Volume 18 - Friction, Lubrication, and Wear Technology Part 13 ppsx

rolling bearings according to rolling-element type, such bearings are also identified according to the predominant loading they are designed to support for example, radial load or thrust

Fig 11 Empirical wear mechanism map for steel (pin-on-disk configuration)

References

1 N.P Suh, Tribophysics, Prentice-Hall, 1986, p 73

2 P.J Blau, Friction and Wear Transitions of Materials, Noyes Publications, 1989

3 H Czichos, Tribology A Systems Approach to the Lubrication and Wear, Elsevier, Amsterdam, 1978, p

195, 196

4 K.-H Zum Gahr, Microstructure and Wear of Materials, Elsevier, Amsterdam, 1987, p 379

5 N.C Welsh, The Dry Wear of Steels, Philos Trans R Soc (London) A, Vol 257, 1965, p 31-70

6 K.-H Habig, Wear and Hardness of Materials, Hanser-Verlag, München, 1980 (in German)

7 T.F.J Quinn, D.M Rowson, and J.L Sullivan, Applications of the Oxidational Theory of Mild Wear to the

Sliding Wear of Low Alloy Steel, Wear, Vol 65, 1980, p 1-20

8 M Woydt, D Klaffke, K.-H Habig, and H Czichos, Tribological Transition Phenomena of Ceramic

Materials, Wear, Vol 136, 1990, p 373-380

9 H Czichos, Influence of Adhesive and Abrasive Mechanisms on the Tribological Behaviour of

Thermoplastic Polymers, Wear, Vol 88, 1983, p 27-43

10 M Godet, Third Bodies in Tribology, Proceedings of EUROTRIB 1989, K Holmberg and I Nieminen, Ed.,

The Finnish Society for Tribology, ESPO, Vol 1, 1989, p 1-15

11 H Czichos and K Kirschke, Investigations into Film Failure (Transition Point) of Lubricated Concentrated

Contacts, Wears, Vol 22, 1972, p 321-336

12 C.M Lossie, J.W.M Mens, and A.W.J de Gee, Practical Applications of the IRG Transition Diagram

Technique, Wear, Vol 129, 1989, p 173-182

13 H Czichos, Failure Criteria in Thin Film Lubrication: The Concept of a Failure Surface, Tribol Intl., Vol 7,

1974, p 14-20

14 S.C Lim and M.F Ashby, Wear-Mechanism Maps, Acta Metall., Vol 35, 1987, p 1-24

15 S.C Lim, M.F Ashby, and J.H Bruton, Wear-Rate Transitions and their Relationship to Wear

Mechanisms, Acta Metall., Vol 35, 1987, p 1343-1348

Concepts of Reliability and Wear: Failure Modes

Horst Czichos, BAM (Germany)

Introduction

METHODS TO CHARACTERIZE THE RELIABILITY of mechanical equipment on the basis of measurements or estimations of wear are often tried in mechanical engineering applications (Ref 1) In this article, statistical techniques and probability concepts for the evaluation and presentation of wear and reliability data are briefly outlined More detailed

information on reliability analysis can be found in the references provided as well as Vol 17 of ASM Handbook (formerly 9th Edition Metals Handbook)

Acknowledgements

The author would like to thank his tribology colleagues at BAM, and in particular Karl-Heinz Habig and Erich Santner for their help in the preparation of this Section Special thanks are also due to BAM mathematicians Wolfgang Gerisch and Thomas Fritz for their review and valuable contributions

Characteristics of Reliability

Reliability is defined as "the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered." (This is the classic definition of reliability given by the Radio Electronics and Television Manufacturers Association in 1955.) In a quantitative way, the reliability of systems, devices, or products may be characterized by the probability concepts outlined in Table 1

Table 1 Reliability probability concepts

Relationship Between Wear and Reliability

Consider as a starting point for the reliability considerations of tribosystems that wear behavior is a function of time (Ref 2) In the previous article on "Presentation of Friction and Wear Data," it was explained that for time-dependent wear of a tribosystem, three different wear stages can be distinguished:

• Self-accommodation or running-in wear

• Steady-state wear

• Self-acceleration (catastrophic damage) of wear

These wear mode changes in the system behavior may follow each other with time, as indicated in Fig 1 In this figure,

Wlim denotes a maximum admissible level of wear losses At this level the system structure has changed in such a way that the functional input-output relations of the system are disturbed severely Repeated measurements show random variations in the data, as indicated by the dashed lines in Fig 1

Fig 1 Simple curves of wear and failure and reliability functions

From sample curves of wear, a probability density function, f(t), of the time for reaching the maximum admissible level of wear (Wlim = constant) is obtained For a given time, t0, the shaded area under the curve f(t), that is, the value of F(t0), is a

measure of the probability that the system fails within the time t < t

Statistical Distributions of Wear and Reliability

For the modeling of the distribution of measured wear data and the estimation of reliability data, statistical distributions may be used In the following paragraphs, some of the statistical distributions that have been applied for these purposes are briefly reviewed in a highly simplified manner in order to illustrate the given probability concepts With respect to the estimation of the occurring parameters, the calculation of confidence intervals, and related subjects, the reader is referred

to Ref 3, 4, 5, 6

For exponential distribution:

(t) = = const

f(t) = · exp (- t) R(t) = exp (- t)

MTTF = 1/

(Eq 1)

In this case, the failure rate is constant, which means that failure occurs accidentally without an accumulation of fatiguelike effects during service time Components in a machine fail in this mode, for example, when the failure is brittle fracture In Fig 2 the density function of the failure of a diesel engine control unit is plotted showing an exponential distribution (Ref 7)

Fig 2 Failure density function of diesel engine control units

For normal distribution:

For lognormal distribution:

(Eq 3)

This distribution is concentrated on the positive t-axis Its failure rate increases to a maximum and then decreases to zero

Therefore, it can be used for modeling survival times after extreme stress

For the Weibull distribution:

(Eq 4)

In its simplest form, this is a distribution with two key parameters: t0, the nominal life, and the constant C This distribution is found to represent failure of many kinds of mechanical systems, such as fatigue in ball bearings As an

example, Fig 3 shows the probability distribution function of the time to failure, F(t), as determined by testing 500

grease-lubricated ball bearings at 1000 rpm (Ref 8)

Fig 3 Failure distribution function of ball bearings

For the Gamma distribution:

7)

Fig 4 Failure density function of diesel engine pistons

Wear and Failure Modes

The aforementioned examples of statistical distributions indicate that different failure modes and different elementary failure processes are associated with different types of failure distribution functions It follows that from the experimental determination of failure distribution curves, conclusions may be drawn as to the type of failure mechanism For most tribosystems failing as a consequence of wear processes, the failure behavior is characterized by the normal distribution

or the Weibull distribution If for a given type of tribosystem the failure mode and the type of failure distribution are known, this knowledge can be used to improve the reliability of the system (Ref 9) For instance, this approach can be used to select the type of a ball or roller bearing system to operate under a given set of operating conditions with high operational safety (Ref 10) More general treatments concerning correlations between life data, statistical lifetime distribution, and failure models can be found in Ref 3, 4, 5, 6, 11 and 12

Dependence of Failure Rate on Operating Duration

To conclude the brief discussion on the failure and reliability of tribosystems, and dependence of the failure rate on the operating duration of a system should be considered If the failure rate is plotted as a function of time, a curve known as the "bathtub curve" is generated (Fig 5)

Fig 5 "Bathtub" failure rate curve

In this curve, three regimes can be distinguished: (1) early failures, (2) random failures, and (3) wear-out failures None of the distribution curves discussed above have this bathtub-shaped failure curve, but an approximation can be obtained by selecting an appropriate probability density function for each of the three regimes Regime (1) describes the region of the

"infant death" of the system This regime is characterized by a decrease of the failure rate with time during running-in wear Regime (2), which exhibits a constant failure rate, is the region of normal running Here failure occurs as a consequence of statistically independent factors Regime (3) is characterized by an increase of the failure rate with time Here failure may be due to aging effects As described above, for a great deal of tribo-induced failures, the failure rate increases with time Thus region (3) of the bathtub curve of Fig 5 appears to be relevant for the normal mode of wear-induced failure of mechanical systems

3 W Nelson, Applied Life Data Analysis, John Wiley, 1982

4 J.F Lawless, Statistical Models and Methods for Lifetime Data, John Wiley, 1982

5 N.R Mann, R.E Schafer, and N.D Singpurwalla, Methods for Statistical Analysis of Reliability and Life Data, John Wiley, 1974

6 J McCormick, Reliability and Risk Analysis, Academic Press, 1981

7 G Fleischer, Problems of the Reliability of Machines, Wiss Z Tech Univ Magdeburg, Vol 16, 1972, p

289 (in German)

8 G Bergling, Reliability of Rolling Bearings, Kugellager-Zeitschrift, Vol 51, 1976, p 1 (in German)

9 A Holfeld, Wear and Life Time Determination on a Statistical Basis, Schmierungstechnik, Vol 20, 1989, p

167-171 (in German)

10 A Sturm, "Rolling Bearing Diagnosis in Machines and Plants," Verlag TÜV Rheinland, Cologne, 1986 (in German)

11 H.F Martz and R.A Walter, Bayesian Reliability Analysis, John Wiley, 1982

12 A.E Green and A.J Bourne, Reliability Technology, Wiley-Interscience, London, 1972

Friction and Wear of Rolling-Element Bearings

Tedric A Harris, Pennsylvania State University

friction characteristics compared to fluid film bearings or simple sliding bearings In addition to the components cited

above (that is, balls or rollers, inner rings, and outer rings), most rolling bearing have a cage (also called a separator or

retainer) that spaces the rolling elements during operation The cage also serves to retain the rolling elements in the

bearing prior to assembly and also in the subsequent application Figure 1 illustrates the components in a typical ball bearing Note that the rolling elements run on an inner ring track called the inner raceway; similarly, the outer ring track is called the outer raceway

Fig 1 Cutaway view of radial ball bearing showing inner ring, outer ring, balls, and cage assembly

Rolling bearings have much less friction torque than conventional hydrodynamic bearing types, and starting friction torque is only marginally greater than operating friction torque In addition, rolling-element bearing deflection is not as sensitive to load fluctuation as is deflection in a hydrodynamic bearing In most applications, only a small quantity of lubricant is required for satisfactory operation, eliminating the need for expensive and space-consuming lubricating systems Moreover, rolling-element bearings require less space than corresponding hydrodynamic bearings, and they can

be selected or designed in compact units to support combination loads (for example, radial, thrust, and moment loads) The load and speed ranges to which a given rolling-element bearing may be subjected and function efficiently under each condition are significantly wide In general, if a rolling-element bearing can satisfy the operating conditions for a given application, it represents the economical choice

Types of Rolling-Element Bearing

There are two basic rolling-element types: balls and rollers Ball bearings enjoy the most universal usage However, for applications in which very heavy loads must be supported, roller bearings find extensive usage In addition to categorizing

rolling bearings according to rolling-element type, such bearings are also identified according to the predominant loading they are designed to support (for example, radial load or thrust load [also called axial load]) Within each subcategory type (for example, radial ball bearings, thrust ball bearings, radial roller bearings, and thrust roller bearings), there are several different basic variations, the usage of each depending on the load and speed conditions to be accommodated

Ball Bearings

Ball bearings can be further classified as either radial ball bearings, angular-contact ball bearings, or thrust ball bearings

Radial Ball Bearings. The most common ball bearing type is the nonseparable Conrad assembly (Fig 2) The nominal contact angle between a ball and a raceway is 0° (the contact angle is defined as the angle the ball-raceway load vector makes with the bearing radial plane) The bearing is designed to carry moderate radial road The bearing can, however, support some thrust (axial) and moment load in addition to the radial load In this case, the contact angles between balls and raceways increase beyond 0° with the application of thrust In most cases, the bearings can operate at high speeds of rotation ( 5 × 105 n · dm, where n is the speed of rotation in rev/min and dm is the pitch diameter, above which special cooling is often required to keep operating temperatures at <170 °C, or 338 °F) Because the bearing balls and rings form

an inseparable unit when assembled, cages are either two-piece riveted assemblies or one-piece snap-on plastic (generally fiberglass-filled polyamide [nylon]) units When using bearings with plastic cages, care must be exercised to ensure the compatibility of the cage material with the bearing lubricant and operating temperatures The latter must not be >120 °C (>248 °F)

Fig 2 Schematic showing assembly process for a nonseparable Conrad-type ball bearing , assembly angle

Self-aligning ball bearings are principally double-row radial bearings that can accommodate radial load simultaneously with substantial misalignment (for example, from 1.5 to 3° depending on internal design), without detriment to bearing endurance In conjunction with the principal radial load, they can also support some axial loading Because the outer raceway is a portion of a sphere (Fig 3), the conformity of the outer raceway to the ball is not close Accordingly, the outer raceway has less load-carrying capacity than does the inner raceway The reverse is true for almost all other basic types of radial rolling-element bearings

Fig 3 Typical construction of a self-aligning ball bearing incorporating a spherically shaped outer raceway

Angular-contact ball bearings are radial bearings designed to support substantial amounts of axial load in addition

to radial load Basic catalog bearing designs have nominal contact angles from 15 to 40° (Fig 4); the bearings having the higher contact angles can carry the greater amount of axial loading For the 40° contact angle bearing, applied thrust load must be at least equal to radial load for satisfactory operation The bearings can also support simple axial loading The bearings are always mounted in pairs to accommodate thrust loading induced by applied radial loading; they may be mounted in back-to-back or face-to-face duplex arrangements (Fig 5) The former provides substantial resistance to moment loading (that is, high stiffness), whereas the latter provides greater ability to accommodate misalignment In addition, angular-contact bearings can be mounted in tandem for increased axial load-carrying capacity (Fig 6) Duplex angular-contact ball bearings can be axially preloaded to achieve increased stiffness (that is, reduced deflection under applied loading)

Fig 4 Key components of an angular-contact ball bearing

Fig 5 Duplex angular-contact ball bearing arrangements used to accommodate thrust loading induced by

applied radial loading (a) Face-to-face mounting (b) Back-to-back mounting

Fig 6 Pair of angular-contact ball bearings mounted in tandem

The bearings may be assembled with one-piece pressed (stamped) or precision-machined cages fabricated from steel, brass, or bronze Bearings having the machined cages are capable of higher speeds Bearings can also be supplied with plastic (mainly polyamide 6/6, nylon) cages; these also have high-speed capability The operating speed capability of angular contact ball bearings is somewhat less than that of other radial ball bearings

Split inner ring ball bearings (Fig 7) are double-direction angular-contact ball bearings (that is, they can support thrust load in either axial direction) When compared to duplex angular-contact bearings, however, they are narrower in width Radial load can be supported only in conjunction with thrust loading sufficient to load all balls Generally, the balls are spaced apart by a one-piece cage precision machined from steel, brass, or bronze The bearings are capable of high-speed operation

Fig 7 Typical construction in a split inner-ring ball bearing

Thrust Ball Bearings

Thrust ball bearings (contact angles from 45 to 90°) are designed to carry predominantly axial load; 90° contact angle thrust bearings (Fig 8) cannot carry any radial load Owing to substantial amounts of ball spinning, they are limited to slow- to moderate-speed operation unless means to remove high friction heat associated with high-speed operation is provided

Fig 8 Thrust ball bearing designed to carry axial load only due to 90° contact angle

slightly crowned rollers (Fig 10) so that, except under extremely heavy loading and/or bearing misalignment, edge loading and its deleterious effects on bearing endurance are avoided The bearings are capable of supporting very heavy radial loading and operating at very high speeds They tend to be sensitive to misalignment; only a few minutes of misalignment can be tolerated without a substantial reduction in endurance In general, the bearings permit axial float of the shaft because neither the inner ring nor the outer ring usually has any guide flanges When both rings have guide flanges (Fig 11), however, the bearing can support some thrust load in conjunction with a greater amount of applied radial load The bearing can be assembled with pressed metal; precision-machined brass, bronze, or steel; or molded plastic cages, depending on the application These bearings are manufactured in two-row and four-row versions for greater load-carrying capacity

Fig 9 Radial roller bearing having cylindrical roller elements

Fig 10 Crowned roller geometry used in radial roller bearings (a) Fully crowned (spherical roller) (b) Partially

crowned (cylindrical roller) Roller length, I; roller diameter, D; crown radius, R

Fig 11 Radial cylindrical roller bearing with guide flanges on both inner and outer rings

Tapered Roller Bearings. A common form of radial roller bearing is the tapered roller bearing As shown in Fig 12, the basic form of the tapered roller is a portion of a cone; generally the rollers are crowned The outer and inner raceway surfaces are also portions of cones, the outer ring being called the cup and the inner ring the cone Because the raceways are angled relative to the shaft, radial tapered roller bearings can carry combined radial and axial loading; very heavy loading can be supported To provide increased load-carrying capacity, the bearings may be obtained in two-row and four-row units

Fig 12 Key components of a tapered roller bearing (a) Photograph showing cone assembly and cup of the

typical roller bearing shown in background (b) Schematic of a cross section of a tapered roller bearing

The bearings are sensitive to misalignment, tending to have substantially reduced endurance under only a few minutes of misalignment Generally, operating misalignment is limited to 3 min to achieve expected performance Because the rolling-contact surfaces are portions of cones, the rollers are driven against a fixed guide flange during operation, usually

on the inner ring The contacts between the roller ends and the guide flange, sometimes called the large end rib, are sliding contacts creating substantial friction as compared to the raceway rolling contacts; therefore, the bearings cannot

operate at high speed without a lubrication system capable of removing the friction heat thereby generated Generally, the bearing cages are manufactured from stamped or pressed steel

Radial spherical roller bearings are generally two-row bearings having one raceway that is a portion of a sphere; therefore, the bearings are internally self-aligning In their most common form, the bearings have an outer raceway that is

a spherical surface, and the rollers are symmetrical or barrel-shaped (Fig 13) In this bearing design, a floating flange is usually employed to provide roller guidance; in another design using asymmetrical rollers, the rollers (as in tapered roller bearings) are driven against, and guided by, a fixed axial central flange Some bearings with symmetrical rollers also use

a fixed central guide flange Depending on the bearing dimension series, from 1 to 2.5° of misalignment can be accommodated without detriment to bearing endurance Because they have design contact angles that are >0° (usually

>10°), double-row bearings can support combinations of very heavy radial and thrust loading Conversely, a single-row spherical roller bearing has a nominal 0° contact angle and can only support a small amount of thrust load in conjunction with a much greater radial load

Fig 13 Typical construction in a radial spherical roller bearing

Because of the relatively close matching of the curved roller profile to the raceways (that is, close osculations to achieve high load-carrying capacity) and bearing contact angle >0°, spherical roller bearings operate with substantial sliding in the roller-raceway contacts Thus, the bearings are constrained to operate at relatively slow speeds unless lubrication systems are employed that can effectively remove the substantial amounts of friction heat generated Cages in spherical roller bearings are usually either pressed steel or machined brass or bronze Double-row bearings may be assembled with a cage for each row or with a one-piece cage

Radial needle roller bearings (Fig 14) are radial cylindrical roller bearings whose rollers have length/diameter ratios 1 (for example, roller length is 3D to 10D, where D is the roller diameter); roller diameter is generally not

greater than 5 mm (0.2 in.) The bearings are used in moderate radial load and speed applications where radial space is at

a premium Needle roller bearings may be assembled as full complement bearings (that is, with no cage and a drawn steel cup outer ring or with machined and ground inner and outer rings and a pressed steel or molded plastic cage) Sometimes the bearings are supplied as outer ring-roller cage assemblies with rollers that ride directly on a properly hardened shaft

Fig 14 Two types of radial needle roller bearing (a) Machined ring with cage (b) Drawn cup

The allowable operating speed of a full complement assembly is less than that of a bearing having precision-machined rings and cage; the allowable operating speeds of needle roller bearings are less than those of standard cylindrical roller bearings owing to the tendency of longer rollers to skew and cause increased friction heating

Thrust Roller Bearings

Thrust roller bearings are available in cylindrical roller, needle roller, tapered roller, and spherical roller versions

Thrust cylindrical roller bearings (Fig 15) are 90° contact angle bearings designed to support axial load only The rollers are similar to those of radial cylindrical roller bearings; however, because of the high contact angle, they operate with considerable sliding motion, causing substantial friction heating and limiting use of the bearings to slow-speed applications To minimize friction, several rollers of relatively small length-diameter ratio may be used in a single-cage pocket as compared to use of a single roller of greater length

Fig 15 Thrust cylindrical roller bearing limited to use with axial loads only due to its 90° contact angle

Thrust needle roller bearings operate with characteristics similar to those of thrust cylindrical roller bearings

Thrust tapered roller bearings have steep contact angles to accommodate primarily axial load However, in combination with relatively heavier axial load, thrust tapered roller bearings can also support radial load Similar to radial tapered roller bearings, thrust tapered roller bearings are limited to relatively slow-speed operational unless means to remove friction heating are employed This type of bearing is similarly sensitive to even small amounts of misalignment

Spherical roller thrust bearings (Fig 16) are usually single-row bearings with an outer raceway that is a portion of

a sphere and with asymmetrical rollers that are of a continuously curved profile They can support heavy combined thrust and radial loading, provided that thrust loading predominates and is sufficient to ensure the loading of all rollers They are internally self-aligning and, depending on specific design, can accept 2 to 3° misalignment without detriment to endurance They are generally constrained to relatively slow operation because of roller-raceway and roller end-flange friction heating unless means to remove such heat are provided in the application

Fig 16 Spherical roller thrust bearing, which incorporates asymmetrical rollers that tolerate a misalignment of

±3°

Bearing Component Materials

Rolling-Contact Component Steels. Most modern ball and roller bearing rings, balls, and rollers are manufactured from vacuum-processed AISI 52100, a high-carbon through-hardening steel, heat treated to at least 58 HRC High-quality grades of this steel are required for ball and roller bearings to achieve the standard load rating generally published in the catalogs of bearing manufacturers for each bearing The heat-treated steel is highly resistant to rolling-contact fatigue, but

is considered brittle and susceptible to fracture in heavy load applications where ring bending can occur

Some bearing types, principally tapered roller bearings, are fabricated from case-hardening steels such as SAE 4320,

4620, and 8620 These low-carbon steels are carburized (that is, heat treated in a carbonaceous atmosphere), such that the case, in which carbon is absorbed (surface and near-surface material), is hardened to 58 HRC while the remaining core

is hardened to 45 HRC This provides a case that resists rolling-contact fatigue and a core that resists fracture The carburized bearing material has a fracture toughness of 40 MPA (36 ksi ), approximately twice that of through-hardened 52100 steel Bearing components fabricated from both 52100 and the case-hardening steels cited above can operate continuously at temperatures up to 160 °C (320 °F) without any reduction of fatigue endurance capability

For bearings that must operate in corrosive environments (for example, water and salt-laden atmospheres), bearings with rings and rolling elements manufactured from AISI 440C, a stainless steel, are frequently used Instrument and miniature ball bearings, which must have smooth uninterrupted minimum friction operation at all times, are fabricated from 440C material This high-carbon chromium-rich steel can be through-hardened to 58 HRC; however, bearing fatigue endurance

is somewhat less than that of the same bearing fabricated from AISI 52100 Satisfactory bearing operation at temperatures

up to 160 °C (320 °F) can be expected

Bearings that must operate at elevated temperatures are usually manufactured from tool steels, AISI M50 being most prevalent in use Bearings with rolling-contact components fabricated from M50 are capable of steady-state operation to

at least 300 °C (572 °F), provided that bearing internal design, cage materials, lubricants, and materials of other components associated with the bearing operation can accommodate the operating temperatures The steel is routinely through-hardened to 58 HRC M50 steel is supplied as consumable vacuum-melted (CVM) M50 and as vacuum induction melted/vacuum arc remelted (VIMVAR) highly homogeneous, minimum inclusion variants that provide exceptional resistance to rolling-contact fatigue in most applications M50 Nil, a carburizing variant, provides similar properties in addition to increased fracture toughness

Rolling-Element Ceramics. As an alternative to steel in machine tool bearing applications, hot isostatically pressed silicon nitride (Si3N4) ceramic balls are being used Bearings with steel rings and ceramic balls are called hybrid ball bearings Because of the lower density of silicon nitride and its increased rigidity, these high-speed bearings tend to operate with less friction, lower temperatures, and increased stiffness than bearings with steel balls These bearings also tend to be more expensive

Cage Materials. The most common materials used for rolling bearing cages are low-carbon steels that can be pressed or stamped (for example, AISI 1010 or 1020) Alternatively, stamped cages are fabricated from brass Such cages can be either rolling-element riding or land riding In many applications, molded polyamide 6/6 (nylon) is used in place of metal The nylon is generally supplied with 25% glass fiber filling for appropriate strength and satisfactory continuous operation

at temperatures up to 100 °C (212 °F); they can be used at slightly higher temperatures if operation at these temperatures

is intermittent Bearings with plastic cages tend to operate with slightly less friction and can therefore achieve higher operating speeds without special attention to friction heat removal

Precision-machined cages are manufactured from steel (for example, AISI 4349, brass, bronze, and variations such as silicon-iron-bronze and alcop (aluminum-copper bronze) Bearings with such machined cages are either inner or outer ringland riding (Fig 17) Bearings with such cages can generally achieve higher operating speeds than bearings with stamped metal cages Precision cages are also machined from fabric-reinforced phenolic resin for very high-speed operating bearings (for example, for machine tool applications); however, operating temperatures are limited to 120 °C (248 °F)

Fig 17 Schematic showing types of rolling bearing cages (a) Inner ringland riding (b) Ball riding (c) Outer

ringland riding

Lubrication Requirements and Methods

To obtain satisfactory performance and rated endurance of rolling bearings, adequate fluid lubrication is necessary The lubricant is required to:

• Form fluid films between the rolling elements and raceways, rolling elements and cage pockets, cage rails and ring lands, roller ends and abutting flanges, thereby minimizing metal-to-metal contact,

friction, and wear

• Contain chemical additives to minimize rolling-contact surface corrosion and wear

• Transport friction heat away from the bearing

In general, only a small amount of lubricant is required to perform the first two functions In fact, too much lubricant in the bearing free space or cavity will cause excessive fluid churning, increased bearing friction, and higher operating temperatures Therefore, the amount of circulating lubricant required to remove friction heat must be carefully determined

to avoid overheating and potential early failure

Grease Lubrication. Most rolling-element applications are lubricated with grease because such lubrication is the most economical and simplest mechanical means to accomplish the task Greases are combinations of fluid lubricants (oils) with metallic soap thickeners; the oil contained in the grease provides most of its lubricating ability For grease lubrication to be effective, however, bearing operating speeds must be relatively slow (<3 × 105 n · dm) This is due to the inability of the grease to dissipate friction heat generation caused by high speed and also its inability to replenish rolling-contact surface fluid lubricant due to insufficient bleeding (flow) rate (lubricant starvation) Heat dissipation from the bearing is achieved mainly by conduction through metal structures

Many bearings are supplied in the greased-for-life form, in which the grease charge is kept in the bearing by integral seals (Fig 18) The elastomeric material used as the sealing element must be compatible with the application operating temperatures and environment to obtain satisfactory seal endurance The amount of grease charge must be carefully metered because excessive grease can cause churning (which produces immediate overheating) and insufficient grease can result in inadequate replenishment of lubricant films (which leads to eventual overheating) When operating temperatures exceed the temperature capability of the grease, aging (oxidation) occurs that reduces the capability of the grease to lubricate Generally, the charge of grease should occupy from one-third to one-half of the free volume Lithium soap (thickener) greases are most frequently used; the type of grease used depends on the operating temperatures and application requirements The upper temperature limit for a grease is determined by the type of thickener A rule of thumb

is that grease life is halved with each 11 °C (20 °F) increase in bearing temperature

Fig 18 Location of elastomeric integral seals in a ball bearing (a) Single-face seal (b) Dual-face seal

Rolling bearings are frequently mounted in pillow blocks (housings), which have fittings for regreasing (Fig 19) In this case, the bearings are open and the pillow blocks are supplied with seals to prevent the loss of grease Regreasing intervals, as recommended by bearing manufacturers, depend on the bearing design and application conditions When a bearing is regreased, it is essential that the new grease pushes through the bearing and the used grease is effectively purged

Fig 19 Location of regreasing fitting in a pillow block mounting

For additional information about the composition and application of grease, see the article "Grease" in this Volume

Bath Lubrication. Many rolling bearings are effectively operated using oil bath lubrication For horizontally mounted bearings, a portion of the bearing ball or roller complement is covered by the lubricant bath (Fig 20) As the cage-rolling element set rotates, each rolling element in succession dips into the bath, carrying sufficient oil with it to adequately lubricate the entire bearing Lubricant returns by gravity to the bath The level of the bath must be such that the process is achieved without lubricant starvation at the rolling contacts most remote from the bath If the lubricant level is too high, excessive lubricant churning occurs, with potential bearing overheating and failure In general, the lubricant level should not be higher than the center of the lowest rolling element under nonoperating conditions

Fig 20 Oil bath lubrication suitable for low speeds of rotation When the bearing is not rotating, oil should

come to level just below center of lowest ball or roller When the bearing rotates, oil is drawn up by bearing moving components, transported through the bearing, and returned by gravity to the bath

For vertically mounted bearing applications, the optimum lubricant levels must be established according to the operating speeds and bearing internal design

Bath-lubricated bearings can operate at higher speeds than grease-lubricated bearings because the bearing components transfer most of their friction heat to the lubricant by convection The lubricant subsequently splashes on the bearing housing internal surfaces, transferring heat by mass transfer and convection This heat is then conducted through the housing structure for dissipation by free or forced convection to the environment

Circulating-Oil Lubrication. When bearing operating speeds are high and applied loading is very heavy, it is frequently necessary to utilize circulating-oil lubrication In this case, lubricant that is supplied to the bearing is subsequently passed through a heat exchanger to remove friction heat (that is, reduce the lubricant temperature prior to returning the lubricant to the bearing) In applications where the generation of friction heat is exceptionally great, a jet

supply of lubricant can be used in which one or more jets of lubricant impinges directly on the bearing rotating components (Fig 21) Where jet supply of lubricant is used, significant amounts of lubricant churning can be expected, with attendant high friction heating This extra heat must also be removed, increasing the bearing cooling requirements

Fig 21 Oil jet lubrication suitable for high speeds of rotation Oil is injected into the bearing under pressure to

gain access to the bearing interior to remove heat Oil jet velocity must be high enough to piece air vortex caused by bearing rotation

the bearing to resist permanent indentations Frequently, many other criteria must be considered to establish the suitability

of a given rolling bearing for a given application (for example, elastic deflection, friction torque, friction heat generation, operating temperatures, corrosion resistance, operating vibration, noise level, and son on) Nevertheless, most bearings are selected for given applications based on their resistance to rolling-contact fatigue and permanent deformation, and based on the load ratings published in the catalogs of manufacturers

Fatigue failure of the surfaces in rolling contact was selected as the endurance criterion for ball and roller bearings because it was considered that all other modes of bearing failure could be prevented if the bearing rolling contact components were:

• Accurately manufactured from high-quality bearing steel

• Properly lubricated

• Keep free of contaminants

• Properly mounted and operated in the application

Bearing endurance as limited by rolling-contact fatigue represented the longest period of time a bearing could reliably perform its intended function The failure mode manifested itself as a spall or flaking of material from a rolling-contact surface This failure mode is considered a form of wear because material is removed from the rolling-contact surfaces (Fig 22) Moreover, bearing endurance is a statistical phenomenon; that is, apparently identical roller bearings subjected

to apparently identical conditions of operation will not achieve identical failure endurance Instead, they will tend to fail according to a statistical distribution (Fig 23) A Weibull distribution (Ref 6) has been shown to adequately approximate

the bearing fatigue life dispersion For ball bearings, it has been demonstrated that the median life, L50, is approximately

equal to five times the rating life, L10:

Standard ball and roller bearing dynamic load ratings are based on the work of Lundberg and Palmgren (Ref 7, 8) Their method of determining basic dynamic load ratings was based on rolling-contact fatigue testing of ball and roller bearings during the 1930s and 1940s Because of the substantial improvements in bearing steels, bearing steel processing, and bearing manufacturing methods since that time, the standard calculation methods have been modified several times to

accommodate the improvements The basic static load rating is based on the work of Lundberg et al (Ref 9); the current

standard method reflects relatively recent improvement in the accuracy of determining permanent deformations during testing Both basic dynamic load ratings and basic static load ratings have undergone substantial increases since the original rating methods were established Because bearing load ratings have increased substantially over time, it follows that to resist specific loading, smaller bearings are now being employed (that is, downsizing of bearings has occured)

Fig 22 Fatigue spall centered on a ball bearing race-way

Fig 23 Plot of fatigue life versus probability of survival to indicate rolling bearing fatigue life distribution

Basic Load Rating

Basic load rating (also called basic dynamic load rating or basic dynamic capacity) is defined as that load which 90% of a group of apparently identical rolling bearings will survive (rolling-contact fatigue) with a life of one million revolutions For radial ball bearings, the International Standards Organization (ISO) (Ref 2) gives the following equations:

Cr = basic radial load rating (in newtons)

bm = rating factor for contemporary, normally used material and manufacturing quality, the value of which varies with the bear- ing type and design

fc = factor that depends on the composition of the material, the geometry of the bearing components, and the accuracy to which the various components are made

• i = number of rows of balls

• = nominal contact angle (in degrees)

• Z = number of balls per row

• D = ball diameter (in mm)

bm can be obtained from Table 1 for different bearing types, and fc can be obtained from Table 2 as a function of the

geometry parameter (D · cos )/d, in which d is the bearing pitch diameter (in mm) The tabular data pertain strictly to

radial and angular-contact bearings having inner ring groove radii 0.52D and outer ring groove radii 0.53D and to

self-aligning bearings having inner ring groove radii 0.53D

Table 1 bm factors for selected rolling bearing types

Ball bearings

Radial and angular-contact ball 1.3

Needle roller with machined rings 1.1

Drawn cup needle roller 1

Cylindrical roller thrust 1

Spherical roller thrust 1.15

Table 2 fc factors for radial ball bearings and angular-contact ball bearings

fc

(D · cos )/

d(a) Single-row radial contact

groove ball bearings and single-row

and double-row angular contact

groove ball bearings

Double-row radial contact groove ball bearings

Single-row and double- row self-aligning ball bearings

Single-row radial contact separable ball bearings (magneto bearings)

(a) fc values for intermediate values of (D · cos )/d are obtained by linear interpolation

Standard Bearing Internal Geometry

The ratio of the raceway curvature radius (ring groove radius) to the ball diameter, f = r/D, together with the parameter (D

· cos )/d, internal radial clearance, and applied load determine the normal stresses in the rolling element-raceway

contacts The standard formulas for basic radial load rating are based on the nominal clearance that produces a radial load distribution among the rolling elements (Fig 24) Normal stresses depend on the contact geometry and rolling-element load; hence, maximum stress occurs colinear with the applied radial load Moreover, the contact areas are elliptical in shape, and the distribution of stress in each contact is as shown in Fig 25 In most bearing applications, maximum normal stress in the contacts rarely exceeds 2000 MPa (290 ksi); however, maximum stresses as high as 3300 MPa (475 ksi) can

be carried (by properly hardened steel bearings) without significant permanent deformation of the contact geometry If bearing raceway groove curvatures are different from those indicated above, then the standard load rating formulas cannot

be used If the raceway curvature radius is greater than standard, normal stresses will be greater than standard and the basic load rating can be considerably less than standard Also, if a bearing has an internal radial clearance greater than

standard, maximum rolling-element load will be greater than standard, and the basic load rating will accordingly be less than standard Harris (Ref 10) provides methods for rating bearings with nonstandard internal geometries

Fig 24 Distribution of radial load among rolling elements in a bearing

Fig 25 Normal (Hertzian) contact stress distribution obtained over an elliptical rolling element-raceway contact

area in a bearing max is the maximum normal contact stress at the center of contact and is the contact

stress anywhere else

For thrust ball bearings the following equations pertain:

(a) fc values for D/d or (D · cos )/d and

other than shown in the table are obtained by

linear interpolation or extrapolation

(b) Values for = 45° permit interpolation of

values for 45° < < 60°

Standard Bearing Contact Geometry

As with radial ball bearings, standard formulas for thrust ball bearing load ratings apply only for bearings having standard internal geometry Moreover, it is presumed that the thrust load carried by each ball is identical (that is, the internal load distribution shown in Fig 26 applies)

Fig 26 Distribution of (simple) thrust load among rolling elements in a bearing

For radial roller bearings:

Cr = bmfc(il · cos )7/9 Z3/4 D29/27 (Eq 9)

where l is the roller effective length (in mm) Roller effective length is the total length of the roller minus corner radii or raceway undercuts, whichever length is smaller Values of bm are given in Table 1; fc values are given in Table 4

Table 4 Maximum fc factors for radial roller bearings

(a) fc values for intermediate values of (D · cos )/d

are obtained by linear interpolation

Similarly, for thrust roller bearings:

Table 5 Maximum fc factors for thrust roller bearings

(a) fc values for intermediate values of D/d or (D · cos )/d

are obtained by linear interpolation

(b) Applicable for 45° < < 60°

(c) Applicable for 60° < 75°

(d) Applicable for 75° < 90°

Standard Roller Geometry

Use of Eq 9, 10, 11, and 12 presumes that the rollers are crowned as in Fig 10 so that under loads as heavy as 4C, where

C is the bearing capacity, stress concentrations due to edge loading (Fig 27) in the contacts are avoided If appropriate

crowning is not employed, basic load ratings can be significantly reduced from standard With regard to nonstandard bearing internal clearance, the load rating situation is identical to that for ball bearings (that is, excessive clearance will result in reduced load-carrying capacity)

Fig 27 Roller axial load distribution associated with edge loading (a) Schematic showing load, Q, applied to

roller of length, l (b) Load distribution across roller

Bearing Fatigue Life

Using the basic load rating obtained either from a catalog supplied by a bearing manufacturer or from the appropriate equation, bearing rolling-contact fatigue life in a given application can be determined using the following equation:

(Eq 13)

where

• Lna = bearing life (in millions of revolutions)

• a1 = life adjustment factor for reliability

• a2 = life adjustment factor for special bearing properties

• a3 = life adjustment factor for operating conditions

• P = dynamic equivalent load (in N)

In Eq 13, the exponent x = 3 for ball bearings and x = 10/3 for roller bearings; a1 values for desired levels of reliability can be obtained from Table 6

Table 6 Life adjustment factor for reliability, a1

For bearings specified in the catalogs of manufacturers, a2 factors of 1 are appropriate in the calculation of fatigue life;

however, a2 values >1 may be applicable if the bearings are fabricated from steel of particularly low impurity content or

of special analysis Conversely, if hardness reduction occurs due to a special heat treatment, a2 < 1 should be used Moreover, special internal design involving increased or reduced uniformity of stress in the rolling contacts can be

accommodated by appropriate selection of a2

The a3 operating conditions factor depends strongly on the effectiveness of lubrication and the presence of foreign matter

(contaminants) in the application In the calculation of bearing fatigue life, lubrication is considered normal (a3 = 1) when the lubricant films generated in the rolling element-raceway contacts have thicknesses equal to, or slightly greater than,

the composite root-mean-square (rms) roughness of the contacting surfaces a3 < 1 should be considered when kinematic viscosity of the lubricant at the bearing operating temperature is <13 cSt for ball bearings or <20 cSt for roller bearings

and bearing operating speed in rev/min, n, times pitch diameter in mm, dm, is <104 (ndm < 104) When lubricant films are insufficient to completely separate the rolling-contact surfaces, it is possible that a chemical interaction will occur

between the bearing material and the lubricant that will necessitate a reduction in a2 Accordingly, it cannot be assumed

that a reduced value of a3 can be compensated by use of a steel nominally having a2 > 1 a3 values > 1 can be considered only where lubrication conditions are so favorable that the probability of failure by surface-oriented distress is virtually

eliminated Bearing manufacturers can recommend appropriate values of a3

Equivalent Load. The dynamic equivalent load for a radial bearing is that purely radial load which, if applied to the bearing, would result in the same fatigue life as the actual applied load For bearings subjected to combined radial and thrust loading, it can be determined from Eq 14:

where Fr is the applied load (in N), and Fa is the applied thrust load (in N) For radial ball and roller bearings, the factors

X and Y can be obtained from Tables 7 and 8, respectively

Table 7 X and Y factors for radial ball bearings

Single-row bearings Double-row bearings Bearing type Relative axial load(a)(b)

Radial contact ball bearings

For this type use the Xo, Yo, and e values

applicable to single row-radial contact groove ball bearings

1 1.21 0.78 1.63 0.52 0.175 0.172 1 0 0.46 1.88 1 2.18 0.75 3.06 0.29 0.35 0.345 1 0 0.46 1.71 1 1.98 0.75 2.78 0.32 0.7 0.689 1 0 0.46 1.52 1 1.76 0.75 2.47 0.36 1.05 1.03 1 0 0.46 1.41 1 1.63 0.75 2.29 0.38 1.4 1.38 1 0 0.46 1.34 1 1.55 0.75 2.18 0.4 2.1 2.07 1 0 0.46 1.23 1 1.42 0.75 2 0.44 3.50 3.45 1 0 0.46 1.10 1 1.27 0.75 1.79 0.49 5.25 5.17 1 0 0.46 1.01 1 1.17 0.75 1.64 0.54

= 10°

7 6.89 1 0 0.46 1 1 1.16 0.75 1.63 0.54 0.178 0.172 1 0 0.44 1.47 1 1.65 0.72 2.39 0.38 0.357 0.345 1 0 0.44 1.4 1 1.57 0.72 2.28 0.4 0.714 0.689 1 0 0.44 1.3 1 1.46 0.72 2.11 0.43 1.07 1.03 1 0 0.44 1.23 1 1.38 0.72 2 0.46 1.43 1.38 1 0 0.44 1.19 1 1.34 0.72 1.93 0.47 2.14 2.07 1 0 0.44 1.12 1 1.26 0.72 1.82 0.5 3.57 3.45 1 0 0.44 1.02 1 1.14 0.72 1.66 0.55 5.35 5.17 1 0 0.44 1 1 1.12 0.72 1.63 0.56

1 0 0.4 0.4 cot 1 0.42 cot 0.65 0.65 cot 1.5 tan

Single-row radial contact separable ball bearings (magneto

bearings)

1 0 0.5 2.5

0.2

(a) Permissible maximum value depends on bearing design internal clearance and raceway groove depth Use

first or second column depending on available information

(b) Values of X, Y, and e for intermediate "relative axial loads" and obtained by linear interpolation

(c) For fo values, see Ref 3

Table 8 X and Y factors for radial roller bearings

Single row, 0 1 0 0.4 0.4 cot 1.5 tan

Double row, 0 1 0.45 cot 0.67 0.67 cot 1.5 tan

Similarly, the dynamic equivalent load for a thrust bearing is that purely thrust load which, if applied to the bearing, would result in the same fatigue life as the actual applied load Equation 14 can be used to determine the dynamic

equivalent thrust load; however, X and Y factors are obtained from Tables 9 and 10 for thrust ball and roller bearings,

(b) Fa/Fr < e is unsuitable for single-direction bearings

(c) For thrust bearings > 45° Values for = 45° permit interpolation for

(a) tan 1 1.5 tan

(a) Fa/Fr < e is unsuitable for single-direction bearings

Nonstandard Application Conditions. The determination of bearing load rating and fatigue life using Eq 2, 3, 4, 5,

6, 7, 8, 9, 10, 11, 12, 13, 14 and the appropriate tables assumes that the bearing internal design and materials meet the limiting criteria and that operating conditions are not unusual; that is, they do not involve high speed, exceptionally heavy

or light loading, high temperatures, and so on Such conditions alter the bearing internal load distributions and contact stresses from those on which the load and life rating methods are based For these situations, more sophisticated means of evaluation are available as detailed by Harris (Ref 10); these frequently require the use of a computer to perform the required analyses

Fatigue Load Limit. Use of Eq 13 implies that even under extremely light loading, ball and roller bearing endurance is limited by rolling-contact fatigue Ioannides and Harris (Ref 11), however, demonstrated that if a certain limiting stress is not exceeded in a given application, then rolling-contact fatigue can be eliminated as a consideration for bearing failure This limiting stress is a function of the bearing internal design, the bearing material, and lubrication conditions Use of a fatigue limit stress or endurance limit as a bearing selection criterion is demonstrated in Ref 12, which includes a fatigue

load limit, Pu, for each bearing Even if applied load exceeds the fatigue load limit, bearing fatigue endurance is longer

than that predicted by Eq 13, depending on the magnitude of P/Pu For P Pu, Eq 12 remains substantially accurate and

is not conservative

Effect of Contamination on Fatigue Life. In the selection of a bearing, the level of contamination in the application must be considered Sayles and MacPherson (Ref 13) reported the effect of lubricant filtration on rolling-contact fatigue endurance To obtain the fatigue lives predicted using Eq 13, especially for high-precision bearings manufactured from high-performance steels, it is necessary to minimize the contamination amount and particle size entering the bearing Hard contaminants of sufficient size will dent the rolling-contact surfaces causing stress concentrations, interrupting

lubricant film formation and reducing fatigue endurance Hamer et al (Ref 14) have shown that, depending on the

application operating conditions, even soft contaminants can cause dents, thereby reducing endurance Contamination can

be precluded by providing a bearing with integral seals or by employing effective sealing means in the application In the use of a fatigue load limit in the fatigue endurance calculation, Ref 12 takes into account the effect of contamination

Basic Static Load Rating. According to Ref 3, 4, 5, experience shows that a total permanent deformation

approximating 0.0001D at the center of the most heavily loaded rolling element-raceway contact can be tolerated in most

bearing applications without impairing the operation of the bearing Such indentation can occur due to loading when the bearing is not rotating or due to heavy shock load during operation The basic static load rating is the load applied in such

a way that it results in this permanent deformation magnitude Furthermore, for most ball bearings, static loading that produces 4200 MPa (610 ksi) stress at the center of the most heavily loaded contact will also cause permanent

deformation approximating 0.0001D This equivalent stress is 4600 MPa (670 ksi) for self-aligning ball bearings and

4000 MPa (580 ksi) for roller bearings Using the appropriate stress criterion, basic static load ratings are created for catalog ball and roller bearings

For radial ball bearings, the basic static radial load rating (in newtons) can be determined from Eq 15:

for which fo values are given in Table 11 The values of Table 9 pertain to bearings having the same groove radii dimensional limitations as defined for basic radial load rating tabular data

Table 11 fo factor for ball bearings

Data based on the Hertz point contact formula with elastic modulus of 207 GPa (3.00 × 107 psi) and Poisson's ratio of 0.3

Factor fo (a)

Radial ball bearings (b)

(D · cos )/d

Radial and angular-contact groove ball bearings

Self-aligning ball bearings

Thrust ball bearings (c)

(a) fo values for intermediate values of (D · cos )/d are obtained by linear interpolation

(b) It is assumed that load distribution results in maximum ball load of 5Fr/(Z · cos )

(c) It is assumed that load distribution results in maximum ball load of Fa/(Z · sin )

For thrust ball bearings, the basic static axial load rating (in newtons) is given by:

for which fo, values are also given in Table 11 and were Z is the number of balls carrying load in one direction The basic

static radial load rating for radial roller bearings is obtained from Eq 17:

(Eq 17)

Similarly, the basic static axial load rating for thrust roller bearings is obtained from Eq 18:

(Eq 18)

where Z is the number of rollers carrying load in one direction In cases where rollers have different lengths, Zl is the sum

of the lengths of all rollers carrying load in a given direction

As with dynamic loading, a static equivalent load must be defined For a radial bearing, it is that purely radial static load which, if applied to the bearing, would produce the same permanent deformation as the applied static loading For a radial bearing subjected to combined radial and thrust loading, Eq 19 gives the static equivalent radial load:

for which the factors Xo, and Yo can be obtained from Tables 12 and 13 for radial ball and roller bearings respectively If

Fr > Por as calculated using Eq 19, then Por = Fr is used

Table 12 Xo and Yo factors for radial ball bearings

Single-row

bearings

Double-row

bearings Bearing type

Xo Yo Xo Yo

Radial contact groove ball bearings (a) 0.6 0.5 0.6 0.5

Angular-contact groove ball bearings, =

Self-aligning ball bearings, 0° 0.5 0.22 cot 1 0.44 cot

(a) Permissible maximum value of Fa/Co depends on bearing design

internal clearance and raceway groove depth

Table 13 Xo and Yo factors for radial roller bearings with > 0°

Bearing type Xo Yo

Single-row 0.5 0.22 cot

Double-row 1 0.44 cot

For thrust ball and roller bearings with < 90°, static equivalent axial load is given by Eq 20:

Equation 20 is valid for all combinations of radial to axial load for double-direction bearings It is strictly valid where

Fr/Fa 0.44 cot ; it gives satisfactory (but less conservative) results for 0.44 cot < Fr/Fa < 0.67 cot Thrust

bearings with = 90° can only support axial loading; in this case Poa = Fa

Frequently, loading applied to the bearing is more complex than that which has been considered using Eq 15, 16, 17, 18,

19, 20 In such cases, the specific load distributions corresponding to maximum permanent deformation of 0.0001D, or

the equivalent stress, can be determined using methods given in Ref 10

Rolling Bearing Friction

The principal sources of friction in roller bearings are due to sliding in the contact zones Some friction occurs due to elastic hysteresis in rolling but the magnitude is insignificant compared to that caused by sliding motions The magnitude

of component sliding friction depends on the effectiveness of lubrication For example, if adequately thick lubricant films are formed to effectively separate the contacting surfaces, friction forces will be relatively small In the latter case, the friction torque of a rolling bearing will be substantially less than that of an oil-lubricated hydrodynamic or hydrostatic bearing in a given application

The sources of sliding friction in a rolling bearing are as follows:

• Sliding in rolling element-raceway contacts due to geometry of contacting surfaces

• Sliding due to deformation of contacting elements (Heathcote slip)

• Sliding between the cage pockets and rolling elements