Bearings, Lubrication and Sealing Systems

Introduction

Bearings support rotating or oscillating shafts while transmitting loads and controlling friction, wear, heat generation, and positional accuracy. A bearing system is not merely a catalogue component: its performance depends on load magnitude and direction, speed, stiffness, lubrication, fits, clearances, contamination control, sealing, installation, and maintenance.

Rolling-element bearings use balls or rollers between raceways. Sliding bearings, also called plain bearings, support motion through relative sliding between a journal and a bearing surface, usually separated by a lubricant film. Both types can provide long service life when correctly selected, but either can fail rapidly when subjected to incorrect loading, inadequate lubrication, contamination, misalignment, or excessive temperature.

This chapter develops a systematic method for selecting and sizing bearings and associated lubrication and sealing systems.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Explain the operating principles and applications of rolling-element and sliding bearings.
2. Select bearing types according to load, speed, stiffness, misalignment, and environmental requirements.
3. Calculate equivalent dynamic load, rating life, static safety, and reliability effects for rolling bearings.
4. Explain hydrodynamic, hydrostatic, boundary, and mixed lubrication regimes.
5. Estimate frictional power loss and assess thermal operating limits.
6. Specify shaft and housing fits, internal clearances, seals, and lubrication methods.
7. Develop practical installation, condition-monitoring, and maintenance procedures.
8. Evaluate a complete bearing arrangement in an applied design case.

1. Bearing Functions and Design Requirements

A bearing performs several functions simultaneously:

• supports radial, axial, or combined loads;
• permits rotation or oscillation with acceptable friction;
• locates a shaft axially or allows controlled axial displacement;
• maintains geometric accuracy and stiffness;
• transfers heat from the contact region;
• excludes contaminants and retains lubricant.

The principal design inputs are radial load, axial load, speed, required life, operating temperature, shaft and housing geometry, shock or vibration, misalignment, contamination, available space, maintenance policy, and cost.

Bearing selection should begin with a load and duty description rather than with a preferred product. A bearing that is satisfactory in a clean, lightly loaded electric motor may be unsuitable in a dusty conveyor, a high-temperature furnace, or a slow oscillating joint.

Important terminology

The inner ring normally rotates with the shaft, while the outer ring is mounted in the housing. Rolling elements are balls or rollers. A cage separates rolling elements and guides them. Raceways are the contact tracks on rings. In a sliding bearing, the rotating member is the journal, and the stationary bearing surface is the bush or bearing shell. Bearing clearance is the space permitting relative movement before thermal and elastic effects are considered.

2. Rolling-Element Bearings

2.1 Types and load capability

Deep-groove ball bearings carry radial load and moderate axial load in both directions. Angular-contact ball bearings carry combined radial and axial loads; their contact angle strongly affects axial capacity. Cylindrical roller bearings provide high radial capacity and stiffness, while some designs permit axial displacement. Tapered roller bearings carry combined loads and generate a substantial axial reaction. Spherical roller bearings tolerate misalignment and carry high radial loads. Thrust ball and thrust roller bearings are primarily intended for axial loads.

2.2 Dynamic load rating and rating life

The basic rating life, L₁₀, is the number of revolutions that 90% of an apparently identical group of bearings can complete or exceed before fatigue failure. It is a statistical rating, not a guaranteed individual life.

For a rolling bearing, the basic rating life in millions of revolutions is:

Here, C is the basic dynamic load rating, P is the equivalent dynamic bearing load, and p = 3 for ball bearings and p = 10/3 for roller bearings. C and P must use the same force unit. The relation assumes fatigue is the governing failure mode, the bearing is correctly manufactured and installed, and lubrication, contamination, and speed are within the conditions represented by the rating.

If the shaft rotates at n revolutions per minute, the life in hours is:

The factor 10⁶ converts millions of revolutions to revolutions, and 60 converts minutes to hours.

The equivalent dynamic load combines radial and axial components:

Fᵣ is radial load, Fₐ is axial load, and X and Y are bearing-specific factors obtained from the manufacturer’s catalogue. For a purely radial load in a suitable radial bearing, P may equal Fᵣ. The factors cannot be assumed universally because they depend on bearing type, internal geometry, contact angle, and the ratio Fₐ/Fᵣ.

Worked example: dynamic life

A deep-groove ball bearing has C = 30 kN and carries a radial load of 2.5 kN at 1,200 r/min. Assume axial load is negligible, so P = 2.5 kN and p = 3.

Therefore,

This is the calculated 90% rating life under the stated assumptions. It does not imply that every bearing will last 24,000 hours, because contamination, mounting errors, lubrication failure, and other non-fatigue mechanisms may dominate.

2.3 Reliability and modified life

L₁₀ corresponds to 90% reliability. Higher reliability requires a reliability adjustment factor. A generalized life expression may be written as:

where L_na is the adjusted life at reliability level corresponding to a₁, a₂ represents material or manufacturing effects where applicable, and a₃ represents lubrication and contamination effects. Modern standards and manufacturers may combine these effects differently; therefore, catalogue procedures should be followed rather than applying an arbitrary factor.

The essential engineering lesson is that nominal dynamic capacity alone does not guarantee service life. Clean lubricant, correct viscosity, adequate film thickness, and controlled contamination can increase practical life substantially, whereas abrasive particles can reduce it severely.

2.4 Static load rating and permanent deformation

When a stationary or slowly rotating bearing experiences a high load, local contact stress may cause permanent indentation. The basic static load rating, C₀, is used to calculate a static safety factor:

P₀ is the equivalent static load, calculated using catalogue factors for radial and axial loading. The required value of s₀ depends on shock, vibration, rotational smoothness, and application precision. A higher value is appropriate for impact-loaded or precision applications. Static safety is distinct from fatigue life: a bearing can have adequate L₁₀ life but insufficient static capacity.

2.5 Preload, clearance, and stiffness

Bearing internal clearance is the total relative movement possible between rings before mounting. Radial clearance is commonly designated by a clearance class. When a ring is pressed onto a shaft, elastic expansion of the inner ring consumes part of the clearance. Temperature differences can consume additional clearance because the inner and outer rings may expand by different amounts.

Too little clearance can cause high friction, overheating, and seizure. Too much clearance causes vibration, reduced stiffness, poor load distribution, and possible skidding. Preload intentionally applies an internal axial or radial force to reduce clearance and increase stiffness, but it increases friction and heat. Preload is therefore used selectively in machine-tool spindles, precision gearboxes, and high-stiffness arrangements.

3. Sliding Bearings

Sliding bearings are often preferred for high loads, shock loads, oscillating motion, low noise, large diameters, or applications where a replaceable bush is economical. Common materials include bronze, babbitt, sintered metals, polymer composites, and engineered plastics.

3.1 Hydrodynamic lubrication

In a hydrodynamic bearing, shaft rotation drags lubricant into a converging wedge. Pressure generated within the lubricant film supports the load, so the surfaces are substantially separated during normal operation. This regime provides low wear but requires adequate speed, lubricant viscosity, correct clearance, and a suitable geometry.

The Sommerfeld number is a useful dimensionless parameter for journal-bearing analysis:

μ is dynamic viscosity, N is rotational speed in revolutions per second, P is average bearing pressure, r is journal radius, and c is radial clearance. The exact form varies with convention and bearing geometry. The parameter is used with appropriate journal-bearing charts or numerical solutions; it is not, by itself, a complete life equation.

Average bearing pressure is:

where W is radial load, L is bearing length, and D is journal diameter. For a journal bearing, the projected area is conventionally LD, not the curved surface area.

The bearing characteristic number often used in design is the product PV:

where v is sliding velocity. PV is useful for screening material and lubrication limits, but manufacturer limits must be respected because allowable PV depends on temperature, lubricant, surface finish, load duration, and motion type.

3.2 Boundary and mixed lubrication

During start-up, shutdown, low-speed operation, overload, or inadequate viscosity, the lubricant film may not fully separate the surfaces. In boundary lubrication, molecular films and additives carry much of the load. Mixed lubrication combines partial fluid-film support with asperity contact. Wear and friction are higher than in full-film lubrication, and additive chemistry becomes important.

Hydrostatic bearings differ from hydrodynamic bearings because an external pump supplies pressurized lubricant. They can support loads at zero speed and provide very low friction, but they require pumps, restrictors, filtration, and control of leakage.

4. Lubrication Selection and Friction

The lubricant must form a load-carrying film, remove heat, protect surfaces from corrosion, remain chemically stable, and avoid damaging seals or cage materials. Selection depends on viscosity, operating temperature, speed, load, water exposure, contamination, compatibility, and relubrication method.

4.1 Grease and oil

Grease is a semisolid lubricant consisting of base oil, thickener, and additives. It is retained more easily, often provides sealing assistance, and suits moderate speeds and routine maintenance. Excess grease can increase churning and temperature.

Oil is preferable for high speeds, high temperatures, accurate heat removal, and systems requiring continuous filtration or circulation. Oil may be supplied by bath, splash, oil mist, drip, jet, or circulating systems. Oil systems demand effective seals and contamination control.

Grease consistency is commonly classified using an NLGI grade, but consistency is not the same as viscosity. Grease compatibility must be checked before mixing products with different base oils, thickeners, or additive packages.

4.2 Friction and power loss

Bearing friction can be represented approximately by a friction torque M. The power loss is:

where ω is angular speed in radians per second. If speed is n revolutions per minute:

Thus, if a bearing has friction torque 0.18 N·m at 1,500 r/min,

This estimate assumes the stated torque represents total operating friction torque. In practice, torque varies with load, speed, lubricant quantity, temperature, seals, and preload. The heat generated must be dissipated through the shaft, housing, lubricant, and surrounding air.

4.3 Temperature and thermal balance

A bearing reaches a steady operating temperature when heat generation approximately equals heat removal. Excess temperature reduces lubricant viscosity, accelerates oxidation, damages seals, and can eliminate internal clearance. Thermal analysis should consider frictional power, ambient temperature, housing conduction, cooling airflow, lubricant circulation, and transient start-up behavior.

A practical design process is to calculate or estimate frictional power, identify the worst operating speed and load, estimate heat rejection, and verify the result using manufacturer speed ratings and a prototype temperature test. A rising temperature trend is often more informative than a single temperature value.

5. Fits, Clearances, and Mounting

A rotating ring generally requires an interference fit relative to the component against which it rotates. For example, a bearing inner ring rotating with a loaded shaft commonly uses a shaft interference fit to prevent creep. A stationary outer ring may use a clearance fit if the load direction is fixed relative to the housing. If the load rotates relative to the outer ring, an interference fit may also be needed.

Fit selection must account for load, ring rotation, temperature difference, shaft and housing material, wall thickness, assembly method, and required accuracy. Excessive interference can reduce internal clearance and damage the bearing during mounting. Insufficient interference permits fretting and circumferential wear known as creep.

The bearing should be mounted by applying force only to the ring being fitted. Force transmitted through rolling elements can brinell the raceways. Induction heating is suitable for many large bearings, provided temperature limits and cleanliness are controlled. Open flames and uncontrolled heating are unacceptable.

Shaft shoulders, housing shoulders, fillets, chamfers, and abutment dimensions must conform to catalogue requirements. Misaligned shoulders or an incorrect fillet radius can prevent proper seating and introduce distortion.

6. Sealing Systems

Seals retain lubricant and exclude contaminants. Common arrangements include:

• Shielded bearings, which reduce entry of large particles but provide limited contact sealing;
• Contact seals, which provide better contamination exclusion but add friction and heat;
• Labyrinth seals, which provide non-contact sealing and low friction, particularly at high speed;
• V-ring and lip seals, which are effective for rotating shafts when correctly installed;
• Mechanical face seals, used in demanding leakage-control applications;
• Gaskets and O-rings, used for static or limited-motion interfaces.

Seal choice is governed by speed, pressure, temperature, lubricant, shaft finish, runout, contamination, and allowable leakage. A seal can fail through wear, hardening, chemical attack, thermal damage, incorrect installation, or shaft groove formation.

No seal is perfect. The design must distinguish between exclusion, retention, and controlled leakage. Labyrinths are durable and low-friction but may require a grease cavity or multiple stages in severe contamination. Contact seals provide stronger exclusion but consume power and may limit speed.

7. Bearing Arrangements and System Design

A shaft commonly uses a locating bearing and a floating bearing. The locating bearing controls axial position in both directions. The floating bearing supports radial load but permits thermal axial expansion. Fixing both bearings axially can create harmful thermal preload unless the structure is specifically designed for it.

Tapered roller and angular-contact arrangements require attention to contact angle, adjustment, thermal expansion, and preload. Back-to-back arrangements provide high moment stiffness; face-to-face arrangements tolerate some misalignment more readily. The arrangement must match the direction and variation of axial load.

Design should also address electrical currents. In variable-frequency motor drives, shaft currents can damage raceways through electrical discharge machining. Insulated bearings, ceramic rolling elements, shaft grounding, and suitable cable and grounding practice may be required.

8. Maintenance and Condition Monitoring

Good maintenance begins with cleanliness. Bearings should remain in their original packaging until installation. Tools, hands, shafts, housings, and lubricants must be clean. Lubricant quantities should be measured rather than guessed.

Useful condition-monitoring methods include:

• temperature and temperature trend;
• vibration analysis, including envelope detection for rolling-element defects;
• acoustic or ultrasound monitoring;
• lubricant sampling for viscosity, particles, water, and wear debris;
• visual inspection of seals and lubricant condition;
• speed, load, and operating-history records.

A maintenance interval should be based on speed, temperature, load, contamination, lubricant type, and manufacturer guidance. Relubrication should occur before lubricant degradation causes surface distress, but over-lubrication must be avoided. When a bearing is replaced, the cause of failure should be investigated rather than simply replacing the component.

Typical failure patterns include fatigue spalling, adhesive smearing, false brinelling, true brinelling, corrosion, electrical fluting, fretting, overheating, cage damage, and seal failure. Each pattern provides evidence about the underlying mechanism.

9. Illustrative Case: Conveyor Drive Bearing System

Background

Consider a belt conveyor drive shaft rotating at 900 r/min. The design radial load on one deep-groove ball bearing is 3.0 kN, with negligible axial load. The required L₁₀ life is 20,000 h. The conveyor operates in a dusty mineral-processing environment with ambient temperatures from 10 °C to 40 °C.

Problem

Select the minimum basic dynamic load rating, specify an arrangement and sealing strategy, and identify maintenance controls.

Analysis

For a ball bearing, p = 3. Convert the required hours into millions of revolutions:

Substitution gives:

With P = 3.0 kN,

A catalogue bearing should therefore have C greater than approximately 30.7 kN. Selection should not stop at this value. The bearing must also satisfy static-load, speed, bore, dimensional, seal, and temperature requirements.

Approach and solution

A locating/floating arrangement is appropriate if the shaft and housing experience appreciable thermal expansion. The bearing on the rotating loaded shaft should have a suitable interference fit, while the floating location should permit controlled axial movement. Because the environment is dusty, contact seals or a bearing combined with external labyrinth seals should be considered. Grease should be selected for the expected temperature and load, and its compatibility with the seal material should be verified.

The housing should provide a protected grease cavity, and the shaft should have a suitable surface finish where a lip seal runs. Installation should use clean tools and force applied to the fitted ring. A temperature baseline and vibration baseline should be recorded after commissioning.

Outcome

The calculated rating requirement establishes a minimum dynamic capacity, but the final design is a system decision. Contamination protection and correct relubrication are likely to influence actual life more strongly than a modest increase in nominal C. A larger bearing may be justified if it improves static safety, seal availability, stiffness, or contamination tolerance.

Learning points

1. Convert the required operating hours into revolutions before using the rating-life equation.
2. Use catalogue factors when axial load is present.
3. Treat sealing and lubrication as part of bearing selection.
4. Provide for thermal expansion through a locating/floating arrangement.
5. Use monitoring data to validate design assumptions.

10. Design Limitations, Safety, and Contemporary Practice

Catalogue calculations are necessary but not sufficient. They often idealize load distribution, temperature, contamination, installation quality, and dynamic transients. Shock loads, vibration, misalignment, electrical current, lubricant starvation, and corrosion may dominate actual failure.

Designers should apply relevant standards and manufacturer instructions for bearing rating, dimensional tolerances, fits, lubricant specifications, and safety. Pressure-containing lubrication systems require appropriate guarding and relief provisions. Used lubricants and contaminated components should be handled according to environmental and occupational regulations.

Digital tools increasingly support bearing selection through finite-element analysis, multibody simulation, sensor networks, and machine-learning-based condition monitoring. These tools can identify trends and anomalies, but they do not replace sound failure analysis. AI-based alerts require representative data, controlled false-alarm rates, cybersecurity, and human verification. Engineers remain responsible for validating sensor quality, operating context, and safe intervention procedures.

Best-Practice Design Procedure

1. Define radial and axial loads, speed range, duty cycle, temperature, contamination, and required life.
2. Decide whether rolling or sliding support is more appropriate.
3. Select a bearing family based on load direction, stiffness, speed, misalignment, and space.
4. Calculate equivalent dynamic load and rating life.
5. Check static capacity, speed, clearance, preload, and thermal behavior.
6. Specify shaft and housing fits using load rotation and temperature effects.
7. Select lubricant quantity, viscosity, additives, and relubrication method.
8. Select seals for contamination, speed, temperature, pressure, and chemical compatibility.
9. Design locating/floating behavior and verify shaft and housing geometry.
10. Define installation, commissioning, monitoring, and failure-investigation procedures.

Chapter Summary

Bearings are integrated mechanical systems whose performance depends on load, speed, geometry, materials, lubrication, sealing, fits, clearance, temperature, and maintenance. Rolling-element bearing fatigue life is estimated using the equivalent dynamic load and the load-life relation, with p = 3 for ball bearings and p = 10/3 for roller bearings. Static capacity must be checked separately because permanent deformation can occur even when fatigue life is adequate.

Sliding bearings operate through surface contact and, under suitable conditions, hydrodynamic lubricant films. Boundary and mixed lubrication become important during start-up, shutdown, low speed, overload, and poor lubrication. Lubricant choice must consider viscosity, temperature, load, speed, compatibility, contamination, and heat removal.

Correct fits prevent ring creep but excessive interference can eliminate internal clearance. Locating and floating arrangements accommodate thermal expansion. Seals retain lubricant and exclude contaminants, but every seal involves trade-offs among friction, speed, leakage, and protection. Clean installation, measured lubrication, vibration and temperature monitoring, and systematic failure analysis are essential to achieving dependable service.

Key Terms

Bearing: A machine element that supports relative motion and transmits load.

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

Sliding bearing: A bearing in which surfaces slide relative to each other.

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

Basic dynamic load rating, C: Constant load associated with the rated fatigue life.

Equivalent dynamic load, P: Catalogue-equivalent constant load representing combined radial and axial loading.

L₁₀ life: Life reached or exceeded by 90% of an apparently identical bearing group.

Basic static load rating, C₀: Load associated with a specified permanent contact deformation.

Internal clearance: Movement available within an unmounted bearing.

Preload: Intentional internal bearing force used to reduce clearance and increase stiffness.

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

Boundary lubrication: Regime in which surface films and additives carry much of the load.

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

Viscosity: Resistance of a fluid to shear flow.

PV value: Product of bearing pressure and sliding velocity.

Locating bearing: Bearing that controls axial shaft position.

Floating bearing: Bearing arrangement that permits controlled axial displacement.

Creep: Relative circumferential movement between a fitted ring and its seat.

Labyrinth seal: Non-contact seal using tortuous passages to restrict contaminant entry and lubricant escape.

False brinelling: Surface damage caused by small oscillatory movements, often during vibration while stationary.

Review Questions

Short Answer Questions

1. What is the meaning of L₁₀ bearing life?
2. Why are fits required between a bearing ring and its shaft or housing?
3. Distinguish hydrodynamic lubrication from boundary lubrication.
4. What is the purpose of a floating bearing arrangement?
5. State two advantages and one limitation of grease lubrication.

Long Answer Questions

1. Explain the selection process for a rolling-element bearing carrying combined radial and axial loads.
2. Discuss how internal clearance, preload, temperature, and fits interact in a bearing system.
3. Compare rolling-element and sliding bearings for heavy-load, high-speed, and oscillating applications.
4. Explain the functions and selection criteria of contact, labyrinth, and mechanical seals.
5. Develop a maintenance strategy for bearings operating in a contaminated industrial environment.

Analytical / Application Questions

1. A ball bearing carries P = 4.0 kN at 1,000 r/min. If C = 32 kN, calculate L₁₀ in millions of revolutions and hours.
2. A bearing has friction torque 0.25 N·m and rotates at 1,800 r/min. Calculate its approximate frictional power loss and discuss two factors that could make the actual value different.
3. Design a locating/floating bearing arrangement for a shaft exposed to large temperature changes. Justify the fits, clearance, lubrication, sealing, and monitoring methods you would specify.

Multiple Choice Questions with Answers

Question 1

For a ball bearing, the basic rating-life exponent p in L₁₀ = (C/P)^p is:

A. 1

B. 2

C. 3

D. 10/3

Correct Answer: C. 3

Question 2

A bearing has C = 24 kN and P = 3 kN. For a ball bearing, its basic rating life is:

A. 8 million revolutions

B. 64 million revolutions

C. 512 million revolutions

D. 1,728 million revolutions

Correct Answer: C. 512 million revolutions

Question 3

Which bearing arrangement normally permits thermal axial expansion of a shaft?

A. Two axially fixed bearings

B. A locating bearing and a floating bearing

C. Two preloaded thrust bearings only

D. Two interference-fitted outer rings

Correct Answer: B. A locating bearing and a floating bearing

Question 4

Which lubrication regime generally provides the greatest surface separation?

A. Boundary lubrication

B. Mixed lubrication

C. Hydrodynamic lubrication

D. Dry friction

Correct Answer: C. Hydrodynamic lubrication

Question 5

The principal purpose of an interference fit on a rotating bearing ring is to prevent:

A. Lubricant oxidation

B. Ring creep on its seat

C. Hydrodynamic pressure

D. Axial thermal expansion

Correct Answer: B. Ring creep on its seat

Question 6

If friction torque is 0.20 N·m and speed is 1,200 r/min, the approximate frictional power loss is:

A. 2.5 W

B. 12.6 W

C. 25.1 W

D. 251 W

Correct Answer: C. 25.1 W

Question 7

Which seal generally has the lowest friction because it does not contact the shaft?

A. Labyrinth seal

B. Lip seal

C. V-ring seal

D. Mechanical face seal

Correct Answer: A. Labyrinth seal

Question 8

The static safety factor for a bearing is commonly expressed as:

A. s₀ = P₀/C₀

B. s₀ = C₀/P₀

C. s₀ = C/P

D. s₀ = P/C

Correct Answer: B. s₀ = C₀/P₀

Question 9

Applying mounting force through the rolling elements can cause:

A. Improved lubrication

B. Raceway indentation or brinelling

C. Reduced seal friction only

D. Automatic preload optimization

Correct Answer: B. Raceway indentation or brinelling

Question 10

For a plain journal bearing, projected average pressure is conventionally calculated using:

A. W/(πDL)

B. W/(LD)

C. W/(2πrL)

D. W/(D/L)

Correct Answer: B. W/(LD)