5.3 Elastohydrodynamic lubrication

Elastohydrodynamic lubrication (EHL) is a critical concept in friction and wear engineering. It describes how heavily loaded, non-conforming contacts are lubricated, combining fluid mechanics and elastic deformation principles to explain thin-film lubrication under high pressure.

EHL is essential for reducing friction and extending component life in applications like gears and bearings. Understanding EHL helps engineers optimize lubricant selection, component design, and operating conditions to improve machine performance and durability.

Fundamentals of elastohydrodynamic lubrication

• Elastohydrodynamic lubrication plays a crucial role in reducing friction and wear in heavily loaded, non-conforming contacts
• Combines principles of fluid mechanics and elastic deformation to describe lubrication in high-pressure, thin-film conditions

Definition and basic principles

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• Lubrication regime characterized by elastic deformation of contacting surfaces and pressure-induced viscosity changes in the lubricant
• Occurs in non-conforming contacts with high loads and relative motion (rolling element bearings, gears)
• Relies on the formation of a thin lubricant film (typically 0.1-1 μm thick) to separate surfaces and reduce friction

Historical development

• Concept introduced in the 1940s by Ertel and Grubin to explain unexpected film thickness in rolling contacts
• Dowson and Higginson developed the first comprehensive EHL theory in the 1960s
• Advancements in computational methods and experimental techniques led to refined models in subsequent decades

Importance in engineering

• Enables efficient operation of heavily loaded machine elements with minimal wear
• Critical for extending the lifespan of components in automotive, aerospace, and industrial applications
• Allows for higher load-carrying capacity and reduced energy losses in mechanical systems

Fluid film formation

• Formation of a lubricant film in EHL contacts depends on the balance between hydrodynamic pressure and elastic deformation
• Understanding fluid film formation helps engineers optimize lubricant selection and component design for improved performance

Pressure-viscosity relationship

• Describes how lubricant viscosity increases exponentially with pressure in EHL contacts
• Barus equation: $η = η_0 e^{αp}$ where η is viscosity, η_0 is ambient viscosity, α is pressure-viscosity coefficient, and p is pressure
• More accurate models (Roelands equation) account for limitations of Barus equation at very high pressures

Film thickness equations

• Central film thickness (hc) equation for line contacts: $h_c = 1.95R(αη_0U/E'R)^{0.727}(W/E'R)^{-0.091}$
• Minimum film thickness (hmin) equation for point contacts: $h_{min} = 3.63R(αη_0U/E'R)^{0.68}(W/E'R)^{-0.073}(1-e^{-0.68k})$
• R is equivalent radius, U is entrainment velocity, W is load, E' is reduced elastic modulus, k is ellipticity parameter

Minimum film thickness

• Occurs near the outlet of the contact zone where pressure gradient is highest
• Critical parameter for determining the onset of asperity interactions and potential surface damage
• Lambda ratio (λ) compares minimum film thickness to composite surface roughness to assess lubrication regime

Contact mechanics

• Understanding contact mechanics helps predict stress distributions and deformations in EHL contacts
• Crucial for analyzing fatigue life and wear resistance of machine elements

Hertzian contact theory

• Describes elastic deformation and stress distribution in idealized, smooth contacting bodies
• Assumes perfectly elastic, frictionless contact with small strains and continuous surfaces
• Provides analytical solutions for contact area, pressure distribution, and maximum contact pressure

Non-Hertzian contacts

• Account for real-world deviations from idealized Hertzian conditions
• Include effects of surface roughness, non-elliptical contact geometries, and plastic deformation
• Require numerical methods or semi-analytical approaches for accurate analysis

Surface roughness effects

• Influences local pressure distribution and film thickness in EHL contacts
• Can lead to asperity interactions and mixed lubrication conditions
• Affects friction, wear, and fatigue life of contacting surfaces
• Characterized by parameters such as Ra (average roughness) and Rq (root mean square roughness)

Lubricant properties

• Lubricant properties significantly influence EHL performance and film formation
• Selection of appropriate lubricants requires consideration of operating conditions and desired tribological outcomes

Viscosity vs temperature

• Viscosity generally decreases with increasing temperature following an exponential relationship
• Viscosity index (VI) quantifies the rate of viscosity change with temperature (higher VI indicates less temperature sensitivity)
• ASTM D341 equation models viscosity-temperature relationship: $log log(ν + 0.7) = A - B log T$

Pressure-viscosity coefficient

• Measures the sensitivity of lubricant viscosity to pressure changes
• Typically ranges from 10-20 GPa^-1 for mineral oils to 5-10 GPa^-1 for synthetic oils
• Determined experimentally using high-pressure viscometers or inferred from EHL film thickness measurements

Thermal conductivity

• Affects heat dissipation and temperature distribution in EHL contacts
• Generally increases with pressure and decreases with temperature
• Typical values range from 0.1-0.2 W/mK for mineral oils to 0.2-0.4 W/mK for some synthetic lubricants

Operating conditions

• Operating conditions significantly impact EHL performance and film formation
• Understanding these effects helps engineers optimize component design and lubrication strategies

Speed and load effects

• Increasing speed generally increases film thickness due to enhanced hydrodynamic action
• Higher loads lead to larger contact areas and higher pressures, potentially reducing film thickness
• Speed and load effects combined in dimensionless speed (U) and load (W) parameters in EHL equations

Temperature influence

• Higher temperatures reduce lubricant viscosity, potentially leading to thinner films
• Thermal effects can cause viscosity variations across the film thickness (thermal EHL)
• Temperature changes affect material properties of contacting surfaces (thermal expansion, elastic modulus)

Starvation vs fully flooded

• Fully flooded conditions ensure adequate lubricant supply to the contact inlet
• Starvation occurs when lubricant supply is insufficient, leading to reduced film thickness
• Starvation effects more pronounced at high speeds and in grease-lubricated contacts
• Degree of starvation quantified by film thickness reduction factor or inlet distance parameter

Numerical modeling

• Numerical modeling enables detailed analysis of complex EHL problems
• Helps predict performance and optimize designs for various operating conditions

Reynolds equation

• Governs pressure distribution in thin lubricant films
• Modified for EHL to include elastic deformation and pressure-viscosity effects
• General form for incompressible, isoviscous flow: $\frac{\partial}{\partial x}\left(\frac{h^3}{\eta}\frac{\partial p}{\partial x}\right) + \frac{\partial}{\partial y}\left(\frac{h^3}{\eta}\frac{\partial p}{\partial y}\right) = 6U\frac{\partial h}{\partial x} + 12\frac{\partial h}{\partial t}$

Energy equation

• Describes temperature distribution in EHL contacts
• Accounts for heat generation due to shearing and compression of the lubricant
• Coupled with Reynolds equation and elastic deformation equations for thermal EHL analysis

Finite element analysis

• Enables solution of complex EHL problems with irregular geometries and non-linear material behavior
• Can incorporate multiphysics effects (thermal, structural, fluid dynamics)
• Allows for detailed stress analysis and optimization of component designs
• Commercial FEA software packages (ANSYS, COMSOL) offer specialized EHL modules

Measurement techniques

• Experimental measurements provide crucial validation for EHL theories and numerical models
• Help characterize lubricant properties and evaluate component performance

Film thickness measurement

• Optical interferometry measures film thickness in transparent EHL contacts (glass or sapphire discs)
• Electrical capacitance technique for opaque contacts
• Ultrasonic methods enable in-situ measurements in real machine elements

Friction measurement

• Measures overall friction in EHL contacts using load cells or torque sensors
• Enables calculation of friction coefficient and evaluation of lubricant performance
• Mini traction machine (MTM) commonly used for laboratory-scale friction measurements

Traction coefficient determination

• Traction coefficient relates tangential force to normal load in EHL contacts
• Measured using specialized test rigs (disc machines, ball-on-disc tribometers)
• Provides insights into lubricant rheology and shear behavior under EHL conditions

Applications in engineering

• EHL principles apply to numerous engineering applications involving heavily loaded, non-conforming contacts
• Understanding EHL helps optimize component design and lubrication strategies for improved performance and longevity

Rolling element bearings

• EHL crucial for efficient operation of ball and roller bearings
• Film thickness predictions used to determine appropriate lubricant selection and bearing design
• EHL analysis helps estimate fatigue life and predict potential failure modes

Gears and cam-follower systems

• EHL governs lubrication in gear tooth contacts and cam-follower interfaces
• Film thickness calculations used to optimize gear geometry and surface finish
• EHL models help predict scuffing resistance and micropitting in gears

Metal forming processes

• EHL principles apply to lubrication in cold rolling and wire drawing processes
• Film thickness predictions used to optimize lubricant selection and process parameters
• EHL analysis helps reduce friction and improve surface quality in formed products

Failure modes

• Understanding EHL-related failure modes helps engineers design more reliable and durable machine elements
• Proper lubrication and operating conditions can mitigate these failure mechanisms

Micropitting and wear

• Occurs when asperity interactions lead to localized surface fatigue
• More prevalent in mixed lubrication regimes with insufficient film thickness
• Characterized by shallow pits (typically <10 μm deep) on the surface
• Can be mitigated by improving surface finish and using higher viscosity lubricants

Scuffing and seizure

• Results from breakdown of the lubricant film and direct metal-to-metal contact
• Often occurs under high loads, high speeds, or inadequate lubrication conditions
• Characterized by rapid adhesive wear and material transfer between surfaces
• Prevention strategies include using extreme pressure (EP) additives and optimizing surface textures

Fatigue and spalling

• Subsurface fatigue caused by repeated stress cycles in EHL contacts
• Leads to formation of cracks that propagate to the surface, resulting in material removal (spalls)
• Influenced by factors such as material cleanliness, residual stresses, and lubrication conditions
• Life prediction models (e.g., ISO 281) incorporate EHL effects on fatigue life

Advanced concepts

• Advanced EHL concepts address more complex scenarios and refine existing models
• Help improve accuracy of predictions and extend applicability to a wider range of conditions

Thermal elastohydrodynamic lubrication

• Incorporates temperature effects on lubricant properties and surface deformation
• Accounts for heat generation due to shearing and compression of the lubricant
• Requires coupled solution of Reynolds, energy, and elasticity equations
• Important for high-speed applications and those with significant sliding

Transient elastohydrodynamic lubrication

• Addresses time-dependent effects in EHL contacts
• Relevant for applications with varying loads, speeds, or geometries (cam-follower systems)
• Considers squeeze film effects and time-dependent rheological behavior
• Requires solution of time-dependent Reynolds equation and elasticity equations

Mixed lubrication regime

• Occurs when film thickness is insufficient to fully separate surface asperities
• Combines aspects of boundary lubrication and EHL
• Requires consideration of asperity interactions and load sharing between fluid film and asperity contacts
• Modeled using statistical approaches or deterministic methods for known surface topographies

Future trends

• Emerging trends in EHL research aim to address new challenges and improve understanding of lubrication phenomena
• Advancements in these areas will lead to more efficient and reliable machine elements

Nano-scale elastohydrodynamic lubrication

• Investigates EHL phenomena at the nanometer scale
• Relevant for micro/nanoelectromechanical systems (MEMS/NEMS) and ultra-thin film lubrication
• Considers effects of surface forces (van der Waals, electrostatic) and molecular-scale fluid behavior
• Requires new experimental techniques and molecular dynamics simulations

Bio-inspired lubricants

• Develops new lubricants based on principles found in nature (synovial joints)
• Explores use of water-based lubricants and biolubricants for environmentally friendly applications
• Investigates surface texturing and smart materials for improved lubrication performance
• Aims to achieve low friction and wear in challenging operating conditions

Computational advancements

• Utilizes machine learning and artificial intelligence to improve EHL modeling
• Develops multiscale modeling approaches to bridge nano, micro, and macro-scale phenomena
• Implements high-performance computing for more detailed and efficient EHL simulations
• Enables real-time monitoring and predictive maintenance of EHL systems through digital twin technology