High Pressure Rheology for Quantitative Elastohydrodynamics

Computational elastohydrodynamics, a part of tribology, has existed happily enough for about fifty years without the use of accurate models for the rheology of the liquids used as lubricants. For low molecular weight liquids, such as low viscosity mineral oils, it has been possible to calculate, with precision, the film thickness in a concentrated contact provided that the pressure and temperature are relatively low, even when the pressure variation of viscosity is not accurately modelled in detail. Other successes have been more qualitative in nature, using effective properties which come from the fitting of parameters used in calculations to experimental measurements of the contact behaviour, friction or film thickness.

High Pressure Rheology for Quantitative Elastohydrodynamics is intended to provide a sufficiently accurate framework for the rheology of liquids at elevated pressure that it may be possible for computational elastohydrodynamics to discover the relationships between the behaviour of a lubricated concentrated contact and the measurable properties of the liquid lubricant. The required high-pressure measurement techniques are revealed in detail and data are presented for chemically well-defined liquids that may be used as quantitative reference materials.

• Presents the property relations required for a quantitative calculation of the tribological behaviour of lubricated concentrated contacts.
• Details of high-pressure experimental techniques.
• Complete description of the pressure and temperature dependence of viscosity for high pressures.
• Some little-known limitations on EHL modelling.

For engineers and researchers concerned with high-pressure lubrication

Chapter 1. An Introduction to Elastohydrodynamic Lubrication
1.1 Lubrication
1.2 Concentrated Contact Lubrication
1.3 Full Elastohydrodynamic Lubrication
1.4 Experimental Elastohydrodynamics
1.5 Conclusion

Chapter 2. An Introduction to the Rheology of Polymeric Liquids
2.1 Background
2.2 The Newtonian Model
2.3 Material Functions for Polymeric Liquids
2.4 Rheological Models
2.5 Time-Temperature-Pressure Superposition
2.6 Liquid Failure

Chapter 3. General High-Pressure Experimental Techniques

3.1 Background
3.2 Pressure Containment
3.3 Closures
3.4 Feed-throughs
3.5 Pressure Generation and Measurement
3.6 Hydrostatic Media and Volume Compensation

Chapter 4. Compressibility and the Equation of State
4.1 Background
4.2 PVT Measurement Techniques and Results
4.3 Empirical Equations of State

Chapter 5. The Pressure and Temperature Dependence of the Low-Shear Viscosity

5.1 Background
5.2 High-Pressure Viscometers
5.3 General Pressure-Viscosity Response and Results for Pure Organic Liquids and Lubricants

Chapter 6. Models for the Temperature and Pressure Dependence of the Low-Shear Viscosity

6.1 Introduction

6.2 Models for the Temperature-Viscosity Response
6.3 Pressure Fragility and Empirical Models for High Pressure Behavior
6.4 The Pressure-Viscosity Coefficient and Empirical Models for Low Pressure Behavior
6.5 Empirical Models for Large Pressure Intervals
6.6 Models Based on Free Volume Theory
6.7 Generalized Temperature-Pressure-Viscosity Models
6.8 Multi Component Systems

Chapter 7. Measurement Techniques for the Shear Dependence of Viscosity at Elevated Pressure
7.1 Introduction
7.2 Phenomena Producing Behavior Similar to Shear-Thinning
7.3 Rheometers for High Pressure

Chapter 8. The Shear Dependence of Viscosity at Elevated Pressure

8.1 Introduction
8.2 Normal Stress Differences at Elevated Pressures
8.3 The Origin of Non-Newtonian Behavior in Low-Molecular-Weight Liquids at Elevated Pressures
8.4 Time-Temperature-Pressure Superposition 8.5 The Competition between Thermal Softening and Shear-Thinning
8.6 Multi Component Systems
8.7 The Power-Law Exponent and the Second Newtonian Viscosity

Chapter 9. Glass Transition and Related Transitions in Liquids under Pressure
9.1 Measurements of Glass Transition at Elevated Pressure
9.2 Measurements of Dielectric Transition at Elevated Pressure
9.3 The Transitions as Isoviscous States
9.4 The Pressure Variation of Viscosity across the Transition

Chapter 10. Shear Localization, Slip and the Limiting Stress
10.1 Introduction
10.2 Measurements of Rate Independent Shear Stress
10.3 Flow Visualization of Shear Bands
10.4 Mohr-Coulomb Failure Criterion
10.5 Change of Character of the Piezoviscous Navier-Stokes Equations
10.6 Thermal Localization, Adiabatic Shear Bands
10.7 Interfacial Slip

Chapter 11. The Reynolds Equation

11.1 Background
11.2 Reynolds Equations for Generalized Newtonian Fluids

Chapter 12. Applications to Elastohydrodynamics
12.1 Introduction
12.2 Film Thickness for Shear Thinning Liquids
12.3 The Calculation of Traction from Material Properties