Scott Bair

A Rheological Model for Elastohydrodynamic Contacts Based on Primary Laboratory Data

A shear rheological model based on primary laboratory data is proposed for concentrated contact lubrication. The model is a Maxwell model modified with a limiting shear stress. Three material properties are required: Low shear stress viscosity, limiting elastic shear modulus, and the limiting shear stress the material can withstand. All three are functions of temperature and pressure. In applying the model to EHD contacts the predicted response possesses the characteristics expected from several experiments reported in the literature and, in one specific case where direct comparison could be made, good numerical agreement is shown.

Shear Strength Measurements of Lubricants at High Pressure

Measurements of lubricant shear rheological behavior in the amorphous solid region and near the liquid-solid transition are reported on three lubricants under pressure. Elastic, plastic and viscous behavior was observed. The maximum yield shear stress (limiting shear stress) is a function of temperature and pressure and is believed to be the property which determines the maximum traction in elastohydrodynamic contacts such as traction drives.

Thermodynamic scaling of the viscosity of van der Waals, H-bonded, and ionic liquids

Viscosities eta and their temperature T and volume V dependences are reported for seven molecular liquids and polymers. In combination with literature viscosity data for five other liquids, we show that the superpositioning of relaxation times for various glass-forming materials when expressed as a function of TV(gamma), where the exponent gamma is a material constant, can be extended to the viscosity. The latter is usually measured to higher temperatures than the corresponding relaxation times, demonstrating the validity of the thermodynamic scaling throughout the supercooled and higher T regimes. The value of gamma for a given liquid principally reflects the magnitude of the intermolecular forces (e.g., steepness of the repulsive potential); thus, we find decreasing gamma in going from van der Waals fluids to ionic liquids. For some strongly H-bonded materials, such as low molecular weight polypropylene glycol and water, the superpositioning fails, due to the nontrivial change of chemical structure (degree of H bonding) with thermodynamic conditions.

An Application of a Free Volume Model to Lubricant Rheology I—Dependence of Viscosity on Temperature and Pressure

Analyses of the dependence of lubricant viscosity on temperature and pressure, μ(T,P), have been carried out by using a modified WLF equation in which pressure effects on viscosity are given in terms of the pressure dependence of the glass transition temperature, Tg , and of thermal expansivity of free volume, αf . log μ(T,P)= log μg−C1•(T−Tg(P))•F(P)C2+(T−Tg(P))•F(P) where C1 and C2 are well known WLF constants, and μg is a viscosity at Tg . Tg (P) and F(P) are functions for describing the pressure dependence of Tg and αf , respectively. On the basis of the iso-viscous concept for Tg (P), μg has been assumed to have a constant value, 1 TPa•s, at any pressure (SCHEME I). SCHEME I yields a reasonable variation in Tg and αf with pressure for synthetic lubricants, while this analysis suggests a lower μg for mineral oils. In order to improve the applicability of the free volume model, a reference temperature Ts (P), at which the viscosity is 10 MPa•s, has been introduced instead of Tg (P) (SCHEME II). Analyses of dielectric transition for some lubricants and of μ(T,P) in the ASME Pressure-Viscosity Report have confirmed the excellent applicability of the present free volume model over wide ranges of temperature and pressure.

Some Observations in High Pressure Rheology of Lubricants

Experimental data are presented on viscosity, elastic shear modulus, and limiting shear stress of 12 liquid lubricants. It is shown that transition histories do affect the limiting shear stress of the materials in the form of isothermal compression resulting in a lower density and lower limiting stress than isobaric cooling. The measured limiting shear stress agrees with EHD traction data at slide-to-roll ratios of 0.1 or more. In pressure viscosity measurements of the polymer solutions, it is found that for some temperatures, the pressure viscosity coefficient of the blend is slightly less than that of the base, which results in the crossing of the viscosity-pressure isotherms at high pressures.

High-pressure rheology of lubricants and limitations of the Reynolds equation

Abstract A review of high pressure rheology leads to the conclusion that the results from rheometers may be used to generate empirical rate equations which are useful in modelling elastohydrodynamic traction. However, an analytical treatment of piezoviscous liquids reveals that the Reynolds equation adequately captures the mechanics of the piezoviscous liquid only when the shear stress is much less than the reciprocal of the pressure viscosity coefficient. Otherwise the cross film pressure gradient may be significant and secondary flows result.

Pressure-Viscosity Relationships for Elastohydrodynamics

The numerical simulation of elastohydrodynamic lubrication has evolved in terms of solution detail, speed and robustness. However, if EHL is to begin to solve practical quantitative problems involving differences among lubricants, practitioners must begin to utilize pressure-viscosity relationships in their numerical schemes that can describe real liquid response. The authors begin with the simple empiricisms that can be used to describe the pressure-viscosity response piecewise over the entire range from ambient to glass transition. Then various free volume formulations are introduced and compared. Finally, empirical expressions that can describe some essential features over the entire pressure range are presented. An example of the utility of one empirical equation is offered. Scheduled for Presentation at the 58th Annual Meeting in New York City April 28–May 1, 2003

The Generalized Newtonian Fluid Model and Elastohydrodynamic Film Thickness

The nature of real shear-thinning in elastohydrodynamic contacts is well-known from both experimental measurement and nonequilibrium molecular dynamics to follow a power-law. Shear-thinning will affect the film thickness when the Newtonian limit is low enough to occur in the inlet zone (less than about I MPa shear stress). Then kinetic theory tells us that film thinning should occur for molecular weight greater than 2000 kg/kmol. We present a review of generalized Newtonian models, flow curves for real lubricants and comparison of calculated and measured film thickness. The calculations utilize measurable liquid behavior, in contrast to most previous work.

The temperature, pressure and time dependence of lubricant viscosity

Abstract The general form of the pressure (Proc. Am. Acad. Arts Sci. 77 (1949) 117) and temperature (Physical properties of molecular crystals, liquids and glasses (1968) 350) dependence of viscosity has been known for at least 50 years. Viscosity varies with temperature in a greater than exponential manner and temperature–viscosity equations generally allow for an unbounded viscosity at some characteristic temperature. At high-pressures the pressure–viscosity response is likewise greater than exponential, often following a less than exponential response at low-pressures. In spite of this known behavior, tribologists working in EHL have generally assumed less than exponential pressure response as a means of applying the Eyring stress aided thermal activation theory to the viscous regime of EHL traction. As justification, time dependence of the lubricant properties in the response to a pressure transient has been advanced. We present acoustic, capillary and impact measurements for timescales less than EHL. While time dependence of properties may be important in the viscoelastic regime of traction, this paper will show that for the timescale of viscous response, a significant time dependence of viscosity is unlikely.

A unified shear-thinning treatment of both film thickness and traction in EHD

A conclusive demonstration has been provided that the nature of the shear-thinning, that affects both film thickness and traction in EHL contacts, follows the ordinary power-law rule that has been described by many empirical models of which Carreau is but one example. This was accomplished by accurate measurements in viscometers of the shear response of a PAO that possesses a very low critical stress for shear-thinning and accurate measurements in-contact of film thickness and traction under conditions which accentuate the shear-thinning effect. The in-contact central film thickness and traction were entirely predictable from the rheological properties obtained from viscometers using simple calculations. These data should be invaluable to researchers endeavoring to accurately simulate Hertz zone behavior since the shear-thinning rheology is extensively characterized and accurate in-contact data are available to test. In addition, a new model has been introduced that may be useful for the rheological characterization of mixtures.