1. Introduction
The global biolubricant market was estimated at USD 1.9 billion in 2020 and is projected to reach USD 2.7 billion by the year 2027 [
1]. The estimated growth in the biolubricant sector at a compound annual growth rate (CAGR) of 5.2% is driven by concerns about the rapid depletion of fossil fuel resources and environmental pollution arising from improper disposal of lubricants derived from such resources. Biolubricants are an alternative to conventional lubricants derived from fossil fuel resources. They are biodegradable (70–100% [
2]) and renewable, with the most common type being vegetable oil or its derivatives (approximately 45% of the global biolubricant market [
1]). In addition to not being toxic, vegetable oil also has excellent lubrication properties, attributed to its unique combination structure of polar and nonpolar molecular groups. The carboxyl polar group of vegetable oil adsorbs to the rubbing surfaces to form a lubricant film, protecting them from undesired wear and tear.
Vegetable oil’s high fatty acid content (between 80–90%) is the primary factor in its lubricating efficacy [
3]. However, the
-hydrogen atoms in the hydroxyl groups and unsaturated free fatty acids (FFA) of the vegetable oil triglycerides promote fast crystallisation, resulting in poor thermo-oxidative stability. Therefore, converting vegetable oil into synthetic esters through chemical modifications (e.g., epoxidation, hydrogenation and transesterification [
4]) can remedy this deficiency. One of the economically feasible solutions is to convert vegetable oil into a synthetic polyol ester, namely, trimethylolpropane ester (TMP ester), using transesterification. On top of an improved thermo-oxidative stability [
4,
5], numerous research studies on such polyol esters derived from vegetable oil have produced biolubricants with a lubricity that is on par or superior to conventional lubricants [
6,
7]. To date, vegetable oils, such as palm oil [
8], jatropha oil [
9], rice bran [
4], karanja oil [
4], sunflower oil [
9], soybean oil [
9,
10] and cotton seed oil [
11], have been transesterified to produce TMP esters. Recently, studies on TMP esters have shifted towards specific fatty acid chains, namely, from TMP trioleate [
12,
13]. TMP trioleate, synthesised from oleic acid, has been demonstrated to possess a good lubricity and has often been suggested for use as hydraulic oil.
A recent bibliometric study by Lee et al. [
14] highlighted the importance of correlational studies on the lubricity of vegetable oil biolubricant and its fatty acid composition. The chemical structure of vegetable-oil-derived biolubricants and their fatty acid composition is vital to their physicochemical and tribological properties [
15,
16,
17]. According to the study by Biresaw and Bantchev [
18], the lubricant film is influenced by the degree of unsaturation, fatty acid chain length and the polar group of the vegetable oil. Correlating the fatty acid compositions of vegetable-oil-based lubricants with rheological properties has been reported on numerous occasions in the literature [
9,
19,
20]. For example, the monounsaturated or polyunsaturated fatty acids influence the viscosity of vegetable oil [
19]. Specifically, Kim et al. demonstrated that the viscosity of vegetable oil increased with a higher concentration of oleic acid (C18:1) while it decreased with a higher linoleic acid (C18:2) content [
20]. Apart from viscosity, it has also been reported that a low thermo-oxidative stability is attributed to higher levels of unsaturation [
9] while high pour points are attributed to higher levels of saturation [
21].
On the other hand, the influence of fatty acid profiles on vegetable oil’s frictional and wear properties have also been studied. For example, stearic acid in vegetable-oil-based lubricants could reduce friction and wear [
3]. High linoleic and oleic acid concentrations in vegetable oils, namely soybean oil, have also produced a lower friction and wear, arising from the formation of denser fatty acid monolayer film [
22,
23]. Hamdan et al. suggested that decreasing the ratio of monounsaturation to total saturation level could result in reducing the friction of vegetable-oil-derived fatty acid methyl ester (FAME) [
24]. A reducing ratio would also reflect an increasing saturation level (assuming a constant monounsaturation). Similarly, the increasing saturation level of vegetable oil FAME has also been reported to lead to a friction drop by Rajasozhaperumal and Kannan [
23]. They explained that saturated fatty acid molecules adsorbed more efficiently on the surface to form a more effective lubricating film.
The literature mentioned above often highlights the effect of the fatty acid composition of vegetable-oil-based lubricants with little effort on mathematically quantifying the effect. Neat vegetable oil feedstocks are often investigated along with different chemical modification and additivation approaches. Instead of using a trial-and-error approach, a proper quantification of such effect would be imperative for optimising the tribological properties of vegetable oil for developing more effective biolubricants, allowing an optimum fatty acid configuration of biolubricant to be attained for the desired applications. Therefore, machine learning techniques should be explored when determining the effect of fatty acid composition on the tribological properties of vegetable-oil-based biolubricants. Machine learning allows complex processes to be systematically quantified in an efficient manner [
25], suitable for tribological systems, often involving multiphysics phenomena.
Marian and Tremmel recently reviewed the penetration of machine learning techniques in the field of tribology research [
26]. Their review showed that most tribological research adopting machine learning techniques are related to composite or advanced materials, lubrication systems for motion generation or power transmissions (including bearings, seals, brakes and clutches), surface texturing and lubricants. With relation to lubricants, the reported literature focuses more on additive studies [
27,
28,
29]. Artificial Neural Networks (ANNs) and genetic algorithms are the majority of machine learning techniques adopted in tribology. Machine learning techniques solve the identified problem by training using available data from a simulation, experiment or the literature. To date, ANNs have been demonstrated to produce predictive models with a high coherence to experimental data [
30]. However, it remains a challenge to derive an empirical formulation of an ANN model for practical applications due to the complex nature of ANN models [
31].
An alternative machine learning technique is gene expression programming (GEP), an extension of genetic programming that incorporates simple and linear chromosomes to generate small programs with explicit equations [
32]. GEP has the genetic algorithm’s simplicity and the abilities of genetic programming [
33]. This technique produces simple mathematical expressions in the form of subexpression trees with high prediction capabilities that can be adopted for practical applications. More importantly, the expressions from GEP have been reported in the literature to have a good generalisation and predictive capability, not limited to correlations [
30,
34,
35]. Recently, GEP has been adopted to study material removal via machining [
36], with most studies still revolving around civil engineering applications [
30,
37].
Knowing the influence of different fatty acid compositions on the physicochemical and tribological properties of vegetable-oil-based biolubricant is essential. A lubricant’s fluid film lubrication performance is heavily influenced by its viscosity. However, the same cannot be said of its boundary lubrication properties. Therefore, as a first approximation, the present study aims to develop a practical empirical expression using GEP to describe the effect of vegetable-oil-based trimethylolpropane (TMP) ester’s fatty acid composition on its boundary frictional performance. The generated GEP model prepares an empirical platform to further explore the boundary lubricity of TMP esters as an alternative to conventional mineral-oil-based lubricants. More importantly, the GEP model is expected to predict the frictional performance of vegetable-oil-based TMP esters following the operating conditions of the desired applications. To the authors’ knowledge, adopting the GEP technique in deriving a generalised empirical model for vegetable-oil-derived TMP esters’ boundary frictional performance, considering fatty acid composition, has yet to be reported in the literature.
3. Results and Discussion
Table 3 summarises the physicochemical properties of the vegetable-oil-derived TMP esters. Based on the kinematic viscosity values, the palm and grapeseed–canola TMP esters fell under the ISO VG 22 grade. On the other hand, the olive and canola–palm-soybean TMP esters could be classified under ISO VG 68, while canola and canola–sunflower followed ISO VG 150. Contrary to the observation by Kim et al. [
20], instead of a lower viscosity, higher viscosity values for canola and canola–sunflower could result from the coupled effect of the high mono- and polyunsaturation levels as shown in
Table 1. On the other hand, the derived coconut TMP ester produced the lowest viscosity, attributed to its shorter alkyl carboxylic chain (predominantly C12 to C16). At the present state, this TMP ester also could not be satisfactorily classified as its viscosity fell between ISO VG 10 and 15. However, the coconut TMP ester could be modified with suitable viscosity modifiers to suit either viscosity grade.
The viscosity index (VI) values for most of the derived TMP esters were calculated to be higher or comparable to reported typical values of oil-based engine lubricants. The canola and canola–sunflower TMP esters’ VI values were lower among the derived TMP esters at 121 and 132, respectively. By referring to
Table 1, the lower VI values from these TMP esters could be attributed to their high PU levels (>50%). The highest VI value was recorded by the coconut TMP ester at 259, potentially resulting from its high SA levels. Such a high VI value shows potential for the coconut TMP ester to be adopted for systems operating under harsh conditions. The thermal decomposition onset temperature determined using TGA can indicate the lubricant’s thermal stability. In the present study, all the derived TMP esters exhibited a decomposition onset temperature above 300 °C, which was much higher than the values reported for engine lubricants (230 to 260 °C) [
45].
The flash point is affected by the unsaturated carbon–carbon bonds in the fatty acid chain of an ester. It is also subjected to the numbers and the location of the double bond in the chain. The double bond in the fatty acid chain act as the active side for oxidation [
46]. In other words, the flash point of the TMP ester is expected to be higher with increasing SA. Referring to
Table 3, the palm TMP ester (46% SA) had the highest flash point while TMP-canola (2.7% SA) had the lowest flash point, corresponding to 152 °C and 98 °C. Contrary to the pour point characterisation, defined as the lowest temperature fluidity of a lubricant, a lower degree of SA gives a better cold flow behaviour [
47]. The obtained pour point for each TMP ester was found to follow the expected trend, where the pour point of canola was much lower than that of palm and coconut. It is noted that the flash and pour points of the TMP esters remained undesirable compared to commercial engine lubricants (≈ 220 °C for flash point and ≈ −50 °C for pour point) and hydraulic oil (≈ −20 °C for pour point). Thus, it can be surmised that the derived TMP esters would need further enhancements through flash point additives and pour point depressants.
The friction force measured for the derived vegetable-oil-derived TMP esters is given in
Figure 4. The friction forces changed linearly with the applied loads for all the TMP esters. It is noted that the determination coefficient (
) for the friction forces as a function of load was above 0.85 when considering a linear regression. Such a trend followed the ones expected of boundary lubrication. However, the coefficient of friction (slope of the friction curve) varied when the sliding speed was increased. Another noticeable trend presented in
Figure 4 is the vertical shift or offset of the measured friction force with the increasing sliding speeds. The offset indicated a varying intercept at the friction force axis. The observed nonzero intercept, also known as a dynamical friction parameter, could result from the TMP ester molecules adsorbing on the rubbing surfaces to form a boundary film [
48], generating an interfacial shear resistance that needs to be overcome to sustain the sliding action. Overall, the frictional property of the palm TMP ester improved with higher speeds, leading to a lower friction coefficient than the other TMP esters. Such an improvement in boundary lubricity could result from the balanced saturation and monounsaturation levels of palm TMP ester, not seen in other TMP esters.
Figure 5 plots the coefficient of friction for the TMP esters against the lambda parameter (
). It is noted that the coefficient of friction was taken as the slope of the measured friction force against the load provided in
Figure 4 at its respective speed. An average
was taken upon observing that the ratio was relatively constant for each load at its respective sliding speed. It is shown that all the TMP esters operated in mixed and boundary lubrication regimes (
< 1.15). Interestingly, the coefficient of friction for all the TMP esters, except for the olive and coconut TMP esters, exhibited a Stribeck like property. The coefficient of friction dropped with increasing
values until reaching a minimum before increasing slightly or saturating at higher
values. Such a behaviour could result from an increased hydrodynamic effect even with a fixed amount of lubricant supply, encouraging the contact to transition from boundary to mixed lubrication regimes. The coefficient of friction for the olive and coconut TMP esters was observed to keep increasing with larger
values. Such a trend indicated that these TMP esters might not sustain the film under a high shear stress, potentially attributed to the molecules’ lesser ability to adsorb to the wear disks. It is noted that the coefficient of friction for all TMP esters was in the range of 0.03 and 0.14, much lower than the measured coefficient for a dry contact (0.34), indicating mixed and boundary lubrication regimes that were consistent with the
values.
GEP Model for TMP Ester Boundary Lubricity
The measured friction forces for the vegetable-oil-derived TMP esters were demonstrated to vary among each other. Considering the tested loads and speeds were fixed, such variation could be due to the influence of the fatty acid composition. However, such a correlation can only be qualitatively observed via the measured friction or coefficient of friction plots, but it remains challenging to quantify them mathematically. Even when it is possible to correlate them using typical regression models, the lack of generalisation capability limits the usage of the obtained correlations. Therefore, as a first approximation, the present study used the GEP model to describe the friction force as a function of the fatty acid composition of the TMP esters.
Figure 6 illustrates the values for the training, validation and testing subsets, randomly assigned using a stratified sampling technique. The values for the validation and testing subsets were shown to sufficiently cover the range of data points represented by the training set. The GEP used the training subset to generate subexpression trees for the model, while the validation and testing subsets were adopted independently to validate the generated GEP model.
The GEP model generated for the TMP ester friction is represented by six subexpression trees, each representing a gene from the GEP, in
Figure 7 and
Figure 8. Each subexpression tree forms a term in the expression produced by the GEP model. Translating the subexpression trees would result in a correlation for the friction force that follows Equation (
2). The friction force,
(mN), can be predicted using the following empirical equation:
where
;
;
The terms A to E are taken from subexpression trees one to five, while the terms and are from subexpression tree six6. The terms , , and refer to SA (%), MU (%), load (mN) and speed (m/s), respectively.
Figure 7.
Subexpression trees 1 to 3 of the generated GEP model for vegetable-oil-derived TMP ester boundary lubricity. (a) Subexpression tree 1. (b) Subexpression tree 2. (c) Subexpression tree 3. (Note: "3Rt" refers to cubic root, "+" refers to addition, "-" refers to subtraction and "/" refers to division).
Figure 7.
Subexpression trees 1 to 3 of the generated GEP model for vegetable-oil-derived TMP ester boundary lubricity. (a) Subexpression tree 1. (b) Subexpression tree 2. (c) Subexpression tree 3. (Note: "3Rt" refers to cubic root, "+" refers to addition, "-" refers to subtraction and "/" refers to division).
Figure 8.
Subexpression trees 4 to 6 of the generated GEP model for vegetable-oil-derived TMP ester boundary lubricity. (a) Subexpression tree 4. (b) Subexpression tree 5. (c) Subexpression tree 6. (Note: 3Rt refers to cubic root, "+" refers to addition, "-" refers to subtraction and "/" refers to division).
Figure 8.
Subexpression trees 4 to 6 of the generated GEP model for vegetable-oil-derived TMP ester boundary lubricity. (a) Subexpression tree 4. (b) Subexpression tree 5. (c) Subexpression tree 6. (Note: 3Rt refers to cubic root, "+" refers to addition, "-" refers to subtraction and "/" refers to division).
Figure 9 gives the friction force comparison between the experiment (target) and model. The absolute error values are also provided in the exact figure. It can be observed that the model predicted friction force trends that followed the experimentally measured values for the training, validation and testing subsets.
Table 4 summarises the statistical parameters for evaluating the GEP model performance. The determination coefficient (
) for the training, validation and testing subsets were 0.858, 0.824 and 0.916, respectively. On the other hand, the correlation coefficients (
R) were 0.926, 0.908 and 0.957 for the training, validation and training subsets, respectively. These values were larger than 0.8 [
34], indicating a strong correlation between experiment and model. The values for
,
,
and
were fairly similar among the training, validation and testing sets, indicating good generalisation capability of the model. Along with the near zero performance index,
, the generalisation capability of the generated GEP model was shown to be statistically reliable. The
values for the validation and testing subsets were 0.078 and 0.076, respectively. The near-zero values for
also indicated there were no overfitting issues [
34].
The GEP model was also externally validated using other statistical parameters as highlighted by Iqbal et al. [
30]. The external validation’s purpose was to evaluate the GEP model’s generalisation capability further.
Table 5 tabulated the statistical parameters adopted in the present study for the external validation of the GEP model. The slopes of the regression lines,
k and
, for the training, validation and tests subsets were 0.976, 0.998 and 0.957, respectively. The values, close to unity, verified the correctness of the correlation produced by the GEP model [
35]. The squared correlation coefficient through the origins (
) and the coefficient between the experiment and model (
) were close to unity for all sets of data. Such trends strongly indicated that the generated GEP model had a statistically reliable generalisation capability and was not merely a correlation. More importantly, it can be surmised that the GEP model possessed a high generalisation capacity and excellent ability to predict reliable outcomes for unseen data or values.
The variable importance level for the GEP model is also highlighted in
Figure 10 along with the influence of each variable on the friction of the derived vegetable-oil-derived TMP esters. The GEP model highlighted that the load (38% contribution) was an essential variable, where increasing the load applied to the contact increased the friction force of the vegetable-oil-derived TMP esters. The saturation level, SA, was the second most important variable at 29%, where higher SA levels would result in a friction reduction. On the contrary, the GEP model indicated that the MU level (21%) and sliding speed (12%) were less significant in affecting the TMP ester friction force than load and SA. The lesser significance of the sliding speed from the GEP model was an expected trend as this corroborates the characteristic of boundary lubrication following the Stribeck curve, where the sliding speed has little influence on the boundary friction. Referring to
Figure 10e, the friction force gradually increased with the sliding speed. The significance could be amplified further when the sliding speed increases beyond the range selected for the present study, potentially attributing to the growing hydrodynamic effect. However, it can be said that the present GEP model could be less accurate at higher sliding speeds, especially when the operating lubrication regime transitions more towards fluid film lubrication, attributed to the lack of information on lubrication regimes outside of the ones provided for the present model.
4. Conclusions
The present study synthesised TMP esters from different vegetable oil feedstocks with varying fatty acid profiles using a two-stage transesterification process. Except for the coconut TMP ester, the TMP esters could be mapped to ISO VG 22 (palm and grapeseed–canola TMP esters), ISO VG 68 (olive and canola–palm–soybean TMP esters) and ISO VG 150 (canola and canola–sunflower TMP esters). The VI values of the TMP esters were comparable to typical engine lubricants. Lower VI values could be attributed to higher polyunsaturation levels while the opposite could be achieved with higher saturation levels.
The study then determined the boundary lubricity of vegetable-oil-derived TMP esters using a purpose-built ball-on-disc tribometer. The TMP esters were spin-coated on stainless steel wear discs, allowing the friction test to be carried out in a boundary lubrication regime. The coefficient of friction for all TMP esters, except olive and coconut TMP esters, exhibited a Stribeck like trend, potentially indicating the transition of operating lubrication regimes from boundary to mixed. Among the studied TMP esters, the palm TMP ester exhibited improved frictional performance with higher speeds, potentially due to its more balanced saturation and monounsaturation levels of fatty acid profile compared to the other tested TMP esters.
A gene expression programming (GEP) was adopted to model the boundary lubricity of the TMP esters. A set of simple and explicit equations was produced to describe the boundary lubricity of the TMP ester considering the fatty acid composition (saturation and monounsaturation levels), load and speed. The GEP model was empirical and agreed well with the measured friction force. The statistical evaluation of the GEP model, including an external validation, demonstrated that the model had a high generalisation and prediction capability. The model also showed that the friction force for the TMP esters decreased with higher saturation levels. On the contrary, the lesser influence of the speed followed the characteristics of boundary lubrication, where hydrodynamic action is negligible. Thus, the GEP model is expected to provide a fundamental and empirical platform for further studies to optimise the boundary tribological properties of vegetable-oil-based TMP esters, encouraging the widespread adoption of such a biolubricant as an alternative to conventional lubricants.