A discussion on simplified modeling of lubricants, presented at the 15th International Colloquium Tribology-Automotive and Industrial Lubrication (Ostfildern, Germany 1/17-19/2006), covers algorithms based on empirical data, leading to a more facile handing of the mesoscale state; computation of lubricants; general aspects; and variables influencing the life of machinery elements.

Previous studies have revealed that friction behave in unexpected ways as pressure increase in a lubricating film. It has been determined that it is not a viscosity-related but rather originating directly from molecular structure. This study strives to elucidate the importance of understanding the properties that govern friction, when undertaking simulation of elastohydrodynamic events. A thorough investigation of the maximum transferable shear stress in the film for a paraffinic mineral oil has been undertaken. A previously stated theory of decreasing friction coefficient with increasing pressure is further substantiated by the current measurements. Classical thermodynamics, in the shape of transient "hot-wire" measurements, have been used to study macro-molecular changes (as function of pressure). The instance of global relaxation correlates nicely to measurements.

Lubricated transient elastohydrodynamic (EHD) conjunctions are extremely difficult to simulate numerically since lubricant properties such as temperature and viscosity vary significantly during the loading-unloading event. Nevertheless, industry has invested considerable time and effort in trying to create such models in order to improve performance and to reduce emissions and friction. One of the essential requirements for a successful model is accuracy in the implementation of frictional properties. The experimental method presented in this paper used an impact on the end surface of a beam to generate propagating waves that were subjected to fast Fourier transform analysis. The method yielded detailed information about the build-up and decay of normal and frictional forces as a function of time for various lubricants at three different initial temperatures (20, 40 and 80 °C) and at relevant EHD pressures. A variety of lubricants were studied to a peak Hertzian pressure of 2.5 GPa for loading-unloading times of 200-400 µs (typical for elastohydrodynamically lubricated conjunctions in ball bearings and gears). A qualitative study of the thermal properties of the lubricants and their influence on viscosity and friction coefficient was also undertaken and, finally, a plausible explanation of the observed behaviour is presented and parallels to dynamic simulations of polyatomic gases are drawn.

In the design and evaluation of mechanical system performance it is important to know the frictional qualities of the lubricant. Without correct numerical treatment of the lubricant during simulations of large systems, e.g., drive trains in trucks and buses, the results will, to a large extent, be inaccurate. However, obtaining detailed information places demands on the test equipment as the events are both transient and highly loaded. Under quasi-static conditions, forces are measured with force transducers, but in elasto-hydrodynamically lubricated conjunctions, where pressures are so high that the surrounding surfaces deform elastically, this cannot be done without permanently damaging the equipment. The conceptual design of the test equipment must therefore incorporate the measuring process in transient conditions (loading-unloading times of 200-500 μs) being performed in real time, and allow extreme pressures of up to 3 GPa without component destruction. One way to obtain accurate friction data successfully is to apply a concentrated force pulse to a non-instrumented surface and to measure the response from that pulse elsewhere. The development of a measurement technique, the Lulea ball and bar apparatus, which utilises wave propagation theory, is presented in this paper. An oblique impact on a robust end plate on a rod was used to generate both non-dispersive compression waves and dispersive flexural waves. The normal force created by the axial wave was measured using strain gauges, while the transverse force was derived from the fast Fourier transforms of two lateral acceleration histories, using dynamic beam theory. The relation between the normal and tangential force histories showed the frictional properties at the impact as a function of time. A variety of lubricants was also studied at Hertzian pressures of up to 2.5 GPa, and the development of the method and results are presented. Experiments indicate that different lubricants exhibit different frictional properties and that the resolution in the test equipment is sufficient to indicate this

The objective of this work was to increase the understanding of which lubricant properties control transient friction, and during what environmental conditions friction is minimized. The experiments have been conducted during conditions relevant to an elastohydrodynamic contact, with pressures extending up to 2.5 GPa, initial temperatures between 20-80°C in the lubricant and loading durations of approximately 200-400 ms. A major revision of an existing work on the relation between pressure and dilatation, for mineral- and synthetic oils, using a modified split Hopkinson pressure bar was undertaken. A quadratic expression with lubricant specific constants, describing the pressure-dilatation relationship without an asymptotic behavior, was presented. A thermal study of isothermal and adiabatic effects on the result was added to the report. One significant observation was that the difference between adiabatic- and isothermal dynamic behavior of the compressed lubricants was small. The proposed idea was that, in practical calculations, it is unnecessary to distinguish between adiabatic and isothermal material data for dynamic calculations. Time-dependent processes on a molecular level must explain the difference found. A new type of experimental set-up was developed, utilizing the flexural response to an exerted load and dynamic beam theory, enabling simultaneous measurement of transverse and normal forces, and thus friction coefficient, as a function of time or pressure. The reproducibility of the load exertion was found to be low but the accuracy of the measurements were encouraging. Differences in friction histories between lubricated and dry contacts were found. Improvement of the developed friction coefficient measurement device was made to enhance reproducibility and accuracy. The experimental set-up was in many ways inverted and a new theory was developed, encompassing both rotational inertia and shear deformation in the energy of motion consideration. Reproducibility between experiments, along with accuracy, went from low to excellent. Five different lubricants were tested and frictional data, as a function of time, were presented. Several phenomena concerning friction were observed and discussed. Two interesting observations were that: Friction increases with increasing pressure during each load cycle (and decreases again as the loading is removed). Friction decreases with increasing maximum pressure of the loading pulse. This apparent contradiction inspired further work in the field and indications suggested that the solution might be embedded in the thermodynamic properties of the lubricants. Enhanced environmental control, added to the set-up, enabled initial temperature increase up to 60°C above ambient. Focus on thermodynamic properties was rewarded with a number of observations and a suitable explanation to the previously described contradiction was formed. It was found that increased coefficient of heat conduction lowered the friction coefficient, as did an increase in specific heat capacity. Both effects strive to reduce the temperature in the contact (by different means) but the tendency is clear: colder contact temperature, lower friction. Further support through the finding that increased initial temperature correspondingly increased friction was acknowledged. The main conclusion was that solid friction is lower than fluid friction during the prevailing test conditions and that a numerical analysis is considered necessary. Frictional data for 12 different lubricants and model hydrocarbons with different physical- and thermodynamic properties were presented. A numerical study of the thermal, shear stress and velocity gradient profiles along with friction coefficients for a paraffinic mineral oil, subjected to a transient pressure pulse in-between two infinite, rigid plates with relative motion was undertaken. Two rheological models were used: one nonlinear viscous and one nonlinear viscoelastic (Ree-Eyring). It was concluded that a Ree-Eyring rheological model together with pressure and temperature dependent viscosity and heat conduction can be used to qualitatively simulate transient rheology experiments. A localized temperature increase occurs in the lubricant film. It is associated with a viscosity decrease and a velocity gradient increase and a “slip plane” is formed. The slip plane will be more pronounced as the pressure pulse peak becomes higher until eventually all motion is localized to that region. The observed contradiction in friction is not viscosity related. The simulation indicated that the friction coefficient increased with increasing pressure, for the rheological model used, in total contradiction to measured data on a real EHL contact. It was consequently concluded that that the frictional properties of the localized shear bands, occurring in the solidified lubricant, were the origin of the detected anomaly and refined rheological models are necessary to bring crisp clarity to the matter.

In theoretical calculations of film thickness, pressure distribution and friction in an elastohydrodynamically lubricated (EHL) conjunction it is necessary to model the physical/mechanical behaviour of the lubricant. It is important to know, for example, the dilatation-pressure or the density-pressure relationship. In this paper a modified split Hopkinson pressure bar system for determination of the compressibility of oil is presented. It makes it possible to test oils under conditions similar to those found in real EHL contacts: loading duration in the range of 100-300 μs and pressures of almost 2 GPa. An empirical model has been suggested for mathematical description of the dilatation-pressure relation of the specific oils. A naphthenic mineral oil and a synthetic oil, 5P4E, have been tested under adiabatic conditions and at pressures up to 1.5 and 1.9 GPa respectively. The adiabatic results have been recalculated to isothermal conditions for comparison

In assessment of lubricant properties and in various contact applications, it is of importance to know the frictional qualities. Under quasi-static conditions, normal and transverse forces are measured using force transducers, but the task is more difficult when loads are high and transient as they often are in elastohydrodynamic conjunctions. The experimental method presented in this paper is based on analysis of propagating waves in a beam, due to an impact on its end surface, using FFT analysis. Since the impact is oblique, both non-dispersive compression waves and dispersive flexural waves are generated. The normal force originating from the axial wave is measured using strain gauges, while the transverse force is derived from the FFT's of two lateral acceleration histories using Timoshenko dynamic beam theory. The relation between normal and tangential force histories displays the frictional properties at the impact as a function of time; i.e., variations in frictional properties during loading and unloading (typically 200 400 s in ball bearings and gears) can be observed. A variety of lubricants has been studied up to a Hertzian pressure of 2.5 GPa, and the method and results are presented

In the assessment of lubricant properties and in various contact applications, it is of importance to know the frictional qualities. Under quasi-static conditions, normal and transverse forces are measured using force transducers but the task is more difficult when loads are high and transient, as they often are in elastohydrodynamic conjunctions. The experimental method presented in this paper is based on analysis of propagating waves in a beam, due to an impact on its end surface, using FFT analysis. Since the impact is oblique, both non-dispersive compression waves and dispersive flexural waves are generated. The normal force originating from the axial wave is measured using straingauges, while the transverse force is derived from the FFT's of two lateral acceleration histories using Euler-Bernoulli dynamic beam theory. The relation between normal- and transverse force histories displays the frictional properties at the impact as a function of time, i.e. variations in frictional properties during loading and unloading (typically 200-400 μs in ball bearings and gears) can be observed. A variety of lubricants have been studied up to a Hertzian pressure of 2.5 GPa, and the method and results are presented.

The lack of published data on the chemical structures of lubricants makes it almost impossible to investigate the influence of structure on lubrication properties. In this investigation, the lubricating properties of three esters with known chemical structure have been investigated and compared with a commercial ester. The lubrication properties that were expected to be dependent on chemical structure such as film thickness and traction, viscosity and friction coefficients were compared by experiment. To measure the film thickness a Ball and Disc Apparatus was used, the traction coefficient was measured in a Jumping Ball Apparatus, the viscosity in a rotational cylindrical viscometer and the friction coefficient in a reciprocating friction and wear test apparatus. The results showed that molecular length has a significant influence on lubrication properties, with longer molecules giving the highest viscosity and greatest film thickness. The length of the molecule did not influence the coefficients of friction, but the traction coefficient, Υ, decreased with increasing molecular length.

This licentiate thesis deals with the influence of transient loading, at high pressures, on the pressure-dilatation relation and frictional properties of lubricants. A Split-Hopkinson pressure bar and a Ball and Bar apparatus have been used for the experiments. Both methods share the same type of evaluation approach: evaluation by analysis of wave propagation in structures. The advantage with this method is that results are presented as function of time, i.e. every experiment yields a history of the studied event, not just a single value. Different theoretical evaluation methods have been used and refinements have been made by introducing compensation terms in order to enhance accuracy. Several lubricants have been studied and an empirical second-degree polynomial has been suggested, for a naphthenic mineral oil and a synthetic 5P4E oil, describing the pressure-dilatation relation over a wide pressure range. It is found that 5P4E exhibits lower compressibility, i.e. higher stiffness than the naphthenic oil. Curves representing friction coefficient as function of time for different lubricants at different pressures are included. It is evident that the Naphthenic- and Paraffinic mineral oils have the highest friction coefficient followed by Polyglycol, Polyalphaolefin and Rape seed oil. The observed distinctions agree well with the expected outcome on basis of molecular structure and pressure variation and correlates well with other density and friction investigations. A general trend of decreasing friction coefficient with increasing pressure is discovered.