Bearings, Lubrication, Seals and Tribology

Introduction

Bearings support relative motion between machine components while carrying radial, axial, or combined loads. Their performance affects frictional power loss, noise, temperature, accuracy, reliability, and maintenance cost. A bearing cannot be selected independently of its lubricant, seals, shaft geometry, housing stiffness, alignment, contamination control, and operating temperature. These elements form a tribological system: interacting surfaces, lubricant, environment, load, speed, and time.

This chapter develops the principles required to select and design rolling-contact and sliding bearings. It also explains lubrication regimes, friction and wear, seals, thermal balance, alignment, maintenance, and condition monitoring.

Learning Objectives

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

• distinguish rolling-contact and sliding bearings and select between them;
• calculate equivalent bearing load, basic rating life, and static load capacity;
• explain hydrodynamic, hydrostatic, boundary, mixed, and elastohydrodynamic lubrication;
• select lubricants according to viscosity, load, speed, temperature, and contamination;
• evaluate friction, wear, heat generation, and thermal balance;
• specify seals and account for misalignment and installation conditions;
• develop practical inspection, lubrication, and replacement practices.

1. Bearing Function and Classification

A bearing constrains relative motion while transmitting forces between a moving member and its support. The principal bearing types are:

1. Rolling-contact bearings, in which balls or rollers separate the raceways. They include deep-groove ball, angular-contact ball, cylindrical-roller, spherical-roller, tapered-roller, and thrust bearings.
2. Sliding bearings, in which a journal slides against a bearing surface, usually separated by a lubricant film. They include plain cylindrical bushes, flanged bushes, split journal bearings, thrust pads, and self-lubricating composite bearings.

Rolling bearings generally provide low starting friction, standardized dimensions, and convenient replacement. Sliding bearings can carry very high loads, tolerate shock, operate quietly, and accommodate large diameters at relatively low cost. They may also be preferable where damping, electrical insulation, or very high speed is required.

Important bearing terminology includes the inner ring, outer ring, rolling elements, cage, raceway, journal, bearing clearance, preload, bearing span, and static or dynamic load rating. Bearing clearance is the internal free movement before mounting; preload is an intentional internal force that removes clearance and increases stiffness, friction, and heat generation.

Selection criteria

Bearing selection should consider:

• magnitude, direction, and variation of load;
• speed and acceleration;
• required life and reliability;
• shaft and housing dimensions;
• radial and axial stiffness;
• shock, vibration, and misalignment;
• operating temperature;
• contamination and moisture;
• lubrication method and relubrication access;
• noise, precision, installation, and cost.

A bearing that satisfies only the static load requirement may still fail from fatigue, inadequate lubrication, excessive temperature, contamination, or incorrect mounting.

2. Rolling-Contact Bearing Design

2.1 Load components and equivalent dynamic load

A rolling bearing may carry radial load F_r, axial load F_a, or both. Catalogues commonly express the equivalent dynamic bearing load as:

where P is the equivalent dynamic load, X and Y are manufacturer-supplied factors, and F_r and F_a are radial and axial loads. The factors depend on bearing type, contact angle, internal clearance, and the ratio of axial to radial load. For a purely radial deep-groove ball-bearing load, a frequently applicable special case is P = F_r, provided the axial-load threshold specified by the manufacturer is not exceeded.

For variable loading, a constant equivalent load may be estimated by a cycle-weighted relation:

Here P_i is the load during operating interval i, L_i is the number of revolutions or proportional operating duration in that interval, and p is the life exponent: approximately 3 for ball bearings and 10/3 for roller bearings. This relation assumes that loads are represented consistently and that the bearing experiences rolling-contact fatigue rather than a dominant other failure mode.

2.2 Basic rating life

The basic rating life is the number of revolutions that 90% of an identical group of bearings can reach or exceed under specified conditions. It is denoted L₁0 and is calculated from:

where C is the basic dynamic load rating, P is the equivalent dynamic load, and p is 3 for ball bearings or 10/3 for roller bearings. If life is required in millions of revolutions, L₁0 is commonly reported as L₁₀ = (C/P)^p million revolutions, with C and P in the same force units.

At rotational speed n in revolutions per minute, life in hours is:

This is a statistical fatigue relation, not a guaranteed service life. It does not directly account for contamination, inadequate lubrication, electrical erosion, misalignment, mounting damage, or seal failure. Modern catalogue life methods may introduce reliability, lubrication, contamination, and material factors; these should be applied using the relevant manufacturer or standard procedure.

Worked Example 1: Dynamic rating and life

A ball bearing carries a constant equivalent load of 4 kN. The required basic rating life is 20 million revolutions. For a ball bearing, p = 3. Determine the required dynamic rating.

Using L₁₀ = (C/P)³:

A bearing with a catalogue dynamic rating of at least 10.86 kN is required, subject to checks for static load, speed, temperature, lubrication, and mounting. If it rotates at 1200 r/min, its basic rating life in hours is:

The result illustrates that a large revolution life can correspond to a modest number of hours at high speed.

2.3 Static load rating

The basic static load rating C₀ relates to a specified permanent deformation at the most heavily loaded contact. The equivalent static load is commonly represented by:

where X₀ and Y₀ are static-load factors supplied for the bearing type. The static safety factor is:

The required value depends on noise, precision, shock, and deformation limits. High static safety is needed where indentation would impair smooth motion or accuracy. Static checking is especially important for stationary loads, oscillation, shock, and low-speed applications.

2.4 Speed, preload, and internal clearance

The limiting speed stated by a manufacturer depends on bearing size, cage design, lubrication, heat dissipation, load, and permissible temperature. A bearing operating near its speed limit requires careful lubricant selection and thermal analysis.

Preload improves stiffness, reduces vibration and axial movement, and may improve running accuracy. However, excessive preload raises frictional torque and temperature and can cause early fatigue. Internal clearance must account for interference fits, thermal expansion, shaft and housing materials, and operating temperature. Cylindrical roller bearings may use controlled radial clearance; angular-contact bearings often use matched preload classes.

3. Sliding Bearings

A sliding bearing supports a shaft, or journal, on a lubricated surface. In a full-film journal bearing, the rotating shaft drags lubricant into a converging wedge, generating pressure that supports the load. A simplified performance parameter is the Sommerfeld number:

where μ is dynamic viscosity in Pa·s, n is rotational speed in revolutions per second, p is average bearing pressure in Pa, r is journal radius, and c is radial clearance. The exact definition varies with convention and bearing geometry; therefore, design charts or validated numerical solutions must be used with the same definition.

Average bearing pressure is:

where W is radial load in newtons, L is bearing length in metres, and d is journal diameter in metres. The pressure–velocity product is:

where v = π d n is the journal surface speed in metres per second. PV is useful for preliminary screening of plain-bearing materials, but it is not a complete design criterion because temperature, lubrication, edge loading, and transients also matter.

The minimum film thickness must be adequate relative to surface roughness. A useful film parameter is:

where h_min is minimum film thickness and R_q1 and R_q2 are the root-mean-square roughness values of the two surfaces. Large λ indicates greater separation and a full-film condition; small values indicate mixed or boundary interaction. Threshold values vary with surface texture and contact type, so λ should be treated as an engineering indicator rather than an absolute boundary.

Plain bearings require checks for projected pressure, surface speed, heat generation, lubricant supply, start-up and stopping, shaft hardness, and allowable wear. They are particularly vulnerable during start-up, when the shaft may contact the bearing before a full hydrodynamic film forms.

4. Tribology and Lubrication Regimes

Tribology is the study of friction, lubrication, and wear between interacting surfaces. The coefficient of friction is:

where F_t is tangential friction force and F_n is normal force. This dimensionless coefficient depends on material, load, speed, temperature, roughness, lubricant, and environment.

Lubrication regimes

• Boundary lubrication: surfaces are separated mainly by chemically adsorbed or reacted films. Friction and wear can be significant; additives are important.
• Mixed lubrication: part of the load is carried by the lubricant film and part by asperity contact.
• Hydrodynamic lubrication: surfaces are fully separated by a pressure-generating fluid film; viscosity, speed, geometry, and load determine performance.
• Hydrostatic lubrication: an externally pressurized lubricant supplies the supporting film, even at zero speed.
• Elastohydrodynamic lubrication: elastic deformation and pressure-dependent viscosity are important, especially in rolling contacts such as gears and rolling bearings.

A Stribeck-type relationship shows that friction generally decreases as the viscosity–speed product increases relative to load, reaches a minimum near mixed lubrication, and rises again when viscous drag dominates. It is a conceptual model, not a universal equation.

Lubricant selection

The principal lubricant classes are mineral oils, synthetic oils, greases, solid lubricants, and water-based fluids. Selection should consider:

• viscosity at operating temperature;
• viscosity index and temperature range;
• oxidation and thermal stability;
• load-carrying and antiwear performance;
• compatibility with seals, coatings, and plastics;
• water resistance and corrosion protection;
• foaming, air release, and cleanliness;
• food, environmental, or fire-safety requirements.

Oil is preferred for high speed, high temperature, heat removal, and continuous filtration. Grease is often preferred for simple sealing, intermittent service, and low-to-moderate speed. Over-greasing is a common cause of overheating because churning increases viscous losses.

Grease consistency is classified by an NLGI grade, while oil viscosity may be specified using ISO viscosity grades. These classifications do not by themselves establish suitability; the operating viscosity and additive chemistry must also be verified.

Lubricants should not be mixed unless compatibility has been established. Different thickener systems, base oils, additives, or contamination levels can cause softening, hardening, separation, or loss of protection. Clean transfer equipment and correct quantities are essential.

5. Friction, Wear, and Thermal Balance

Wear mechanisms include adhesive wear, abrasive wear, fatigue wear, corrosive or chemical wear, fretting, and erosive wear. Wear debris is both a symptom and a cause of damage. Hard particles can indent raceways, cut surfaces, and accelerate fatigue.

A simplified adhesive/abrasive screening relation is Archard’s law:

where V is wear volume, k is a dimensionless wear coefficient, W is normal load, s is sliding distance, and H is hardness of the softer wearing material. The equation assumes a simplified wear process and is useful for comparative estimates, not as a substitute for test data.

Bearing friction produces heat. A preliminary estimate is:

where P_f is frictional power in watts, M_f is friction torque in N·m, and ω = 2πn is angular speed in rad/s, with n in revolutions per second. An alternative sliding estimate is P_f = μ_f W v.

For steady operation, a thermal balance requires:

If heat is removed approximately through a thermal resistance R_th in K/W, the temperature rise may be estimated as:

This is a lumped approximation. Actual bearing temperature depends on conduction through shaft and housing, lubricant flow, convection, radiation, seals, and transient operation. If generated heat exceeds dissipation, temperature rises until failure or a new balance occurs; lubricant oxidation, viscosity loss, clearance change, and seal degradation may follow.

6. Seals, Shields, and Contamination Control

Seals retain lubricant and exclude water, dust, chemicals, and abrasive particles. Common arrangements include:

• contact lip seals, which provide effective exclusion but create friction and heat;
• non-contact labyrinth seals, which have low friction and high-speed capability but require suitable geometry and orientation;
• shields, which protect against larger particles and reduce grease loss but are not fully sealed;
• mechanical seals, common in pumps and rotating equipment where leakage control is critical;
• V-rings, wipers, and axial seals, selected according to movement and contamination.

Seal selection depends on shaft speed, pressure differential, temperature, fluid compatibility, surface finish, shaft hardness, runout, and expected contamination. Seal lips should be installed without damage, and the shaft seal track should be free from burrs. A seal cannot compensate for excessive shaft misalignment, poor surface finish, or inadequate housing design.

Contamination control is often more important than increasing bearing size. Protective measures include clean assembly areas, filtered oil, properly fitted breathers, positive-pressure systems where appropriate, correct storage, and inspection of seal condition.

7. Alignment, Fits, and Installation

Misalignment causes uneven load distribution, edge loading, increased torque, and premature fatigue. Sources include bent shafts, incorrect shoulder geometry, housing distortion, thermal growth, soft foot, and inaccurate assembly.

A locating or fixed bearing generally controls axial position, while a floating bearing permits axial displacement caused by thermal expansion. If both bearings constrain the shaft without provision for expansion, substantial axial forces can develop.

Fits must prevent ring creep without creating excessive internal clearance reduction. A rotating ring under a stationary load may require a looser fit than a ring subjected to a rotating load. Exact fit recommendations depend on load, speed, shaft material, temperature, and bearing size and should be taken from the manufacturer or applicable standard.

Installation practices include:

1. verify bearing identity and cleanliness;
2. inspect shaft shoulders, fillets, and housing bores;
3. apply force only to the ring being fitted;
4. use controlled heating or hydraulic methods for interference fits;
5. never transmit mounting force through rolling elements;
6. set clearance or preload using the specified method;
7. protect seals and provide correct lubricant quantity;
8. rotate by hand and check for abnormal resistance;
9. record bearing, lubricant, fit, and installation data.

Induction heating is preferable to open flame because it gives controlled, uniform heating and avoids local overheating. Excessive heating can alter material properties or damage seals and lubricant.

8. Maintenance and Condition Monitoring

A maintenance program should combine preventive, predictive, and corrective practices. Important measurements include temperature, vibration, ultrasound, lubricant condition, speed, torque, and leakage. A rising vibration trend is generally more informative than one isolated reading.

Common diagnostic patterns include:

• high-frequency vibration and spalling-related frequencies: possible rolling-contact fatigue;
• repeated fluting or electrical discharge marks: possible stray-current damage;
• temperature rise after relubrication: possible over-greasing or incompatible grease;
• discoloured lubricant: overheating or oxidation;
• dents and regular impact marks: contamination or static shock loading;
• fretting corrosion near fits: insufficient interference, vibration, or micro-motion.

Relubrication intervals depend on bearing size, speed, temperature, load, grease type, contamination, and orientation. The interval and quantity should be obtained from a validated manufacturer method rather than guessed. Oil systems require filtration, sampling, level control, venting, and periodic replacement based on condition and degradation.

Lubrication records should identify lubricant brand and grade, quantity, date, technician, equipment condition, and observed abnormalities. Mixing products without documented compatibility is unacceptable in professional maintenance.

9. Applied Case: Conveyor Drive Bearing Failure

Background

This illustrative case concerns a belt conveyor driven by a motor and gearbox. The drive shaft used two sealed rolling bearings. The conveyor operated continuously in a dusty aggregate plant.

Problem

The outboard bearing repeatedly failed after approximately three months, although its calculated basic rating life exceeded one year. Failures appeared as raceway indentations, discoloured grease, and seal damage.

Analysis

Inspection found three interacting causes. First, the shaft seal had been installed with a damaged lip, allowing abrasive dust and moisture to enter. Second, maintenance personnel added grease weekly without considering the sealed bearing’s original fill, causing churning and temperature rise. Third, the shaft was not adequately supported during installation; mounting force passed through the rolling elements and created indentation marks.

The nominal dynamic rating was therefore not the controlling design factor. Contamination, thermal degradation, and installation damage dominated the failure process. The fixed/floating arrangement was also checked because thermal growth had produced slight axial preload during hot operation.

Approach and solution

The maintenance team replaced the damaged seal arrangement with a contamination-resistant labyrinth and auxiliary contact seal, while retaining a suitable grease-filled bearing. A controlled installation fixture applied force to the correct ring. The grease procedure was changed to manufacturer-specified quantity and interval, with no routine addition to sealed-for-life units. Shaft alignment and housing distortion were measured, and vibration and temperature trends were recorded.

Outcome

After the changes, operating temperature stabilized, vibration decreased, and bearing replacement intervals increased substantially. The principal improvement resulted not from selecting a larger bearing but from controlling contamination, installation, lubrication, and alignment.

Learning points

1. Catalogue fatigue life is not a complete reliability prediction.
2. Seals and lubricant are part of the bearing system.
3. Installation errors can create damage before service begins.
4. Trending temperature and vibration supports early intervention.
5. Correct maintenance procedure may yield more benefit than oversizing.

10. Design Workflow and Professional Practice

A robust bearing design proceeds as follows:

1. define duty cycle, loads, speed, environment, life, and allowable motion;
2. identify radial and axial load components and calculate equivalent loads;
3. select bearing type based on load direction, stiffness, speed, misalignment, and space;
4. calculate dynamic life and static safety;
5. check speed, preload or clearance, fits, thermal growth, and alignment;
6. select lubricant and sealing arrangement together;
7. estimate frictional power and verify thermal balance;
8. specify installation, inspection, and maintenance procedures;
9. validate the design using testing, monitoring, or field data.

Engineers must apply applicable standards, manufacturer data, occupational safety requirements, environmental regulations, and equipment-specific procedures. Lubricant disposal, leakage prevention, noise exposure, and safe handling of heated or hydraulically mounted bearings are also professional responsibilities. Digital monitoring and machine-learning tools can identify abnormal trends, but they require representative data, sensor validation, explainable alarm limits, and human engineering judgment. They should assist—not replace—failure analysis and safe decisions.

Challenges and Limitations

Bearing calculations rely on idealized loads, material data, and statistical assumptions. Real machines experience transient shock, contamination, thermal gradients, manufacturing variation, electrical effects, and uncertain maintenance. A calculated L₁₀ is neither a guaranteed life nor a failure date. Lubricant viscosity changes strongly with temperature, while seals may degrade through chemical attack or wear. Numerical simulations can improve prediction but require accurate geometry, material properties, contact conditions, and validation. Therefore, design calculations should be combined with standards, supplier data, testing, and condition monitoring.

Chapter Summary

Bearings transmit load while permitting controlled relative motion. Rolling bearings are selected primarily through equivalent dynamic load, basic rating life, static load capacity, speed, clearance, preload, and environmental requirements. Sliding bearings depend on pressure, speed, viscosity, geometry, film formation, and thermal balance. Tribology links friction, lubrication, wear, surfaces, and operating environment.

Hydrodynamic and elastohydrodynamic films can separate surfaces and greatly reduce wear, whereas boundary and mixed regimes require appropriate materials and additives. Lubricant viscosity, compatibility, cleanliness, and quantity are central design variables. Seals retain lubricant and exclude contaminants, while alignment, fits, installation, and thermal expansion determine whether the bearing can perform as intended. Frictional heat must be dissipated, and maintenance should use correct relubrication, cleanliness, vibration and temperature trends, and documented procedures. Effective bearing design is therefore a system-level engineering activity rather than a catalogue-rating exercise.

Key Terms

Bearing: A machine element that supports load while permitting relative motion.

Rolling-contact bearing: A bearing using balls or rollers between raceways.

Sliding bearing: A bearing in which surfaces slide relative to one another.

Journal: The rotating cylindrical surface supported by a plain bearing.

Dynamic load rating: Catalogue load associated with a specified rolling-fatigue life.

Static load rating: Load rating associated with a specified permanent contact deformation.

Equivalent dynamic load: A single load used to represent combined radial and axial loading.

Basic rating life: Statistical life reached or exceeded by 90% of identical bearings.

Preload: Intentional internal bearing force that removes clearance.

Internal clearance: Free internal movement before mounting and operation.

Tribology: Study of friction, lubrication, and wear.

Boundary lubrication: Regime in which surface films and asperities carry substantial load.

Hydrodynamic lubrication: Full-film lubrication generated by relative motion and fluid viscosity.

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

Viscosity: Resistance of a fluid to shear flow.

Wear: Progressive material loss or damage caused by interacting surfaces.

Seal: Device that retains lubricant and excludes contaminants.

Fretting: Damage caused by small-amplitude oscillatory motion.

Thermal balance: Equality between heat generated and heat dissipated.

Condition monitoring: Measurement-based assessment of equipment health.

Review Questions

Short Answer Questions

1. What is the difference between a rolling-contact bearing and a sliding bearing?
2. Define basic rating life L₁₀.
3. Why can excessive grease cause bearing overheating?
4. Name three important lubrication regimes.
5. What is the purpose of a floating bearing arrangement?

Long Answer Questions

1. Explain the procedure for selecting a rolling-contact bearing for combined radial and axial loading.
2. Compare hydrodynamic, boundary, mixed, and elastohydrodynamic lubrication.
3. Discuss the influence of seals and contamination on bearing reliability.
4. Explain how preload, internal clearance, fits, and thermal expansion interact.
5. Describe a complete bearing maintenance and condition-monitoring program.

Analytical / Application Questions

1. A ball bearing carries a constant equivalent load of 5 kN and has a dynamic rating of 25 kN. Calculate its basic rating life in millions of revolutions and comment on the assumptions.
2. A plain bearing carries 12 kN on a 60 mm diameter journal that is 60 mm long. Calculate its projected average pressure and identify additional data needed before final design approval.
3. A bearing shows rising temperature immediately after relubrication and increasing high-frequency vibration in a dusty environment. Diagnose the likely causes and propose a staged engineering response.

Multiple Choice Questions with Answers

Question 1

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

A. 1

B. 2

C. 3

D. 10/3

Correct Answer: C. 3

Question 2

If a bearing has C = 12 kN and P = 4 kN, its basic life in millions of revolutions, assuming a ball bearing, is:

A. 3

B. 9

C. 27

D. 64

Correct Answer: C. 27

Question 3

Which lubrication regime relies mainly on a pressure-generating fluid wedge produced by relative motion?

A. Boundary lubrication

B. Hydrodynamic lubrication

C. Dry friction

D. Solid-film lubrication

Correct Answer: B. Hydrodynamic lubrication

Question 4

What is the principal purpose of a floating bearing in a two-bearing shaft system?

A. To increase electrical conductivity

B. To prevent all radial motion

C. To permit axial thermal expansion

D. To eliminate the need for lubrication

Correct Answer: C. To permit axial thermal expansion

Question 5

In the relation P = X F_r + Y F_a, X and Y are:

A. Material hardness values

B. Manufacturer-supplied load factors

C. Thermal resistance factors

D. Seal friction coefficients

Correct Answer: B. Manufacturer-supplied load factors

Question 6

Which condition most directly increases the risk of abrasive bearing damage?

A. Clean, filtered lubricant

B. Controlled preload

C. Entry of hard contaminant particles

D. Correct shaft alignment

Correct Answer: C. Entry of hard contaminant particles

Question 7

The approximate frictional power relation P_f = M_f ω requires M_f to be expressed in:

A. N·m

B. kPa

C. mm²/s

D. kg/m³

Correct Answer: A. N·m

Question 8

Which installation practice is correct for an interference fit on a bearing inner ring?

A. Apply force through the rolling elements

B. Apply force to the ring being fitted

C. Strike the seal to seat the ring

D. Heat locally with an open flame

Correct Answer: B. Apply force to the ring being fitted

Question 9

For a plain bearing with load W, length L, and diameter d, the projected average pressure is:

A. W/(L d)

B. W L d

C. L d/W

D. W/(π L d)

Correct Answer: A. W/(L d)

Question 10

A rising temperature immediately after adding grease most plausibly suggests:

A. Guaranteed increase in bearing life

B. Possible over-greasing or lubricant incompatibility

C. Zero friction in the bearing

D. A reduction in lubricant churning

Correct Answer: B. Possible over-greasing or lubricant incompatibility