Bearings, Lubrication and Sealing Systems

Introduction

Bearings support shafts, constrain motion, transmit forces, and reduce friction between moving members. Their reliability directly affects efficiency, noise, temperature, dimensional accuracy, maintenance cost, and safety. A bearing is not selected merely by matching shaft diameter: the designer must consider radial and axial loads, speed, duty cycle, life, stiffness, misalignment, temperature, lubrication, contamination, installation, and sealing.

This chapter develops a practical design method for rolling-element and journal bearings. It also explains friction and heat generation, lubrication regimes, lubricant selection, seals, contamination control, monitoring, and failure analysis. The objective is not only to calculate a bearing rating, but to design a dependable bearing system.

Learning objectives

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

• distinguish rolling-element and journal bearings and select suitable types;
• resolve combined radial and axial loads into bearing-equivalent loads;
• calculate basic rating life and estimate reliability effects;
• evaluate speed, lubrication, temperature, stiffness, and static-load requirements;
• explain boundary, mixed, and hydrodynamic lubrication;
• estimate frictional power and heat generation;
• design practical lubrication, sealing, and contamination-control arrangements;
• diagnose common bearing failures and recommend corrective action.

1. Bearing functions and selection philosophy

A bearing performs four related functions:

1. It supports a rotating or oscillating shaft.
2. It locates the shaft radially and, where required, axially.
3. It permits relative motion with acceptable friction and wear.
4. It transfers forces into the housing while maintaining alignment.

The bearing system includes the bearing, shaft, housing, fits, lubricant, seals, cooling provisions, and maintenance practice. Failure of any one of these elements can produce the appearance of a “bearing failure.” For example, a bearing may be correctly sized for fatigue life yet fail early because water entered through an unsuitable seal.

Selection normally proceeds in this order:

• define loads, speed, motion, environment, and required life;
• choose a bearing family and arrangement;
• calculate dynamic and static loading;
• check life, speed, stiffness, and temperature;
• specify lubricant, seals, fits, and contamination controls;
• verify installation and condition-monitoring requirements.

2. Principal bearing types

2.1 Rolling-element bearings

Rolling-element bearings use balls or rollers between inner and outer raceways. Balls have low friction and are suitable for high speed and moderate loads. Rollers provide greater contact area and load capacity but generally have higher friction and lower speed capability.

A locating–non-locating arrangement is common. The locating bearing fixes the shaft axially; the non-locating bearing permits thermal expansion. If both bearings locate the shaft rigidly without allowance for expansion, thermal preload may cause overheating.

2.2 Journal bearings

A journal bearing supports a shaft on a continuous sliding surface, commonly made from bronze, babbitt, polymer, or a composite material. In a hydrodynamic bearing, shaft rotation drags lubricant into a converging wedge, producing pressure that separates the surfaces. At sufficiently high speed and suitable clearance, metal-to-metal contact is avoided.

Journal bearings offer high damping, low noise, excellent shock-load capability, and potentially long life. They require an adequate starting lubricant film and correct clearance. At start-up and shutdown, the film may collapse, so boundary lubrication or a solid/low-friction lining may be necessary.

3. Loads, bearing arrangements, and basic terminology

The principal loads are radial load F_r, axial or thrust load F_a, and sometimes overturning moment. Static load acts without significant relative motion; dynamic load occurs while the bearing rotates and causes rolling-contact fatigue.

Important terms include:

• Basic dynamic load rating, C: constant load that gives a basic rating life of 1 million revolutions for a group of apparently identical bearings under standard conditions.
• Basic static load rating, C₀: load producing a specified permanent deformation at the most heavily loaded contact.
• Rating life, L₁₀: life that 90% of an apparently identical group is expected to attain or exceed under stated conditions.
• Equivalent dynamic load, P: a calculated constant load producing the same life as the actual combined loading.
• Internal clearance: difference between ring and rolling-element dimensions before mounting; it changes with fits and temperature.
• Preload: intentional application of internal force to reduce clearance and increase stiffness.

The bearing arrangement must also account for shaft bending, housing rigidity, thermal expansion, assembly access, and the direction of axial loads. A pair of angular-contact or tapered bearings may be arranged back-to-back, face-to-face, or in tandem. Back-to-back arrangements generally provide greater moment stiffness; face-to-face arrangements tolerate some misalignment better.

4. Rolling-element bearing life calculations

4.1 Basic rating life

For a constant equivalent dynamic load and constant speed, the basic rating life in millions of revolutions is:

where L₁₀ is in million revolutions, C is the basic dynamic load rating, P is the equivalent dynamic bearing load, and p is 3 for ball bearings and 10/3 for roller bearings. The formula assumes appropriate lubrication, cleanliness, alignment, mounting, and a load that is reasonably constant. It describes rolling-contact fatigue, not every possible failure mode.

For speed n in revolutions per minute, life in hours is:

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

4.2 Equivalent dynamic load

For many single-row radial bearings under combined loading:

Here X and Y are manufacturer-supplied factors determined by bearing geometry and the ratio of axial to radial load; F_r and F_a are radial and axial loads. This expression is not universal: thrust bearings, oscillating bearings, variable loads, and special bearing arrangements require the manufacturer’s method.

For variable operating conditions, divide the duty into intervals. If P_i acts for a fraction q_i of the total revolutions, an approximate equivalent load is:

This relationship applies when the load exponent and operating conditions are suitable for the bearing and when loads can be represented by discrete duty segments.

4.3 Reliability and modified life

The L₁₀ value is a statistical reference, not a guarantee that 10% of bearings will fail exactly at that life. Reliability-adjusted or modified-life calculations may include reliability, lubrication, contamination, material quality, and stress effects. The exact factors depend on the bearing standard and manufacturer. Designers should therefore use current catalogue methods rather than applying undocumented correction factors.

Worked example 1: dynamic life

A deep-groove ball bearing carries F_r = 2.0\ kN and F_a = 0.6\ kN. Catalogue factors for the selected bearing are X = 0.56 and Y = 1.6. Its dynamic rating is C = 18\ kN, and speed is n = 1200\ rpm. Calculate the basic rating life.

First,

P = 0.56(2.0) + 1.6(0.6) = 2.08\ kN.

For a ball bearing, p = 3. Therefore,

L₁₀ = (18/2.08)³ = 648.\ million\ revolutions\ (approximately).

In hours,

L_10h = (10⁶ × 648)/(60 × 1200) ≈ 9000\ h.

This is a basic fatigue life. It does not prove that the bearing will operate for 9000 hours if lubrication, sealing, alignment, or installation is poor.

4.4 Static load and safety

When a bearing is stationary, oscillating, shock-loaded, or rotating very slowly, permanent deformation may govern. A simplified static safety factor is:

where s₀ is the static safety factor, C₀ is the basic static load rating, and P₀ is the equivalent static load. P₀ is calculated using the bearing manufacturer’s static-load factors for radial and axial components. The acceptable value depends on noise, vibration, shock, precision, and consequences of deformation; it is not a universal constant.

5. Journal-bearing theory and design considerations

For a plain cylindrical journal bearing, the diametral clearance is the difference between bearing diameter and journal diameter. The radial clearance is half the diametral clearance. Excessive clearance reduces load capacity and increases vibration; insufficient clearance risks seizure when the shaft and bearing expand.

Useful first-order quantities include projected bearing pressure and surface speed:

where W is radial load in newtons, L is bearing length in metres, d is journal diameter in metres, p_b is projected pressure in pascals, v is surface speed in metres per second, and n is speed in revolutions per minute. These are screening quantities, not complete hydrodynamic design equations.

The viscosity ratio and bearing geometry determine whether a full lubricant film develops. A central concept is the minimum film thickness relative to the combined surface roughness. This is commonly expressed through the specific film thickness:

where h_min is minimum film thickness and σ_c is the composite root-mean-square roughness of the two surfaces. Large λ indicates stronger separation; small values indicate mixed or boundary contact. Exact interpretation depends on surface texture, material, additives, and operating conditions.

Hydrodynamic analysis normally uses Reynolds’ equation with assumptions such as Newtonian lubricant behaviour, an isoviscous or specified-viscosity model, smooth surfaces, and known geometry. Real bearings may require thermal, cavitation, turbulence, and misalignment corrections. Consequently, detailed journal-bearing design commonly uses validated software, test data, or established design charts.

6. Friction, power loss, and heat generation

Bearing friction arises from rolling and sliding contact, lubricant shear, seals, cage motion, and churning. A useful engineering estimate is:

where M_f is friction torque in newton-metres, μ_b is an effective friction coefficient, P is bearing load in newtons, and d_m is mean bearing diameter in metres. The coefficient is not a material constant; it varies with bearing type, load, speed, lubricant, temperature, seals, and operating condition. Manufacturer friction-torque data are preferred.

Frictional power is:

where P_f is watts, ω is angular speed in radians per second, and n is revolutions per minute. At steady temperature, heat generated must be removed by conduction, convection, lubricant flow, or a cooling system. If heat removal is inadequate, viscosity falls, the film weakens, and the bearing may enter a thermal runaway condition.

Seal friction can be significant at high speed. Grease churning may dominate at excessive fill levels. Thus, reducing lubricant quantity does not always reduce risk: insufficient lubricant causes wear, while excessive grease raises temperature.

7. Lubrication systems

7.1 Lubrication regimes

• Boundary lubrication: surfaces are separated mainly by adsorbed or chemically reacted films; asperity contact is substantial. It occurs at start-up, low speed, high load, or inadequate viscosity.
• Mixed lubrication: both asperity contact and fluid-film support carry load.
• Hydrodynamic lubrication: motion and lubricant viscosity generate pressure that separates surfaces.
• Elastohydrodynamic lubrication: elastic deformation of rolling contacts and pressure-dependent viscosity create a load-bearing film; it is central to rolling-element bearing contacts.

The lubricant must provide separation, remove heat, resist oxidation, protect against corrosion, and remain compatible with seals and materials.

7.2 Oil and grease

Oil is preferred for high speed, high temperature, heat removal, oil circulation, and gearbox integration. Grease is preferred where simple retention, low leakage, and long relubrication intervals are important. Grease consists of base oil, thickener, and additives; the thickener is not a measure of base-oil viscosity.

Important oil-selection variables are viscosity at operating temperature, viscosity index, oxidation stability, additives, compatibility, and cleanliness. Important grease variables are base oil, thickener type, consistency grade, operating temperature range, water resistance, mechanical stability, and compatibility with the existing grease.

Never mix greases solely because their consistency grades match. Thickener incompatibility can cause softening, hardening, oil separation, or loss of lubrication. When compatibility is uncertain, remove the old grease and follow the lubricant supplier’s guidance.

7.3 Lubrication methods

Common methods include grease pack, periodic grease replenishment, oil bath, oil ring, splash lubrication, circulating oil, oil mist, and air–oil systems. Selection depends on speed, heat, contamination, accessibility, environmental restrictions, and required reliability.

A good relubrication program specifies quantity, interval, lubricant identity, application point, purge route, and safe procedure. Over-greasing is a frequent cause of temperature rise. Automatic lubricators improve consistency but must be correctly sized and protected from pressure buildup.

8. Sealing and contamination control

A seal retains lubricant and excludes water, dust, chemical vapour, and process debris. Common arrangements include non-contact labyrinth seals, contact lip seals, shields, bearing-integrated seals, V-rings, mechanical seals, and exclusion flingers.

Non-contact labyrinth seals have low friction and good high-speed capability but may admit liquid under immersion or pressure washing. Contact seals exclude contaminants more effectively but generate heat and wear. A multi-stage arrangement may use a flinger, labyrinth, and internal bearing seal.

Seal design should consider shaft surface finish, shaft runout, lip speed, pressure differential, temperature, chemical compatibility, and installation damage. A drain or purge path is often essential; a seal that traps water or excess grease can still fail.

Contamination is frequently more damaging than nominal overload. Hard particles create indentations that produce stress concentrations and early fatigue. Water reduces lubricant film strength, promotes corrosion, and can cause hydrogen-related damage in susceptible materials. Best practices include:

• clean assembly areas and lint-free handling;
• capped, labelled lubricant containers;
• filtered oil and clean transfer equipment;
• protected breathers, preferably desiccant breathers where moisture is severe;
• magnetic or fine filtration where appropriate;
• shaft flingers and correctly oriented seals;
• contamination monitoring and scheduled lubricant analysis.

9. Fits, mounting, and installation

A ring subjected to a rotating load relative to its seat generally requires an interference fit to prevent creep. A stationary load ring may use a looser fit, subject to vibration and accuracy requirements. Excessive interference reduces internal clearance; insufficient interference permits fretting and raceway creep.

Mounting force must be applied through the ring being fitted. Pressing through rolling elements can damage raceways. Heating a bearing uniformly by an induction heater is often safer than flame heating. Do not exceed the manufacturer’s temperature limit, and never strike a bearing directly with a hard hammer.

Tapered-bore bearings use an adapter sleeve or withdrawal sleeve and require controlled tightening. The correct internal clearance reduction or axial drive-up must be verified according to the manufacturer’s instructions. Incorrect adjustment is a major cause of premature failure.

Shaft and housing shoulders must be square, seats must be clean and correctly sized, and locking devices must prevent axial movement. After installation, rotate the assembly by hand, check for abnormal resistance, confirm seals and lubricant, and record the bearing identification and mounting data.

10. Failure modes and condition monitoring

Condition monitoring may include temperature, vibration, acoustic emission, motor-current analysis, lubricant particle count, viscosity, water content, and ferrous-debris analysis. Trends are more informative than isolated readings. Monitoring should lead to an action threshold and a defined response, not merely data collection.

11. Illustrative case: conveyor head-pulley bearing system

Background. An enclosed conveyor operates continuously at 900 rpm in a dusty aggregate plant. Each pulley shaft is supported by two bearings. The existing open spherical roller bearings require frequent replacement.

Problem. Bearings fail after approximately four months, although a catalogue L₁₀ calculation predicts more than two years. Inspection finds dark grease, abrasive particles, and corrosion marks near the seal. One bearing also shows evidence of axial restraint at both housings.

Analysis. The life calculation considered radial load but not contamination. The two fixed housings prevented thermal expansion of the shaft. Grease was replenished with a high-pressure gun until visible leakage occurred, forcing contaminants through the seal. The existing contact seal was unsuitable for aggressive washdown.

Approach and solution. The redesigned arrangement uses one locating bearing and one non-locating bearing. The shaft and housing fits are checked to preserve operating clearance. A multi-stage flinger–labyrinth arrangement with an appropriate contact element is installed. Grease quantity and interval are calculated from the bearing supplier’s recommendations, with a purge path and automatic metering system. Grease is stored in sealed, labelled containers, and a desiccant breather is fitted where the housing design permits. Vibration and temperature trends are recorded monthly.

Outcome. In this illustrative case, the design change is expected to improve reliability because it addresses thermal expansion, contamination, lubrication quantity, and maintenance consistency rather than simply increasing bearing size. Verification requires field measurements and a defined operating trial.

Learning points. Catalogue fatigue life is conditional. The complete bearing system—including seals, fits, lubricant, housing, and maintenance—must be designed as one system. Increasing capacity without controlling contamination may produce little benefit.

12. Contemporary developments and professional practice

Modern bearing systems increasingly use ceramic rolling elements, advanced polymer cages, special coatings, electrically insulating designs, and improved synthetic lubricants. Hybrid ceramic bearings can reduce electrical-current damage and may offer lower friction, but they cost more and do not remove the need for correct lubrication and sealing.

Sensors embedded in bearing housings can measure temperature, vibration, speed, and load. Data-driven and AI-assisted maintenance can identify deviations from a learned baseline, but the output must be checked against physical evidence. Poor sensor placement, changing operating conditions, and biased failure data can produce false alarms. Safety-critical decisions require engineering judgement, traceable thresholds, and documented validation.

Designers should follow applicable bearing, lubricant, machinery-safety, environmental, and occupational-health standards. Used oil, contaminated grease, and cleaning chemicals require proper handling and disposal. A reliable design also considers worker exposure during relubrication, guarding of rotating parts, lockout procedures, and safe access.

Chapter Summary

Bearings must be selected as complete mechanical systems rather than isolated catalogue components. Rolling-element bearings are commonly sized using equivalent dynamic load and the basic rating-life relationship L₁₀ = (C/P)^p, while static safety, speed, clearance, stiffness, and temperature require separate checks. Ball and roller bearings have different life exponents and load capabilities. Journal bearings rely on sliding surfaces and, under suitable conditions, a hydrodynamic or elastohydrodynamic lubricant film.

Friction produces heat through rolling, sliding, lubricant shear, churning, and seal contact. Lubricant choice and quantity must match load, speed, temperature, and environment. Seals retain lubricant and exclude contaminants, but contact seals add friction and non-contact seals may provide weaker exclusion. Clean assembly, correct fits, controlled mounting, suitable breathers, filtration, and condition monitoring are central to dependable operation. Finally, bearing reliability depends on the interaction of design, manufacture, installation, lubrication, sealing, and maintenance.

Key Terms

Bearing: Machine element that supports and guides relative motion.

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

Journal bearing: Sliding bearing supporting a shaft on a lubricated surface.

Basic dynamic load rating, C: Reference load associated with a 1-million-revolution rating life.

Basic static load rating, C₀: Rating related to permanent deformation under stationary or slow loading.

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

Equivalent dynamic load, P: Constant calculated load representing a combined actual load.

Static safety factor: Ratio of static load rating to equivalent static load.

Internal clearance: Pre-mounting dimensional freedom between bearing components.

Preload: Intentional internal bearing force that removes clearance.

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

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

Boundary lubrication: Regime in which surface films carry load with substantial asperity interaction.

Viscosity: Resistance of a fluid to shear flow.

Fretting: Surface damage caused by small-amplitude relative motion.

Labyrinth seal: Non-contact seal using a tortuous path to restrict contaminant entry.

Contact seal: Seal whose lip or surface physically contacts a rotating member.

Contamination control: Measures that prevent harmful particles, water, and chemicals from entering a bearing system.

Locating bearing: Bearing that fixes shaft axial position.

Non-locating bearing: Bearing that permits axial displacement, often for thermal expansion.

Review Questions

Short Answer Questions

1. What is the difference between basic dynamic load rating and basic static load rating?
2. Why is a locating–non-locating bearing arrangement used?
3. State the three principal lubrication regimes discussed in this chapter.
4. Why can excessive grease cause bearing overheating?
5. What is the purpose of a labyrinth seal?

Long Answer Questions

1. Explain the procedure for selecting a rolling-element bearing from load, speed, life, and environmental requirements.
2. Compare rolling-element and journal bearings in terms of load capacity, friction, damping, lubrication, and failure modes.
3. Derive the conversion from rating life in million revolutions to rating life in hours.
4. Discuss how fits, internal clearance, mounting, and thermal expansion influence bearing reliability.
5. Explain how lubricant selection, sealing, filtration, and maintenance form an integrated contamination-control strategy.

Analytical / Application Questions

1. A ball bearing has C = 24\ kN, P = 3\ kN, and operates at 1500 rpm. Calculate its basic L₁₀ life in revolutions and hours, then state two reasons why the actual service life may be shorter.
2. A conveyor bearing repeatedly overheats after grease replenishment. Develop a diagnostic sequence covering lubricant quantity, seal friction, speed, load, clearance, and heat removal.
3. Design a preliminary bearing and sealing arrangement for a shaft exposed to water, abrasive dust, variable radial load, and thermal expansion. Justify the bearing arrangement, seal type, lubricant method, and monitoring plan.

Multiple Choice Questions with Answers

Question 1

For a ball bearing, what value of p is normally used in the basic rating-life equation L₁₀ = (C/P)^p?

A. 1

B. 3

C. 10/3

D. 5

Correct Answer: B. 3

Question 2

A bearing has C = 12 kN and P = 3 kN. For a ball bearing, its basic life is:

A. 4 million revolutions

B. 16 million revolutions

C. 64 million revolutions

D. 144 million revolutions

Correct Answer: C. 64 million revolutions

Question 3

Which bearing arrangement primarily permits shaft thermal expansion?

A. Two rigidly fixed locating bearings

B. Two thrust bearings facing the same direction

C. One locating and one non-locating bearing

D. A bearing with zero internal clearance

Correct Answer: C. One locating and one non-locating bearing

Question 4

Which lubrication regime involves substantial asperity contact while also having some fluid-film support?

A. Hydrodynamic

B. Mixed

C. Full-film only

D. Vacuum lubrication

Correct Answer: B. Mixed

Question 5

What is a principal disadvantage of a contact lip seal compared with a non-contact labyrinth seal?

A. It cannot retain any lubricant

B. It always permits water entry

C. It generates friction and wear

D. It cannot operate at low speed

Correct Answer: C. It generates friction and wear

Question 6

For a roller bearing, the basic rating-life exponent p is normally:

A. 1

B. 2

C. 3

D. 10/3

Correct Answer: D. 10/3

Question 7

Which condition most directly promotes fretting corrosion at a bearing ring seat?

A. Correct interference fit

B. Ring creep caused by an inadequate fit

C. Clean filtered oil

D. Adequate thermal expansion allowance

Correct Answer: B. Ring creep caused by an inadequate fit

Question 8

If friction torque is 2 N·m and speed is 3000 rpm, approximate frictional power is:

A. 314 W

B. 628 W

C. 942 W

D. 1885 W

Correct Answer: B. 628 W

Question 9

Which practice is most likely to reduce abrasive contamination during relubrication?

A. Mixing unlabelled greases

B. Using open lubricant containers

C. Using clean, capped, labelled lubricant equipment

D. Forcing grease until seals rupture

Correct Answer: C. Using clean, capped, labelled lubricant equipment

Question 10

What is the main purpose of a non-locating bearing in a thermally expanding shaft system?

A. To eliminate all radial load

B. To permit controlled axial displacement

C. To increase lubricant viscosity

D. To prevent every form of misalignment

Correct Answer: B. To permit controlled axial displacement