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PII: DOI: Reference:

S0301-679X(17)30106-8 http://dx.doi.org/10.1016/j.triboint.2017.02.046 JTRI4627

To appear in: Tribiology International Received date: 11 August 2016 Revised date: 20 January 2017 Accepted date: 27 February 2017 Cite this article as: K. Simonovic and M. Kalin, Experimentally derived Friction Model to evaluate the Anti-Wear and Friction-Modifier Additives in Steel and DLC Contacts, Tribiology International, http://dx.doi.org/10.1016/j.triboint.2017.02.046 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.

Experimentally derived Friction Model to evaluate the Anti-Wear and Friction-Modifier Additives in Steel and DLC Contacts K.Simonovic, M.Kalin*

University of Ljubljana, Laboratory for Tribology and Interface Nanotechnology, Bogisiceva 8, 1000 Ljubljana, Slovenia *

Corresponding author. Tel.: +38614771462; fax: +38614771469, [email protected]

ABSTRACT Individual and synergistic contributions of Anti-Wear wear (Zinc dialkyldithiophosphate, ZDDP) and Friction-Modifier (Glycerol isostearate, GIS) additives to the friction of steel and DLC contacts across a broad range of boundary-lubrication contact conditions are evaluated. A design-of-experiments was used to enable broad-range experimental matrix and carefully selected regression technique was used to develop friction models and friction maps depending on the most relevant contact parameters ( , , , ). Apart from many specific conclusions, one of the major conclusions is that statistically identified interactions of the experimental parameters show which of the parameters interfere and compete in their influence on the coefficient of friction, hence, which of the investigated parameters must be simultaneously considered if proper conclusions are to be made.

Keywords: anti-wear, friction modifier, boundary lubrication, design of experiments.

List of Symbols Symbol

Units

Meaning

GPa

Hertzian pressure

m/s

Sliding speed Sample bulk temperature Surface roughness

/

Coefficient of friction

/

Coefficient of determination

1. INTRODUCTION Modern automotive lubricants are mainly designed for pure steel contacts and are a mixture of several additives and the base oil, which are blended together for optimized tribological performance, i.e., low friction and wear [1]. Nevertheless, out of the many different components, two are the most important ones for the boundary-lubrication (BL) regime, i.e., anti-wear (AW) and friction-modifier (FM) additives. AW extend the life of the tribological contact by modifying the surface, thereby preventing the asperityasperity contact in the BL regime and, consequently, preventing wear [1]. These AW additives are commonly added in the range 1–3% percent of the total weight of the fully-formulated oil depending on the specific application and environmental requirements [2]. On the other hand, high friction in the BL regime needs to be reduced in order to decrease fuel consumption and so reduce the environmental impact. For this reason, FMs are commonly added to the formulated blends in a similar weight percent as the AW additives [3]. Today, the most commonly used AW additive is ZDDP, which was introduced as early as the 1940s as an antioxidant agent before its antiwear properties were discovered [1]. As for the FM additives for automotive applications, the most important one is molybdenum dithtiocarbamate (MoDTC), as engine lubricants are based on ZDDP and it is proven that MoDTC combined with ZDDP provides good synergetic results in terms of both friction reduction and wear prevention [3]. However, due to the environmental requirements, organic friction modifiers (OFMs) [4] were considered as a possible replacement for the Mo-based FMs; they have shown good results, both in terms of friction reduction and their interactions with ZDDP [5].

2

The effects of the AW and the combination of the AW and the FM additive were extensively studied for the traditional steel-steel contact [6-30], mostly from the point of view of the tribochemical or tribological mechanisms. From these comprehensive studies it was determined that the effects of the AW and the FM additives are very dependent on the experimental parameters, i.e., contact pressure (

, sliding speed ( , and the surface roughness (

, test temperature

). Tabular overview of the friction dependence from

the experimental parameters for the steel-steel contact lubricated with the AW and the combination of the AW and the FM additive is presented in the table 1. In order to reduce the friction coefficient even further, tribologists have invested great efforts in replacing the classical steel materials used for automotive applications with diamond-like-carbon (DLC) coatings, due to their superior wear and friction properties as well as their resistance to corrosion, high hardness and chemical stability [31-38]. Therefore, many studies (summarized in table 2) have been devoted to understanding the behavior of the AW and the FM additives in steel-DLC contacts because of their prospective role in automotive applications [39-59]. Although these studies are valuable in terms of a tribochemical understanding of the AW and the FM additive’s influence on the steel-steel and steel-DLC contact, not much can be concluded about the influence of the broader range of parameters in the whole BL regime on the coefficient of friction when contacts are lubricated with the AW and the FM additive, since most of the experiments are conducted using a fixed set of parameters or with the variation of the only one experimental parameter. To summarize, from tables 1 and 2 it follows that despite many extensive mechanistic studies conducted on both steel-steel and steel-DLC contacts, it is still unclear how both individual and simultaneous variations of the contact pressure ( ), surface roughness (

), sliding speed ( ) and temperature ( )

influence the activation of the AW and FM additive (in model oils) and how these additives effect friction performance in the boundary lubrication (BL) regime. Therefore, to be able to fully understand and predict the performance of the AW and FM additives in the BL regime we need to establish the friction response to variations of the contact parameters across a wide range of BL-relevant conditions. However, to do this a design-of-experiments (DOE) methodology that enables us to perform simultaneous variation of the experimental parameters through a systematically built broad experimental matrix must be employed [60]. The results obtained from such a matrix are suitable for a statistical analysis and the generation of empirical models (equations), which are further used to plot the friction maps. Once the maps have been generated, we obtain the following new information about the investigated contact–additive combination: the range of friction values, the value of the coefficient of friction for a particular set of parameters, the absolute and relative response of the coefficient of friction to a change of certain (or to a simultaneous

3

change of multiple) experimental parameters, and an understanding of the friction behavior of the investigated additive across a wide BL regime [60]. Accordingly, in this investigation we study the two most relevant types of additives for automotive applications, i.e., anti-wear and friction-modifier additives on the steel-steel and steel-DLC contacts. As an anti-wear additive, ZDDP was chosen due to its widespread application in automotive lubricants. However, in order to avoid the frequently reported and catastrophic failures of DLC coatings when Mobased FMs are used [47, 49, 53, 54], and also to make a step towards greener lubrication, we decided to use Glycerol isostearate (GIS) as the FM additive. GIS is an isomer of the well-researched Glycerol monooleate (GMO), for which excellent results in steel-DLC contacts were reported [48, 58, 61-63], and although it should yield similar results as the GMO there are no reports about the properties of the GIS in automotive applications, which means it is interesting to establish the performance of GIS for both steelsteel and steel-DLC contacts.

2. EXPERIMENTAL The step-by-step experimental procedure is presented in figure 1, while Appendix A gives a more detailed description of the applied statistical techniques. Extensive discussion on the used statistical techniques, their advantages and drawbacks compared to alternatives is presented in our companion paper [60]. The generation of the design matrix and the subsequent analysis of the results was performed using SAS JMP 11 pro software.

2.1 Oils and Additives The performance of individual additives was studied by comparing three different oils: Group III base oil (BO) ( (BOAW) (

⁄

⁄ ), base oil additivated with w.t. 1% AW additive ⁄

w.t. 1% FM additive (BOAWFM) (

⁄ ) and base oil additivated with w.t. 1% AW and ⁄

⁄ ). Mineral oil has been

selected because it widely used in automotive application and it is known that additives dissolve better in the mineral then in the synthetic oil [64]. The AW additive investigated in this study was a mixture of 0.5 wt. % of the primary and 0.5 wt.% of the secondary ZDDP, while the FM additive used was a preprepared solution of the Glycerol isostearate. Both additivated oils were stir mixed at room temperature, and in order to prevent possible sedimentation the oils were constantly stirred for the duration of the experiments. Due to a fact that in a real engineering application the AW and FM additives are always

4

combined, we did not conduct a separate study for the FM additive on its own. The base oil and additives were supplied by Total Marketing and Services (Solaize, France).

2.2 Materials Two representative types of contacts were selected for the investigation and comparison of the additive performance: steel-steel and steel-DLC. The friction of the DIN 100Cr6 steel ball (10mm in diameter) was studied against the DIN 100Cr6 steel and the DLC-coated discs (24mm in diameter, 7.9mm in thickness) in the boundary-lubrication (BL) regime. The steel samples were prepared as flat discs in a sequence of grinding and polishing steps, only through mechanical treatment, by using the abrasive discs to reach the desired roughness. The roughness was measured with a stylus-tip profilometer according to the ISO 4287 standard (T8000, Hommelwerke GmbH, Schwenningen, Germany). The DLC coating was a conventionally hydrogenated, amorphous DLC coating, with a hydrogen content of 33 at. % deposited on the polished side of the discs by a plasma-assisted, chemical-vapor-deposition (PA CVD) process. The thickness of the DLC coating was 0.8 µm, with an additional adhesive interlayer and an overall thickness of about 2 μm. The DLC coatings were supplied by Oerlikon Balzers (Limoges, France).

2.3. Design of Experiments and data analysis The test sequence and the test-to-test parameter combination were determined according to the chosen split-plot DOE method, which is described in our previous study [60]. The main property of the split-plot design is that it allows us to define hard-to-change parameters, meaning that for a certain number of experimental runs a chosen parameter (e.g., the temperature) will remain constant, without violation of the randomization principle, thereby reducing the testing time (i.e. the heating and cooling times) [60]. The data obtained from the design matrix were first analyzed with Elastic-net regression. Elastic-net regression removes the danger of overfitting with a combination of two penalization factors, and yields a good balance between the accuracy of the prediction and the simplicity of the obtained model [60]. From Elastic-net we obtain the friction-prediction equations that mathematically describe the investigated system through the used experimental parameters and as a final result friction maps are plotted. Furthermore, we identify statistically significant experimental parameters and their interactions that tell us which experimental parameters have most of the influence on the coefficient of friction and which of these parameters have a simultaneous effect and therefore cannot be studied separately. Obtaining the friction prediction equation is the two-step process (figure 1). In the first step, elastic-net regression is used to determine which experimental parameters are statistically highly significant. In the second step, quadratic effects of the highly significant parameters are included in the second order model

5

which is then again analyzed with the Elastic-net regression. In its general form, second order model is shown in the equation 1[60]: k

k

i 1

i 1

y 0 i xi ii xi2 ij xi x j

(1)

i j

where ’s are predictors and ’s are the coefficient to be estimated. The statistical significance of the parameters is determined by the probability of rejection (P): if P<0.0001 then the parameter is statistically highly significant, and if P≤0.005 then the parameter is statistically significant. However, in order to make the paper easier to follow, in tables A1 to A6, the statistically highly significant parameters are denoted as HS and the statistically significant as S. To check if the experimental results have been properly modeled the residuals (

)

are checked for normality. Normally distributed residuals indicate that the modeling procedure has been properly completed. The quality of the obtained model is checked with the determination coefficient (

),

which can take values between 0 and 1 (with 1 being the best, i.e., 100% of the experimental data are covered by the model)[65].

2.4 Tribological tests This experimental study was performed on an SRV Optimol reciprocating tribometer, which was chosen for its easy sample manipulation and because it was already shown that results obtained on an SRV Optimol are directly applicable on other devices (i.e., the Phoenix Tribology-TE 77), while trends and relative variations of friction are valid for any other reciprocating tribometer [60]. We have considered the four parameters that are widely accepted as the key parameters for the BL regime across broad ranges that describe most of the engineering-relevant BL conditions: mean Hertzian contact pressure ( , from 0.68 GPa to 1.3 GPa), initial surface roughness (

, from 0.01 μm to 0.1 μm), sliding

speed ( , from 0.02 m/s to 0.1 m/s) and sample bulk temperature ( , from 50

to 150

). The value of

the λ parameter for all of the tests was below 1, hence all tests were conducted inside the BL regime. In order to capture the quadratic effects of the experimental parameters, each parameter had to be studied at three levels. The specific values of the experimental parameters are given in table 3. Altogether, 36 tests were performed for every combination of oil and contact.

3. RESULTS The obtained friction maps are presented in figures 2 to 7. To make the presentation of the results easier to follow, based on the measured friction data, we have arbitrarily divided the values into three ranges: 6

low (μ≤0.113), medium (0.113<μ≤0.128) and high (μ>0.128). On the obtained friction maps, these ranges are marked as shades of green, yellow and red, respectively. The mean absolute errors and the coefficients of determination (

) for each contact/oil combination are given in table 4.

3.1 Steel-Steel contact 3.1.1 Base oil The friction maps for the steel-steel contact lubricated with the base oil (figure 2) are plotted using the friction-prediction equation (2), which was obtained using the procedure explained in figure 1.

steel , BO 0.131542 0.0000213121T 0.207833v 0.00294497Tv 4.08902v 2 p 0.0209825 0.0679303Ra 0.000226636T 0.153708v

(2)

Ra 0.162406 0.00250956T 3.26699v 0.0330594Tv From figure 2 it is clear that the friction coefficient is almost independent of the investigated parameters and it is very high (i.e., above 0.15) for any combination of experimental parameters. However, a detailed observation of figure 2 reveals that the friction coefficient slightly increases with an increase of the sliding speed. Surprisingly, the friction coefficient decreases with an increase of the sample bulk temperature at a low sliding speed, while it shows no temperature dependence at a higher sliding speed. The regression method (Table A1) identified one HS experimental parameter, i.e., the sliding speed, and the joint effect of the sample’s bulk temperature and the contact pressure as being HS. Furthermore,

for

the steel-steel contact lubricated with BO was calculated as 0.667, meaning that 66.7% of the experimental data is covered by the model, which is a very low coverage of the experimental data, meaning that the used methodology is not the best for a study of the base oil in the BL regime. Very high friction values for all the combinations of the experimental parameters, the small number of statistically significant factors (interactions) and the very low

value indicate that the severity of the BL

regime is too high for the base oil and that is fully clear from both the tribological and statistical points of view. For the reasons stated previously, the base oil should only be considered as a reference for the comparisons with the other investigated oils.

3.1.2 Base oil + AW (BOAW) The equation describing the dependence of the friction coefficient of the steel-steel contact lubricated with the BOAW oil from the investigated experimental parameters is given below:

7

steel , BOAW 0.339754 0.0355744 p 2 2.26361Ra 2 8.91144v 2 0.0019768T 0.824023v 0.0230692Tv Ra 3.71411 0.0386909T 39.8545v 0.390985Tv

(3)

p(0.302241 0.00191874T 2.09858v 0.0215424Tv) pRa 4.36558 0.0394273T 42.3973v 0.401056Tv

Figure 3 shows the friction map for the steel-steel contact lubricated with BOAW oil plotted using equation (3). At a low sliding speed ( =0.02 m/s) the friction decreases with an increase of the temperature, while at a medium sliding speed ( =0.06 m/s) this trend is not so clearly expressed; the friction remains in the high region and barely changes with an increase of the temperature. At a high sliding speed ( =0.1 m/s) the coefficient of friction increases with an increase of the sample bulk temperature and it remains in the medium and high regions regardless of the other experimental parameters. Looking at the map from the temperature perspective we can see that there is no single friction trend that can be established for any of the investigated temperatures. At 50

the friction coefficient first increases

with an increase of the sliding speed from =0.02 m/s to =0.06 m/s (figures 3-g and 3-h), but decreases slightly when the speed is further increased to =0.1 m/s (figure 3-i). Identical behavior occurs at 100 , while at 150

there is slight increase in the values of the friction coefficient when the speed is increased

from 0.06 m/s to 0.1 m/s. Coefficient of friction decreases with an increase of the contact pressure, however, there is an exception to this rule; namely, for a high roughness at a low speed and temperature (for example, figure 3-g). Hence, the final effect of the pressure also depends on the sample roughness, the sliding speed and the temperature. Finally, the friction coefficient increases with an increase of the surface roughness for most of the experimental range; again, there is an exception to this rule, depending on the contact pressure, the coefficient of friction can either increase or decrease with an increase of the surface roughness (figure 3g). Table A2 shows that three experimental parameters were identified as highly significant, i.e., roughness, pressure and speed, which means that these three parameters will predominantly influence the friction coefficient. This was also confirmed by the fact that their quadratic effects were identified as statistically significant as well. The influence of the sample bulk temperature, although not directly visible, is present 8

through multiple interactions identified by the regression algorithm; see the temperature interactions with other experimental parameters denoted as HS or S in Table A2. The fact that there were so many parameter interactions identified means that the experimental parameters interfere and compete in their influence on the friction coefficient and that we cannot describe this system without considering all four selected experimental parameters. This is best illustrated during low-speed sliding ( =0.02 m/s) in figures 3-g, -d, -a, where the removal of either one of the experimental parameters would lead to the wrong conclusions about the investigated tribological system. was calculated as 0.8573, meaning that 85.73% of the experimental data are covered by the developed model. Although this represents rather good coverage, when combined with the large number of identified interactions in table A2 it points to the fact that ZDDP (as the only additive in the BO) in the steel-steel contact can behave unpredictably, and as such it is difficult to control over a wider range of conditions.

3.1.3 Base oil + AW + FM (BOAWFM) The equation describing the dependence of the friction coefficient of the steel-steel contact lubricated with BOAWFM oil from the investigated experimental parameters is given below:

BOAWFM , steel 0.0507298 0.0501784 p 2 1.83677 Ra 2 2.62383v 2 0.000883221T 2.52263v 0.0133375Tv Ra 2.18887 0.0145533T 38.5092v 0.293283Tv

(4)

p 0.00174206 0.00103526T 2.37935v 0.0158011Tv pRa 1.73602 0.0140575T 37.4606v 0.283845Tv

Figure 4 shows a friction map for the steel-steel contact lubricated with BOAWFM oil plotted from equation (4). Firstly, it is immediately noticeable that the friction coefficient is significantly reduced, compared to the BOAW oil (figure 3) meaning that the selected FM is truly an effective friction reduction additive. At a low sliding speed ( =0.02 m/s) the friction coefficient decreases with an increase of the temperature, while at higher sliding speeds ( =0.06 m/s and =0.1 m/s) this trend is reversed, i.e., the friction increases with an increase of the sample bulk temperature. In terms of the temperature dependence, at low temperature ( temperatures (

) the friction decreases with an increase of the sliding speed, while at higher and

increase of the sliding speed.

9

) there is a steady increase in the friction coefficient with an

Furthermore, coefficient of friction decreases with an increase of the contact pressure; however, there is an exception to this rule, i.e., for high roughness at high speed and low temperature (for example, figure 4-i). Hence, the final effect of the pressure also depends on the sample roughness, the sliding speed and the temperature. Finally, the friction coefficient increases with an increase of the surface roughness for most of the experimental range. However, this is not valid at low temperatures and high sliding speeds (figure 4-g): for a low contact pressure the coefficient of friction decreases with an increase of the surface roughness, while for the higher pressures the coefficient of friction increases with an increase of the surface roughness. Surprisingly, identified behaviors and exceptions in behaviors are the same as the ones identified of the AW additive. Looking at the efficiency of the friction modifier, from figure 4, the parameters where the FM is the most effective are =0.02 m/s and

, while the effectiveness of the friction modifier generally

decreases with an increase of the sliding speed, except at

where the effectiveness is improving

with an increase of the sliding speed (figures 4-g, -h, -i). In terms of pressure and roughness, it is clear that the FM is always effective over a wide range of pressures (always at the highest possible pressure); however, specific values of the surface roughnesses for which the effect of the friction modifier is maximized depend on the specific temperature and speed. Moreover, comparing figures 3 (BOAW oil) and 4 it is obvious that the FM does not significantly modify the friction trends, i.e., the general trends remain the same with the friction drastically reduced. This proves the effectiveness of the FM on the steelsteel contact as a “pure” friction modifier with little direct effect on the anti-wear additive performance. Table A3 shows that three experimental parameters were identified as highly significant, i.e., roughness, pressure and speed, meaning that these parameters have a dominant effect on the coefficient of friction. Further proving their significance, the second order of all the mentioned parameters was confirmed. The influence of the sample bulk temperature, although not directly visible, is present through multiple interactions identified by the regression analysis (Table A3). All these interactions among several parameters, again points to the fact that we cannot observe any of the experimental parameters separately from the others, as the results are only valid for a specific combination of parameters and otherwise lead to the wrong system interpretation. As an example, the importance of these interactions is best illustrated for low temperatures, where it is clear that the effectiveness of the friction modifier is preserved with an increase of the speed only if the pressure and the surface roughness are adjusted simultaneously (figures 4g,-h,-i).

10

was calculated to be 0.974, meaning that 97.4% of the data is covered by the model. Such a high value for the

coefficient is excellent and comparable to the one obtained for the fully-formulated oils in our

previous study [60]. On the other hand, the number of statistically highly significant interactions (P<0.0001) is comparable to the one obtained for the BOAW oil (Section 3.1.2), meaning that the experimental parameters are still highly correlated among each other. However, the difference is that in the BOAWFM case only one multi-parameter ( interaction of more than two parameters) interaction remained as highly significant, which is an improvement over the BOAW oil and indicates the beneficial effect of the FM in terms of the reduction of the experimental parameters’ correlation level. The high value of the

coefficient, together with the fact that the number of identified interactions is comparable

to the one obtained for the BOAW oil (Table A3), points to the fact that GIS works not only as an excellent friction modifier but also as a stabilizer of the friction coefficient and a unifier of the friction values, thus making the friction behavior easier to predict.

3.2 Steel-DLC contact 3.2.1 Base oil (BO) Friction maps for the steel-DLC contact lubricated with the base oil are plotted from equation (5) in figure 5

BO, DLC 0.151768 0.0398733 p 2 p 0.094266 0.11644 Ra 0.000094668T 0.00012878T Ra 0.380239 0.000622611T 2.57562v 0.141659v

(5)

From figure 5 it is clear that the friction coefficient is significantly reduced for the BO and this is due to the well-known low friction nature of the DLC coating. Furthermore, coefficient of friction almost independent of the investigated experimental parameters, although closer examinations reveal that the friction coefficient slightly decreases with an increase in the sliding speed. Temperature wise, with an increase of the sample bulk temperature, the friction coefficient remains practically constant, except for high pressures and roughnesses, where the friction decreases with an increase of the temperature. A regression analysis identified the contact pressure as the only statistically significant parameter (Table A4) and no interactions were identified. Comparing these results with those obtained for the steel-steel contact (table A1) reveals that the lower reactivity and polarity of the DLC surfaces caused a reduction in the number of significant parameters and interactions. Later, the

coefficient was calculated to be 0.63, meaning that only 63% of the experimental data are

covered by the model. This small coverage of the experimental data together with the fact that only the contact pressure is said to influence the friction coefficient (Table A4) points out that the BL conditions 11

are too severe for the BO. Finally, the results for the base oil in the steel-DLC contact are very similar to the ones obtained for the steel-steel contact (Section 3.1.1) in terms of the small number of significant parameters and the low

coefficient, meaning that despite the DLC coating, BO is absolutely inadequate

for the BL regime which is intuitively clear from the tribological point of view.

3.2.2 Base oil + AW (BOAW) The equation describing the dependence of the friction coefficient of the steel-DLC contact lubricated with the BOAW oil from the investigated experimental parameters is given below:

BOAW , DLC 0.0859261 0.0220413 p 2 5.3403Ra 2 0.00063346T 0.831869v 0.0076399Tv Ra 1.22776 0.00676762T 1.07126v 0.0451227Tv p(0.00871689 0.000662724T 0.833683v 0.00699497Tv)

(6)

pRa 0.700446 0.0077507T 2.37997v 0.0553547Tv Figure 6 shows a friction map for the steel-DLC contact lubricated with the BOAW oil plotted from equation (6). From the map it is clear that the friction strongly depends on the sliding speed. At a low sliding speed ( =0.02 m/s) the friction coefficient increases with an increase of the sample bulk temperature for low values of the surface roughness and the contact pressure, while at a medium sliding speed ( =0.06 m/s) the friction decreases slightly with an increase of the sample bulk temperature. Finally, at a high sliding speed ( =0.1 m/s) there is strong tendency for the friction to decrease with an increase of the sample bulk temperature. Temperature wise, there is a stable trend in the increase of the friction coefficient with the sliding speed for all the tested temperatures. This is most pronounced at 50

where the increase of the friction

coefficient is the highest. With an increase of the sample bulk temperature the increase in the friction coefficient is less clear and at 150

the friction coefficient remains mostly inside the same range of

values. Coefficient of friction reduces with an increase of the contact pressure, without any exceptions. However, figure 6 clearly shows that the magnitude of the friction reduction depends on the sliding speed. The friction coefficient becomes more sensitive to changes in the contact pressure at higher sliding speeds, while at a low sliding speed and temperature the coefficient of friction is less sensitive to the variations of the contact pressure (see figure 6-g).

Finally, coefficient of friction increases with an increase of the

surface roughness; however, this is not valid for the low sliding speed. Namely, at the low sliding speed, depending on the pressure and temperature, the coefficient of friction either increases or decreases with an increase of the surface roughness.

12

The regression method identified the pressure and roughness as statistically highly significant parameters (Table A5); however, only the quadratic effect of the surface roughness is confirmed, meaning that the roughness has the dominant influence on the friction coefficient over the contact pressure. This is interesting as it was not noticed for the BO and because the initial surface roughness is generally not considered to be a key contact parameter. Another important finding is that the sample temperature as a single parameter is identified as a statistically significant for the first time in this study. This finding confirms the direct influence of the sample bulk temperature on the friction of a steel-DLC contact lubricated with the ZDDP-additivated oil in the BL regime. Table A5 shows that there is only one three-parameter interaction identified as being statistically significant (temperature, roughness and pressure) and that the total number of statistically significant parameters is smaller than the one obtained for the steel-steel contact (see Table A2). The model presented in equation 5 covers 86.14% of the experimental data (

=0.8614), which is almost identical to the

coverage obtained for the steel-steel contact (Section 3.1.2). The small number of interactions (compared to the steel-steel contact) and the almost identical coefficient of determination point to the fact that the lower surface reactivity of the DLC reduces the number of statistically significant parameters and interactions. However, the behavior of the ZDDP remains similar as to the steel-steel contact lubricated with the BOAW oil (see Section 3.1.2).

3.2.3 Base oil + AW + FM (BOAWFM) The equation describing the dependence of the friction coefficient for the steel-DLC contact lubricated with the BOAWFM oil from the investigated experimental parameters is given below:

BOAWFM , DLC 0.236517 0.0128173 p 2 4.56401Ra 2 0.0011574T 2.47951v 0.0252374Tv Ra 0.852028 0.0159583T 30.8832v 0.284468Tv

(7)

p(0.145367 0.000968687T 2.1387v 0.020883Tv) pRa (1.55914 0.0151153T 27.3124v 0.246934Tv) Figure 7 shows the friction map for the steel-DLC contact lubricated with the BOAWFM oil plotted from equation (7). It should be emphasized that unlike the steel-steel contact, the reduction of friction with the addition of the friction modifier to the AW additive is much smaller for the steel-DLC contact, confirming the well-known low-friction property of the DLC coatings and so much less importance of the FM in the formulations then for the steel-steel contact. From the map it is clear that both the sliding speed and the sample bulk temperature influence the friction coefficient. At a low sliding speed ( =0.02 m/s) the friction coefficient decreases with an increase in the 13

sample bulk temperature, while at higher sliding speeds ( =0.06 m/s, =0.1 m/s) this trend is reversed and the friction coefficient increases with an increase of the sample bulk temperature. From the temperature perspective, at low temperature (

) the friction coefficient decreases with an increase of the

sliding speed, while at higher temperatures (

,

) the trend is reversed and the friction

coefficient steadily increases with an increase of the sliding speed. Note that the identified behavior is identical to that obtained for the steel-steel contact lubricated with the BOAWFM oil (Section 3.1.3), meaning that it derives from the properties of the friction modifier. The coefficient of friction reduces with an increase of the contact pressure without any exceptions. The identified trend is not conditioned by any other parameter; it is consistent across the whole experimental range. However, figure 7 shows that the sensitivity of the friction coefficient to the variations of the contact pressure depends on the speed, temperature and roughness. Namely, at a low speed and temperature (figure 7-g) for almost any roughness the friction remains constant, irrespective of the pressure variations. On the other hand, at the highest speed and temperature (figure 7-c), for any surface roughness the friction coefficient becomes very sensitive to variations in the contact pressure. Finally, the coefficient of friction increases with an increase of the surface roughness and this trend is identical to the one obtained for the BOAW oil. However, this is not valid for the low sliding speed and low temperature. Namely, at a low sliding speed and temperature (figure 7-g), at low pressures, the coefficient of friction either increases or decreases with an increase of the surface roughness. On the other hand, at high pressures the coefficient of friction increases consistently with an increase of the surface roughness. From the performance point of view, i.e., the reduction of friction with the FM, it follows from figure 7 that the GIS is the most effective at a low sliding speed ( =0.02 m/s) and the highest temperature ( ), figure 7-a. In contrast, the smallest effect of the FM is obtained at the highest speed ( =0.02 m/s) and temperature (

), figure 7-c. Furthermore, GIS is always effective across the whole range of

pressures, but only for specific

values. These specific roughnesses on which the maximum

effectiveness is achieved depend on a combination of the sliding speed and temperature (for example, compare figures 7-g and 7-b). Moreover, a comparison of figures 6 and 7 reveals that the effect of the GIS is not always only positive. Namely, friction reduction is present in some regions; however, there are also regions where the friction increases compared to the one obtained for the BOAW oil (for example, figures 6-d and 7-d). This implies that if the only desired effect is friction reduction, the operating parameters need to be carefully chosen in order to maximize the effect of the FM additive.

14

Table A6 shows that three experimental parameters were identified as highly significant, i.e., roughness, pressure and sliding speed, meaning that these parameters have a major effect on the coefficient of friction; however, only the quadratic effect of the roughness was confirmed, meaning that the roughness has a dominant effect on the coefficient of friction compared to both pressure and speed. Again,

is not

the most relevant parameter for steel, but it is for the DLC. The influence of the sample bulk temperature was not directly confirmed; however, it is present through multiple interactions identified by the regression analysis in Table A6. As mentioned before, these interactions imply that for the steel-DLC contact all the contact parameters need to be considered simultaneously if proper conclusions are to be made. was calculated to be 0.976, meaning that 97.6% of the experimental data are covered by the model. The calculated coefficient of determination is not only comparable with the one obtained for the fullyformulated oil [60], but it is practically identical to the one obtained for the steel-steel contact lubricated with BOAWFM oil (Section 3.1.3). However, unlike for the steel-steel contact the addition of the FM increased both the number of statistically highly significant parameters and the number of interactions. This is just the opposite of the results for the steel-steel contact, where the FM decreased the number of statistically highly significant parameters and interactions. Hence, increasing the number of statistically highly significant parameters (and interactions) on the surface of lower reactivity (DLC) together with the high coefficient of determination implies that GIS will create a more unified and easier-to-predict tribological system compared to the one with ZDDP alone (Section 3.2.2.).

4. DISCUSSION 4.1 Validity and applicability of models and maps The present study was designed to determine the individual and combined effects of the AW and FM additives on the friction coefficient of the steel and DLC contacts across a broad range of boundarylubrication (BL) regime, as a function of the most relevant contact parameters (

). The only way

to consider such a broad and comprehensive experimental range is a combination of DOE methods and statistical analyses, which was explained in this work, see figure 1. For all combinations of investigated oils and contacts we have obtained an empirical friction model (equations 2, 3 and 4 for the Steel-steel and equations 5, 6 and 7 for the steel-DLC contact). These equations provide us with the exact friction value (or range of values) for any specific set (or range) of experimental parameters for any of the investigated oils by direct calculation from the equations.

15

Although trends and behavior are obtained for specific oils, these oils have been prepared from base oil and additives which are commonly used in automotive lubricants. It was proved in many studies that these additives have the same or very similar behavior irrespective of producer and slight variations in chemistry or concertation. Therefore, presented maps are expected to be equally broadly valid for any other similar oil, additive and their concentration - similarly as in all other studies explain the mechanisms of this oils. Furthermore, in our previous study [60] we have shown that certain Tribometers can be directly numerically comparable - not just in terms of friction trends, which is often the case. Hence, direct (numerical) application of the equations (2) – (7) is not limited only to the device used in this work, but also expanded to the Tribometer which produces statistically equivalent results (i.e. Fenix Tribology, TE77)[60]. Moreover, developed models (equations 2-7) are user-ready, meaning that one can directly insert its own values of the experimental parameters and calculate coefficient of friction for selected oils. Unites to be used in the equations 2-7 are the same as in the table 3. What is more, it needs to be highlighted that obtained models (i.e. friction prediction equations) are not the consequence of the endless fitting process (i.e. super-fitting); equations are based on the experimental parameters and their interactions which have, statistically proven, influence on the coefficient of friction of the investigated oil and contact. From the obtained equations, the friction maps (figures 2 – 7) are generated; these friction maps provide good insight into the effect that investigated additives have on the friction coefficient in the wide range of the BL conditions. Such a wide overview of the friction behavior has not been reported in the literature until now. Therefore, friction maps may be used for readout of the friction trends which are frequently reported in various literature (tables 1 and 2). Moreover, friction maps may be used as a complementary tool for further mechanistic studies and hence assist in explanation of the friction mechanisms, however, any discussion about tribological mechanisms is beyond the scope of this article.

4.2 Findings revealed from the maps Apart from numerous results and findings one can obtain directly from the maps, there are some findings revealed that were not noticed so far in the literature or need special mentioning. Starting with the base oil, it is immediately visible that steel-DLC contact produces on average 22% lower friction coefficient then the steel-steel (figure 2 vs. figure 5), which is well known from the literature [66], but here evidenced in the broad BL range. Furthermore, addition of the AW additive decreases the coefficient of friction for the steel-steel contact up to 37%, but for the steel-DLC contact the coefficient of friction increases up to 25% compared to the base oil. Magnitude of this friction increase is surprising; while friction increase was reported before [36] it was not found of this magnitude. Moreover, from maps 16

in this study we realized that in the steel-steel contact friction is decreased in complete BL regime, while for the steel-DLC contact this behavior is more complex meaning that on average friction increases, but sometimes it also decreases. Addition of the FM additive reduces friction of the steel-steel contact even further, up to 25%. However, similar to the AW effect for the steel-DLC contact there is no unified conclusion; friction can decrease (up to 25%), increase (up to 12.5%) or remain in the same range as for the AW additivated oil depending on parameters. Hence, this example of the steel-DLC contact very clearly illustrates necessity of the friction analysis via friction maps; if test would have been conducted on a single set of experimental parameters, either of the three possibilities could be identified and easily wrongly generalized to the whole BL regime. From the friction maps we further reveal until now unreported property of the FM; comparison with the results for the AW additivated oil reveal that addition of the FM unifies friction values irrespective to parameter variations. Unifying friction effect of the FM is present in both steel-steel and steel-DLC contacts. However, while in the steel-steel contact FM brings both unification and friction reduction, in the steel-DLC contact unification is the primary effect of the FM. It is further found that FM additive effectiveness depends from temperature and speed which have competing effect for both steel-steel and steel-DLC contacts. Namely, FM is the most effective at high temperature and low speed and vice-versa, at low temperature and high speed. While the effectiveness of the FM changes with the variation of these parameters, FM becomes ineffective at high speed and high temperature (figures 4-c and 7-c). Generally speaking, friction behavior (trends) of both steel-steel and steel-DLC contacts lubricated with the AW and the FM additive does not differ from the behavior identified with the AW additivated oil. This means that the AW additive fully determines the friction trends, which are thus obviously strongly related to wear. The wear, however, was not studied in details in this work but strong effect of AW on wear is well documented. Therefore, FM is responsible for the change in the friction values but not in the friction trends. From discussion above it follows that FM is more important as the additive in the steel-steel contact then in the steel-DLC. Namely, in the steel-DLC contact effect of the FM on the friction is not uniform and depends on the contact conditions, while in steel contacts it reduces the coefficient of friction in the whole range of the BL parameters.

17

4.3 Key findings from statistical analysis In the Appendix A, we have presented tables A1-A6 of statistically significant parameters and their interactions as a result of the statistical analysis in this work. These tables offer unique insight into behavior into the friction behavior of the steel-steel and steel-DLC contact with AW and FM additive; for the first statistically proving which parameters and their interactions govern friction mechanism. In practical terms, if a single parameter has been identified as highly significant (HS) or significant (S) this means that the parameter is key contact parameter and that it has to be considered in any experimental study in order to obtain relevant and valid conclusions. Furthermore, if interaction of these parameters has been identified as either highly significant or significant, it shows, which experimental parameters interfere and compete in their influence on the coefficient of friction, hence, which of the investigated parameters must be considered - simultaneously - for any proper conclusions. Since identifying and so discussing interactions is not possible in classical tribological, one factor at a time (OFAT) studies, both experimental design and statistical analysis is absolutely necessary for obtaining these information. Trough performed statistical analysis we have revealed some important and new findings on key contact parameters that define friction in steel-steel and steel-DLC contacts. First of all, sample temperature has no direct influence on the coefficient of friction (tables A3 and A6) with and exception of the steel-DLC contact lubricated with the AW additivated oil (table A5). Although numerous literature reports that temperature does have an effect on the coefficient of friction for the AW additivated oils in the steel-steel contacts [16, 19-22], our statistical analysis clearly shows that temperature influences friction only trough parameter interactions. This means that reported effects are not consequence of the temperature alone, but of the competitive and synergetic effect of multiple parameters and that it is impossible to debate influence of the temperature without consideration of these experimental parameters (i.e. roughness, speed and pressure) Second, effect of surface roughness is mostly neglected in the literature, with only few exceptions for the steel-steel contact [23, 25-29]. Our analysis (tables A2, A3 and A5, A6) for both steel-steel and steel-DLC contacts and AW and FM additives clearly shows that surface roughness is identified even as statistically highly significant. Roughness is therefore one of the key contact parameters defining the coefficient of friction and consequently having great impact on the tribological mechanisms behind the measured friction values. Furthermore, number of interactions can provide us with two information about contact-oil pair; namely and overall importance of certain experimental parameter as well as implicit information about complexity of the investigated oil-contact system [60]. If certain parameter is participating in many of the identified 18

interactions, it is clearly important, and moreover, it is clear that its effect on the friction coefficient cannot be investigated in classical OFAT tribological study. Moreover, large number of interactions indicate that parameters interfere and compete in their influence meaning that the only way to establish how important these interactions are, is through the simultaneous variation of experimental parameters and appropriate statistical analysis. Furthermore, less multi-parameter interaction (consisting of more than two experimental parameters) interactions being identified as highly significant imply more stable and controlled behavior with additives and we have clearly shown this in our results. This is especially visible for the steel-steel contact when AW and AW+FM additivated oils are compared (tables A4 and A5); addition of the FM reduces the number of the multiparameter interactions emphasizing the stabilization effect of the FM additive. Furthermore steel-DLC contact on its own has less highly significant multi-parameter interactions, with both AW and the FM additive, meaning that DLC itself stabilizes (and reduces) the coefficient of friction (Figures 6 and 7). Finally, low value of the

coefficient indicates unpredictable and probably not well controlled

tribological behavior of investigated oil and the whole contact. With the introduction of the additives into the base oil value of the contact, values of the

coefficient grows, and what is surprising, for both, steel-steel and steel-DLC coefficient are almost identical for the observed oils. Hence, value of the

coefficient is predominantly determined by the additives in the oil and the value itself consequently shows appropriateness of the lubricant for the boundary lubrication regime conditions. This is clearly visible from the fact that for the base oil, in both of the contacts,

coefficient was calculated to approximately

0.6 and is well known that base oil alone is inappropriate lubricant for the BL regime. In contrast, for AW additivated oil

was calculated to approximately 0.86, and for the more complex, FM-stabilizing (see

discussion above) AW+FM additivated oil, even 0.97. The fact that values of the

coefficient are almost identical for all investigated oils shows that both AW

and the FM additives are truly activated on both steel-steel and steel-DLC contacts. This is therefore an interesting result about the additives mechanisms and surface reactivity, especially of DLC, which is often discussed.

19

5. CONCLUSIONS

1. AW additive decreases the friction coefficient up to 37% in the complete BL regime in the steelsteel contact while in the steel-DLC contact friction is increased up to 25% compared to the base oil. 2. In the steel-steel contact, FM additive decreases up to 25% compared to the AW additivated oil. However, in the steel-DLC contact effect of the FM depends on the specific set of experimental parameters. 3. Through comprehensive mapping analysis a new property of the FM was discovered; addition of the FM stabilizes friction values irrespective of parameter variations for both of the investigated contacts. 4. AW additive determines friction trends while FM affects values of the friction coefficient, but not its trends, which is true in steel-steel and steel-DLC contacts. 5. In contrast to typical assessment of the temperature effects, we show here that bulk temperature has no direct influence on the coefficient of friction in the selected experimental range. 6. Surface roughness, which is often completely neglected in literature, has been confirmed as one of the key highly significant parameters governing the coefficient of friction. 7. FM additive reduces number of multiparameter interactions thereby supporting the stabilization effect of the FM additive in both of the investigated contacts. 8. Interactions of parameters show, which of the investigated experimental parameters interfere and compete in their influence on the coefficient of friction, hence, which of the investigated parameters must be simultaneously considered if any proper conclusions are to be made; Practically, this means that neither AW, neither FM additive, in the boundary lubrication regime, cannot be investigated without simultaneous consideration of the contact pressure, sliding speed, surface roughness and temperature. 9. Number of multiparameter interactions give information about the control over the contact behavior, more complete additivation means less multiparameter interactions and consequently better control. 10. From the value of the

coefficient we can assess how well the model predicts the behavior of

the investigated oil-contact system; addition of additives increases the

value for both steel-steel

and steel-DLC contacts suggesting less variation in friction with more complex additives. 11. Through the increase of the

coefficient value we confirm that both AW and the FM additives

are truly activated in both of the investigated contacts. 20

ACKNOWLEDGMENT This study was funded by the FP7 program MC-ITN “ENTICE – Engineering Tribochemistry and Interfaces with a Focus on the Internal Combustion Engine” [290077] and was carried out at the Laboratory for Tribology and Interface Nanotechnology, at the University of Ljubljana. The authors would like to express their gratitude to Dr. Frédéric Meunier (Oerlikon Balzers, France) for supplying and assisting us with the DLC coatings and Benoît Thiébaut (Total Marketing and Services, France) for his advice and supply of the lubricants. Finally, many thanks to our colleagues from the Laboratory for Tribology and Interface Nanotechnology, whose suggestions and comments contributed to the quality of this paper

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24

APPENDIX A – STATISTICAL DETAILS Before the model is created, the distribution of the measured results should be determined for two reasons. First, Elastic net regression works with different distributions (i.e., normal, lognormal, binomial, etc.) and this is one of the input parameters. Second, a normal distribution of the results indicates that all of the experimental data were obtained under regular conditions, i.e., no abrupt events occurred, such as possible coating delamination, drying out of the oil, heating failure, excessive vibrations, loose sample clamping, etc.[60] Furthermore, after the model is obtained, residuals (

) should also be

checked for normality because a normal distribution of the residuals is an important indicator that the modeling procedure has been properly completed. The Wald test is represented by the diagnostic plot (figure A1 and A2 for steel-steel and steel-DLC contacts, respectively) on which the thick line is the line of fit and the dotted lines show the 95% confidence interval[60]. If the measured values or residuals fall approximately on the line of fit they are from a normal distribution. From figures A1 and A2 we see that this is the case for all the investigated material/oil combinations. Tables of significant parameters and interactions were obtained using the Wald test [60], which tests the statistical significance of every potential member of the model. In practice, this means that for every explanatory variable hypothesis testing will be conducted in order to determine whether the parameter (or group of parameters) is statistically significant or not. The initial presumption (hypothesis, H0) is that the parameter (or group of parameters) is insignificant and that it should be excluded from the model, while the alternative hypothesis is that the parameter is significant and that it should be included in the model. The Wald test will compute the P value for every parameter (or group of parameters) and compare it to the predefined significance level α (in our case, α=0.005). If P≤ α the null hypothesis is rejected in favor of the alternative one, i.e., we accept that the parameter (or group of parameters) is significant and include it in the model. If P> α we accept the null hypothesis, i.e., the parameter is indeed insignificant and we exclude it from the model [60]. The computed P value is used to determine the significance of the particular parameter (or group of parameters) once it has been accepted to the model (i.e., once the null hypothesis has been rejected). For P<0.05 the parameter is considered as statistically significant (a less than 5% chance of being wrong, denoted as S in the presented tables) and when P<0.0001 the parameter is considered as statistically highly significant (a less than 0.01% chance of being wrong, denoted as HS in the presented tables) [60]. Finally, tables of the statistically (highly) significant parameters and interactions identified in this study are presented in tables A1, A2 and A3 for the steel-steel contact and A4, A5 and A6 for the steel-DLC contact.

25

Figure Captions:

Figure 1 Step-by-step diagram for building the friction model using a statistical approach. Reprinted with permission from [60] Figure 2 Friction map for the steel-steel contact lubricated with the base oil (BO) obtained from the friction model, equation (2), depending on

.

Figure 3 Friction map for the steel-steel contact lubricated with the base oil additivated with the AW additive (BOAW) obtained from the friction model, equation (2), depending on

.

Figure 4 Friction map for the steel-steel contact lubricated with the base oil additivated with the AW and the FM additives (BOAWFM) obtained from the friction model, equation (3), depending on

.

Figure 5 Friction map for the steel-DLC contact lubricated with the base oil (BO) obtained from the friction model, equation (4), depending on

.

Figure 6 Friction map for the steel-DLC contact lubricated with the base oil additivated with the AW additive (BOAW) obtained from the friction model, equation (5), depending on

.

Figure 7 Friction map for the steel-steel contact lubricated with the base oil additivated with the AW and the FM additives (BOAWFM) obtained from the friction model, equation (6), depending on

.

Figure A1 Diagnostic plots for the BO, BOAW and BOAWFM oils, steel-steel contact, showing that the measured friction values and residuals from the predicted values are normally distributed Figure A2 Diagnostic plots for the BO, BOAW and BOAWFM oils, steel-DLC contact, showing that the measured friction values and residuals from the predicted values are normally distributed

26

Table 1 Literature overview on the friction dependence from the experimental parameters for the steel-steel contact lubricated with the AW and the FM additive

27

Investigated experimental parameter

Study

Investigated additive

[16-19]

AW

Increase of the contact pressure causes decrease of the COF.

[22, 23]

AW

Contact pressure has no major influence on the coefficient of friction

[16, 19-22]

AW

Increase of the test temperature leads to the increase of the friction coefficient

[19]

AW

[16, 22]

AW

[24]

AW

[25-29]

AW

[23]

AW

[22]

AW+FM

[30]

AW+FM

Effect on the coefficient of friction

Simultaneous increase of the contact pressure and the test temperature increases the coefficient of friction

,

Increase of the sliding speed increases the coefficient of friction There is a correlation between the sliding speed and the temperature and its effect on the friction coefficient.

,

Increase of the surface roughness increases the coefficient of friction.

,

,

,

, AW/FM concentration ratio

Initial surface roughness and the bulk temperature has a synergetic effect on the coefficient of friction Contact pressure has no significant influence on the coefficient of friction. Coefficient of friction reduces with an increase of both the sliding speed and the temperature. For the same concentration of the FM additive friction increases with the temperature.

Table 2 Literature overview on the friction dependence from the experimental parameters for the steel-DLC contact lubricated with the AW and the FM additive

Investigated experimental parameter

Study

Investigated additive

[57, 59]

AW

COF decreases with the increase of the contact pressure

[54]

AW

COF is insensitive to the variation of the contact pressure

[58]

AW

COF increases with the temperature up to 50 , with the further increase of temperature COF decreases

[52]

AW

COF increases with the temperature.

[39, 40, 52, 56]*

AW

COF decreases with the increase of the entrainments speed

[45]

AW

COF increases with an increase of the sliding speed up to 0.06 m/s and decreases for higher sliding speeds.

[52, 58]

AW+FM (Mo- and organic)

COF decreases with the increase of the temperature

[58]

AW+FM(organic)

[52]*

AW+FM

, FM(organic) concentration

Effect on the coefficient of friction

With the reduction of the OFM concentration, COF becomes insensitive to the variations of temperature COF decreases with the increase of the entrainment speed

*

Sliding rolling contact

Table 3 Testing parameters

Temperature, [ ]

28

Roughness, [

]

Speed, [m/s]

Pressure, [GPa]

50

0.01

0.01

0.68

100

0.055

0.06

0.99

150

0.1

0.1

1.3

Table 4 Prediction errors and coefficient of determinations for the investigated contact and oils.

Contact

Steel-Steel

Steel-DLC

Oil

(%)

(%)

BO

0.003 (2%)

66.7

BOAW

0.002 (1.8%)

85.73

BOAWFM

0.001 (1.1%)

97.4

BO

0.006 (5.2%)

63

BOAW

0.003 (3%)

86.14

BOAWFM

0.002 (1.6%)

97.61

Table A1 Identified parameters and their interactions for the steel-steel contact lubricated with the BO oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

Parameters/Interactions

29

Level of significance

Speed

HS

Temperature x Pressure

S

Speed x Speed

S

Speed x Pressure

/

Parameters/Interactions

Level of significance

Temperature x Roughness x Speed

/

Temperature x Speed

/

Temperature x Roughness

/

Roughness

/

Roughness x Pressure

/

Pressure

/

Roughness x Speed

/

Temperature

/

Temperature x Roughness x Pressure

/

Temperature x Speed x Pressure

/

Roughness x Speed x Pressure

/

Temperature x Roughness x Speed x Pressure

/

Table A2 Identified parameters and their interactions for the steel-steel contact lubricated with the BOAW oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

30

Parameters/Interactions

Level of Significance

Roughness

HS

Pressure

HS

Speed

HS

Temperature x Roughness x Speed x Pressure

HS

Temperature x Speed

HS

Speed x Speed

HS

Temperature x Roughness x Pressure

HS

Roughness x Roughness

S

Temperature x Pressure

S

Roughness x Pressure

S

Roughness x Speed

S

Pressure x Pressure

S

Speed x Pressure

/

Temperature

/

Temperature x Roughness

/

Temperature x Roughness x Speed

/

Temperature x Speed x Pressure

/

Roughness x Speed x Pressure

/

Table A3 Identified parameters and their interactions for the steel-steel contact lubricated with the BOAWFM oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: 31

parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

Parameters Interactions

32

Level of significance

Pressure

HS

Roughness

HS

Temperature x Speed

HS

Roughness x Pressure

HS

Speed

HS

Temperature x Roughness x Speed x Pressure

HS

Temperature x Pressure

S

Pressure x Pressure

S

Speed x Pressure

S

Roughness x Roughness

S

Roughness x Speed x Pressure

S

Speed x Speed

S

Temperature x Roughness x Pressure

/

Temperature x Roughness x Speed

/

Temperature x Roughness

/

Roughness x Speed

/

Temperature x Speed x Pressure

/

Temperature

/

Table A4 Identified parameters and their interactions for the steel-DLC contact lubricated with the BO oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

Parameters/Interactions

33

Level of significance

Pressure

HS

Roughness x Speed

/

Pressure x Pressure

/

Roughness x Pressure

/

Roughness

/

Temperature x Roughness

/

Temperature x Pressure

/

Temperature

/

Speed

/

Temperature x Speed

/

Temperature x Roughness x Speed

/

Temperature x Roughness x Pressure

/

Speed x Pressure

/

Temperature x Speed x Pressure

/

Roughness x Speed x Pressure

/

Table A5 Identified parameters and their interactions for the steel-DLC contact lubricated with the BOAW oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

Parameters/Interactions

34

Level of significance

Pressure

HS

Roughness

HS

Roughness x Speed

HS

Roughness x Roughness

S

Temperature x Roughness x Pressure

S

Speed

S

Temperature x Speed

S

Speed x Pressure

S

Roughness x Pressure

S

Temperature

S

Roughness x Speed x Pressure

/

Pressure x Pressure

/

Temperature x Roughness x Speed

/

Temperature x Speed x Pressure

/

Parameters/Interactions

Level of significance

Temperature x Roughness

/

Temperature x Roughness x Speed x Pressure

/

Temperature x Pressure

/

Table A6 Identified parameters and their interactions for the steel-DLC contact lubricated with the BOAWFM oil. Parameters below the red dotted line have no statistical significance, while parameters above the green line are statistically highly significant (note: parameters marked with HS are statistically highly significant and parameters marked with S are statistically significant).

Parameters/Interactions

35

Level of significance

Roughness

HS

Pressure

HS

Roughness x Roughness

HS

Temperature x Speed

HS

Speed

HS

Temperature x Pressure

S

Speed x Pressure

S

Temperature x Roughness x Speed x Pressure

S

Temperature x Roughness

S

Parameters/Interactions

Level of significance

Roughness x Speed

S

Temperature x Speed x Pressure

S

Roughness x Pressure

/

Temperature x Roughness x Speed

/

Pressure x Pressure

/

Temperature

/

Temperature x Roughness x Pressure

/

Roughness x Speed x Pressure

/

Highlights

36

AW and FM additive influence on the boundary lubrication friction has been described.

AW and FM additives are active in both steel-steel and steel-DLC contacts.

AW additive defines general friction trends in both steel-steel and steel-DLC contacts.

Stabilization effect of the FM is shown for both steel-steel and steel-DLC contacts.

Value of the

coefficient provides qualitative information about the investigated oil.

37

38

39

40

41

42

43

44

45

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