Correlation of Elastohydrodynamic Friction with Molecular Structure of Highly Refined Hydrocarbon Base Oils
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The molecular compositions of a range of low viscosity hydrocarbon base oils spanning API Groups II to IV have been quantified using 13C NMR and correlated with base oil elastohydrodynamic (EHD) friction. A strong correlation has been found between the proportions of paraffin, linear and branched carbons and EHD friction, with a high proportion of linear and paraffinic carbon atoms contributing to low-EHD friction but branched carbons contributing to high-EHD friction. Correlation equations have been developed to predict EHD friction based on base oil composition. At very high temperature and low pressure, this correlation breaks down as the lubricant in the contact does not reach sufficiently high shear stress for shear thinning to occur. For Group IV polyalphaolefin, the correlation must be extended to account for the very high proportion of linear carbons originating from linear alkene oligomerization. The correlations developed in this study can be used to guide the design of low-EHD friction base oils.
KeywordsEHD friction Traction Low friction 13C NMR API groups Base oil structure
To meet challenging carbon dioxide emissions reduction targets, coupled with increasing demands of electric vehicles whose transmissions are subjected to very high torque and thus high contact pressures, industry is increasingly demanding high quality base stocks with superior elastohydrodynamic (EHD) frictional characteristics. Base stock qualities depend primarily on the crude oil feedstock and the refining process technology employed, and these result in widely differing base oil structures, and thus properties and performance, including EHD friction.
Crude oils consist of mixtures of hydrocarbon molecules with primarily paraffinic, naphthenic and aromatic structures. They need to be refined to produce targeted base stocks suitable for lubricant applications. Since crude oils have both undesirable and desirable components, the refining process needs to be a balance between removing, converting and retaining components to achieve an appropriate molecular structural transformation to the target product.
Vacuum gas oil or deasphalted oil from distillation of crude oil is generally used as feedstock to produce base stocks. Unlike Group I base stocks which are rich in aromatics and typically obtained from solvent processes, paraffinic base stocks are produced by catalytic hydroprocessing routes including hydrotreating, hydrocracking, isodewaxing and hydrofinishing. To obtain highly refined and highly paraffinic base stocks featuring high viscosity index, low cold cranking simulator (CCS) viscosity, better oxidation stability and higher boiling temperature, a combination of waxy feedstocks and severe hydroprocessing technology is typically adopted .
Elastohydrodynamic lubrication (EHL) is present in lubricated components such as gears, rolling bearing, cam-tappet systems and constant velocity joints, where non-conforming contacts generate high strain rate and very high pressure. EHD friction is determined by how the lubricant molecules respond to these conditions. It is now recognized that EHD friction is mainly affected by the structure and flexibility of the base oil molecules present, since these control how easily molecular layers move past one another during shear at high pressure when the available free volume is very limited .
Although there have been many studies concerning the EHD friction properties of different base oils, these have mainly focused on synthetic base oils designed to provide high-EHD friction for traction drives [3, 4]. Studies of the EHD friction of conventional, petroleum-derived hydrocarbon base oils has been limited to exploring the impact of base oil viscosity and API group type, with little attempt to relate EHD friction to detailed base oil composition.
In this study, the EHD friction of low viscosity, highly refined paraffinic base oils such as are becoming prevalent in low-friction lubricant formulations is correlated with molecular structural parameters determined by 13C nuclear magnetic resonance (NMR) spectroscopy. The aim is to better understand how to obtain low viscosity, hydrocarbon lubricants that provide low friction in EHD contacts.
2 Previous Work
There has been considerable previous research on the EHD friction properties of base fluids aimed at relating their friction behaviour to their composition. Gunsel and co-workers studied a wide range of base fluids from various refining processes and with different kinematic viscosities, and found that synthetic polyalphaolefin (PAO) and hydro-treated base oils gave lower friction than solvent-treated mineral base oils . This has been recently confirmed by Zhang et al. .
Most systematic exploration of the relationship between EHD friction and molecular structure of base fluids has focused on synthetic base oils and especially fluids that deliver high-EHD friction [3, 4 6–11]. This is unsurprising since the molecular structure of most synthetics is much better defined than that of mineral oil-derived fluids. It has been shown that cyclic saturated ring structures give high-EHD friction [3, 6] and that the extent of alkyl chain branching also contributes to an increase of EHD friction . Tsubouchi identified five key molecular structure features for high-EHD friction to be high molecular stiffness, large size, short alkyl chain length, high melting point and low molecular polarity [7, 8, 9, 10]. Edgar and Hurley applied quantitative structure activity relationships (QSAR) to predict EHD friction based on friction measurements on a learning set of molecules of known structure to aid in the development of new traction fluids .
Oxygen-containing Group V synthetic base oils, such as esters and glycols have been another area of interest in terms of EHD friction behaviour. Hetchshel studied various polyglycols and found that ethylene-based ones gave the lowest EHD friction. He proposed that lubricant molecules with a thread-like shape and a minimum of pendant structural subunits or functional groups reduced the intermolecular interactions that contribute to EHD friction . Chang et al. found that shear stress (and thus friction) was strongly dependent on ester structure, demonstrating that esters with long and linear chains gave low shear stress, while branched chain esters gave relatively high shear stress . Zhang et al. measured the EHD friction properties of a very wide range of base fluids including synthetics and mineral oils. They confirmed the importance of molecular structure of the base fluid on EHD friction and that liquids having linear-shaped molecules with flexible bonds give lower friction than liquids with bulky side groups or rings .
Most of the studies above have employed disc machines or ball-on-disc tribometers and were aimed specifically at measuring EHD friction. A number of studies have also explored the impact of lubricant molecular structure on the friction and efficiency of actual engineering components. Rounds used a thrust ball bearing rig to measure the friction properties of several mineral and synthetic base oils and found that naphthenic base oils gave higher friction than paraffinic base oils . Yang et al. measured the temperature rise of a loaded thrust bearing to correlate with measured EHD friction. Based on this, they suggested that EHD friction is one of the important lubricant properties in determining rolling bearing efficiency and found that Group III + , IV and ester (Group V) have generally low-EHD friction . Yoshizaki et al. studied the influence of base oil structures on friction loss by testing spur gears  while Höhn et al. investigated the influence of base oil type on gear mesh losses . They both noted torque reduction with synthetic base oils including esters, polyglycols and PAO, compared to mineral base oils.
In this study, highly refined hydrocarbon base oils with quite similar compositional types have been selected to conduct a systematic study of the impact of molecular structure on EHD friction. Nuclear magnetic resonance (NMR) spectroscopy has been reported to be a powerful tool to understand the structural parameters of base oils and has been correlated with the latters’ bulk properties such as low-temperature rheology and pressure-viscosity coefficient [18, 19, 20, 21, 22]. In this study, NMR has been applied to derive a range of quantitative structural parameters of the base oils of interest and a series of EHD friction property measurements has been made on the same set of base oils at various conditions. Finally, correlation by multiple regression fit has been made between the quantitative molecular structural characteristics and EHD friction. This correlation between structure and property can be used to inform the design of tailored molecules to create new base oils able to cope with the rising demand for high quality, low-friction base oils.
3 Test Fluids
Hydrocarbon base oils tested
GrII + (A)
GrII + (B)
GrIII + (A)
GrIII + (B)
GrIII + (C)
4 Test Methods
4.1 EHD Friction
EHD friction was measured using a mini traction machine (MTM2, PCS Instruments). In the MTM, a ball is loaded against the flat surface of a disc immersed in lubricant and these are independently driven to enable any desired combination of rolling and sliding speed. Friction curves were obtained at a fixed entrainment speed of 2.0 m/s over a wide range of slide-roll ratio (SRR) values ramped up from 0 to 50%. In this study, 19.5 mm diameter AISI 52100 steel balls and 46 mm diameter AISI 52100 steel discs were employed. Their root mean square surface roughnesses, Rq, were 11 and 5.5 nm, respectively.
The tests were conducted at five different temperatures, 40, 60, 80, 100 and 120 °C, and four different applied loads, 15.0, 25.9, 41.1 and 61.3 N, corresponding to mean Hertz pressures of 0.5, 0.6, 0.7 and 0.8 GPa, respectively.
4.2 EHD Film Thickness
The EHD film-forming properties of the test oils were also measured in order both to ensure that friction measurements were made in full-film EHD conditions and also to enable calculation of the mean shear rates present in the frictional contacts. EHD film thickness measurements were made using an ultrathin film measurement system (EHD2, PCS Instruments). This employs optical interferometry to measure lubricant film thickness in a rolling steel ball on coated disc contact .
In this study, the measurements of central film thickness were made as a function of entrainment speed in nominally pure rolling with a steel ball/glass disc combination at an applied load of 20 N.
4.3 Nuclear Magnetic Resonance Spectroscopy
13C NMR analysis was carried out on a 600 MHz NMR spectrometer in deuterated chloroform. The experiments were performed at room temperature and chemical shifts were measured with respect to tetramethylsilane (TMS) used as an internal standard. Neat base oils were analyzed without separation of saturate and aromatic fractions. Structural parameters of the base oils were computed from the data obtained from 13C NMR measurements.
5.1 EHD Friction
5.2 EHD Film Thickness
These film thickness data were also used to determine strain rates (sliding speed/film thickness) to enable conversion of EHD friction curves to plots of mean shear stress versus strain rate as described later in this paper.
5.3 Nuclear Magnetic Resonance Spectroscopy
13C NMR structural parameters of hydrocarbon base oils
GrII + (A)
GrII + (B)
GrIII + (A)
GrIII + (B)
GrIII + (C)
Paraffin carbons (CP), %
Branched carbons (CB), %
Linear carbons (CL), %
6.1 Shape of EHD Friction Curves
At most temperatures and loads, the friction coefficient versus SRR curves as illustrated in Fig. 1 show classical EHD friction behaviour, with a rapid rise in friction with SRR followed at higher SRR by a levelling out and then, at the highest loads, a slight drop in friction coefficient. Johnson and Tewaarwerk have produced the most widely accepted model of this behaviour . At very low SRR and thus low strain rates, the fluid behaves in a Newtonian fashion, though this tends to be overlain at high pressures with an accommodation of some of the strain by a viscoelastic response of the fluid and elastic shear compliance of the contacting surfaces. When the strain rate and thus the shear stress reaches a critical value, often called the Eyring stress, the film starts to shear thin so that its shear stress no longer rises linearly with strain rate and this is responsible for the initial levelling out of the friction curves. At high shear stress and strain rate, the fluid film experiences a significant temperature rise due to shear heating, and this produces a full levelling out and even slight fall in the friction at high SRRs for most lubricants, including the ones tested in this study.
6.2 Isothermal Correction
Figure 5 shows that over much of the SRR range, mean shear stress is proportional to log (strain rate) but that at high strain rate the shear stress curves flatten and at high pressures, actually start to fall. This is due to shear heating of the EHD film at a combination of high shear stress and high strain rate. To determine the intrinsic EHD friction of base oils the effects of shear heating of the EHD film can be subtracted to obtain isothermal shear stress versus strain rate curves.
In Eq. 4, Ksρc = 7.95 × 107 J2 K−2 s−1 m−4, b was 98 µm at a load of 15 N, 118 µm at 25.9 N, 137 µm at 41.1 N and 157 µm at 61.3 N. Koil was estimated from data in  by selecting the nearest fluid type and correcting to the relevant mean contact pressures. For each measured friction value, the mean oil film temperatures in the contact calculated and mean shear stresses obtained from measured friction data were corrected back to their bulk test temperatures as described in .
6.3 Eyring Stresses
6.4 Friction Behaviour at High Temperature and Low Load
As can be seen in Fig. 1e, at very low pressure and high temperature, the friction coefficient versus SRR curves are almost linear and there is relatively little difference in friction between the different groups. This is because under these conditions, all the fluids are behaving in a predominantly Newtonian fashion and do not reach sufficiently high shear stress to experience shear thinning. In this case dynamic viscosity alone will control friction. Evans and Johnson have derived regime maps to describe lubricant film rheological response at different pressures and strain rates [29, 30]. These suggest that fluids behave in a Newtonian fashion at low strain rates, if they have low viscosity or are at modest pressure, but that in high pressure contacts, they show a shear-thinning response.
6.5 Correlation of EHD Friction and Structural Parameters
It is evident from Fig. 1 that base oil groups Group III, III + and IV show relatively low-EHD friction. As suggested by previous researchers [2, 5, 6, 12, 13] this can be attributed to more linear paraffinic molecular structures in higher base oil groups, which enable easier alignment and less interaction with neighboring molecules during shear at high pressure, thus favouring lower EHD friction. In the current study, detailed structural parameters for each base oil were obtained using 13C NMR as listed in Table 2 and multiple linear regression analysis of these parameters with EHD friction was carried out to model the relationship between them. Correlations were made for EHD frictions measured at each temperature and pressure at five different SRR values of 5, 10, 20, 30 and 50%. As expected, the parameters of total paraffin carbons and linear carbons are positively correlated with EHD friction, but the parameter of branch carbons is negatively correlated.
Detailed result of regression analysis relating EHD friction to 13C NMR structural parameters of base oils (in these regression equations, CP, CL and CB are fractional values, not percentages as in Table 2)
0.0716 − 0.0258CP − 0.117CL + 0.0276CB
0.0774 − 0.0275CP − 0.112CL + 0.0289CB
0.0800 − 0.0230CP − 0.101CL + 0.0313CB
0.0767 − 0.0215CP − 0.0848CL + 0.0290CB
0.0477 − 0.0192CP − 0.0864CL + 0.0370CB
0.0585 − 0.0232CP − 0.0929CL + 0.0353CB
0.0683 − 0.0252CP − 0.0863CL + 0.0361CB
0.0689 − 0.0205CP− 0.0829CL + 0.0204CB
0.0421 − 0.0180CP − 0.0731CL + 0.0352CB
0.0528 − 0.0208CP − 0.0831CL + 0.0313CB
0.0636 − 0.0225CP − 0.0798CL + 0.0232CB
0.0642 − 0.0215CP − 0.0724CL + 0.0244CB
0.0373 − 0.0202CP − 0.0523CL + 0.0348CB
0.0477 − 0.0224CP − 0.0636CL + 0.0294CB
0.0586 − 0.0236CP − 0.0629CL + 0.0199CB
0.0597 − 0.0219CP − 0.0589CL + 0.0188CB
Normalized regression equations relating EHD friction to 13C NMR structural parameters of base oils; (in these regression equations, CP, CL and CB are fractional values, not percentages as in Table 2)
μ = 0.0716(1 − 0.360CP − 1.63CL + 0.385CB)
μ = 0.0774(1 − 0.355CP − 1.45CL + 0.373CB)
μ = 0.0800(1 − 0.288CP − 1.26CL + 0.391CB)
μ = 0.0767(1 − 0.280CP − 1.11CL + 0.378CB)
μ = 0.0477(1 − 0.403CP − 1.81CL + 0.776CB)
μ = 0.0585(1 − 0.397CP − 1.59CL + 0.603CB)
μ = 0.0683(1 − 0.369CP − 1.26CL + 0.529CB)
μ = 0.0689(1 − 0.300CP − 1.20CL + 0.300CB)
μ = 0.0421(1 − 0.428CP − 1.74CL + 0.836CB)
μ = 0.0528(1 − 0.394CP − 1.57CL + 0.593CB)
μ = 0.0636(1 − 0.354CP − 1.25CL + 0.365CB)
μ = 0.0642(1 − 0.335CP − 1.13CL + 0.380CB)
μ = 0.0373(1 − 0.542CP − 1.40CL + 0.933CB)
μ = 0.0477(1 − 0.470CP − 1.33CL + 0.616CB)
μ = 0.0586(1 − 0.403CP − 1.07CL + 0.340CB)
μ = 0.0597(1 − 0.367CP − 0.987CL + 0.315CB)
Although the effects of molecular structure on EHD friction such as more linear chains and less branches to give lower EHD friction, have been reported mainly qualitatively, this study has clearly shown the effect of molecular structures quantitatively and a high degree of correlation based on detailed molecular carbon level. Thus, the findings could be applied to design lower EHD friction base oils to maximize fuel economy and energy efficiency.
The above correlations were made using the raw EHD friction data without thermal correction. Correlations were also tested using isothermally corrected friction data. The isothermally corrected average R2 coefficient was 0.964 and increased to 0.984 when results measured at 0.5 GPa and 0.6 GPa at 120 °C, and 0.5 GPa at 100 °C were excluded. These are almost identical to the uncorrected friction correlations of 0.968 and 0.984. This is unsurprising since the isothermal correction is based on friction in a systematic way and should scale linearly with friction.
6.6 EHD Friction and Structural Parameters of PAO
PAO has been included in this study to compare the effectiveness of the correlation for synthetic hydrocarbon base oils that have considerably different structures from mineral base oils. As generally recognized, PAO shows relatively low-EHD friction based on a very high proportion of linear paraffin chains. Although PAO is synthesized paraffinic base oil, 13C NMR structural parameters showed 6.9% of naphthenic carbons when a baseline correction is applied as was done for the rest of base oils. However, it was confirmed that the PAO sample has more than 99% paraffinic carbons by the mass spectrometry (MS)-based ASTM test method D2786.
Multiple linear regression analysis between EHD friction and 13C NMR structural parameters of hydrocarbon base oils including PAO (with CP: 93.1, CB: 10.5, CL: 50.6) give considerably lower R2 coefficients than when PAO is not included and the average R2 coefficient falls down to 0.908 (0.925 except for results measured at 0.5 GPa and 0.6 GPa at 120 °C and 0.5 GPa at 100 °C). This can be explained in terms of the unique molecular architecture of PAO, which has long chain branches on a main backbone. Based on the assignment rule applied to 13C NMR, carbons that are located 4 or more carbon atoms away from a backbone chain on long chain branches, corresponding to ε, δ, γ, β, α in Fig. 4a, are defined as linear carbons, but they are obviously on long branches.
This study shows quantitatively the impact of molecular structures of highly refined hydrocarbon base oils on EHD friction. The relationship between the EHD friction and the molecular structural parameters of base oil has been established with very high R2 coefficient, especially at high pressure and low and mid-range temperature. The critical average structural parameters for the EHD friction are total paraffin carbons, linear carbons and branched carbons determined by 13C nuclear magnetic resonance (NMR) spectroscopy.
Distinguishable EHD friction curves are achieved depending on API base oils (Group II, II + , III, III + , IV) with similar kinematic viscosity, reflecting the obvious differences in their molecular structures.
The authors would like thank SK innovation Institute of Technology Innovation for their support for this study.
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