Measurement of tribology at the micro and nano scales has been limited by the lack of dedicated instrumentation. The Scanning Force Microscope (SFM) has been the instrument of choice for investigating friction, wear and lubrication at such small scales. However, the SFM often produces contact pressures in the gigapascal range owing to the small dimensions of the tip. The Nano Tribometer from Anton Paar allows a much greater variation in contact conditions, and is therefore more suited to the study of lubricants at very low loads.
Different Lubrication Regimes
A recent study has been able to show the transition through differing lubrication regimes as the applied load is varied on a lubricated contact.
Lubricants
The lubricants investigated were of two different types. The first was a mineral oil (MO) consisting of 3% aromatics, 31% naphthenes and 66% paraffins, with viscosities of 40 cSt, 96 cSt and 200 cSt. The second was a synthetic oil composed of polyalphaolefine (PAO) with a base viscosity of 6 cSt, to which two additives were added: The ‘Irgalube 63’ additive contains dithiophosphate and is used as an extreme pressure, antiwear additive for industrial lubricants and greases. The ‘Irgalube211’ additive contains alkylated triphenyl phosphorothionate and is used as an antiwear additive in metalworking fluids and automotive engine oils.
Definitions
In order to fully describe the interaction of two surfaces and an intermediary lubricant layer subjected to both normal and sliding forces, one must look at the definitions that describe not only the geometric and hydrodynamic parameters but also the elastic deformations that occur around the zone of interaction. Elastohydrodynamic lubrication (EHL) between a sphere and a fl at plate can be described by a power law which relates various parameters to the minimum lubricant film thickness (hmin) at the contact point:
_{}
where R is the radius of the spherical partner, U is the sliding velocity, W is the normal load and α and η0 are lubricant properties relating the change of viscosity under increasing pressure. E is the reduced elastic modulus of the surface as described by Hertzian theory.
Nano Tribometer Tests
The Nano Tribometer tests were carried out using a 100Cr6 steel ball of diameter 2mm as the spherical partner with a TiNcoated steel disk as the plate on which the test oils could be applied using a micropipette. Each test was performed with exactly 30μl of oil and the plate was rotated at a rate of 20 rpm giving an effective linear velocity of 4.2 mms^{1} at the point of contact. Seven constantly applied loads of 250μN, 500μN, 1mN, 2mN, 4mN, 10mN and 25mN (which represent Hertzian contact pressures of approximately 110MPa, 140MPa, 180MPa, 225MPa, 280MPa, 385MPa and 520MPa respectively) were used for each test cycle. The frictional force (F) was measured over 200 revolutions of the plate and therefore the coefficient of friction (μ) could be calculated as μ = F/W, with W representing the normal load as applied by the glass spring cantilever assembly (shown in Fig. 1).
Figure 1. Closeup view of the Nano Tribometer glass spring force sensor which allows loading through the range 20μN  1N.
A complete set of measured friction coefficient data for one of the test oils (200cSt) is shown in Fig. 2 for the load range 250μN  25 mN. It can be seen that as the load is increased, the interaction of the ball, sample surface and lubricant fall between three distinct regimes. For loads of 250μN and 500μN the lubricant inhibits the sliding motion of the ball on the surface leading to higher frictional resistance. At 1mN, the friction coefficient is still high but the curve gradually decreases over the duration of the test, characteristic of the “runningin” of the surfaces.
Figure 2. Experimentally measured friction coefficients as a function of rotational laps for a 200 cSt high purity mineral oil, for applied loads in the range 250 μN  25 mN.
For loads greater than 2mN, the curves seem to have a runningin period after which a steady state is reached where the coefficient of friction stabilises to a constant value.
Minimum Lubricant Film Thickness
The minimum lubricant film thickness can be calculated from the power law for various different oil viscosities, as shown in Fig. 3. The results here are shown as a function of normal load, although the equation shows that the sliding velocity and the sphere radius have a much more significant influence on the film thickness than the applied load.
Figure 3. Calculated oil film thicknesses as a function of normal load for four different oil viscosities (sphere radius of 1 mm).
Power Law Equation
The power law equation shows that for any given ballonflat system, decreases in normal load or increases in sliding speed lead to increases in the lubricant film thickness. At some point the film thickness will be so great as to completely separate the surface asperities of the two opposing surfaces. Such a condition is referred to as full film or hydrodynamic lubrication and, because there is no longer any interaction between mating material surfaces, the lubricant film thickness becomes governed by the viscosity, speed and normal load.
Increase in Friction Coefficient
An exponential increase in the friction coefficient is shown in Fig. 4 (a) as the film thickness increases. This behaviour is evident for all four viscosities plotted. For low loads where the Hertzian contact pressures fall to around 110MPa, the friction is at a maximum. As the load is subsequently increased, the friction decreases (seen as the initial decrease of each curve). In the cases of the 40cSt and 96cSt viscosities, it is clearly visible that there is an optimum film thickness/normal load which causes a minimum friction coefficient.
Elastohydrodynamic to Hydrodynamic Transitions
The transition between different lubrication regimes can be seen if the coefficient of friction is plotted as a function of the Stribeck number, L, where L = ηU/W. The results for the same four viscosities are shown in Fig. 4 (b) where the transition from elastohydrodynamic to hydrodynamic regimes can clearly be seen. In order to investigate the boundary lubrication regime, a much lower sliding speed would be required at the contact. At such low speeds, there is no pressure buildup in the lubricant and therefore the load is totally carried by the asperities in the contact area.
Figure 4. Experimental results for the friction coeffi cient of a 100Cr6 ball of radius 1 mm in contact with a TiNcoated steel sample. Sliding velocity was 4.2 mms1 and four different oil viscosities are shown. The film thickness is plotted in (a) whereas a Stribeck representation is given in (b).
Nano, Micro and Macro Scales
Although the Nano Tribometer is ideally suited to the characterisation of lubricant properties at the micro and nano scales, it can also be of interest to correlate such results with measurements made at the macro scale on a different instrument. By using three different instruments it has been possible to map the three lubrication regimes of a 200cSt mineral oil. A standard pinondisk machine was used to measure the friction coefficient from the boundary condition with μ being initially stable at around 0.3 (for L values of 0.15  1) after which it drops to a minimum μ of 0.11 (at L = 20). The Nano Tribometer is then used to measure μ from L values of about 10 up to 5000. This covers the transition from mixed to hydrodynamic regimes (contact conditions are radius of 1mm and sliding velocity 4.2mms^{1}).
Higher Sliding Speeds
For higher sliding speeds, the Nano Scratch Tester is used with a contact radius of 20 μm and a sliding velocity of 1cms^{1}. This allows μ to be measured up to an L value of around 70000. This is a good example of how the measurement capabilities of three instruments can be combined to give frictional information from the macro down to the micro scales.
