure rolling, pH=431 MPa, t0=25
14
hmin/hminff
1
0.1
Oil-air (0.036ml/s) Oil-air (0.072ml/s) Oil-air (0.11ml/s) Oil-air (0.18ml/s) Oil-jet (0.57ml/s) Oil-jet (0.85ml/s) Oil-jet (1.13ml/s) 0.01
0.1
1
10
100
2
u /S
Fig. 9 Relative film thickness as a function of u2/S under oil-air lubrication (Lub II in Table 2) and under oil-jet lubrication (Lub III in Table 2), pure rolling, pH=431 MPa, t0=25 , PAO8
℃
1E-5
Oil-air( 0.036ml/s) Oil-air( 0.11ml/s) Oil-air( 0.22ml/s)
Oil-jet (0.57ml/s) Oil-jet (0.85ml/s) Oil-jet (1.13ml/s)
The parameter η (s)
1E-6
1E-7
1E-8
1E-9
1E-10 10
Entrainment speed (m/s)
Fig. 10 The parameter η as a function of entrainment speed for oil-air lubrication (Lub II in Table 2) and oil-jet
℃
lubrication ( Lub III in Table 2), pure rolling, pH=431 MPa, t0=25 , PAO8
15
30 25 20
O
15 1 10
R1
Temperature rise ( C)
Temperature rise Dimensionless size of inner side oil reservoir Lub I (0.22ml/s,3 bar) Lub I (0.22ml/s,6 bar) Lub II (0.22ml/s) Lub III (2.83ml/s)
5 0.1 1
10
Entrainment speed (m/s)
Fig. 11 Temperature rise and dimensionless size of inner side oil reservoir as a function of entrainment speed for fully flooded under all lubrication conditions
900 800 700
(a)
600
Film thickness (nm)
500 400 300
200
Lub I (0.036ml/s,3 bar) Lub I (0.036ml/s,6 bar) Lub II (0.036ml/s) Lub III (0.85ml/s) 100 1
10
Entrainment speed (m/s)
16
10
(b)
O
Temperature rise ( C)
Tempearature rise Dimensionless inner side oil reservoir Lub I (0.036ml/s,3 bar) Lub I (0.036ml/s,6 bar) Lub II (0.036ml/s) Lub III (0.85ml/s)
10
R1
1
0.1 1
10
Entrainment speed (m/s)
Fig. 12 (a) Minimum film thickness as a function of entrainment speed (b) Temperature rise and dimensionless size of inner side oil reservoir as a function of entrainment speed for starvation under all lubrication conditions.
Appendix: the calculation of the oil reservoir’s volume
Fig.13 The oil reservoir’s approximate model for volume calculation
An approximate model for oil reservoir is built as the oil reservoir is divided into three cylinders shown in Fig.13(a). V=v1+v2+v
(5)
For ever cylinder, the calculation is similar. Take v1 as an example (Fig.13(b)) (6)
v1=vOBCD-vOBG
vOBCD represents for the volume of a cylinder. Its undersurface is a sector whose radius is r1 and central angle is α1 ( The area
°)( Fig.13(a)). Its height is BC.
S1 =
α1π r12
(7)
360
The height BC = GD + OG = hc + R −
R 2 − r12
(8)
Where R represents the radius of the ball. Therefore,
vOBCD = S1 × BC =
α1π r12 360
× (hc + R − R 2 − r12 )
(9)
vABG represents for the volume of part of the ball. Its undersurface is a sector whose radius is r1 and 17
central angle is α1 (
°). Its height is OG
OG = R − R 2 − r12
vOBG =
α1 360
× π × OG 2 × ( R −
(10)
OG ) 3
(11)
Highlights
EHL film thicknesses were measured up to 30 m/s under oil-air lubrication.
The minimum film thicknesses decrease linearly against speed in starved regime.
A defined parameter η shows 30 times higher under oil-air lubrication at 30m/s.
The roles of micron-order oil droplets were verified and discussed.
18
The film forming behavior at high speeds under oil-air lubrication He Liang, Dan Guo, Liran Ma, Jianbin Luo
www.elsevier.com/locate/triboint
PII: DOI: Reference:
S0301-679X(15)00248-0 http://dx.doi.org/10.1016/j.triboint.2015.06.010 JTRI3715
To appear in:
Tribology International
Received date: 11 February 2015 Revised date: 1 June 2015 Accepted date: 2 June 2015 Cite this article as: He Liang, Dan Guo, Liran Ma, Jianbin Luo, The film forming behavior at high speeds under oil-air lubrication, Tribology International, http: //dx.doi.org/10.1016/j.triboint.2015.06.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The film forming behavior at high speeds under oil-air lubrication He Liang; Dan Guo*; Liran Ma, Jianbin Luo*
State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China. Corresponding authors: [email protected] (Dan Guo); [email protected] (Jianbin Luo)
Abstract The film forming behavior has been investigated under oil-air lubrication, compared with that under oil-jet lubrication in present work. Images of microscopic oil reservoir and interference were obtained up to 30 m/s. A parameter η describing the oil supply effects is 30 times higher and the film thickness reduces in starved regime much slower under oil-air lubrication compared with that under oil-jet lubrication. The contribution of micron-order oil droplets on film forming is discussed. More micron-order oil droplets can spread onto the disc while less of them are driven away by centrifugal effects. As a result, the oil supply efficiency of oil-air lubrication is improved. The high pressure compressed air can blow off the oil and intensify the film oscillation.
：High speeds, Elastohydrodynamic lubrication, Oil-air lubrication, Starvation
Keywords
Nomenclature h
Lubricant film thickness (m)
t0
Operating temperature (K)
η0
Ambient viscosity (Pa s)
u
Lubricant entrainment speed, u =(u1 + u2)/2
u1 , u2
Surface velocities of disc and ball (m/s)
E’
Reduced modulus (Pa)
pH
Maximum Herzian pressure (Pa)
b
Theoretical Hertz contact radius (m)
Re
Reynolds Number, ρud/η0
d
Diameter of oil droplets, m
1 Introduction The lubrication film thickness distribution in a point contact could be measured experimentally by optical interferometry introduced by Gohar and Cameron[1, 2] in the 1960s. Following this, different interferometry-based film thickness measurement techniques were developed [3-5]. These interferometry-based techniques made it easier to measure film thickness directly with high resolution up to a few nanometers under different conditions. For fully flooded lubrication, the film thicknesses under high speed [6, 7], high pressure [8-10] and high slide-roll-ratio [11, 12] were measured and showed deviations compared with those predicted by Hamorock and Dowson equations [13]. Many 1
new phenomena of lubrication films showed close relation to the speed, i.e. thin film lubrication phenomenon [4, 14, 15] and superlubricity phenomenon [16-19]. For starved lubrication, the characteristics and the judge of starvation degree were on the focus. The mechanism in point contact was investigated by Wedeven et al. [20] and Chiu [21] using a ball-on-disc test rig, indicating that the starvation was determined by the fluid replenishment ability into the track. Later, the inlet film was adopted to define the degree of starvation by Chevalier et al.[22] and Damiens et al.[23] in numerical models of starved elastohydrodynamic lubrication and Svoboda et al. [24] in ball-on-disc experiments. Criteria were proposed by Liu and Wen[25] to determine lubrication conditions between fully flooded, starved and parched lubrication. The influence of operational parameters conditions, including speed, viscosity, load and lubricant volume, on the onset of starvation in EHL contacts were performed experimentally [7, 26] later. However, roller bearings in high-speed spindles and aircraft engines are likely to run at much higher speeds. Numerical studies by van Zoelen et al.[27, 28] and experiments by Liang et al. [7, 29]suggested that centrifugal effects might drive the lubricant to flow vertically and the film thickness distribution was asymmetric under starved lubrication. Most of above works were under immersed or half immersed lubrication, which was proper for low speed conditions, but not for high-speed rolling ball-bearings in aircraft engine, high-speed spindles and other machine tools due to the high oil loss by splashing. Therefore, the oil-air lubrication, oil-mist lubrication and oil-jet lubrication were developed for improving the oil supply efficiency. Under the oil-air lubrication and oil–mist lubrication, the oil is broken down into micro-droplets and then make their way precisely into the friction point continually by high pressure compressed air flow. The difference is that under oil-air lubrication, the oil droplets are not atomized. Therefore, the oil-air lubrication system has the advantages of high lubricating efficiency and environmental benefits [30, 31]. Under oil-jet lubrication, the oil is jetted into the bearings. It needs to deliver much more oil into the bearings compared with the other two ways. As a result, the oil-jet lubrication obtains lower bearing temperature and higher power losses [32]. The researches on oil-air lubrication mainly focus on its thermal effects. Ramesh et al. [33] found that convection was the major component of heat transfer in this method. Materials, rotating speed, preload, oil supply rate and other factors [34-36] were optimized to reach the lowest temperature rise. Few efforts were made on the film thickness measurement under oil-air lubrication system. It was proved that thin film maintained in bearing up to 20 000 rpm using the capacity method under oil-air lubrication by Ramesh et al. [33] and under oil-jet lubrication by Gorse et al.[37]. However, the film distribution and the film forming characteristic are still invisible perhaps due to the difficulties in validating experimental measurements. In this article, the film forming behavior was investigated under the oil-air lubrication and compared with that under the oil-jet lubrication. Film thicknesses and temperature rises near the inlet zone were recorded on a ball-on-disc test rig for speeds up to 30 m/s using relative optical interference intensity (ROII) technology and compared with theories. The roles of high pressure compressed air and 2
micron-order oil droplets on film forming behavior were discussed under oil-air lubrication. 2 Experimental 2.1 Ball on disc test rig A homemade high-speed ball-on-disc test rig is used in the tests. The properties and functions are introduced in Ref.[7] . The material properties of the balls and discs were measured and are quoted in Table 1. Three 1-mm-diameter thermo couples (Omega, US) are located in the oil bath, near the inlet zone and near the outlet region of the contact on the disc separately, to record the temperature variations. The thermo couples are located close to the contact at macro level (about 5 mm away from the contact), however, it is still far away from the contact at micro level. What the thermo couples can detect is the temperature rise of the disc surface. If the thermo couples get closer to the contact, the temperature rise will increase. Therefore, during all tests, the positions of the thermo couples are fixed so that temperature rise of different tests can be compared. Interference images are taken by use of a high speed camera. Film thicknesses are determined by the relative optical interference intensity (ROII) technique [4, 38] and are given by the following expression[39]:
h=
λ nπ [( n + sin ) ⋅ π + arc cos( I ) ⋅ cos nπ − arc cos( I 0 )] 4π k 2
(1)
where λ represents wave length of the incident light, k is reflective index of lubricant, n is interference ¹
order, I is light intensity,
I max , I min is maximum or minimum interference light intensity, I is ¹
relative interference light intensity ( I
¹
= (2 I − I max − I min ) / ( I max − I min ) ) and I 0 is relative light
intensity when the lubricant film thickness is zero. 2.2 Lubrication systems The oil supply system is an autonomous system (Fig.1). In the tests, both the oil-air lubrication system and the oil-jet lubrication system are used and can be replaced. The basic structures of used oil-air lubrication device (SKF Vogel, Germany) are shown in Fig.2. It consists of an oil reservoir, an oil pump and mixing valves. The oil pump delivers the oil intermittently into the mixing valves, where the oil and the compressed air are mixed and distributed to oil-air supply pipes. Finally, oil-air stream is ejected by means of the nozzle and shoots onto the disc. The oil flow rate, oil supply position and air pressure can be controlled. The oil-jet lubrication is used as comparison. It contains an oil reservoir, a peristaltic pump and pipes. The oil is delivered from the oil reservoir via a pipe by the pump and then jets onto the disc through a nozzle near the inlet zone. The splashing oil is collected and flows back to the oil reservoir to form a supply circulation. 2.3 Test conditions In the present work, all tests are carried out at pure rolling. The operating conditions are shown in Table 1. One kind of polyalphaolefin oil (PAO8) is used in the tests. The viscosity and density of PAO8 is about 86.55 mPa s and 833 kg/m3 at 25 oC, as measured by a viscometer (Anton Paar, Austria) and the 3
surface tension is 29.4 mN/m as measured by a surface tension-meter (Dataphysics DCAT21, Germany). Three lubrication conditions are used as shown in Table 2 and Table 3. The changes of film thickness and temperature rise as a function of entrainment speed are studied at various speeds from 3 m/s to 30 m/s. 3. Results and discussions 3.1 The effects of high pressure compressed air on film forming The oil is supplied firstly near the inlet zone under oil-air lubrication, shown in Fig.3. (Labelled as Lub I in Table 2). The oil supply of 0.11 ml/s and the high pressure compressed air of 3 bar and 6 bar are utilized. Figure 4 shows the minimum film thickness as a function of entrainment speed. The film thickness seems to oscillate under 5 m/s and above 10 m/s under high pressure compressed air of 3 bar and 6 bar and the amplitude is larger for a stronger air pressure (6 bar). As the oil supply by the oil-air lubrication and oil-jet lubrication used in the tests is periodic. The oil reservoir and film thickness may oscillate. It is normally believed that there is a critical inlet distance where the film thickness starts to decrease[40]. The oscillation of oil reservoir starts to influence the film thickness onwards 10 m/s as the volume of oil reservoir shrinks with entrainment speed. The amplitude of film thickness oscillation is influenced by the oil supply, frequency and other factors. In such conditions, the amplitude of film thickness oscillation is about 50 nm and 80 nm under high pressure compressed air of 3 bar and 6 bar. The amplitude of film thickness under oil-air lubrication avoiding the impact of compressed air and under oil-jet lubrication is 15 nm and 30 nm separately (see Fig. 8). The comparison of oscillation amplitude of film thickness indicates that the high pressure compressed air intensifies the oscillation of film thickness. For speeds lower than 5 m/s, the oscillation amplitude of film thickness is quite large and the contact may experience parched starvation as the oil can be blown off the contact region directly (the images of oil reservoir is shown in Fig.5). The oil reservoir still exists but has been separated from the contact. It is of interest to find that the starvation degree is reduced when the speed is higher than 5 m/s. A comparison test is made to remove the oil on the disc by adding a wiper behind the contact. Figure 6 shows the images of oil reservoir changes about the whole process. First step [Fig.6 (a)], the contact achieves fully flooded lubrication under oil-air lubrication (Lub I, 5 m/s, 0.11 ml/s, 6 bar). Second step [Fig.6 (b)], a wiper is added to block the oil on the disc. The oil from oil-air lubrication is the only way to supply the contact. The oil reservoir immediately shrinks and the minimum film thickness decreases from 600 nm to about 120 nm although the oil supply is continuing. Third step [Fig.6 (c)], the wiper is removed. The oil reservoir slowly grows and recovers after 10 seconds. It indicates that only small part of oil from oil-air lubrication can reach near the contact directly, most of the other oil droplets will be blown off or spread on the disc. The spreading oil will rotate with the disc and accumulate. It can replenish the oil reservoir after one revolution or more. The oil reservoir should be a result of comparison between oil loss intensified by high pressure compressed air and the oil supply in the inlet zone. At lower speeds, it takes longer to go around one revolution, during this time, the oil loses more 4
by high pressure air than that can flow back. While at higher speeds, the interval between revolutions is reduced, the high pressure air still blow off the oil in the inlet zone at high speeds, however the spreading oil accumulates fast and replenishes the oil reservoir promptly to avoid the film from collapsing. The high pressure compressed air is commonly regarded to transport oil droplets and to help with heat dissipation. In this section, it shows that the high pressure compressed air blow off the oil in the inlet zone and intensify the oscillation of film thickness. 3.2 The effects of oil droplets on film forming 3.2.1 Film thickness measurement and oil supply effects There are two significant characteristics for oil-air lubrication: high pressure compressed air and homogenous oil droplets with diameter of tens of micrometers. The effects of the oil droplets on film forming are detected in this section. In order to avoid the impact of high pressure compressed air on lubricant flowing near the inlet zone, the oil is supplied far from the contact under oil-air lubrication, shown in Fig. 7 (labelled as Lub II in Table 2). Figure 8(a) shows the measured minimum film thicknesses for different oil supply against entrainment speed under oil-air lubrication far from the inlet zone (Lub II). For starved lubrication, the minimum film thicknesses decrease linearly against entrainment speed. The distribution of film thickness along y axis is asymmetric at high speeds because of centrifugal effects [7]. The film thicknesses (Fig. 8(b)) under oil-jet lubrication were measured as comparison. For fully flooded lubrication, the minimum film thicknesses under oil-air lubrication are little smaller than those under oil-jet lubrication with errors less than 10%. This may be mainly caused by the thermal effects which will be discussed in section 3.3. If compared with predicted ones by Hamrock-Dowson equations, the film thicknesses show increasing discrepancies at speeds higher than 4 m/s which may be mainly caused by the inlet shear heating [41]. For starved lubrication, the changes of film thickness under oil-jet lubrication show different patterns: the minimum film thicknesses collapse higher than a critical speed, decrease rapidly and finally maintain at about 30 nm. The film thickness under starved conditions are compared with Cann et al. [26] in which a parameter using the ratio speed/volume can superpose curves under different oil supply at lower speeds. However, it may not proper for high speed conditions. The film thickness descending is more impacted by speed due to the centrifugal effects [7]. Therefore, the ratio u2/S (S represents the oil supply, the unit is µL/s) is used and superposition of curves under a range of oil supply is obtained (see Fig. 9). There are two main differences between curves of oil-air lubrication and that of oil-jet lubrication. The first one is the starting point of starvation, where the relative film thickness starts to decrease. Both of them are larger than what Cann et al. found because the parameter u2 is used and the oil is supplied continuously instead of a limited volume used by Cann et al. [26]. Apparently, the starting point under oil-air lubrication is much larger than that under oil-jet lubrication. The second one is the curvature of film thickness against u2/S under starvation. The film thickness under oil-jet lubrication decreases faster than that of oil-air lubrication. It indicates that the film 5
thickness decreasing under oil-jet lubrication is more affected by speed. A parameter
η
is defined to describe the oil supply effects:
η=
V S
(2)
where V represents the volume of oil reservoir calculated by integration according to its shape, and S represents the oil supply per second. The oil supply S is fixed for a test while the volume of oil reservoir V reduces with entrainment speed. Therefore the parameter entrainment speed (Fig. 10). Under oil-air lubrication, the parameter
η
η
also decreases with
decreases from 10-6 s to 10-8 s
as the entrainment speed increases from 3 m/s to 30 m/s. It means that the oil needed to support the lubrication is quite minor compared with the large amount of oil supply and most of the oil is lost or spread on the disc though it is higher than that under oil-jet lubrication, which is almost 5 times higher at 3 m/s and 30 times higher at 30 m/s under such conditions. 3.2.2 The oil droplets effects The whole oil supply process can be divided into two steps both for oil-air lubrication far from the contact (Lub II) and oil-jet lubrication: Firstly, oil is ejected out from the nozzle with an initial speed and then impacts on the disc. Some oil may spread on the disc while some other may rebound or splash. Then, the oil spreading on the disc will rotate with the disc at high speeds and be driven outwards by the centrifugal force simultaneously. Only the oil on the track close to the radius of the contact can flow into the inlet zone. The difference between two kinds of lubrication systems in these two steps are discussed. 1.
Oil droplets impact on the disc
When the oil droplets impact on a disc at a certain speed, four cases of conditions may occur and a parameter Weber Number (We) is normally used to decide the conditions. This is achieved through the evaluation of the splashing parameter K (K=We0.5Re0.25, Re=Reynolds Number )[42]. The critical value Kc, above which the droplets will breakup and splash is determined experimentally by Cossali et al.[43]. If the droplet does not splash, it is further classified as sticking (We <5), rebounding (5
ρU 2 d σ K c = 649 + 3.76 / ( Ra / d )0.63 We =
Where
ρ , d , σ represents
(3) (4)
the density, diameter and surface tension of oil droplets separately, U
represents the vertical velocity (perpendicular to the disc) of oil droplets, Ra represents the roughness of the disc. To calculate the Weber Number, the mean diameter of oil droplets for oil-air lubrication is selected and the diameter of oil droplets by oil-jet lubrication is assumed to be the same with the diameter of jet nozzle (Table 3). For oil-air lubrication, the mean diameter of oil droplets is about 60 µm, and the jetting speed of oil is about 3~5 m/s, therefore the calculated Weber Number is 15~43, just locating in the spreading stage. For oil-jet lubrication, the mean diameter of oil droplets is about 2 mm. The jetting speed is proportional to the oil supply in this test. As the oil supply ranges from 0.57~1.13 6
ml/s, the jetting speed is 0.18~0.36 m/s and the Weber Number is 1.84~7.38. The comparison of Weber Number indicates that chances of oil spreading on the disc under oil-air lubrication are higher than that of oil-jet lubrication. 2.
Centrifugal effects on oil droplets
When the spreading oil droplets on the disc rotate with the disc at high speeds, they suffer from high centrifugal forces which will drive them to move along the direction of centrifugal forces and slowly get far away from the contact. The mass of a 2 mm-diameter oil droplet from oil-jet lubrication is 37 000 times larger than that of a 60 µm-diameter oil droplet from oil-air lubrication. Therefore, the oil droplets from oil-jet lubrication deposited on the disc are under stronger centrifugal forces due to their larger size. More of them are driven away faster from the track at higher speeds. As a result, the parameter
η
of oil-air lubrication decreases more slowly than that of oil-jet lubrication with
increasing speed as shown in Fig.10. In summary, under oil-air lubrication, more oil droplets can deposit on the disc while less of them are driven away by centrifugal effects. Therefore, the parameter η is much higher than that of oil-jet lubrication. 3.3 The thermal effects on film forming The temperature rise near the inlet zone is recorded under three different lubrication conditions (as described in Table 2). A dimensionless parameter R1 is used to represent the change of oil reservoir which is defined to be the ratio of inner side oil reservoir radius, r1 in Fig.2, to Hertz radius, b [7]. Under fully flooded lubrication (Fig. 11), the temperature rise increases linearly while R1 decreases as a power-law with entrainment speed under all lubrication conditions and the slopes of the exponent of the power-law are about -0.95 and -0.36 for oil-jet lubrication and oil-air lubrication (Lub II), respectively. Lub II (oil-air lubrication far from the inlet zone shown in Fig.7 and Table 2) results in smaller size of inner side oil reservoir, and the highest temperature rise while Lub III (Oil-jet lubrication) results in largest oil reservoir (When the R1 is larger than 14, it is out of the field of view) and lowest temperature rise. Lub I (oil-air lubrication near the inlet zone shown in Fig.3 and Table 2) gets almost the same size of oil reservoir as Lub II while the temperature rise is little lower which shows 1
℃ of decrease at 30m /s. The real temperature rise near the inlet zone should be much higher
than what can be detected 5 mm away from the inlet zone. Because of the temperature discrepancy, the film thicknesses under oil-air lubrication are little lower than those under oil-jet lubrication (as shown in Fig.8). As it is almost the same film forming conditions under pure rolling, the discrepancy of temperature rise should be based on the difference of heat loss mainly via heat conduction through ball and disc and heat convection through oil flowing. As only little part of oil supply can get to contact or go cross the contact successfully, it can be suggested that bigger oil reservoir may represent that more oil goes across the contact and thus intensifies the heat convection. The high pressure compressed air also help of heat convection to a limited extent. Under starved lubrication, the results are quite different from those of fully flooded lubrication [Fig.12 (b)]. Cases of similar turning point under three lubrication conditions are chosen so that the 7
thermal effects can be compared. The turning point of starvation is near 8 m/s under all lubrication. [Fig.12 (a)]. Under Lub III (Oil-jet lubrication) the temperature rise gets the highest as the film thickness and oil reservoir decreases the fastest. Lub I with high pressure compressed air still gets lower temperature rise which shows 1
℃ of decrease at 30 m/s compared with Lub II. Although the
oil-jet lubrication entails quite low temperature rise under fully flooded lubrication, the oil-air lubrication shows more stable thermal effects from fully flooded lubrication to starved lubrication. 4 Conclusion In present work, the film forming behavior was investigated under oil-air lubrication. Film thickness and temperature rise were recorded and compared with those under oil-jet lubrication. A parameter η is defined as the ratio of oil reservoir’s volume to the oil supply to describe the oil supply effects. The results show that the parameter η under oil-air lubrication is 5 times higher than that under oil-jet lubrication at 3 m/s and 30 times higher at 30 m/s. A parameter u2/S is used and superposition of curves under a range of oil supply is obtained The film thickness reduces in starved regime under oil-air lubrication is much slower than that under oil-jet lubrication and the temperature rise at 30 m/s is 2 oC lower than that under oil-jet lubrication in starved regime while it is 2 oC higher for fully flooded lubrication. The roles of micron-order oil droplets and high pressure compressed air were verified and discussed separately. The lubricating efficiency and stability are improved because more micron-order oil droplets can spread to the disc judged by Weber Number while less of them are driven away by centrifugal effects. The high pressure compressed air is used to transport the oil droplets. It can blow off the oil and cause oscillation of oil reservoir and film thickness, meanwhile, it helps to cool down the contact to a limited extent. Acknowledgments The work is financially supported by National Natural Science Foundation of China (51335005, 51375 255, 51321092), and National Key Basic Research Program of China (No.2014CB046404)
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Table 1 Operating conditions for measurements Material properties
Operating conditions
ball
disc
Load(N)
15
Material
Steel
Glass with Cr coating
E’(GPa)
117
Radius(mm)
11.1125
45
pH(GPa)
0.43
Roughness(nm)
5
3
b (µm)
128
t0(oC)
25
Table 2 Lubrication conditions (t0=25 oC) Label
Lub I
Lubrication System Oil-air
Oil supply position Near the inlet zone (Fig.3) 10
Air pressure 3/6 bar
Oil supply
0.036~0.22ml/s
Lub II
Oil-air
In the lower disc (Fig.7)
/
0.036~0.22ml/s
Lub III
Oil-jet
Near the inlet zone
/
0.57~2.83ml/s
Table 3 Lubrication conditions (t0=25 oC) Lubrication
Supply
Jetting speed
Mean diameter of oil
Weber
System
(ml/s)
(m/s)
droplet (m)
Number
Oil-air
0.036~0.22
3~5
60µm
15~43
Oil-jet
0.57~1.13
0.18~0.36
2mm
1.84~7.38
Fig.1 Diagram of oil supply system
Fig. 2 Diagram of oil-air lubrication system (a) Schematic of oil-air lubrication; (b) Homogenous oil droplets under oil-air lubrication; (c) Poor wetting under oil-jet lubrication
11
Fig. 3 Schematic of oil supply position under oil-air lubrication (Lub I in Table 2), the oil is supplied near the inlet zone.
Filmthickness (nm)
Oscillation region for 6 bar Oscillation region for 3 bar
Lub I (0.11ml/s, 3 bar) Lub I (0.11ml/s, 6 bar) Hmin (HD) 1
10
Entrainment speed (m/s)
Fig. 4 Measurements of minimum film thickness under oil-air lubrication which the oil is supplied near the inlet zone (Lub I in Table 2). The error bars indicates the oscillation of film thickness induced by high pressure compressed air.
12
Fig. 5 Images of oil reservoir blown off at u=1.4m/s under oil-air lubrication (Lub I in Table 2), the dashed lines show the edge of oil reservoirs, oil supply: 0.11ml/s, air pressure: 6 bar
Fig. 6 Images of oil reservoir of a comparison test under oil-air lubrication (Lub I in Table 2). The dashed lines represent the edge of oil reservoirs. (a) Start of the test, fully flooded (b) A wiper was added to block the oil on the disc (c) Oil reservoir recovered after the wiper was removed. u=5m/s, oil supply: 0.11ml/s, air pressure: 6 bar
Fig. 7 Schematic of oil supply position under oil-air lubrication (Lub II in Table 2), the oil is supplied on the lower disc, far from the contact.
13
(a) Oil-air lubrication (Lub II) 0.036ml/s 0.072ml/s 0.11ml/s 0.18ml/s 0.22ml/s Hmin(HD)
Film thickness (nm)
1000
1
10
Entainment speed (m/s)
(b) Oil-jet lubrication (Lub III) 0.57ml/s 0.85ml/s 1.13ml/s 2.83ml/s Hmin(HD)
Film thickness (nm)
1000
100 1
10
Entrainment speed (m/s)
Fig. 8 Minimum film thickness as a function of entrainment speed (a) under oil-air lubrication (Lub II in Table 2);
℃, PAO8
(b) under oil-jet lubrication (Lub III in Table 2), pure rolling, pH=431 MPa, t0=25
14
hmin/hminff
1
0.1
Oil-air (0.036ml/s) Oil-air (0.072ml/s) Oil-air (0.11ml/s) Oil-air (0.18ml/s) Oil-jet (0.57ml/s) Oil-jet (0.85ml/s) Oil-jet (1.13ml/s) 0.01
0.1
1
10
100
2
u /S
Fig. 9 Relative film thickness as a function of u2/S under oil-air lubrication (Lub II in Table 2) and under oil-jet lubrication (Lub III in Table 2), pure rolling, pH=431 MPa, t0=25 , PAO8
℃
1E-5
Oil-air( 0.036ml/s) Oil-air( 0.11ml/s) Oil-air( 0.22ml/s)
Oil-jet (0.57ml/s) Oil-jet (0.85ml/s) Oil-jet (1.13ml/s)
The parameter η (s)
1E-6
1E-7
1E-8
1E-9
1E-10 10
Entrainment speed (m/s)
Fig. 10 The parameter η as a function of entrainment speed for oil-air lubrication (Lub II in Table 2) and oil-jet
℃
lubrication ( Lub III in Table 2), pure rolling, pH=431 MPa, t0=25 , PAO8
15
30 25 20
O
15 1 10
R1
Temperature rise ( C)
Temperature rise Dimensionless size of inner side oil reservoir Lub I (0.22ml/s,3 bar) Lub I (0.22ml/s,6 bar) Lub II (0.22ml/s) Lub III (2.83ml/s)
5 0.1 1
10
Entrainment speed (m/s)
Fig. 11 Temperature rise and dimensionless size of inner side oil reservoir as a function of entrainment speed for fully flooded under all lubrication conditions
900 800 700
(a)
600
Film thickness (nm)
500 400 300
200
Lub I (0.036ml/s,3 bar) Lub I (0.036ml/s,6 bar) Lub II (0.036ml/s) Lub III (0.85ml/s) 100 1
10
Entrainment speed (m/s)
16
10
(b)
O
Temperature rise ( C)
Tempearature rise Dimensionless inner side oil reservoir Lub I (0.036ml/s,3 bar) Lub I (0.036ml/s,6 bar) Lub II (0.036ml/s) Lub III (0.85ml/s)
10
R1
1
0.1 1
10
Entrainment speed (m/s)
Fig. 12 (a) Minimum film thickness as a function of entrainment speed (b) Temperature rise and dimensionless size of inner side oil reservoir as a function of entrainment speed for starvation under all lubrication conditions.
Appendix: the calculation of the oil reservoir’s volume
Fig.13 The oil reservoir’s approximate model for volume calculation
An approximate model for oil reservoir is built as the oil reservoir is divided into three cylinders shown in Fig.13(a). V=v1+v2+v
(5)
For ever cylinder, the calculation is similar. Take v1 as an example (Fig.13(b)) (6)
v1=vOBCD-vOBG
vOBCD represents for the volume of a cylinder. Its undersurface is a sector whose radius is r1 and central angle is α1 ( The area
°)( Fig.13(a)). Its height is BC.
S1 =
α1π r12
(7)
360
The height BC = GD + OG = hc + R −
R 2 − r12
(8)
Where R represents the radius of the ball. Therefore,
vOBCD = S1 × BC =
α1π r12 360
× (hc + R − R 2 − r12 )
(9)
vABG represents for the volume of part of the ball. Its undersurface is a sector whose radius is r1 and 17
central angle is α1 (
°). Its height is OG
OG = R − R 2 − r12
vOBG =
α1 360
× π × OG 2 × ( R −
(10)
OG ) 3
(11)
Highlights
EHL film thicknesses were measured up to 30 m/s under oil-air lubrication.
The minimum film thicknesses decrease linearly against speed in starved regime.
A defined parameter η shows 30 times higher under oil-air lubrication at 30m/s.
The roles of micron-order oil droplets were verified and discussed.
18