Hydrodynamic Lubrication of Non-Newtonian Fluids

Front Cover
Hydrodynamic Lubrication of Non-Newtonian Fluids
Copyright Page
Contents
Preface
Introduction
I. Universal equation of non-Newtonian hydrodynamic lubrication
1 Viscosity of fluid
1.1 Overview
1.2 Viscosity of Newtonian fluid
1.2.1 Definition of viscosity
1.2.2 Units of viscosity
1.3 Rheological property of non-Newtonian fluid
1.3.1 Types of non-Newtonian fluids
1.3.1.1 Pseudoplastic fluid
1.3.1.2 Bloated fluid
1.3.1.3 Bingham fluid
1.3.1.4 Grease
1.3.1.5 Viscos-plastic fluid
1.3.1.6 Thixotropy fluid and rheopexy fluid
1.3.1.7 Viscoelastic fluid
1.3.2 Viscosity of non-Newtonian fluid
1.3.2.1 Total viscosity
1.3.2.2 Incremental viscosity
1.3.2.3 Comparison of two viscosities
1.3.2.4 Negative (incremental) viscosity
1.4 Factors influencing viscosity
1.4.1 Relationship between viscosity and temperature
1.4.2 Relationship between viscosity and pressure
1.4.3 Combinational relationship of viscosity, temperature and pressure
1.5 Common rheological experiment devices
1.5.1 Coaxial cylinder rheometer
1.5.2 Cone-plate rheometer
1.5.3 Parallel plate rheometer
References
Further reading
2 Basic equations of hydrodynamic lubrication
2.1 Basic equations and assumptions of hydrodynamic lubrication
2.1.1 Basic equations
2.1.2 Basic assumptions
2.2 Continuity equation
2.3 Equilibrium equations
2.3.1 Expression of equilibrium equations
2.3.2 Derivation of equilibrium equations
2.3.2.1 Simplification of Navier-Stocks equation
2.3.2.2 Simplification by force balancing
2.3.2.2.1 Micro element analysis
2.4 Fluid constitutive equation
2.4.1 Newtonian fluid constitutive equation
2.4.2 Non-Newtonian fluid constitutive equations
2.4.2.1 Power constitutive equation
2.4.2.2 Prandtl-Eyring constitutive equation
2.4.2.3 Circular fluid model
2.4.2.4 Buckling fluid constitutive equation
2.4.2.5 Viscos-plastic fluid model
2.4.2.6 Bingham fluid
2.4.2.7 Eyring constitutive equation
2.4.2.8 Carreau constitutive equation
2.4.2.9 Ellis fluid model
2.5 Boundary conditions of hydrodynamic lubrication
2.5.1 Boundary conditions between fluid-solid interface
2.5.1.1 Velocity boundary conditions
2.5.1.2 Shear stress boundary conditions
2.5.1.3 Mixing boundary conditions
2.5.2 Pressure boundary conditions
2.5.2.1 With all convergent zone
2.5.2.2 With some divergent zone
Reference
3 Reynolds equation and non-Newtonian hydrodynamic lubrication
3.1 Derivation of Reynolds equation
3.1.1 Analysis of basic equations
3.1.2 Elimination of shear stress
3.1.3 Elimination of flow velocities
3.2 General nonlinear problems
3.2.1 Linear problems
3.2.2 Nonlinear problems
3.2.3 Non-Newtonian hydrodynamic lubrication
3.3 Difficulties during derivation of Reynolds equation of non-Newtonian hydrodynamic lubrication
3.3.1 Reynolds equation of power constitutive equation
3.3.2 Difficulties to derive a general Reynolds equation of non-Newtonian fluid
Reference
4 Universal hydrodynamic lubrication equation
4.1 Separated flow velocity method
4.1.1 Basic principles of separated flow velocity method
4.1.2 Steps to solve non-Newtonian hydrodynamic lubrication problems with separated flow velocity method
4.1.3 Theoretical basis of the separated flow velocity method
4.2 Derivation of universal hydrodynamic lubrication equation
4.2.1 Derivation steps of universal hydrodynamic lubrication equation
4.2.2 Simplified universal hydrodynamic lubrication equation
4.2.3 Solution of universal hydrodynamic lubrication equation
4.3 Determining conditions of separated flow velocity method
4.3.1 Separated flow velocity method satisfies all basic equations
4.3.2 Boundary conditions
4.4 Common non-Newtonian universal hydrodynamic lubrication equations
4.4.1 Power constitutive equation
4.4.2 Universal hydrodynamic lubrication equations of commonly used non-Newtonian fluids
II. Lubrication failure due to limit shear stress
5 Experimental study on rheological properties of fluids
5.1 Non-Newtonian fluid experiments under atmospheric pressure
5.1.1 Preparation of non-Newtonian fluids
5.1.1.1 Base solution and additive
5.1.1.2 Rheological experiment
5.1.2 Experimental results of non-Newtonian fluids
5.1.2.1 Rheological experiments of low shear rate
5.1.2.2 Rheological experiments of high shear rate
5.1.2.3 Constitutive equation and viscosities
5.1.3 Viscosity-temperature relationship of polyethylene oxide solutions
5.2 Experimental devices of fluid rheological property under high pressure and high shear rate
5.2.1 Double disc type
5.2.2 Impact type
5.2.3 Shear type
5.2.4 Capillary type
5.2.5 Pure shear type
5.2.6 Impact and shear type
5.2.7 Impact and squeeze type
5.2.8 Falling column type
References
6 Interface slip models and slip measurement
6.1 Interface slip models
6.1.1 Slip length model
6.1.1.1 Interface slip length
6.1.1.2 Slip length theory
6.1.2 Limit shear stress slip model
6.2 Experimental study on interface slip
6.2.1 Interface slip measurement
6.2.1.1 Direct measurement of fluid velocity near interface
6.2.1.2 Flow measurement based on micro pipeline
6.2.1.3 Measurement based on hydrodynamic pressure
6.2.2 Influencing factors of interface slip
6.2.2.1 Influence of wettability
6.2.2.2 Influence of viscosity
6.2.2.3 Influence of squeezing velocity
6.2.2.4 Comparison of two models
References
7 Lubrication failure of non-Newtonian fluid
7.1 Interface slip and its conditions
7.1.1 Interface slip
7.1.2 Slip boundary conditions
7.1.3 Flow velocity distribution at slip zone
7.1.3.1 Couette flow in slip zone
7.1.3.2 Poiseuille flow in slip zone
7.2 Difference of rolling and sliding for lubrication failure
7.2.1 Slide-roll ratio
7.2.2 Reynolds equation of pure rolling
7.2.3 One-dimensional Reynolds equation of pure rolling
7.2.4 Shear stress of hydrodynamic lubrication in pure rolling
7.2.5 Lubrication failure of non-Newtonian fluid in sliding
7.3 Criterial point of lubrication failure
7.3.1 Stribeck curve and lubrication failure
7.3.2 Friction coefficient of hydrodynamic lubrication
7.3.2.1 Film thickness
7.3.2.2 Pressure distribution
7.3.2.3 Load per width
7.3.2.4 Frictional force per width
7.3.2.5 Friction coefficient
7.3.3 Relationship between friction coefficient and lubrication failure
7.3.4 Influence of friction coefficient
7.3.4.1 Friction coefficient and load
7.3.4.2 Friction coefficient and film thickness
7.3.4.3 Minimum friction coefficient of hydrodynamic lubrication
Reference
8 Analysis of lubrication failure of non-Newtonian fluid with limit shear stress
8.1 Lubrication failure of viscos-plastic fluid
8.1.1 Constitutive equation of viscos-plastic fluid
8.1.1.1 Constitutive equation
8.1.1.2 Shear stress in film
8.1.2 Basic equations of viscos-plastic fluid
8.1.2.1 Lubrication equations of viscous zone
8.1.2.2 Lubrication equations of plastic zone
8.1.3 Numerical analysis of lubrication failure of viscos-plastic fluid
8.2 Lubrication failure of buckling fluid
8.2.1 Constitutive equation of buckling fluid
8.2.2 Basic equations of buckling fluid
8.2.2.1 Shear rate
8.2.2.2 Pressure flow velocity
8.2.2.3 Total flow velocity
8.2.2.4 Total flow
8.2.3 Numerical analysis of lubrication failure of buckling fluid
8.2.3.1 Numerical solution
8.2.3.2 Steps to solve pressure
8.2.3.3 Result analysis
8.3 Lubrication failure of circular fluid
8.3.1 Circular constitutive equation
8.3.2 Basic equations of circular fluid
8.3.2.1 Shear rate
8.3.2.2 Pressure flow velocity
8.3.2.3 Total flow velocity
8.3.2.4 Total flow
8.3.3 Numerical analysis of lubrication failure of circular fluid
References
III. Calculation method and program
9 Calculation method and program of hydrodynamic lubrication of non-Newtonian fluids
9.1 Basic equations, numerical method and program of one-dimensional hydrodynamic lubrication
9.1.1 Basic equations
9.1.1.1 Dimensional basic equations
9.1.1.1.1 Lubrication equation
9.1.1.1.2 Pressure boundary conditions
9.1.1.1.3 Load equation
9.1.1.2 Dimensionless basic equations
9.1.1.2.1 Dimensionless lubrication equation
9.1.1.2.2 Dimensionless pressure boundary conditions
9.1.1.2.3 Dimensionless load equation
9.1.2 Numerical method
9.1.2.1 Iteration method
9.1.2.2 Calculation method of pressure
9.1.2.3 Adjustment of H0
9.1.3 Calculation procedure
9.1.3.1 Procedure introduction
9.1.3.2 Program diagram
9.1.3.3 Calculation example and results
9.1.3.4 Source program
9.2 Basic equations, numerical method and program of two-dimensional hydrodynamic lubrication
9.2.1 Basic equations
9.2.1.1 Dimensional basic equations
9.2.1.2 Dimensionless basic equations
9.2.2 Numerical method
9.2.3 Calculation procedure
9.2.3.1 Procedure introduction
9.2.3.2 Program diagram
9.2.3.3 Calculation example and results
9.2.3.4 Source program
10 Calculation method and program of elastohydrodynamic lubrication of non-Newtonian fluid
10.1 Basic equations, numerical method and program of non-Newtonian EHL in line contact
10.1.1 Basic equations
10.1.1.1 Dimensional basic equations
10.1.1.1.1 Lubrication equation
10.1.1.1.2 Film thickness equation
10.1.1.1.3 Viscosity and density of lubricant
10.1.1.1.4 Load equation
10.1.1.2 Dimensionless basic equations
10.1.1.2.1 Dimensionless lubrication equation
10.1.1.2.2 Other dimensionless equations
10.1.1.3 Discretization of dimensionless basic equations
10.1.1.3.1 Discrete lubrication equation
10.1.1.3.2 Other equations
10.1.2 Numerical method
10.1.2.1 Pressure iteration method
10.1.2.2 Adjustment of rigid film thickness H0 to balance load
10.1.3 Calculation procedure
10.1.3.1 Procedure introduction
10.1.3.2 Program diagram
10.1.3.3 Calculation example and results
10.1.3.4 Source program
10.2 Basic equations, numerical method and program of non-Newtonian EHL in point contact
10.2.1 Basic equations
10.2.1.1 Dimensionless basic equations
10.2.1.2 Discretization of dimensionless equations
10.2.2 Numerical method
10.2.2.1 Pressure iteration method
10.2.2.2 Adjustment of rigid film thickness H0
10.2.3 Calculation procedure
10.2.3.1 Procedure introduction
10.2.3.2 Program diagram
10.2.3.3 Calculation example and results
10.2.3.4 Source program
References
11 Temperature calculation method and program of hydrodynamic lubrication
11.1 Basic equations of hydrodynamic lubrication
11.1.1 Basic equations
11.1.1.1 Constitutive equation
11.1.1.2 Balance equation
11.1.1.3 Flow velocities
11.1.2 Flow continuity equation
11.2 Energy equation and calculation method
11.2.1 Energy equation
11.2.1.1 One-dimensional energy equation
11.2.1.2 Two-dimensional energy equation
11.2.2 Numerical calculation of energy equation
11.2.2.1 Calculation of flow velocity and its gradient
11.2.2.1.1 Flow velocity
11.2.2.1.2 Flow velocity gradient
11.2.2.2 Calculation of energy equation
11.2.2.3 Temperature boundary conditions
11.2.2.4 Temperature calculation
11.2.3 Temperature calculation flow chart
11.3 Calculation program of thermal hydrodynamic lubrication of Newtonian fluid
11.3.1 One-dimensional temperature calculation program
11.3.1.1 Calculation procedure
11.3.1.2 Calculation results
11.3.2 Two-dimensional temperature calculation
11.3.2.1 Calculation procedure
11.3.2.2 Calculation results
Reference
12 Calculation method and program of thermal hydrodynamic lubrication of non-Newtonian fluids
12.1 Equations, numerical method and program of one-dimensional thermal hydrodynamic lubrication of non-Newtonian fluids
12.1.1 Basic equations
12.1.1.1 Basic equations
12.1.1.1.1 Lubrication equation
12.1.1.1.2 Velocity and its gradient equations
12.1.1.1.3 Energy equation
12.1.1.1.4 Viscosity-temperature equation
12.1.1.2 Dimensionless basic equations
12.1.1.2.1 Dimensionless lubrication equation
12.1.1.2.2 Dimensionless velocity and velocity gradient equations
12.1.1.2.3 Dimensionless energy equation
12.1.1.2.4 Dimensionless viscosity-temperature equation
12.1.2 Numerical method
12.1.3 Calculation program
12.1.3.1 Program introduction
12.1.3.2 Flow chart
12.1.3.3 Calculation example
12.1.3.4 Source program
12.2 Equations, numerical method and program of two-dimensional thermal hydrodynamic lubrication of non-Newtonian fluids
12.2.1 Basic equations
12.2.1.1 Dimensional basic equation
12.2.1.1.1 Lubrication equation
12.2.1.1.2 Energy equation
12.2.1.1.3 Viscosity-temperature equation
12.2.1.2 Dimensionless basic equations
12.2.1.2.1 Dimensionless lubrication equation
12.2.1.2.2 Dimensionless energy equation
12.2.1.2.3 Dimensionless viscosity-temperature equation
12.2.2 Numerical method
12.2.3 Calculation program
12.2.3.1 Program introduction
12.2.3.2 Calculation flow chart
12.2.3.3 Calculation example
12.2.3.4 Source program
Reference
13 Calculation method and program of thermal elastohydrodynamic lubrication of non-Newtonian fluids
13.1 Basic equations, numerical method and program of non-Newtonian TEHL in line contact
13.1.1 Basic equations
13.1.1.1 Dimensional basic equations
13.1.1.1.1 Lubrication equation
13.1.1.1.2 Film thickness equation
13.1.1.1.3 Energy equation
13.1.1.1.4 Viscosity and density equations
13.1.1.1.5 Load equation
13.1.1.2 Dimensionless equations
13.1.1.2.1 Dimensionless lubrication equation
13.1.1.2.2 Dimensionless film thickness equation
13.1.1.2.3 Dimensionless energy equation
13.1.1.2.4 Dimensionless viscosity and density equations
13.1.1.2.5 Dimensionless load equation
13.1.1.3 Discretization of dimensionless basic equations
13.1.1.3.1 Lubrication equation
13.1.1.3.2 Other equations
13.1.2 Numerical method
13.1.3 Calculation program
13.1.3.1 Program introduction
13.1.3.2 Program diagram
13.1.3.3 Calculation example and results
13.1.3.4 Source program
13.2 Basic equations, numerical method and program of non-Newtonian TEHL in point contact
13.2.1 Basic equations
13.2.1.1 Dimensional basic equations
13.2.1.1.1 Lubrication equation
13.2.1.1.2 Film thickness equation
13.2.1.1.3 Energy equation
13.2.1.1.4 Viscosity and density equations
13.2.1.1.5 Load equation
13.2.1.2 Dimensionless basic equations
13.2.1.2.1 Lubrication equation
13.2.1.2.2 Film thickness equation
13.2.1.2.3 Energy equation
13.2.1.2.4 Velocity equations
13.2.1.2.5 Velocity gradient equations
13.2.1.2.6 Viscosity and density equations
13.2.1.2.7 Load equation
13.2.1.3 Discretization of dimensionless equation
13.2.2 Numerical method
13.2.3 Calculation program
13.2.3.1 Program introduction
13.2.3.2 Block diagram
13.2.3.3 Calculation example and results
13.2.3.4 Source program
References
14 Calculation method and program of lubrication failure
14.1 Lubrication failure calculation of viscos-plastic fluid
14.1.1 Basic equations
14.1.1.1 Constitutive equation
14.1.1.2 Lubrication equations
14.1.2 Discrete iterative formula
14.1.3 Calculation flow chart
14.1.4 Source program
14.1.5 Pressure distributions of Newtonian fluid and viscos-plastic fluid
14.2 Lubrication failure calculation of buckling fluid
14.2.1 Basic equations
14.2.1.1 Constitutive equation
14.2.1.2 Pressure flow velocity
14.2.1.3 Total flow velocity
14.2.1.4 Total flow
14.2.1.5 Lubrication equation
14.2.2 Discrete iterative formula
14.2.3 Calculation flow chart
14.2.4 Source program
14.2.5 Pressure distribution of Newtonian fluid and buckling fluid
14.3 Lubrication failure calculation of circular constitutive fluid
14.3.1 Basic equations
14.3.1.1 Constitutive equation
14.3.1.2 Increment of pressure flow velocity
14.3.1.3 Lubrication equation
14.3.1.4 Discrete iterative formula
14.3.2 Source program
14.3.3 Pressure distributions of Newtonian fluid and circular fluid
Index
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