Tribology, Bearings and Lubrication

Introduction and context

Tribology is the interdisciplinary science and engineering of interacting surfaces in relative motion. It includes friction, wear, lubrication, surface engineering, materials, fluid mechanics, heat transfer, dynamics and reliability. In a machine, tribological interfaces may account for a substantial fraction of energy loss and are frequent sites of premature failure. Bearing and lubrication design therefore cannot be treated as an afterthought to strength design: the load, speed, temperature, contamination, alignment and maintenance strategy must be considered together.

A tribosystem consists of two surfaces, an intervening medium, applied load, relative motion, environment and time. Its behaviour is governed not only by bulk material properties but also by roughness, surface chemistry, oxide films, debris and lubricant condition. The same pair of materials can exhibit very different friction and wear in dry air, oil, water or vacuum.

Learning objectives

After studying this chapter, the reader should be able to:

1. Explain the mechanisms of friction, lubrication and wear.
2. Distinguish boundary, mixed, hydrodynamic, hydrostatic and elastohydrodynamic lubrication.
3. Select and preliminarily size sliding and rolling bearings.
4. Apply bearing-life, friction, heat-generation and lubrication relationships.
5. Diagnose common tribological failures and propose corrective action.
6. Evaluate modern monitoring, materials and sustainability issues in bearing systems.

1. Friction and contact mechanics

1.1 Friction

For dry sliding, the classical engineering approximation is

where F_f is friction force (N), μ is the coefficient of friction (dimensionless), and N is normal load (N). This law is useful for preliminary calculations but is not a universal material constant. The coefficient depends on pressure, velocity, temperature, surface finish, lubrication, contamination and running history. Static friction is usually represented by a limiting value μ_s, while kinetic friction is represented by μ_k.

At a real interface, apparent contact area is much larger than the actual area of contact. Load is transmitted through microscopic asperities. Adhesion, ploughing, deformation and third-body effects contribute to friction. Consequently, friction may increase when surfaces are extremely smooth because adhesive junctions become more significant.

1.2 Elastic and plastic contact

For two elastic bodies in contact, Hertz theory gives the circular contact radius for a sphere of radius R under normal load W:

The reduced elastic modulus is

Here a is contact radius (m), E₁,E₂ are Young’s moduli (Pa), ν₁,ν₂ are Poisson ratios, and E* is the effective modulus (Pa). The maximum Hertzian pressure is

These equations assume smooth, isotropic, homogeneous elastic bodies, nonconforming contact and negligible adhesion. Rolling-element contacts often operate at high pressure while remaining predominantly elastic; local plasticity, inclusions and residual stress can nevertheless initiate fatigue.

2. Wear mechanisms

Wear is progressive material loss or damage caused by relative motion. Important mechanisms are:

• Adhesive wear: asperity junctions form and tear, transferring material between surfaces.
• Abrasive wear: hard asperities or particles cut or plough a softer surface.
• Surface-fatigue wear: repeated contact stress produces cracks, pitting and spalling.
• Tribochemical or corrosive wear: chemical reactions weaken the surface and are accelerated by motion.
• Erosive wear: moving particles or droplets impact a surface.
• Fretting: small-amplitude oscillation produces oxidized debris and severe local damage.

A useful first estimate for sliding wear is Archard’s relationship:

where V is wear volume (m³), k is a dimensionless wear coefficient, W is normal load (N), L is sliding distance (m), and H is hardness of the softer material (Pa). It assumes wear is proportional to load and distance and that the wear regime remains unchanged. The coefficient is empirical and can vary by orders of magnitude; therefore the equation is a comparison tool, not a substitute for testing.

Designers reduce wear by lowering contact stress, preventing particle entry, choosing compatible materials, improving surface hardness and finish, and maintaining a lubricant film. Wear particles are both a failure cause and a diagnostic signal.

3. Lubrication regimes

Lubrication separates surfaces, reduces shear, removes heat and protects against corrosion. The principal regimes are:

1. Boundary lubrication: the film is too thin to separate asperities. Adsorbed molecular layers, additives and surface chemistry control friction and wear.
2. Mixed lubrication: some load is carried by the fluid film and some by asperities.
3. Hydrodynamic lubrication: relative motion draws lubricant into a converging wedge and generates pressure sufficient to separate surfaces.
4. Hydrostatic lubrication: an external pump supplies pressurized lubricant, allowing separation even at zero speed.
5. Elastohydrodynamic lubrication (EHL): elastic deformation of contacting bodies and pressure-induced viscosity increase produce a separating film, especially in gears and rolling bearings.

Film adequacy is often expressed by the specific film-thickness ratio:

where h_min is minimum film thickness (m), and Rq₁,Rq₂ are root-mean-square surface roughness values (m). As a qualitative guide, λ < 1 indicates substantial asperity interaction, approximately 1 ≤ λ ≤ 3 indicates mixed lubrication, and λ > 3 indicates predominantly full-film separation. These boundaries are approximate and depend on surface texture and operating conditions.

The dimensionless Sommerfeld number for a journal bearing is commonly written as

where μ is dynamic viscosity (Pa·s), N is rotational speed (rev/s), p is mean bearing pressure (Pa), r is journal radius (m), and c is radial clearance (m). It is used with experimentally or numerically obtained bearing charts. Definitions of speed and clearance must be consistent with the selected chart.

For an incompressible Newtonian lubricant, shear stress in a simple film is

where τ is shear stress (Pa), η is dynamic viscosity (Pa·s), and du/dy is velocity gradient (s⁻¹). This relation assumes laminar flow and constant viscosity. Real lubricants may be non-Newtonian, particularly when additives or polymers are present.

Lubricant selection

Viscosity is the primary selection variable. Excessively low viscosity causes film collapse and wear; excessively high viscosity increases churning losses, starting torque and temperature. Other requirements include oxidation stability, viscosity–temperature behaviour, antiwear and extreme-pressure performance, demulsibility, foaming tendency, seal compatibility and food or environmental compliance.

Oil is suitable for high speed, heat removal and centralized circulation. Grease is convenient where leakage must be limited and relubrication is infrequent, but it generally removes heat less effectively. Solid lubricants such as graphite, molybdenum disulfide and polytetrafluoroethylene are useful in vacuum, high-temperature or chemically incompatible environments, subject to load and atmosphere limitations.

Additives are functional chemicals, not universal improvements. Antiwear additives form protective films under moderate severity; extreme-pressure additives react under high temperature and pressure; detergents, dispersants, antioxidants and corrosion inhibitors address other service needs. Compatibility with seals, coatings and other lubricants must be verified.

4. Sliding bearings

A sliding bearing supports a shaft through a lubricated conforming or partially conforming surface. Common forms are full journal, partial journal, thrust, sleeve, tilting-pad and foil bearings.

For a journal bearing, mean bearing pressure is

where W is radial load (N), L is bearing length (m), and D is journal diameter (m). The projected area LD is used; it is not the actual curved contact area. Bearing clearance, load direction, speed, viscosity and alignment determine the pressure distribution.

The friction torque is approximately

and power loss is

where f is an effective friction coefficient, r is journal radius (m), N is rotational speed (rev/s), and P_f is power loss (W). These expressions are preliminary estimates; hydrodynamic analysis should account for eccentricity, side leakage and temperature-dependent viscosity.

A practical design must check pressure, pv value, minimum film thickness, starting and stopping conditions, thermal balance, shaft hardness, bearing material and lubrication supply. Babbitt offers conformability and embedment; bronze provides strength and compatibility; polymeric and ceramic materials can perform well under special conditions but require careful thermal and counterface analysis.

Thermal balance

Bearing temperature is determined by generated heat, lubricant flow, conduction, convection and radiation. A steady-state energy balance is

If heat removal is approximated by convection,

where h is heat-transfer coefficient (W·m⁻²·K⁻¹), A_s is effective cooling area (m²), T_b is bearing temperature (K), and T_∞ is surrounding-fluid temperature (K). This lumped model assumes a representative uniform temperature and known heat-transfer coefficient. In practice, lubricant flow and viscosity feedback require iterative analysis.

5. Rolling-element bearings

Rolling bearings use balls or rollers between inner and outer raceways. They offer low starting friction, standardized dimensions and predictable life, but are sensitive to contamination, misalignment, installation damage and lubrication failure. Ball bearings suit moderate loads and high speed; cylindrical rollers carry high radial load; tapered rollers carry combined radial and axial load; spherical rollers accommodate limited misalignment.

Static and dynamic capacity

Static rating concerns permanent deformation under stationary or slowly rotating load. Dynamic rating concerns rolling-contact fatigue life. For a bearing carrying equivalent dynamic load P, the basic rating life in millions of revolutions is

where C is basic dynamic load rating (N), and p = 3 for ball bearings and p = 10/3 for roller bearings. L₁0 is the life that 90% of an adequately manufactured population is expected to reach or exceed under stated conditions. The relationship assumes proper lubrication, clean conditions, correct mounting and predominantly constant load.

In hours,

where n is speed (rev/min). For variable loads, an equivalent load based on time fractions is often estimated as

where f_i is the fraction of operating time at load P_i, and Σf_i = 1. Manufacturer standards and catalogue factors should be used for axial load, reliability, lubrication and contamination adjustments.

Worked example: preliminary bearing life

A ball bearing has C = 30 kN, carries P = 5 kN, and rotates at 1,200 rev/min. With p = 3,

Therefore,

This is a basic rating life, not a guarantee. Contamination, inadequate film thickness, electrical current passage or misalignment can reduce actual life substantially.

Bearing preload and internal clearance

Preload removes internal looseness and improves stiffness, but increases friction and temperature. Excessive preload causes rapid failure. Excessive clearance permits vibration, skidding and poor load distribution. Thermal expansion must be included: operating clearance differs from assembly clearance because rings, shaft and housing may reach different temperatures.

6. Lubrication systems and failure diagnosis

Delivery methods include oil bath, splash, drip, circulating oil, oil mist, grease packing, automatic lubricators and centralized systems. Selection depends on speed, heat generation, accessibility, contamination and consequence of failure. Seals should exclude contaminants while limiting friction and lubricant loss; labyrinth seals are low-friction but may not stop pressure-driven liquid ingress, whereas contact seals provide stronger exclusion with greater drag.

A structured diagnostic process is preferable to replacing a failed bearing without identifying cause:

1. Record operating load, speed, temperature, vibration and lubrication history.
2. Preserve the failed component and document mounting orientation.
3. Inspect raceways, rollers, cages, seals and lubricant debris.
4. Distinguish fatigue spalling, smearing, false brinelling, corrosion, electrical fluting, indentation and overheating.
5. Correct the root cause and verify through condition monitoring.

Vibration analysis detects characteristic defect frequencies; oil analysis measures viscosity, oxidation, water and particle contamination; thermography identifies abnormal heat; acoustic-emission methods can detect early rolling-contact damage. Data-driven and AI methods can classify trends, but they require representative training data, sensor validation and human review. A model should support—not replace—physical failure analysis.

7. Illustrative industrial case: repeated conveyor-drive bearing failures

Background. A mineral-processing conveyor repeatedly failed its drive-end spherical roller bearing after three to five months, although the catalogue rating predicted several years.

Problem. Failures occurred as darkened grease, raceway smearing and localized spalling. Operators increased grease quantity, but temperature rose and failures accelerated.

Analysis. Review showed intermittent high speed, a dusty environment, shaft misalignment and manual relubrication without a measured quantity. Vibration spectra indicated cage and rolling-contact distress. Grease inspection found abrasive mineral particles and evidence of overgreasing. The nominal life calculation had assumed clean lubrication and constant load; it did not represent the actual tribosystem.

Approach. The team aligned the shaft and housing, replaced damaged seals with a labyrinth-plus-contact arrangement, installed an automatic metered lubricator, specified a compatible high-load grease, added temperature and vibration monitoring, and established a contamination-control procedure. Operating limits were revised to include transient loads.

Outcome. Bearing temperature decreased, vibration stabilized and service life exceeded the maintenance interval. The financial benefit arose not merely from a different bearing, but from controlling alignment, contamination, lubricant quantity and operating data.

Learning points. Rating life is conditional; overgreasing is a failure mode; cleanliness and installation quality are design variables; and condition monitoring is most effective when linked to a corrective maintenance decision.

8. Advanced design considerations and sustainability

Tribological design increasingly uses surface texturing, diamond-like carbon coatings, thermal-spray coatings, ceramic rolling elements, solid-lubricant films and hybrid bearings. These technologies can reduce friction or improve electrical insulation, but their performance depends on counterface preparation, coating adhesion, thermal expansion and debris tolerance.

Electrically driven systems create new bearing risks. Variable-frequency drives can generate shaft voltages and electrical discharge machining damage, producing fluting. Insulated bearings, ceramic rolling elements, grounding brushes and correct cable installation are possible countermeasures.

Sustainability requires considering total energy and life-cycle impact rather than lubricant consumption alone. Lower friction reduces operating energy, while longer life reduces replacement materials and downtime. Bio-based and biodegradable lubricants may reduce environmental impact but can have limitations in oxidation stability, hydrolysis, seal compatibility and low-temperature performance. Used oils and contaminated grease require regulated collection and disposal. Safety data sheets, local environmental law and machinery standards must guide procurement and maintenance.

Best practice is to:

• define the complete operating envelope, including transients;
• calculate load, speed, temperature and life using consistent units;
• specify cleanliness, fit, clearance, alignment and mounting procedures;
• choose lubricant viscosity and additives for the actual regime;
• control storage, handling and relubrication quantity;
• monitor temperature, vibration, lubricant condition and contamination;
• validate catalogue calculations through testing or field evidence;
• document assumptions and revise them when operating conditions change.

Chapter Summary

Tribology explains the interaction of surfaces in motion and integrates friction, wear, lubrication, materials, contact mechanics and reliability. Friction is influenced by asperity adhesion, deformation, ploughing, lubricant films and contaminants. Wear may be adhesive, abrasive, fatigue-based, chemical, erosive or fretting-related. Lubrication regimes range from boundary to full-film hydrodynamic, hydrostatic and elastohydrodynamic states; the film-thickness ratio provides a useful qualitative indicator.

Sliding-bearing design requires pressure, clearance, film thickness, friction and thermal checks. Rolling-bearing selection requires equivalent load, dynamic capacity, speed, reliability, lubrication and contamination assessment. The basic rating-life equation is conditional and must not be interpreted as a guaranteed service life. Effective practice combines sound design, controlled installation, suitable lubricant delivery, sealing, condition monitoring and root-cause analysis. Contemporary developments include engineered coatings, hybrid bearings, electrical-damage protection, sensor systems and data-assisted maintenance, all of which require validation within the complete tribosystem.

Key Terms

Tribology: Science and engineering of interacting surfaces in relative motion.

Friction: Resistance to relative motion between surfaces.

Wear: Progressive material loss or surface damage caused by motion.

Asperity: Microscopic peak on a surface.

Boundary lubrication: Regime in which asperity contact carries a significant part of the load.

Mixed lubrication: Regime combining fluid-film and asperity load support.

Hydrodynamic lubrication: Film generation by relative motion through a converging lubricant wedge.

Hydrostatic lubrication: Film support produced by externally pressurized lubricant.

Elastohydrodynamic lubrication: Lubrication involving elastic deformation and pressure-dependent viscosity.

Viscosity: Resistance of a fluid to shear flow.

Journal bearing: Sliding bearing supporting a rotating shaft through a lubricated sleeve or pad.

Rolling-element bearing: Bearing using balls or rollers between raceways.

Basic dynamic load rating: Constant load associated with a basic rating life of one million revolutions.

L10 life: Life exceeded by 90% of a sufficiently large bearing population under specified conditions.

Preload: Intentional internal bearing load applied to remove clearance.

Fretting: Damage caused by small-amplitude oscillatory motion.

Archard relationship: Empirical wear-volume relationship involving load, distance and hardness.

Sommerfeld number: Dimensionless parameter used in hydrodynamic journal-bearing analysis.

Condition monitoring: Measurement-based assessment of machine health.

Specific film-thickness ratio: Ratio of minimum lubricant-film thickness to combined surface roughness.

Review Questions

Short Answer Questions

1. Define tribology and identify the elements of a tribosystem.
2. Distinguish boundary, mixed and hydrodynamic lubrication.
3. What is meant by L10 bearing life?
4. State two important causes of rolling-bearing failure.
5. Why can overgreasing increase bearing temperature?

Long Answer Questions

1. Explain the principal mechanisms of friction and wear, with engineering examples.
2. Describe the construction, operation and design checks of a hydrodynamic journal bearing.
3. Explain rolling-bearing dynamic capacity, equivalent load and rating life.
4. Discuss lubricant selection, delivery systems, seals and contamination control.
5. Explain how vibration, temperature and oil analysis contribute to predictive maintenance.

Analytical / Application Questions

1. A bearing operates under two loads for equal periods. Develop the equivalent dynamic load using the appropriate life exponent and explain the assumptions involved.
2. A journal bearing shows rising temperature after a viscosity grade is increased. Analyse the competing effects of film thickness, viscous drag, heat generation and heat removal.
3. A conveyor bearing exhibits spalling, abrasive particles and seal damage. Construct a root-cause investigation and propose design, maintenance and monitoring actions.

Multiple Choice Questions with Answers

Question 1

Which lubrication regime involves significant load sharing between the fluid film and asperities?

A. Hydrostatic lubrication

B. Mixed lubrication

C. Pure hydrodynamic lubrication

D. Vacuum lubrication

Correct Answer: B. Mixed lubrication

Question 2

In Archard’s relationship, increasing the hardness of the softer surface generally causes wear volume to:

A. Increase proportionally

B. Remain unchanged

C. Decrease, for the same load, distance and wear coefficient

D. Become independent of sliding distance

Correct Answer: C. Decrease, for the same load, distance and wear coefficient

Question 3

For a ball bearing, the usual exponent p in the basic rating-life equation is:

A. 1

B. 2

C. 3

D. 10/3

Correct Answer: C. 3

Question 4

A bearing has C = 30 kN and P = 5 kN. Its ball-bearing basic rating life is:

A. 6 million revolutions

B. 36 million revolutions

C. 125 million revolutions

D. 216 million revolutions

Correct Answer: D. 216 million revolutions

Question 5

Which condition most directly promotes abrasive bearing wear?

A. Clean lubricant and correct alignment

B. Hard particles entering the contact

C. Adequate film thickness

D. Correct internal clearance

Correct Answer: B. Hard particles entering the contact

Question 6

Hydrostatic lubrication differs from hydrodynamic lubrication because hydrostatic lubrication:

A. Requires no lubricant

B. Uses externally supplied pressure to support the load

C. Can operate only at high speed

D. Always involves plastic contact

Correct Answer: B. Uses externally supplied pressure to support the load

Question 7

The main purpose of bearing preload is to:

A. Increase internal looseness

B. Remove internal clearance and improve stiffness

C. Reduce all heat generation to zero

D. Permit unlimited misalignment

Correct Answer: B. Remove internal clearance and improve stiffness

Question 8

For a spherical Hertzian contact, the reduced modulus combines:

A. Only the two surface roughness values

B. Young’s moduli and Poisson ratios of both bodies

C. Only lubricant density and viscosity

D. Bearing speed and clearance only

Correct Answer: B. Young’s moduli and Poisson ratios of both bodies

Question 9

Which observation is most characteristic of electrical discharge damage in a rolling bearing?

A. Uniform polishing with no electrical source

B. Fluting on raceways

C. Increased static load rating

D. Reduced lubricant viscosity only

Correct Answer: B. Fluting on raceways

Question 10

At 1,200 rev/min, a bearing with a basic rating life of 216 million revolutions has an L10 life of:

A. 300 h

B. 1,200 h

C. 3,000 h

D. 36,000 h

Correct Answer: C. 3,000 h