On the film thickness behaviour of polymer greases at low and high speeds

Tribology International 90 (2015) 435–444

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Tribology International journal homepage: www.elsevier.com/locate/triboint

On the film thickness behaviour of polymer greases at low and high speeds David Gonçalves a,n, Beatriz Graça a, Armando V. Campos b, J. Seabra c, Johan Leckner d, René Westbroek d a

INEGI, Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal ISEP-IPP, Instituto Superior de Engenharia do Instituto Politécnico do Porto, Portugal c FEUP, Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal d Axel Christiernsson International AB, Sweden b

art ic l e i nf o

a b s t r a c t

Article history: Received 3 February 2015 Received in revised form 22 April 2015 Accepted 7 May 2015 Available online 16 May 2015

Experimental batches of polymer thickened greases, as well as their base and bleed-oils were tribologically characterized through film thickness measurements over a wide range of entrainment speeds on a ball-on-disc test rig using optical interferometry. The results are in agreement with previous observations of several authors. Under fully flooded conditions and low speed it was observed that thickener lumps enter the contact producing a high film thickness plateau. The transition speed at which the film thickness increases with decreasing speed is dependent on the thickener content and operating temperature. At moderate to high speeds, all the tested greases show a film thickness much higher than the base and bleed-oils, even though the bleed-oil's film thickness is closer to the grease's. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Polymer greases Film thickness Grease formulation

1. Introduction The mechanisms which rule the grease lubrication of rolling contacts are still not completely established. While in the case of fully flooded, oil-lubricated contacts, the EHL theory is well defined, in the case of grease lubrication this theory is more complex. However, there has been a growing interest in the topic over the last few decades and many studies from different authors have reached a few generalized conclusions. It was already observed that both oil released from the grease and thickener lumps cross the EHD contact and contribute to EHD film formation at low speeds [1–3]. Many studies also suggest that lubricating greases with the same formulation generate higher film thickness for higher base oil viscosities and thickener content [4]. Furthermore, a few authors also found that the grease builds-up a higher film thickness than its base oil, under fully flooded lubrication [2,3,5,6]. This difference was reported to be mainly dependent on the base oil viscosity, thickener type and its content [4]. Cann et al., measured the grease film thickness in a ball-on-disc device and clearly showed that the film thickness was composed of the sum of static and dynamic film components. The static film is a layer adsorbed on the surfaces whether or not in movement (residual layer), while the dynamic part is due to the elastohydrodynamic n

Corresponding author. Tel.: þ 351 225081742; fax: þ 351 225081584. E-mail address: [email protected] (D. Gonçalves).

http://dx.doi.org/10.1016/j.triboint.2015.05.007 0301-679X/& 2015 Elsevier Ltd. All rights reserved.

effect, like predicted by the EHL equations (typical oil film). Cann [7] also wrote that the thickener will not enter the contact at higher speeds but will be pushed to the side, which means that at moderate to high speeds, the film thickness can be calculated using the standard EHL film thickness equations, using the base oil viscosity as the viscosity of the active lubricant in the contact. Residual films of thickness around 6–80 nm were found, consisting of significant amounts of thickener [8]. Other authors found that the oil released from the grease under static or dynamic conditions (“bleed-oil”) can show, for certain grease formulations, very different properties than the base oil [9– 11] and evidence was found that the film thickness and traction coefficient produced by this bleed-oil is much closer to the greases' [11–13]. More recently, the film thickness behaviour at ultra-low speeds was investigated [14] and the thickener contribution to the film thickness formation at low speeds was addressed again. Moreover, the film thickness in rolling bearings lubricated with grease was also measured and a parallelism between the full rolling bearing tests and the single contact test results was found [14]. Experimental batches of polymer greases, as well as their base and bleed oils were rheological and chemically evaluated by the authors of this paper in previous publications [15,16]. In this work, the film thickness behaviour of polymer greases at both low and high speeds was addressed. To study the grease lubrication mechanisms, film thickness measurements were performed in a

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Table 1 Tested greases' properties. Grease reference

M1

Thickener type

Polypropylene

Thickener content Elastomer content

11 0

13 0

15 0

Worked penetration (ISO 2137) NLGI

290 2

269 2

80 1C

12,035 2574

Consistency factor k Shear-thinning index n

80 1C

15.36 0.49

Base oil viscosity (ASTM D445)

40 1C 100 1C

48 8

20 1C

1.460 1.467 1.460

Storage modulus G0 Loss modulus G″

Base oil refractive index Grease refractive index Bleed-oil refractive index

M2

MLi

Units

Lithium complex

–

13 2.6

17.5 0

% %

249 3

276 2

n.a. n.a.

10  1 mm –

21,347 4596

29,810 6029

16,030 5225

22,285 7102

Pa Pa

31.62 0.43

37.13 0.44

59.67 0.48

104.20 0.31

Pa –

178.7 21.4

mm2/s

1.465 1.483 1.474

– – –

1.468 1.460

M3

1.468 1.460

M5

1.470 1.461

ball-on-disc apparatus with fresh grease, as well as with fresh base and bleed-oils. The aim of this work is to study the behaviour of this poorly studied type of grease in the light of recent discoveries regarding the film thickness of lubricating greases at low speeds [14]. Additionally, this work aims to understand the thickener role in grease lubrication and its contribution to the active lubricant inside the EHD contact.

2. Background on the numerical models for film thickness calculation of grease, base oils and bleed-oils The film thickness behaviour of base oils with Newtonian behaviour is well understood for a long time. Since these oils do not show significant shear thinning, shear degradation or thixotropic behaviour under typical EHL conditions, there are a few equations which can predict the film thickness very accurately [17–22]. The main differences between these models are the way in which the viscosity and the density were treated regarding pressure and temperature. One of the most accepted models to describe the viscosity dependence on pressure and temperature is the Roelands equation. However, this equation has already been criticised by other authors [23] who have performed very high pressure viscosity measurements for many liquids, claiming that the viscosity does not follow the Roelands law. The film thickness equation proposed by Hamrock et al., here given by Eq. (1): H oc ¼ ϕT  1:345  Rx  U 0:670  G0:530  W  0:067  C 0

ð1Þ

was obtained using the Roelands equation to describe the viscosity dependence on pressure and temperature while also considering the fluid to be compressible (Dowson and Higginson [24]). In Eq. (1), the thermal correction ϕT was also included, which contemplates a correction to the film thickness due to lubricant heating at the contact inlet [25]. This equation, although very accurate for Newtonian fluids, largely overestimates the film thickness for shear-thinning lubricants [26]. The film thickness of non-Newtonian fluids, which have been the scope of a few authors for the latest years, must consider not only the viscosity dependence on pressure and temperature, but also the dependence on the shear deformation. Derived by Katyal and Kumar [26] and following a similar approach to Hamrock and Dowson's [27], Eq. (2) predicts the central film thickness for shear-thinning lubricants in EHD point contacts under pure

Fig. 1. Dynamic viscosity curves of the bleed-oils extracted from greases M2, M5 and MLi.

Table 2 Calculated kinematic viscosities of the base and bleed-oils of the fresh greases. Note: viscosity values in cSt. Temperature

60 1C

80 1C

110 1C

PAO base oil M1 bleed-oil M2 bleed-oil M3 bleed-oil M5 bleed-oil

21.58 22.59 22.62 23.67 322.01

13.05 13.22 13.34 13.59 173.76

7.44 7.12 7.44 7.62 88.09

77.78 56.69

42.56 29.40

21.24 14.09

Blend base oil MLi bleed-oil

rolling: H k0 ¼ 1:099  RX  U 0:652  G0:570  W  0:042  R

ð2Þ

The model is a numerical regression based on a full numerical simulation where the Reynolds equation is solved using the

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Fig. 2. Diagram of the optical interference technique used in the EHD2 equipment.

Carreau viscosity model and an exponential pressure–viscosity relation similar to Barus' [28]. In this equation, U, G and W are dimensionless parameters very similar to Hamrock and Dowson's parameters. The R factor is the shear-thinning correction factor and it also depends on the dimensionless parameters U, G and W. If the lubricant oil presents a non-Newtonian shear-thinning behaviour, R will be less than 1, indicating the film thinning. Otherwise, R should be equal to the unity allowing to use Eq. (2), for Newtonian lubricating oils. This R factor follows the Carreau viscosity model represented through Eq. (3): "

η ¼ η0 þ ðη0  η1 Þ  1 þ




η0 γ_ Gcr

2 #ðn  1Þ=2

Parameters

Ball

Disc

Units

Radius – Rx;y Roughness – Ra Material Elastic modulus – E Poisson coefficient – ν

9.525 r 20 AISI 52100 207 0.29

– E5 Glass 64 0.20

mm nm – GPa GPa

Load – L Hertzian pressure – Pmax Entrainment speed - U0 Slide-to-roll ratio - SRR Temperature - T

50 E0.7 0.01–2 3 60, 80, 110

N GPa m/s % 1C

ð3Þ previously referred to Eq. (7) [35].

where η0 is referred to the first Newtonian viscosity at low shear rates and η1 the second Newtonian viscosity at high shear rates (here considered zero, since it was not possible to predict its value). Gcr is the bleed-oil's critical stress (stress at which the first Newtonian plateau ends) and n is the power-law index. The theoretical film thickness H0 can still be corrected to include the inlet shear heating effect, using the thermal reduction factor ϕT, as shown in Eq. (4) [25]. H k0c ¼ ϕT  H 0

Table 3 EHD2—ball-on-disc test conditions.

ð4Þ

Regarding the film thickness of lubricating greases, the EHL theory for rolling contacts under fully flooded conditions is not fully established yet. The initial film thickness is known to be higher than expected with the base oil up to the point where starvation occurs and the film is largely reduced. The initial fully flooded film thickness has been modelled by some authors assuming the initial thickness to be proportional to the thickener concentration. Hurley even developed an empirical formula for this [29]. Other authors however, chose to use the grease rheology as an input, developing a model for fully flooded grease lubricated contacts [30–33]. The Herschel–Bulkley and Bingham rheological models are the most commonly used nonNewtonian models. Using these models the authors found slightly higher values of film thickness compared to those calculated with the base oil viscosity only. Yang and Qian [34], using the Bingham rheology model, showed that the conventional EHL formula could be used for film thickness calculation if the grease's viscosity at high shear rates was used instead of the base oil's. More recently, other researchers developed simple models for film predictions of grease under fully flooded conditions. Examples of these models are shown in Eqs. (5) [4], (6) [34] and the

h ð1 þ B  ΦÞ0:67 þ1 ¼ hoil 100

ð5Þ


0:74 h K ¼ hoil ηoil

ð6Þ

h hR ¼ þ1 hoil hoil

ð7Þ

The film thickness under starvation has also been the scope of work of some authors. Aihara and Downson [36] performed an experimental study in a two-disc machine, suggesting that the grease's film thickness was about 70% of the fully flooded film thickness of the base oil. Kauzlarich and Greenwood pointed that shear degradation of the grease leads to a reduction of the film thickness in time [6].

3. Materials and methods 3.1. Tested greases Five greases were tested in this work: M1, M2, M3, M5 and MLi. The greases' main properties specified by the manufacturer are shown in Table 1. For more information regarding the methods used to characterize the tested greases, refer to [15]. Experimental batches of polymer thickened greases were manufactured and processed so they should reflect the differences in their composition. In short: the samples have been melted and quenched in 1 kg batches using the same settings for each batch. The milling has been done in a colloidal mill where each grease has passed through the mill exactly the same number of times with decreasing gap size. The process is kept as uniform as possible.

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3

Film Thickness [nm]

10

2

10

1

10

-2

-1

10

0

10

10

Entrainment Speed [m/s]

Fig. 3. Film thickness measurements of different formulated greases at 60 1C.

All these greases were formulated with a base oil of the same nature: poly-alpha-olefin (PAO) with exception of grease MLi which was formulated with a mixture of two different grades of PAO and some ester (5% v/v) to facilitate the saponification reaction. None of the grease contains additives or anti-oxidants. Since Lithium thickened greases are the most common lubricating greases in the market, MLi was tested as reference. This grease has no polymer or additives in its formulation, even though its additized version is a fully formulated commercial product on the market.

3.2. Base oils and bleed-oils properties The dynamic viscosities of base oils and bleed-oils were measured on a rotational rheometer at 60, 80 and 110 1C, the same temperatures at which the film thickness curves were measured. The method used to extract the bleed-oil from the grease can be consulted in [15]. The corresponding kinematic viscosities were calculated from the dynamic viscosity values obtained at the first Newtonian plateau (see Fig. 1 for the results at 601 C). The calculated viscosity results are shown in Table 2. From the analysis of this table, it can be concluded that the thickener content does not significantly influence the bleed-oil's viscosity since its value is about the same for the bleed-oils of greases M1, M2 and M3. On the other hand, it is clear that the elastomer (co-thickener) presence greatly increases the bleed-oil's viscosity. The bleed-oil of grease M5 shows a much higher viscosity than the bleed-oil of grease M2, even if they were formulated with the same base oil, which suggests that the elastomer “bleeds” with the oil released from the grease. However, the viscosity of the bleed-oil of grease M5 shows a clear shearthinning behaviour, which should be related to the changes in the elastomer morphology when subjected to high shear rates, therefore decreasing the viscosity increase effect. This shear-thinning effect can be seen in Fig. 1. It is also interesting to see that the bleed-oil extracted from grease MLi shows a smaller viscosity than the corresponding base oil used in its formulation.

3.3. EHD2 equipment The EHD2 is an equipment produced by PCS Instruments which allows the measurement of the ultra-thin lubricant films in ballon-disc or roller-on-disc configuration, over different ranges of temperature, speed, load and slide-to-roll ratio. The device uses the space layer interferometry method which allows the measurement of ultra-thin films using the setup shown in Fig. 2. Light is shone into the contact between the ball and the disc. Part of this light is reflected from the underside of the glass disc and some passes through any lubricant film and is then reflected back from the steel ball. Since the two beams of light have travelled different distances they interfere, resulting in interference fringes captured by the spectrometer and then recorded by a monochrome CCD camera. The system spectrometer measures the wavelength of the light fringes returned from the central plateau of the contact allowing the micro-computer to calculate the central film thickness with better resolution than the conventional optical interferometry (down to 1 7 1 nm). The lubricant's film thickness wavelength is always measured at the same rotational position on the disc – trigger point – and the central film thickness is computed considering the refractive index of the oil and space layer, as well as the initial thickness of the space layer. For careful overview of the ultra-thin film interferometric method check the references [37,38]. The test conditions are shown in Table 3. Before each test a heat period of 30 min was applied to ensure the temperature stabilization. After this period, the space layer thickness was measured at the disc track radius, without any lubricant between the ball and the disc. The entrainment speed was then ramped up three times (each ramp takes 200 s, ranging from E0.01 to 2 m/s) and a combined curve of the three measurements was created. The fully flooded condition was ensured using a grease scoop which forced the grease back into track, avoiding starvation of the contact with test time. The temperature deviation at each ramp up was inferior to 72 1C from the average. At the end of each ramp up, a zero speed film thickness was also measured, allowing us to identify if the disc track has been damaged in the process (measuring a negative film thickness) and at the same time, measuring the residual film thickness between

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439

Fig. 4. Film thickness measurements of grease M1 and MLi at 60 1C. Contact area images are also shown.

Table 4 c Average central film thickness (h0 ), standard deviation (σ) and transition speed (utr) of the plateau at low speeds and test temperature of 60 1C. Grease

h0

σ

σ%

utr

M1 M2 M3 MLi

592.6 690.6 867.9 42.5

85.8 88.5 161.7 5.7

14.5 12.8 18.6 13.4

194 302 460 32

Units

nm

nm

%

mm/s

c

The EHD2 equipment can also be adapted to measure the film thickness profile of the contact area, using the Space Layer Imaging Method (SLIM) [39]. It uses a sensitive RGB (red, green, blue) colour camera to capture an image of the contact area. The colours of the pixels can be used to calculate the film thickness, producing 3D maps of the contact area film thickness. This technique was also used in this work despite not being used to calculate the central film thickness.

4. Experimental results ball and disc. The zero speed film thickness is measured after unloading the ball and without entrainment speed. The full load (50 N) is then re-applied and the static film thickness is measured only after 5 s, allowing the squeezed film to spread. An average of the three measurements for each grease was calculated.

4.1. Influence of the thickener content The central film thickness results of grease M1, M2, M3 and MLi at 60 1C are shown in Fig. 3, in a log–log scale. The film thickness of grease MLi is also shown.

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3

Film Thickness [nm]

10

2

10

1

10 -2 10

-1

0

10

10

Entrainment Speed [m/s] Fig. 5. Film thickness measurements of grease M1 at 60, 80 and 110 1C.

Table 5 Average zero speed film thickness (hR) measurements at different temperatures. Note: Film thickness values in nm. T (1C)

M1

M2

M3

MLi

60 80 110

439.8 433.2 293.8

533.4 559.8 649.4

603.8 701.2 597.7

61.2 19.7 60.9

As verified by several other authors, at moderate to high speeds the film thickness increases with the entrainment speed at rate of  U 0:67 . Following these results, it is interesting to notice that the film thickness behaviour of the Lithium thickened grease (MLi) is quite different from the other three polymer thickened greases. Under the same entrainment speed range tested, the MLi grease shows a higher film thickness under moderate to high entrainment speeds than the polymer greases. This should be related to the fact that grease MLi was formulated with a base oil of higher viscosity than the polymer greases. Moreover, the thickener content difference between the polymer greases does not seem to significantly influence their film thickness at moderate to high speeds, all curves looking very close. At low entrainment speeds, the behaviour between greases formulated with different thickener types becomes more relevant. Below a certain transition speed (utr), the film thickness increases with the decrease of the entrainment speed at a very high rate until it reaches a plateau. In this region, the measurements fluctuate widely and lead to a very high standard deviation which presumably should be related to more frequent thickener lumps entering and leaving the contact [40]. In this particular zone, the polymer greases show much higher film thickness than MLi. To address this difference in behaviour, contact area pictures of the film thickness profile were also obtained for the same entrainment speed range, using the SLIM method which allows us to obtain the complete film thickness profile over the contact area. The resulting images are shown in Fig. 4. The central film thickness curves at 601 C of greases M1 and MLi are also shown, for easier comparison. Analysing the film thickness profiles at low entrainment speeds, it is possible to observe thickener lumps entering the

contact for grease M1 and MLi. However, with the increasing entrainment speed, the film thickness behaviour starts to change and after reaching a certain transition speed, the film thickness profile resembles an oil-like contact, showing the typical horseshoe profile. The transition speed showed poor repeatability and was often found at slightly different values which could be related to the initial amount of grease available. Still, it is interesting to notice that the transition speed happens at much higher speed for the polymer greases than for the MLi. This fact should be related to the thickener size and to how easy it should be for the thickener to be pushed off to the sideways of the contact area. Not only the transition speed is much smaller for grease MLi, but also the plateau is reached at a much lower entrainment speed, resulting into a smaller film thickness in this region. Other authors have tested similar greases also formulated with Lithium Complex and found values of the film thickness plateau higher than those reported in this work [14]. Furthermore, according to Fig. 3, it seems that the transition speed increases with the thickener content and therefore, it also depends on the grease formulation, following this order: M2 M1 MLi uM3 tr 4 utr 4 utr 4 utr

ð8Þ

In this regime at low speeds, a higher thickener content leads also to higher film thickness or at least to more frequent thickener lumps entering the contact. The average film thickness of the plateau at 60 1C, is shown in Table 4. From these average values, it seems that the thickener content influences the film thickness at low speeds, following the order: M3

M2

M1

MLi

hpl 4 hpl 4 hpl 4 hpl

ð9Þ

In Fig. 5, the results of the film thickness measurements of grease M1 at different operating temperatures are shown. It seems that the plateau observed at low speeds is almost independent on the operating temperature. Furthermore, as it was previously observed by other authors [14], it seems that the transition speed increases with increasing temperature, as the curves move down and to the right, reflecting the lubricant's decrease of viscosity. In Table 5, the average zero speed film thickness (hR) results are shown. It is possible to see that the values found are very close to

D. Gonçalves et al. / Tribology International 90 (2015) 435–444

M2

Bleed-oil

PAO base oil

M5

Bleed-oil

PAO base oil

3

3

10 Film Thickness [nm]

10 Film Thickness [nm]

441

2

10

2

10

1

1

10 -2 10

-1

10 -2 10

0

10

10

-1

10

Entrainment Speed [m/s]

10

0

Entrainment Speed [m/s]

MLi

Blend base oil

Bleed-oil

3

Film Thickness [nm]

10

2

10

1

10 -2 10

-1

0

10

10

Entrainment Speed [m/s]

Fig. 6. Film thickness measurements at 60 1C of fresh greases and their base and bleed-oils: (a) Grease M2; (b) Grease M5; (c) Grease MLi.

Table 6 Comparison between the numerical predictions and the film thickness measurements of the lubricating greases M2, M5 and MLi at the entrainment speed of 1 m/s and 60 1C. Grease Measured hexp =hoil Measured h (nm) @ 1 m/s B Eq. (5) Φ (%) hcalc =hoil

M2

M5

MLi

1.46 183.6 2.5 13.0 1.11

2.31 291.6 2.5 13.0 1.11

2.08 472.8 2.5 17.5 1.13

Eq. (6)

k (Pa sn) ηoil (Pa s) hcalc =hoil

338.3 0.018 1485.4

86.1 0.018 539.58

230.9 0.063 436.5

Eq. (7)

hR (nm) hoil (nm) hcalc =hoil

533.4 126.1 5.23

429.6 126.1 4.41

61.2 227.0 1.27

the values of the film thickness plateau at very low speeds shown in Fig. 3 and Table 4. It was not possible to identify any relationship between the zero speed film thickness and the temperature. In fact, it seems that hR is not greatly affected by it, since the value is very similar between temperatures for some greases. Once again, the difference between the polymer greases and grease MLi is very large, even for the zero speed film thickness measured.

4.2. Influence of the elastomer content: base oil versus bleed-oil Several authors point out that at high shear rates, the grease rheology gets close to the base oil's and therefore, also the film thickness of the grease approaches the base oil's one at high speeds [2,3,5,6]. Yet, a few authors also found some correlation between the grease's film thickness and the film thickness produced by the bleed-oil under fully flooded condition [13].

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Fig. A1. Film thickness measurements of base and bleed-oils at different temperatures. The film thickness predictions according to Hamrock and Dowson (H&D) or Kumar et al. are also shown, calculated using the piezo-viscosity value obtained through Gold's equation (αGold) and also its optimized value (αoptim) obtained to match the experimental results.

Fig. 6 shows the measured film thickness of greases M2, M5 and MLi, their corresponding base and bleed-oils, at 601 C. Following this figure, it is possible to observe that each grease produces a film thickness at least 1.4 times higher than the base oil's for both the polymer and the lithium complex thickened greases under fully flooded conditions. In the case of the polymer greases, the bleed-oil shows a higher viscosity than the base oil (see Table 2) and therefore it also produces a higher film thickness. This is specially important in the case of grease M5, even taking into account the shear-thinning behaviour of its bleed-oil at low shearrates. In the case of the grease MLi, the film thickness of the bleedoil is still higher than the base oil, even if the viscosity of the bleed-oil is smaller. The film thickness of the bleed-oils is closer to the greases' but still much smaller, which shows that even if we consider the bleed-oil properties for the film thickness calculation, the value obtained would still be smaller than the film thickness of the greases under fully flooded condition. Still, even it is not due to the increased bleed-oil viscosity of the grease formulated with elastomer, it is clear that its presence is very relevant. From the analysis of Fig. 6, it is possible to see that the elastomer presence greatly contributes to the increase of the film thickness under moderate to high speeds.

5. Film thickness prediction of greases under fully flooded condition Following the film thickness calculation background reported earlier, a comparison between the measured values of the greases' film thickness and its prediction using Eqs. (5)–(7) was performed.

Table A1 Optimized pressure–viscosity coefficient α, obtained for different operating temperatures. Oil

T (1C)

60

80

110

PAO base oil

αGold αoptim

11.12 14.20

10.40 12.95

9.65 11.69

M2 bleed-oil

αGold αoptim

11.12 15.34

10.39 11.78

9.68 10.56

M5 bleed-oil

αGold αoptim

15.96 3.50

14.70 3.40

13.42 3.29

PAO blend oil

αGold αoptim

13.20 9.28

12.18 8.71

11.10 8.09

MLi bleed-oil

αGold αoptim

12.66 21.66

11.59 18.68

10.51 15.82

Units

GPa  1

All these equations try to estimate the film thickness of lubricating greases under fully flooded conditions based on the film thickness of their base oils at moderate to high entrainment speeds. Therefore, these equations are not prepared to represent the film thickness behaviour under low entrainment speeds where the thickener influence is visible. The calculation results are shown in Table 6 for the film thickness measurements at the entrainment speed of 1 m/s for greases M2, M5 and MLi, shown in Fig. 6. At this entrainment speed, the tested greases show similar behaviour to their base and bleed oils, showing parallel slopes. According to the results, none of the equations is capable of giving a good prediction of the

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grease's film thickness, all models showing very high deviations from the measured value. Eq. (5) is the one which best approaches the experimental results but still by defect. On the other hand, Eq. (6) shows the highest deviation from the measured values which might be related to the way the consistency index k is measured, since its value greatly affects the calculation. Finally, Eq. (7) was not able to reproduce the film thickness behaviour based on the base oil's film thickness and the measured zero speed film thickness (hR), since its value was very large for the tested polymer greases. In the case of lithium thickened grease MLi, the approximation using this equation was closer. Not only these equations are not able to describe the film thickness behaviour at low speeds, but they cannot provide a fair approximation to the greases' film thickness at high entrainment speeds and under fully flooded condition. The authors aim to address and propose a new way of predicting the film thickness in a future publication, already considering the film thickness plateau at low speeds.

443

 The film thickness of the lubricating fresh greases could not be accurately predicted using any of the models researched in the bibliography.

Acknowledgements The authors gratefully acknowledge the funding supported by  National Funds through Fundação para a Ciência e a Tecnologia (FCT), under the projects PTDC/EME-PME/122271/2010 and EXCL/SEM-PRO/0103/2012.  COMPETE and National Funds through Fundação para a Ciência e a Tecnologia (FCT), under the project Incentivo/EME/ LA0022/2014.  Quadro de Referência Estratégico Nacional (QREN), through Fundo Europeu de Desenvolvimento Regional (FEDER), under the project NORTE-07-0124-FEDER-000009 - Applied Mechanics and Product Development. without whom this work would not be possible.

6. Conclusions Appendix A. Film thickness prediction of base and bleed-oils This work is intended to characterize the film thickness behaviour of this new type of lubricating greases, thickened with PP polymers. The film thickness under fully flooded conditions was addressed and the active lubricant inside the contact issue was discussed. The current literature regarding greases and oils' film thickness prediction was analysed and discussed regarding the experimental measurements. The main conclusions of this work are summarized here:

 It was found that the polymer greases produce a very high film





 





thickness plateau from low to moderate speeds. After reaching a certain transition speed, the film thickness drops at a very fast rate and then increases again at a rate of U 0:67 . This behaviour change and the high standard deviation of the film thickness in the plateau zone, suggested that thickener lumps were entering the contact very frequently and locally increasing the film thickness, which was in fact observed experimentally. The film thickness of the tested lithium complex thickened grease is higher than the polymer greases at high speeds, but under low to moderate speeds, the film thickness is much smaller. This grease also shows a film thickness plateau but it is reached at lower entrainment speeds and also at much lower value than the polymer greases. This fact should be related to the thickener properties of each grease, since it was observed that thickener lumps enter the contact, being responsible for the film thickness plateau. The transition speed at which the film thickness behaviour changes from to the typical linear slope increases with increasing thickener content, for the polymer greases tested. This transition speed is also influenced by the temperature, increasing with it. The transition occurs at about the same film thickness value which suggests that it should be related to the thickener properties. The film thickness at high speeds follows a parallel slope to the film thickness of base and bleed-oils. The film thickness of the bleed-oils is higher than the base oils, but still much smaller than the greases'. This happened for all tested greases despite thickener type, content or elastomer content. The elastomer content lead to grease with a bleed-oil of increased viscosity, regarding the base oil. However, the film thickness produced by this bleed-oil was still inferior to the film thickness of the grease under fully flooded conditions.

There are several equations commonly used to predict film thickness of lubricating oils. The main differences between these models are related to the way the viscosity and density behaviour is modelled regarding pressure and temperature. The pressure– viscosity coefficient (α) is one of the most important parameters to calculate the film thickness, since it defines the way the viscosity changes with the high pressures involved in the EHL contact. This parameter however, is very hard to measure and it requires the use of very specific and complex equipment. For a certain range of contact pressures, the α-value can be predicted using Gold's equation [41], using specific parameters for each oil nature. Still, quite frequently, the film thickness calculated using this α-value is very far from the experimental measurements. More recently, Van Leeuwen [42] has used film thickness measurements to inversely calculate the pressure viscosity coefficient, which seems to be the suitable way to determine the α-value when high pressure viscosity measurements are not available. However, Bair et al. [43] contested these measurements, showing that the α-value obtained with this process could be much different values depending on the geometry (and consequent scale effect) used for the film thickness measurements. Nevertheless, in this work, a similar approach to Van Leeuwen's was used, and the α-value was optimized to match the experimentally measured film thickness of each base and bleed-oil. The results are shown in Fig. A1. It is clear that using the Hamrock and Downson's (H&D) equation produces a close prediction to the measured film thickness for the base oils and for the non-shearthinning bleed-oils even using Gold's equation for the pressure– viscosity α-value. However, the bleed-oil of grease M5 shows shear-thinning behaviour and therefore, for this bleed-oil, the Katyal and Kumar model was used. Still, even using the shearthinning model, the film thickness predicted is much higher than the measured one. After the optimization of the pressure–viscosity value, the models show a very good agreement with the experimental results. The optimized values calculated are shown in Table A1. As expected, the pressure–viscosity decreases with temperature, following the viscosity decrease. The values obtained are of the same order of magnitude as the ones predicted using Gold's equation but for certain cases the difference between them is quite large, particularly the case of M5's bleed-oil.

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