Conformal & Non-Conformal Surfaces

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Figure 1.1 Conformal Surfaces. [From Hamrock and Anderson (1983).]

Figure 1.2 Nonconformal Surfaces. [From Hamrock and Anderson (1983).]

Hydrodynamic Lubrication

Figure 1.3 Characteristics of hydrodynamic lubrication.

Minimum film thickness:

Pressure Development

Figure 1.4 Mechanisms of pressure development for hydrodynamic lubrication. (a) Slider bearing; (b) squeeze film bearing; (c) externally pressurized bearing.}

Elastohydrodynamic Lubrication

Figure 1.5 Characteristics of hard elastohydrodynamic lubrication

Figure 1.6 Characteristics of soft elastohydrodynamic lubrication

Regimes of Lubrication

Figure 1.5 Film conditions of lubrication regimes. (a) Fluid film lubrication - surfaces separated by a bulk lubricant film; (b) partial lubrication - both bulk lubricant and boundary film play a role; (c) boundary lubrication - performance depends entirely on boundary film.

Friction for Various Lubrication Conditions

Figure 1.8 Bar diagram showing friction coefficient for various lubrication conditions.

Wear Rates for Lubrication Regimes

Figure 1.9 Wear rates for various lubrication regimes.

[From Beerbower (1972)].

Boundary Lubricants

Table 1.1 Fatty acids in oil as lubricants. [From Dorinson and Ludema (1985).]

Figure 1.10 Effect of chain length on the effectiveness of a boundary lubricant. (a) Critical temperature as a function of chain length [From Bowden and Tabor (1950)]; (b) friction coefficient as a function of chain length. [From Zisman (1959).]}

Langmuir-Blodgett Films

Figure 1.11 Effect of boundary lubricant thickness on friction for Langmuir-Blodgett films. [From Bowden and Tabor (1950).]

Boundary Lubricant Mechanisms

Figure 1.12 Physisorption of of n-hexadecane molecules to a metal surface. [From Ku (1970).]

Figure 1.12 Chemisorption of stearic acid to an iron-containing surface to form iron stearate. [From Ku (1970)]

Boundary Lubrication Mechanisms (cont.)

Figure 1.15 Thermal activation of a boundary lubricant during the initial thermal cycle.

Figure 1.14 Formation of sulfide layers on steel, an example of boundary lubrication through chemical reactions involving the substrate.

Stribeck Curve

Bearing Classification

Figure 2.1 Divisions of conformal fluid film bearings. Figure 2.2 Divisions of

rolling-element bearings.

Guide to Journal

Bearings

Figure 1.5 General guide to journal bearing type. Except for rolling-element bearings, curves are drawn for bearings with width equal to diameter. A medium-viscosity mineral oil is assumed for hydrodynamic bearings. [From ESDU (1965).]

Guide to Thrust

Bearings

Figure 2.4 General guide to thrust bearing type. Except

for rolling-element bearings, curves are drawn for typical ratios of inside diameter to

outside diameter. A medium-viscosity mineral oil is

assumed for hydrodynamic bearings. [From ESDU

(1967).]

Surface Profiles

Figure 3.2 Difficulty in interpreting profilometer traces. (a) Surface profile; (b) surface asperity.

Figure 3.1 Geometric characteristics of solid surfaces [From Halling (1976).]

Figure 3.3 Error due to stylus radius.

Compressed Surface Profile

Figure 1.5 True (a) and compressed (b) profile. [From Thomas (1982).]

Atomic Force Microscope

Figure 3.5 Schematic illustration of an atomic force microscope. (a) Principle of operation for an AFM. (b) Typical cantilevers for use in an atomic force microscope. [Source: Digital Instruments Corp.]

Devices for Surface Measurement

Table 3.1 Summary of typical specifications of devices used for surface topography measurement. [From Sherrington and Smith (1988)].

Reference Lines

Figure 3.6 Comparison of three types of reference line: (a) M system; (b) ten-point average; (c) least squares.

Mean or M System: Areas above and below the horizontal line are equal.

Ten-point average: Use five highest peaks and five lowest valleys

Least Squares: Similar to M System, but line can be inclined.

Roughness Issues

Figure 3.7 Geometric profiles having same values of arithmetic average. [From Halling (1976).]

Roughness measures:

Typical Roughness

Table 3.2 Typical arithmetic averages for various processes and components.

Bearing Area Curve

Figure 3.8 Surface profile showing bearing length. [From Persson (1992).]

Figure 3.9 Abbot curves for two different profiles. [From Persson (1992).]

All-Ordinate Distribution

Figure 3.10 Method of deriving all-ordinate distribution. [From Halling (1975).]

Gaussian distribution:

Roughness measures:

Skewness and Kurtosis

Figure 3.11 Illustration of three different kurtosis values. [From Halling (1975).]

Skewness:

Kurtosis:

Autocorrelation Parameter

Figure 3.12 Two different surfaces and resulting autocorrelation functions. (a) Periodicity profile; (b) decay profile. [From Halling (1975).]

Autocorrelation:

Friction vs. Film Parameter

Figure 3.13 Variation of friction coefficient with film parameter. [From Hamrock and Dowson (1981).]

Film parameter:

Friction coefficients:

Paraffins

Table 4.2 Homologous series of hydrocarbons. [From Hess (1981).]

Table 4.1 Straight-chain paraffins [From Pugh (1970)].

Petroleum Products

Table 4.3 Petroleum products with boiling point range and number of carbon atoms present.

Lubricant Formulas

Synthetic Lubricants

Poly-Alpha-Olefin (PAO)

Figure 1.5 Poly-alpha-olefin (PAO) structures. The “star” orientation displays superior lubrication properties. [From Kioupis and Maginn (1999).]

Greases

Table 4.7 Typical characteristics of lubricating greases.

Fluid Viscosities

Figure 4.2 Absolute viscosities of a number of fluids for a wide range of temperatures.

Viscosity of Gases

Figure 4.3 Viscosity of common gases as a function of temperature. [From Cameron (1976).]

Viscosity of Gases

Table 4.8 Viscosity of various gases at 14.7 psia. [From Svehla (1962).]

Properties of Liquids & Gases

Table 4.9 Some properties of common liquids and gases at 68°F and 14.7 psia. [From Gross (1980).]

EmulsionsTypically 5% oil, 95% water.

Oil phase includes additives including emulsifier.

Emulsifier stabilizes emulsion and determines particle size.

Outstanding cooling properties and reasonable lubrication effectiveness.

Figure 4.4 An oil-in-water emulsion stabilized by an emulsifier.

Newtonian Fluids

Figure 4.5 Properties of a Newtonian fluid. (a) Effect of viscosity on shear strain rate; (b) effect of shear stress on shear strain rate.

Figure 4.6 Physical illustration of Newton's postulate, where f = friction force, N; A = area, m2; u=velocity, m/s; h = film thickness, m.

Viscosity Conversion Factors

Table 4.10 Viscosity conversion factors.

Kinematic Viscosity

Table 4.10 Divergence between kinematic and absolute viscosity data with increasing temperature. [From Klaman (1984).]

Kinematic viscosity:

Viscosity Grades

Figure 1.5 Viscosity grade comparisons. [From Litt (1986).]

Viscosity-Pressure Effects

Table 4.12 Absolute and kinematic viscosities of fluids at atmospheric pressure and three temperatures. [From Jones et al. (1975).]

Roelands & Barus

EquationsBarus Law:

Roelands (isothermal):

Figure 4.8 Comparison of absolute viscosity obtained from Barus' and Roelands' formulas for a wide range of pressure. Results are shown for three different lubricants at 38°C; oil 1 --- synthetic paraffinic oil (lot 3); oil 2 --- superrefined napthenic mineral oil; oil 3 --- synthetic hydrocarbon (traction fluid).

Fluid Designations

Table 4.13 Fluids with manufacturer and manufacturer’s designation. [From Jones et al. (1975).]

Pressure-Viscosity Coefficients

Table 4.14 Pressure-viscosity coefficients for fluids at three temperatures. [From Jones et al. (1975).]

Piezo-viscous and Thermo-viscous Behavior

Figure 4.9 Absolute viscosities of SAE lubricating oils at

atmospheric pressure.

Thermal Properties of Liquids

Table 4.16 Typical thermal properties of some liquids.

[From Winer and Cheng (1980).]

Viscosity-Shear Rate Effects

Figure 4.10 Characteristics of different fluids as a function of shear rate. (a) Viscosity; (b) shear stress.

Viscosity Index

Figure 4.11 Graphical explanation of viscosity index where L = low VI oil, x = unknown oil, and H=high VI oil.)

Viscosity Index Data

Table 4.17 Viscosity-index data to be used in Eq. (4.18). [From: An

abridgement from ASTM D567, ``Standard Method for Calculating Viscosity Index''.]

VI Improver Molecules

Figure 4.12 Summary of common viscosity index improver molecules.

Properties of Base Fluids

TAble 4.18 Base fluids tested, with corresponding kinematic viscosity and average molecular weight. [From Hamrock et al. (1987).]

Compressibility

Figure 4.13 Effect of pressure on relative volume for six base fluids. Constant

temperature of 20°C assumed. [From Hamrock et al. (1987).]

Compressibility

Figure 4.14 Effect of pressure on density. [From Hamrock et al. (1987).]

Limiting Shear Stress

Figure 4.15 Comparison of rheological models for isothermal conditions.

Non-Newtonian Rheology

Figure 4.16 Non-Newtonian rheological models represented by (a) effect of shear strain rate on dimensionless shear stress and (b) effect of dimensionless shear stress on dimensionless effective viscosity. [From Myllerup et al. (1993).]

Effective Viscosity

Figure 4.16 Non-Newtonian rheological models represented by (a) effect of shear strain rate on dimensionless shear stress and (b) effect of dimensionless shear stress on dimensionless effective viscosity. [From Myllerup et al. (1993).]

Conformal Bearing Materials

White Metal Bearing Alloys

Alloys in General Use

Bronze & Copper Bearing Alloys

Non-Metallic Bearing Materials

Figure 5.1 Phenolic laminate bearings. (a) Tubular bearing; (b) circumferentially laminated bearing; (c) axially laminated bearing; (d) stave

bearing; (e) molded bearing. [From Kaufman (1980).]

Table 5.5 Limits of application of nonmetallic bearing materials. [Revised from O'Connor et al. (1968)].

Phenolic Bearing Applications

Bearing Surfaces

Figure 5.2 Different forms of bearing surfaces. (a) Solid bearing; (b) lined bearing; (c) filled bearing; (d) shrink-fit bearing.

Bearing Steels

Figure 5.3 Hot hardness of CBS 1000, CBS 1000M, Vasco X-2, and high-speed tool steels. [From

Anderson and Zaretsky (1975).]

Density

Table 5.8 Densities of various metals, polymers, and ceramics at room temperature (20°C; 68°F) [From ESDU (1984).]

Figure 5.4 Illustration of density for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984).]

Elastic Modulus

Figure 5.5 Modulus of elasticity for various metals, polymers, and ceramics at room temperature (20°C; 68°F) [From ESDU (1984).]

Poisson’s Ratio

Table 5.10 Poisson's ratio for various metals, polymers, and ceramics at room temperature (20°C; 68°F) [From ESDU (1984).]}

Thermal Expansion Coefficient

Figure 5.6 Illustration of thermal expansion coefficient for various metals, polymers, and ceramics applied over temperature range 20 to 200°C (68 to 392°F). [From ESDU (1984).]

Thermal Conductivity

Figure 5.7 Illustration of thermal conductivity for various metals, polymers, and ceramics. [From ESDU (1984).]

Specific Heat Capacity

Figure 5.8 Illustration of specific heat capacity for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984).]

Concentric Journal Bearing

Figure 6.2 Developed journal and bearing surfaces for a concentric journal bearing.Figure 6.1 Concentric Journal Bearing.

Petrov’s Equation:

Navier-Stokes Equation

Figure 6.3 Stresses on two surfaces of a fluid element.

Cartesian Coordinates:

Continuity Equation

Figure 6.4 Velocities and densities for mass flow balance through a flux volume element in two dimensions.

Figure 6.5 Flow between parallel flat plates.

Continuity Equation:

Couette & Poiseuille Flow

Figure 6.6 (a) Couette and (b) Poiseuille velocity profiles.

Velocity Profiles

Figure 6.7 Some interesting velocity profiles.

Flow Examples

Figure 6.8 Flow in a circular pipe.

Figure 6.9 Flow down a vertical plane.

Viscosimeters

Figure 6.10 Important features of a capillary viscometer.

Figure 6.10 Rotational circular viscometer.

Figure 6.10 Cone-and-plane viscometer.

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