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Reference liquids for quantitative elastohydrodynamics: selection and rheological characterization

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Abstract

It is essential to the establishment of EHL as a quantitative field, that reference materials be selected and accurately characterized so that calculations may be compared with experiment. Three materials were selected as somewhat representative of the viscosity dependence on temperature, pressure and shear that may be observed in EHL lubrication:

  1. 1.

    Squalane

  2. 2.

    Poly(ethylene glycol-ran-propylene glycol)

  3. 3.

    Squalane +15% by weight of Polyisoprene, cis.

The properties of these materials were measured over a range of temperature and pressure using experimental techniques which have been shown to give accurate measurements for presently established reference materials. Models are provided for use in elastohydrodynamic simulations.

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Abbreviations

a V :

thermal expansivity defined for volume linear with temperature, K−1

B :

Doolittle parameter

D F :

fragility parameter in the VTF equation

G :

liquid critical shear stress or material modulus associated with λ, Pa

h :

film thickness, m

K :

isothermal bulk modulus, Pa

K 0 :

isothermal bulk modulus at p = 0, Pa

K ′0 :

pressure rate of change of isothermal bulk modulus at p = 0

K 00 :

K 0 at zero absolute temperature, Pa

m :

exponent for a shifting rule

N 1 :

first normal stress difference, the tension in the flow direction minus the tension in the cross-film direction, Pa

N 2 :

second normal stress difference, the tension in the cross-film direction minus the tension in the neutral direction, Pa

n :

power-law exponent

p :

pressure, Pa

R 0 :

occupied volume fraction at reference state, T R, p = 0

T :

temperature, K

T ∞ :

divergence temperature, K

T R :

reference temperature, °C

V :

volume at T and p, m3

V R :

volume at reference state, T R, p = 0, m3

V 0 :

volume at p = 0, m3

V ∞ :

occupied volume, m3

V ∞R :

occupied volume at reference state, T R, p = 0, m3

α:

local pressure–viscosity coefficient, Pa−1

α0 :

initial pressure–viscosity coefficient, Pa−1

α*:

reciprocal asymptotic isoviscous pressure coefficient (=1/p ai), Pa−1

αB :

secant pressure–viscosity coefficient, Pa−1

αfilm :

general film-forming pressure–viscosity coefficient, Pa−1

β K :

temperature coefficient of K 0, K−1

\(\dot{\gamma}\) :

shear rate, s−1

ɛ:

occupied volume thermal expansivity, K−1

η:

rate-dependent shear viscosity, Pa s

λ:

characteristic or relaxation time, s

μ:

limiting low-shear viscosity and Newtonian viscosity, Pa s

μR :

low-shear viscosity at reference state, T R, p = 0, Pa s

μ∞ :

viscosity extrapolated to infinite temperature, Pa s

ρ:

mass density, kg/m3

ρR :

mass density, at reference state, T R, p = 0, kg/m3

σ:

regression fit quality, \(\sqrt {\sum\limits_1^N {{{{{[(x_{{\text{meas}}} - x_{{\text{calc}}} )} \mathord{\left/ {\vphantom {{[(x_{{\text{meas}}} - x_{{\text{calc}}} )} {x_{{\text{meas}}} ]^2 }}} \right. \kern-\nulldelimiterspace} {x_{{\text{meas}}} ]^2 }}} \mathord{\left/ {\vphantom {{{{[(x_{{\text{meas}}} - x_{{\text{calc}}} )} \mathord{\left/{\vphantom {{[(x_{{\text{meas}}} - x_{{\text{calc}}} )} {x_{{\text{meas}}} ]^2 }}} \right. \kern-\nulldelimiterspace} {x_{{\text{meas}}} ]^2 }}} N}} \right. \kern-\nulldelimiterspace} N}}}\)

τ:

shear stress, Pa

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Acknowledgment

The measurements reported here were supported by a grant from the Timken Company. The design and construction of the high-pressure rheogoniometer was funded by a grant from Valvoline Corporation.

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Authors and Affiliations

  1. Center for High-Pressure Rheology, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    Scott Bair

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Bair, S. Reference liquids for quantitative elastohydrodynamics: selection and rheological characterization. Tribol Lett 22, 197–206 (2006). https://doi.org/10.1007/s11249-006-9083-y

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