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CAST COPPER ALLOYSLEEVE BEARINGS
Non-Ferrous Founders' Society
CAST COPPER ALLOY SLEEVE BEARINGS
INTRODUCTION TO LUBRICATED BRONZE BEARING DESIGN
HISTORICAL ........................................................................................................................................... 7
WHAT MUST BEARINGS DO? .............................................................................................................. 8
DIFFERENT BEARING CLASSES........................................................................................................... 9
Differences Between Sliding and Rolling Bearings .................................................................. 9 Types of Sliding Bearings .........................................................................................................10
Dry Bearings and Boundary Lubricated Bearings.........................................................10 Mixed-Film Bearings.................................................................................................... 10 Full-Film Bearings........................................................................................................ 10
PRINCIPAL BEARING GEOMETRIES........................................................................................................ 10
BEARING OPERATING CHARACTERISTICS............................................................................................. 11
Bearing Friction, Wear and Temperature ................................................................................... 12
BEARING MATERIAL SELECTION CRITERIA....................................................................................... 14
CAST BRONZE BEARING MATERIALS ................................................................................................ 14
OTHER BENEFITS OF BEARING BRONZES ......................................................................................... 15
SELECTING CAST BEARING BRONZES
BRONZES AND COPPER ALLOYS ....................................................................................................... 17
ECONOMICS AND AVAILABILITY ........................................................................................................ 17
DETAILED DISCUSSION OF SPECIFIC ALLOYS .................................................................................. 19 Tin Bronzes................................................................................................................................ 19 Leaded Tin Bronzes ................................................................................................................... 19 High-Leaded Tin Bronzes.......................................................................................................... 19 High-Strength Brasses ............................................................................................................... 20 Aluminum Bronzes .................................................................................................................... 20 Silicon Brasses........................................................................................................................... 21 Copper Beryllium Alloys........................................................................................................... 21 Lead-Free Bearing Bronzes....................................................................................................... 21 Effect of Other Alloying Elements ........................................................................................... 21
SUMMARY OF CAST BRONZE CHARACTERISTICS AND USAGE ..................................................... 21
TABLE OF CONTENTS\continued
SELECTION PROCEDURE FOR BEARING MATERIALS ......................................................................21 Initial Selection of Candidate Materials Based on Past Usage ..................................................23 Additional Materials Selection Considerations..........................................................................23 Physical Properties of Bearing Materials....................................................................................25 Compatibility with Working Fluids............................................................................................25
DESIGN OF BOUNDARY LUBRICATED BRONZE BEARINGS
CONDITIONS LEADING TO BOUNDARY LUBRICATION .....................................................................29
BOUNDARY LUBRICATED WEAR DATA FOR CAST BRONZE BEARINGS ........................................29
LUBRICATED WEAR LIMITS FOR BEARING BRONZES .....................................................................30
LUBRICATED WEAR RATES FOR BEARING BRONZES ...................................................................... 31
BEARING TEMPERATURES................................................................................................................... 31 Bearing PV factors ..................................................................................................................... 32
DESIGN CONSIDERATIONS .................................................................................................................. 32 Maximum Allowable Bearing Temperatures.............................................................................. 32 Maximum Allowable Bearing Stress .......................................................................................... 32 Clearance ................................................................................................................................... 33 Shafting...................................................................................................................................... 33 Surface Finish ............................................................................................................................ 33 Wall Thickness and Flange Dimensions .................................................................................... 33 Methods of Retaining Bearings.................................................................................................. 34
Press or Shrink Fit ........................................................................................................ 34 Keying Methods............................................................................................................ 35
Grease Grooving Patterns.......................................................................................................... 35 Straight Axial Supply Groove....................................................................................... 36 Cicumferential Grooves ............................................................................................... 36 Recirculating Configurations........................................................................................ 36 Groove Geometry ......................................................................................................... 36
Grease Consumption .................................................................................................................. 37 Regreasing Intervals .................................................................................................................. 38
HYDRODYNAMIC JOURNAL BEARING DESIGN
LOAD CAPACITY OF HYDRODYNAMIC JOURNAL BEARINGS........................................................... 41
THERMAL EFFECTS .............................................................................................................................. 43
TRANSITION TO HYDRODYNAMIC LUBRICATION ............................................................................. 43
DESIGN CRITERIA FOR JOURNAL BEARINGS.................................................................................... 44
Bearing Size .............................................................................................................................. 44 Minimum Recommended Film Thickness...................................................................................44 Design Clearances ......................................................................................................................45 Maximum Temperatures and Temperature Rises........................................................................46 Bearing Stresses and Materials ...................................................................................................46 Safety Factors.............................................................................................................................47
Lubricants and Filtration ............................................................................................................ 47 Geometry Considerations........................................................................................................... 47 Lubricant Grooving.................................................................................................................... 47 Machining Considerations ......................................................................................................... 47
OTHER JOURNAL BEARING DETAILS.................................................................................................. 47 Bearing and Load Rotation........................................................................................................ 47 Geometries to Mitigate Edge Loading due to Shaft Bending.................................................... 48
MATING SURFACES .............................................................................................................................. 48 Shafting Materials...................................................................................................................... 48 Surface Preparation ................................................................................................................... 49 Surface Roughness Levels ......................................................................................................... 49 Hardness of Shafts..................................................................................................................... 49
OTHER ISSUES ...................................................................................................................................... 50
COMPUTER PROGRAMS
BACKGROUND TO THE PROGRAMS.................................................................................................... 63
USING THE HYDRODYNAMIC PROGRAM ...........................................................................................64 Entering Bearing Data ...............................................................................................................55 Lubricant Selection ....................................................................................................................65 Entering Data in Alternate Unit Systems ....................................................................................66
CALCULATING BEARING PERFORMANCE..........................................................................................66 Clearance....................................................................................................................................68 Air-Cooled Design .....................................................................................................................58
APPLYING THE HYDRODYNAMIC PROGRAM RESULTS....................................................................59
USING THE BOUNDARY LUBRICATION PROGRAM ............................................................................60 Entering Bearing Data................................................................................................................60 Friction.......................................................................................................................................60 Units...........................................................................................................................................60 Calculating Bearing Performance ..............................................................................................61
REFERENCES AND APPENDICES
REFERENCES ...........................................................................................................................................65 APPENDIX A. Quantifying Lubricated Wear .............................................................................................67
Archard-Holm Equation .............................................................................................................67 Other Forms of the Archard Equation........................................................................................68 Lubricated Wear under Variable Loading Conditions.................................................................68
APPENDIX B. Thermal Modeling of the Bearing ......................................................................................69 General Heat Transfer Model..................................................................................................... 69 Control of Heat Transfer Mechanisms ....................................................................................... 70
APPENDIX C. Fluid Viscosity Database................................................................................................... 71 Adding Additional Fluids to the Database ................................................................................. 71 Viscosity Conversions................................................................................................................ 71
ACKNOWLEDGMENTS We wish to thank Joseph L. Tevaarwerk for editorial production of this publication. We wish to thank the following for providing photography used in this publication.
Bunting Bearings Corporation
Magnolia Metal Corporation
This Handbook has been prepared for the use of engineers, designers and purchasing managers involved in the selection, design, manufacture or use of copper alloy bearings. It has been compiled from information supplied by testing, research, manufacturing, standards, and consulting organizations that Copper Development Association Inc. believes to be competent sources for such data. However, CDA assumes no responsibility or liability of any kind in connection with the Handbook or its use by any person or organization and makes no representations or warranties of any kind thereby.
Published 1997 by Copper Development Association Inc., 260 Madison Avenue, New York, NY 10016 A1063-00/97
LIST OF SYMBOLS AND UNITS USED
Symbol Explanation Units A apparent area of surface contact m2 AB outer surface area of bearing housing m2 Aj inside bearing area (πBD) m2
Ar real area of surface contact m2 B bearing width m
C radial clearance (Db-Dj)/2 m
CD diametral clearance m Ceff effective radial clearance at θeff m
d diametral wear m d* critical wear depth m
D, Db bearing diameter m
Dj journal diameter m E modulus of elasticity N/m2 e bearing eccentricity m
F bearing radial load N f friction coefficient - Fn applied radial load N
H hardness N/m2 hc convection heat transfer coefficient W/m2 • °K
hmin minimum film thickness m h2min recommended minimum film thickness m
hr radiant heat transfer coefficient W/m2 • °K 4 K wear coefficient -
LIST OF SYMBOLS AND UNITS USED\continued
Symbol Explanation Units k conduction heat transfer coefficient W/m • °K ka heat transfer coefficient to ambient W/m • °K
L total sliding distance m
N journal speed rps
Ne equivalent journal rotation rps Nj original journal rotation rps Nb bearing rotation rps
NF load vector rotation. rps NT transition journal speed rps
P nominal bearing stress Fn/B • D N/m2 Pta heat flow to ambient W R journal radius, D/2 m
Ra arithmetic average of surface roughness µm S Sommerfeld number - T total operational time s
t sliding time s te equivalent sliding time t
ts total sliding time s Tregrease regreasing interval h
U sliding velocity m/s V wear volume m3 Vf bearing grease consumption rate cm3/h
VL total grease volume in bearing m3 w power loss W
α thermal expansion coefficient m/m • °K
ε eccentricity ratio -
εT transition eccentricity ratio - η dynamic fluid viscosity Pa • s ηeff effective viscosity at θeff Pa • s
Λ bearing loading factor - ν kinematic fluid viscosity m2/s θamb ambient temperature °C
θB bearing temperature °C θeff effective bearing temperature °C
θmax maximum lubricant temperature °C ρ material density kg/m3 σy material yield strength Pa 5
Introduction to LubricatedBronze Bearing Design
I. INTRODUCTION
When two surfaces are in relative sliding motion, a normal load may be transmitted between them. Such a system is referred to as a sliding bearing. Under nominally dry conditions, this transmitted load is supported by small irregularities on the bearing surfaces, called asperities. These asperities are in direct contact. Under limited conditions of load and speed, such a bearing will work quite well and experience moderate wear. Materials such as high-leaded tin bronzes have self-lubricating properties that permit fairly high loads to be supported this way.
If a lubricant in the form of a fluid or grease is present between the sliding surfaces, a pressure may develop such that a significant por-tion of the load is transmitted by fluid pressure rather than metal to metal contact. When all the load is supported by fluid pressure, we speak of a full-film or hydro-dynamic bearing. In a truly hydro-dynamic bearing, the two surfaces are thus not in contact at all. Since fluids are easily sheared without damage, and generally have a lower shear resistance than most solids, relative motion between the two bearing surfaces takes place in the fluid film. This results in a lowering of friction and a reduction or elimination of wear. To achieve hydrodynamic or full-film lubrica-tion in bearings requires special attention to several key variables that influence film formation. Most
important among these are the geometry and motion of the bear-ing surfaces, the nature and consis-tency of the fluid employed, and the continual supply of this fluid.
The benefit of having the load supported by fluid pressure is very great indeed. It reduces wear and friction by several orders of magni-tude. Unfortunately we cannot ensure that the correct conditions exist at all times. Contact between two bearing surfaces will invari-ably occur at some point during operation. When contact occurs, behavior of the bearing material is very important in the reliable oper-ation of the bearing. Hence, besides the bearing geometry, bearing kine-matics and lubricant, the bearing materials are of paramount impor-tance. It is thus not difficult to see that the design of lubricated sliding bearings can be quite complex.
Complexity should not, however, be allowed to act as a deterrent to tackling a bearing design because the rewards for a good design are very rich indeed. Well designed bearings often have very long life expectancies and are very low cost from an operational and mainte-nance point of view. One of the first tilting-pad hydrodynamic bearings ever designed and put in service in this country is still oper-ating today, after 80 years of almost continuous service. See Snow1.
The intent of this publication is to describe the principles of lubricated bronze journal bearing
design, including the many alloys now being successfully applied, and to introduce Hydro and Bound, CDA's bearing design software. Together, this text and the software can assist designers in choosing the optimum material and dimensions for anticipated service conditions.
Historical The problem of transporting
heavy loads was significantly reduced by the invention of the wheel. The invention of the wheel was significant, but the bearing sur-face that supported the wheel must be regarded with equal importance. How and when the bearing and wheel were invented is not known, but it may be assumed that once invented, their use spread fairly rapidly. It is also fairly certain that soon it was realized that different types of wood gave different useful lives and that some materials reduced the amount of work required for hauling loads. It was probably also soon realized that smaller shaft bores gave lower friction but also had reduced life.
Today we would quickly under-stand these phenomena through the application of our vast knowledge base. In antiquity these bearing principles would have been deter-mined through experimentation, just like the reduction in effort would have been noticed when wet conditions prevailed, or when animal greases were applied to
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the bearings. It was probably a combination of increased life and reduced effort that made the lubri-cation of wheel axles a regular practice.
Gradual improvements undoubtedly were made all the time to these bearing systems. Materials such as bronze and later, iron, would have increased life, but also increased the attention to be paid to greasing these bearings because of the relative preciousness of these materials. In addition to animal and vegetable fats, the use of pitch-tar, tree resins, and beeswax for bearing lubricants would have developed over time.
How and why bearings worked, and why the introduction of lubri-cants in them lowered the friction remained much of a mystery until the late 18th and into the 19th cen-tury. Most of the developments in bearings during this time were dri-ven by the wheel bearing problems that occurred in the railways. The railways of the time were searching for ways to increase the load and speed capacity of cars and locomo-tives. The limit was always set by the problems encountered by bearing failures.
Matters were not helped along by the almost simultaneous intro-duction of plentiful, but somewhat deficient, mineral oils. Oiliness, the ability to prevent wear under metal-to-metal contact conditions, is almost absent in mineral oils, com-pared to the vegetable and animal oils and fats used up to that time. It was the development of full-film lubrication as we call it today, that gave the breakthrough into bear-ings capable of high loads and high speeds. Advances in both experi-mental techniques and mathematical analysis brought a lot of detail to
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light, fostering an understanding that still serves us quite well today.
The real breakthrough in experimental work, leading directly to the development of the hydrody-namic theory, should be credited to Beauchamp Tower. See Cameron2. Discussing his railroad journal bearing experiments, Tower indicated: "...interesting discovery when oil bath experiments were nearing completion. The bearing seized under increased load (625 psi), and the brass bearing was removed. While the bearing was removed, a 1/2-inch hole was drilled for a lubricator fitting through the cast iron bearing cap and the brass bear-ing. The bearing was reassembled and put in an oil bath lubrication. Oil was observed running out of the hole when the bearing was operated, making a mess. Attempts were made to plug the hole first with a cork and then with a wooden plug. Each one was forced out, indicating high pressure. A 200-psi pressure gage was screwed into the hole and the gage read the maximum gage capacity of 200 psi when the bearing was operated. The estimated bearing pressure was 100 psi."
This indicated to Tower that the shaft was floating on a film of oil whose pressure was more than double the mean bearing pressure. Beauchamp Tower's publications on his landmark bearing experiments stimulated Osborne Reynolds to deve-lop the "physical wedge concept" for hydrodynamic lubrication in 1888.
Once the law of viscous flow was well known, and it was recog-nized that bearings developed their own pressurized lubricant films, the possibility of mathematical prediction of bearing behavior was realized. Petroff developed an
equation in 1883 for estimating the power loss in a journal bearing, knowing the viscosity, diameter, speed and load. He assumed con-stant viscosity and a shaft centered in the bearing. Reynolds, in England, formulated the now famous Reynolds equation in 1886, and actually proceeded to solve it, using the results obtained by Tower in later experiments as an experi-mental verification of his methods. Around the beginning of the 20th century, Stribeck and Sommerfeld in Germany advanced the hydrody-namic lubrication theory toward engineering application. Stribeck established the minimum friction point and experimentally devel-oped the "Stribeck Curve." Sommerfeld produced an analytical solution to the Reynolds equation for journal bearings, making possible the development of a Stribeck curve from theory.
What Must Bearings Do? Bearings are multifunctional
devices. In order to operate effi-ciently and provide long service life, bearings often have to satisfy several requirements simultaneously. These include: ■ Position and support a shaft
or journal and permit motion with minimum energy consumption;
■ Support a fixed load and be able to withstand occasional shock loads;
■ Run quietly and suppress externally generated vibrations;
■ Act as a guide to support reci procating or oscillating motion;
■ Withstand temperature excursions;
■ Accommodate some degree of shaft misalignment;
■ Accommodate dirt particles trapped in the lubricant;
■ Resist corrosion — under normal service conditions as well as during storage or extended down-time; and
■ Provide easy maintenance. As with all engineering endeav-
ors, selection of the type of bearing and the bearing material usually involves some compromise among the often competing design require-ments. Bronze bearing alloys can-not satisfy all needs at all times, but they do offer the broadest range of properties among today's sleeve bearing materials and can perform well under a very wide range of operating conditions.
Different Bearing Classes When we speak of bearings, we
mean a device that can transmit a load from one surface to another, when these surfaces experience a relative motion. This may be achieved by either some form of rolling motion or by some form of sliding action, see Figure 1.1.
Based on this fundamental difference we divide bearings into two broad classes as either: Rolling-Element Bearings (REB) or Sliding-Surface Bearings (SSB). These two classes are then further subdivided according to different forms of surface geometry and dif-ferent types of surface interactions, see Figure 1.2.
Differences Between Sliding and Rolling Bearings
There are important differences between the two classes of bearings that are worth noting. Many of these differences will favor the use of one type of bearing over the other.
Figure 1.1. Load Carried by Rolling (I) and Sliding (r) Motion.
Figure 1.2. Bearing Classes and Different Types within Each Class.
As may be observed in Table 1 on page 10, there are so many inherent advantages in sliding bearings that one should make every available effort to use them. Sliding bearings are used because they are simple, reliable, compact, durable, and
because they can be custom-made economically for an almost limit-less variety of applications—including and exceeding all those to which rolling-element bearings can lay claim.
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Sliding BearingsNeed to be purposefully designedand manufactured.
Bearing, per se, usually less costly.Overall cost is less for small bearingsystems.
Service life not predictable, but can becapable of providing unlimited life.
Offer more design flexibility and versatilityand broader spectrum of materials.
More tolerant of abuse. May requireperiodic maintenance.
Can provide high levels of beneficialdamping.
Sometimes higher friction. Wear, underfavorable conditions, can approach zero.
Little outside help available.
Rolling Element BearingsOff-the-shelf finished bearingsavailable.
Lower overall cost for larger bearings.Small bearings may have higherrelative cost.
Statistically predictable finite life.
Limited by available standard sizes,configurations and materials.
Very sensitive to abuse. Minimalmaintenance, short of replacement.
Minimal damping characteristics.
Finite, generally low frictionand wear.
Lots of outside help available(suppliers).
Table 1. Differences between Sliding and Rolling Bearings.
The use of rolling elementbearings in every conceivableapplication is based more on thelack of suitable design skills insliding bearing design, rather thanan inherent superiority of rollingelement bearings per se.
Types of Sliding BearingsWithin the sliding bearing
category there are various types ofbearings broadly categorized asfollows:
■ Dry bearings and boundarylubricated bearings,
■ Mixed-film bearings, and■ Full-film bearings.
Dry Bearings and BoundaryLubricated Bearings
In the dry bearings, the lubri-cant is provided by solid particlescontained within the bulk material.Besides lead, typical solid lubri-cants include graphite, molybdenum
disulfide (MoS2) and PTFE. A verysuccessful line of dry bearings usesa sintered bronze material on asteel backing. The voids in thesintered material are then filledwith a mix of lead and PTFE.
Boundary lubrication exits inliquid (or grease) lubricated bear-ings when there is no load carryingfilm and the lubricant serves mainlyto keep friction fairly low. Castbronze bearings are used extensivelyfor boundary lubricated applica-tions. We will return to this topiclater.
Mixed-Film BearingsOil-impregnated porous metal
bearings are the most commonlyused lubricated bearings whereinsufficient film exists to carry allthe load. Only under very favorableconditions will the complete loadbe supported by the fluid filmdeveloped. These bearings containvoids within which a liquid lubri-
cant can be maintained and providedin sufficient quantity for successfuloperation. Capillary action withinthe network of voids helps supplythe surface with lubricant. Addition-al lubricant may be available to thebearing in the form of storage infelt reservoirs.
Full-Film BearingsIn these types of bearings the
lubricant is applied to the workingsurface from an external source.Lubricants typically used are oilsor greases. They may also be otherfluids such as water, process fluidsor even gases. Full-film bearingsfall into one of four categories:
■ Hydrodynamic, where theshaft or bearing rotation gener-ates a thin load carrying lubri-cant film,
■ Squeeze-film bearings, wherethe normal motion of thesurfaces generates a thinlubricant film ( connecting rodsin internal combustion engines),
■ Hydrostatic, where lubricant issupplied under very highpressure sufficient to separatethe metal surfaces, and
■ Hybrid bearings, where bothhydrostatic and hydrodynamicfeatures are used.
Principal Bearing GeometriesSliding bearings may be further
categorized by the direction of loadsupport that they provide. Broadlyspeaking this would be the journalbearing and the thrust bearing, seeFigure 1.3.
The journal bearing, alsoknown as a sleeve bearing, a bush-ing or a radial bearing, can supporta radial load on a shaft. This radialload may act in any orientation, andmay vary with time. Each of the
10
different lubrication modesmentioned above is possible witha journal bearing. In its simplestform, a journal bearing consists ofa shaft that fits through a clearancehole in a plate. This simple geometryis such that a full-film lubricationof the shaft and bearing may bepossible under certain circumstances.The clearance space between theshaft and bearing form a naturalwedge, and no complex machiningtechniques are needed to makea simple hydrodynamic journalbearing.
A thrust bearing is intended tosupport an axial thrust load on ashaft. It may consist of a simpleflat washer of suitable material that
with a thrust bearing requiressurface features that need to bemachined into the thrust washersurface. They may consist of sim-ple grooves or dimples, or verysophisticated shapes such aswedges and spiral groove patterns.Because of the additional complexityin designing hydrodynamic thrustbearings, we will limit this discus-sion to journal bearing designs.
Bearing OperatingCharacteristicsSliding bearings can operate inthree fundamental modes, and it isimportant to understand that, for agiven set of system requirements,
Figure 1.3. Machine Member with Journal Bearings and a Thrust Bearing.
rides against a thrust collar on theshaft. This simple form of thrustbearing will only be able to operateunder boundary lubricating condi-tions because no natural wedgeaction takes place. Hence, similarto journal bearings, thrust bearingsbenefit greatly from the boundarylubrication characteristics ofcast bronzes.
To obtain full-film lubrication
their operating modes can be con-trolled by design. A good basisfor the understanding of the funda-mental phenomena in slidingbearings is the modified Stribeckdiagram shown in Figure 1.4. Thisdiagram presents three lubricatedbearing performance parametersthat are critical in slider bearingdesign. They are:
■ Friction coefficient, a measure
of the effort needed to movethe surfaces relative toeach other,
■ Wear coefficient, a measureof the amount of materialloss during the sliding and adetermining factor in bearingdurability, and
■ Local bearing temperature,a measure of the likelihoodof sudden failure that maybe experienced in the system.Variations of these design
parameters are shown as a functionof a so-called hydrodynamic vari-able that contains velocity, viscosityand load as important variables. Inessence, the hydrodynamic variabledetermines how a load is supportedin a sliding bearing.
Hence, the load transmittedbetween two bearing surfaces maybe carried entirely by a continuoushydrodynamic lubricant film,entirely by the surface roughnesspeaks on the two opposing surfaces,or by a combination of the two.Thus, depending on the method bywhich the load is carried betweentwo surfaces, we may define threelubrication and corresponding wearregimes as:
■ Boundary lubrication. Large-scale asperity contact occurs.Load is carried by asperitiesand wear is moderate to heavy,depending on the nature of thesurfaces and the materialsinvolved.
■ Mixed-film lubrication. Alubricant film is present, butintermittent contact occurs.Load is carried partially byfluid pressure and partially byasperity contact. Wear ismoderate to light, dependingon the chemical activity ofthe lubricant and bearing
11
Figure 1.4. Modified Stribeck Curve for Lubricated Sliding Surfaces.
materials and on the contact-ing surfaces.
■ Load carried by Hydrodynamicaction only. When conditionsof full hydrodynamics exist,the surfaces are completelyseparated by a lubricant film,and the load is carried by fluidpressure only. Wear in thisregime is very low to non-existent.Transition from boundary to
hydrodynamic lubrication occurswhen the mean film thickness sep-arating the surfaces is greater thanthe local system roughness. Lowroughness tends to promote earlytransition to hydrodynamics. It isalways the desired goal in bearingdesign to work to the right of thistransition. However several con-
straints may preclude operation inthis domain and the bearing mayhave to operate for considerableperiods of time in the boundarylubricated regime.
Bearing Friction, Wear andTemperature
Examination of the behaviorof bearing friction, wear and tem-perature as a function of the bearingoperating regimes gives us someimportant insight into bearingmaterials selection and overallbearing design.
Bearing Friction (solid line inthe lower half of Figure 1.4.) remainsalmost constant as we start to move
from low to high hydrodynamics,and then experiences a rather suddendrop in the "mixed-film lubrica-tion" region. The lowest frictionoccurs at the "transition point," andafter this the friction rises slowly.The explanation for this frictionbehavior lies in the fact that frictionat low hydrodynamics is almostcompletely governed by surfaceinteraction. At high hydrodynamics,it is almost exclusively fluid fric-tion (dashed line).
Asperity friction may be due toadhesive or abrasive contact. Thefriction level depends on the bear-ing material and its chemical inter-action with the lubricant. Frictionlevel is nearly velocity independent.To achieve low friction in theboundary lubricated region is thus amaterials selection issue.
In the fluid friction region thenature of the bearing surfaces isnot relevant because there is noasperity contact. The direct interac-tion properties of the bearing andshaft materials are not importanthere; however, the material musthave sufficient plastic flowstrength (indicated by hardness)and fatigue resistance to avoidgross dimensional changes due tohigh fluid pressures.
Bearing Wear (upper half ofFigure 1.4.) decreases drastically aswe move from low to high hydro-dynamics, showing a rather suddenreduction in the "mixed film lubri-cation" region. This sudden dropoccurs for the same reason that thefriction drops, namely the reduc-tion in asperity interaction due toload support by the lubricant film.
Bearing wear can occur due toseveral mechanisms. In slidingbearings, we typically encounterwear due to adhesion, two-body
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abrasion, or three-body abrasion.Adhesive wear occurs when inter-acting materials form solid bondsat the points of contact.
Sliding of the surfaces relative toeach other causes the breakage ofthese bonds and results in removal ofsurface material. Two-body abrasionoccurs when metal surfaces are indirect contact and where asperitiesfrom a hard surface penetrate into theother softer surface. Relative motionbetween the two now causes materialremoval of the softer surface. Bothadhesive wear and two-body abra-sive wear occur in sliding bearingswhen the surface separation is lessthan the mean operating roughness.
Adhesive bearing wear can becombated by selecting bearing mate-rials with low solubility into eachother. Materials such as indium,cadmium, lead, tin, silver and bis-muth have low solubility with steeland are thus excellent choices asbearing materials. Note all the mate-rials mentioned are very soft. It isalso possible to add substances to alubricant to contaminate the likelybonding sites.
Two-body abrasion can be min-imized by selecting harder bearingmaterials or by reducing the surfaceroughness on the harder of the twosurfaces. Increasing hardness of thebearing material may be detrimen-tal to some other important aspectof the bearing.
Three-body abrasion is causedby hard particles in the lubricant.They may originate from sourcesoutside the bearing such as dustand sand, or they may be generatedwithin the bearing system itself dueto adhesive or two-body abrasion.
There are several ways inwhich three-body abrasion can be
combated. If the source of particlesis external, we may employ lubri-cant filters and seals to reduce theconcentration in the bearing. Third-body abrasion due to self-generat-ed wear particles can be reducedby increasing the lubricant flushingaction. We could also use harder,more wear resistant bearing materials.To avoid extensive bearing damagedue to very large hard abrasive par-ticles, an accommodation mecha-nism is incorporated by providing afairly thick soft layer. Large, hardparticles embed themselves intothis layer. This however can leadto the two-body abrasion of theharder (normally shaft) material.
Bearing Temperature (dotted linein Figure 1.4.), which results fromthe product of friction and slidingvelocity, is low at low slidingspeed, reaches a peak, and thenreduces due to a drop in friction.Further increases in speed pro-duces a minimum temperature, andthen it starts to rise again. The ini-tial rise in temperature is almostexclusively the result of solid sur-face friction, while at high hydro-dynamics it is completely due tofluid friction.
There are several importantobservations that can be madeabout the bearing temperature.The initial rapid rise is the result ofhigh friction coupled with thevelocity difference between thetwo surfaces. Remember, this is theboundary lubrication regime, andalmost all the bearing load is car-ried by direct asperity contact. Thefriction in this regime is due toadhesive and abrasive asperity con-tact. It is well known that increas-ing temperature tends to promoteadhesion between materials. Hence
the propensity for asperities toweld together increases rapidly inthe boundary lubricated region.
Depending on the materials, asufficiently high temperature maybe reached to cause scuffing dam-age. Scuffing damage may be cata-strophic to a bearing operation inthe form of galling and seizure.
Key factors that tend to keepthe peak bearing temperatures loware low friction (low adhesion),early transition, good heat conduc-tion and low, local normal stress.As far as material selection is con-cerned, we should select soft mate-rials with low friction and highconductivity. Copper based bearingmaterials possess several of thesekey requirements.
From the foregoing discussionof lubrication regimes we shouldnote that a very important consid-eration of the bearing design is thebearing material itself. This iswhere the various bronze materialsare providing us with an excellentchoice.
Readers interested in a more in-depth explanation of asperity inter-action and the impact of materialsmay wish to consult Rabinowicz3.An excellent treatise on the differ-ent wear modes in bearings isgiven by Lansdown4.
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Bearing MaterialSelection Criteria
Alloy selection is obviouslyvery important in the design ofbearings and especially when oper-ating in the boundary lubricatedregime. While the choice of alloyis less critical for full-film bear-ings, it does influence performanceduring the non-hydrodynamicconditions at start-up or upset oper-ation brought about by shockloads, dirt intrusion, temperaturesurges and intermittent lubricantflow. Certainly, the more preciselya bearing's operating conditionscan be defined, the simpler andmore obvious will be the choiceof bearing materials.
Selection of the specific bear-ing alloy requires a very carefulconsideration of the applicationand the characteristics of the mate-rial itself. There is no single bestbearing material. The following areconsidered to be the attributes of a"good" bearing material:
■ A low coefficient of frictionagainst steel. The need for thisproperty is self-evident,however good inherentfrictional properties are partic-ularly important in cases ofunreliable lubrication, i.e.,boundary- or mixed-filmconditions. In such cases, themetal itself must be reliedupon to provide adequate anti-friction behavior until lubrica-tion is restored.
■ High wear resistance. Thisproperty is different from, butrelated to strength, hardness,friction and a number of otherproperties. As with other prop-erties, wear resistance is mostimportant when lubricationmomentarily fails. Wear resis-tance is also essential when
bearings are run against hard-ened steel shafts.
■ The ability to conform tonon-uniformities in the shaftsurface and to shaftmisalignment. Low strengthor relative softness are some-times advantageous in abearing alloy. Not all shaftsare turned to precision toler-ances or finishes, and serviceconditions can provoke mis-alignment; a softer alloy cantolerate such defects.
■ Good corrosion resistance.Pump bearings are routinelyexposed to sea water, sourmine waters, acids and anynumber of corrosive industrialprocess streams. All bearingsoccasionally get wet, and evensome constituents of lubricantsare or can become aggressive.It is therefore important thatbearing materials exhibitsufficient corrosion resistance,both in service and duringstorage.
■ High compressive strengthcombined, where needed, withgood impact strength.Strength obviously determinesthe bearing's load-carryingcapacity, while impactbehavior frequently dictatesthe permissible types ofservice. Alloys with lowimpact strength must beadequately supported insuitable housings.
■ Low shear strength. Thisproperty is characteristic ofcertain leaded alloys, whoseability to smear across theshaft surface provides a formof "internal lubrication." Thisis highly beneficial whennormal lubrication is intermit-tent or unreliable.
■ High creep strength. Somebearings must withstandelevated temperatures. In suchcases, creep and stress-ruptureproperties have to be takeninto account.
■ High fatigue strength. Somebearings are subject torepeated pounding, others topulsating or vibratory stresses.High fatigue strength generallyaccompanies high tensilestrength, but there areexceptions to this rule.
■ High thermal conductivity.Heat is damaging to mostbearings and lubricants, there-fore the ability to conductfrictional heat away from thebearing surface results inlower operating temperatures.
■ A uniform metallurgicalstructure. Sound, non-poroussurfaces are needed to promoteand maintain a stable lubricantfilm.
■ Compatible thermalexpansion. The thermalexpansion of the bearing mustbe known in order to establishproper clearances at the bear-ing's operating temperature.Some of these attributes are
obviously more important thanothers, and only a few may becritical in particular installations.All, however, influence bearingperformance to some degree, andnone should be ignored.
Cast BronzeBearing Materials
Literally hundreds of differentbearing alloys are available for usewith steel mating surfaces. Alongwith sintered and wrought bronzes,aluminum and zinc alloys and avariety of polymers and composites,these materials make up many of
14
the sliding bearings inuse today. For additionalinformation, the readeris referred to an excel-lent detailed reviewby Pratt5 and a moregeneral descriptionby Glaeser6.
Many bearingmaterials offer promis-ing individual proper-ties (light weight, lowfriction) to meet partic-ular service require-ments, but the castbearing bronzes offerthe broadest range ofapplicability. Theirfavorable combinationsof mechanical andphysical propertiesallow the designer tooptimize a bearingdesign without compromisingneeded characteristics unnecessarily.Table 1.2. from CDA7 comparesmany of the tribologically impor-tant criteria for a range of common-ly used materials.
Note the broad range of bear-ing bronzes to choose from, andthe superior load and wear perfor-mance of the copper based materials.These latter two properties becomeextremely important when lessthan ideal lubrication conditionsexist. Chapter 2 contains descrip-tions of the various bearing bronzesin greater detail.
Bearing Alloy Families
Leaded Red Brasses
Tin Bronzes
High-LeadedTin Bronzes
Aluminum Bronzes
High-Strength Brasses
Copper Beryllium Alloys
Leaded Coppers
Tin-Based Babbitts
Lead-Based Babbitts
Aluminum Low-Tinor Lead Alloys
Aluminum High-Tinor Lead Alloys
Load Capacityand FatigueResistance
Moderate
High
Moderate /High
Very High
Moderate
High
Moderate
Moderate
Moderate
High
Moderate
MaximumOperating
Temperature
Moderate
High
High
Very High
Moderate
High
High
Moderate
Moderate
High
High
Conformabilityand
Embeddability
Low
Moderate
Good
Poor
Poor
Poor
Very Good
Excellent
Excellent
Good
Good
Resistance toSeizure
Low
Moderate
Good
Moderate
Moderate
Poor
Very Good
Excellent
Excellent
Low
Moderate
Hardnessand Wear
Resistance
Good
High
High
Very High
High
Very High
Moderate
Low
Low
Moderate
Moderate
Table 1.2. Comparison of Important Bearing Selection Criteria for Commonly Used Materials.
Other Benefits ofBearing Bronzes
Besides the superior strengthand wear properties of bearingbronzes, there are additional bene-fits when using these materials.Some of these are:
■ bearing bronze materials arereadily available,
■ all grades can be produced inalmost any size in large orsmall quantities,
■ normal machine shop facilitiesare adequate for preparation,
■ substantial structural strengthpermits the use of bearingbronzes as an integral part ofthe structure. This inherentstrength also permits their use
without backing,■ no need to rely upon specialist
manufacturers and suppliers,and manufacture can usuallybe in-house,
■ easy to fine tune bearings. If acharacteristic of a specificbearing is found deficient, areview can be made of theimportant material propertiesneeded and a selection madefrom available materials toprovide improved properties.The large selection of castcopper-based bearing alloysprovides a wide choice ofengineering properties, so thatincremental adjustments canbe made.
15
Properties and Selection ofCast Bearing Bronzes
SELECTING CAST BEARING BRONZES
A very important aspect of sliding bearing design is the selec-tion of the actual bearing materials. Literally hundreds of different bearing alloys are available for use with steel mating surfaces. Selection of a specific bearing alloy requires very careful consideration of the application and the material char-acteristics themselves. There is no single best bearing material. Technically, an assessment must be made of component and system requirements to allow placing a priority on the material properties for a given application.
Bronzes and Copper Alloys Many bearing materials offer
promising individual properties (light weight, low friction) to meet particular service requirements, but the cast bearing bronzes offer the broadest range of applicability. Their favorable combinations of mechanical and physical properties allow the designer to optimize a bearing design without compro-mising needed characteristics unnecessarily. The large selection of cast copper-based bearing alloys provides a wide choice of engi-neering properties. Table 2.1, com-piled from data presented in CDA8, gives the composition of the most important cast bearing bronzes in use today.
Economics and Availability As with all engineering, eco-
nomic factors play heavily in the
selection of materials. Therefore, the selection of a material also requires a review of the economic factors. Overall costs are frequently the deciding factor in selection of a bearing material. Some materials cost more than others. Bearing costs are, to a certain extent, sub-jective. The economic assessment should also include factors such as availability, ease of manufacture, replacement cost, the degree of precision required in its manufac-ture and installation, spare parts cost, and ability of making incre-mental adjustments to the bearing.
While bronze bearing alloys are certainly not the least expen-sive engineering materials, they are easily competitive in terms of performance and life-cycle costs. Finally, and not incidentally, bronze sleeve bearings offer the distinct advantage that virtually all grades can be produced in almost any size in large or small quantities.
Cast bronze bearing alloys are available in a large variety of stan-dard and custom shapes and sizes. Bearing blanks are cast as cylindri-cal shapes using the one of several techniques available. They may be sand cast, chill cast, continuous cast or centrifugally cast. The rate of cooling of the molten alloy influences the grain size of the solidified material, and slow cool-ing usually gives a coarser struc-ture with reduced mechanical properties. Chill casting can be used instead of sand casting to get
improved mechanical properties. A further variation is centrifu-
gal casting in which the mold is rotated during casting. Any impuri-ties which are present are usually less dense and are therefore sepa-rated towards the center of the mold where they can be removed, and as a consequence a cleaner alloy is produced. With centrifugal casting methods, however, segre-gation of high lead content alloys can occur. Continuously cast alloys are also of high quality, with prop-erties comparable to alloys cast by centrifugal casting.
The cast bearing bronzes are available in a great variety of sizes and shapes. Particularly suitable for the manufacture of bearings are the following:
Tin and leaded tin bronzes: ■ As finished bearings in sizes
ranging from 3 mm to 152 mm (5/16 in to 6 in ) in diameter, up to 230 mm (9 in) long;
■ As solid bars ranging from 10 mm to 260 mm (3/8 in to 10 in) in diameter, up to 2700 mm (105 in) long; and,
■ As cored bars 25 mm to 300 mm (1 in to 12 in) in diam-eter, in various bore sizes, also up to 2700 mm (105 in) long. Aluminum bronzes:
■ As solid bars 13mm to 200 mm (0.5 in to 8.0 in) in diameter, from 3,000 mm to 3,700 mm (120 in to 144 in) long;
■ As cored bars 30 mm to 260 mm (1.25 in to 10 in) in diameter, in
17
DesignationUNSLeaded Red BrassC83600
Tin BronzesC90300
C90500
C90700
Leaded Tin BronzesC92200
C92300
C92700
High-Leaded Tin BronzesC93200
C93400
C93500
C93600
C93700
C93800
C94100
C94300
C94500
High-Strength BrassesC86300
C86400
Aluminum Bronzes
C95300
C95300HT
C95400
C95400 HT
C95500
C95500 HT
C95520
C95800
Silicon BrassesC87600
C87900
Copper Beryllium AlloysC82800
Leaded Copper
C98820
Lead-Free BronzeC89320
SAE
40
620
62
65
622
-
63
660
-66
M-64
64
67
-
(AMS-4840)
-
430B
68b
-
-
-
-
-
-
_
-
484
-
Cu
85
88
88
88
88
87.3
88
83
84
85
80
80
78
73
68
72
63
59
89
89
85
85
81
81
75
79
90
65
96.6
Rem
89
Sn
5
8
10
11
6
8
10
7
8
5
7
10
7
5.5
5
7
_
-
-
-
-
-
-
-
-
_
-
-
_
6
NominalPb Zn
5
-
-
1.5
0.7
2
7
8
9
12
10
15
20
25
19
_
1
-
-
-
-
-
-
-
_
-
-
42
-
5
4
2
-
4.5
4
-
3
-1
1
-
-1
.8
1.2
25
40
-
-
-
-
-
5.5
34
-
_
-
Composition, Wt%Fe Ni P
--
_
--
--------
3
-
1
1
4
4
4
4
5
4
-
-
_
-
-
-
_
-
-
_
-
-
-
-
-
-1
1
-
-
-
-4 _
4
5
4.5
_
-
-
_
-
Al
--
_
--
--
-----
6
-
10
10
11
11
11
11
11
9
-
-
_
-
Other
_
_
-
_
--
--------
3 Mn
-
-
-
-
-
-3 Mn
1 Mn
4.5 Si
1 Si
2.6Be/
.5Co/
.25Si
_
5 Bi
Table 2 .1 . Nominal Compositions of the Most Common Cast Bearing Bronzes.
18
various bore sizes, up to3,700 mm (144 in) long;and,
■ As rectangles, 6 mm x 26 mm(0.25 in x 1.0 in) to 75 mm(3 in) square, up to 3,700 mm
(144 in) long.
Custom castings are availablein most bearing materials. Theyrange in size from miniatures only6 mm (0.25 in) in diameter to largerings up to 3 m (10 ft) across.
Detailed Discussion ofSpecific Alloys
The broad classification of castbearing bronzes in Table 2.1 arealong composition lines. Differentlevels of alloying elements impartcharacteristics to the individualmaterials that may be used in thematerials selection. The followingis a fairly detailed discussion of thespecific alloys.
Tin BronzesTin increases the strength of
copper alloys. Unless it is presentin high concentrations, it has onlya small effect on thermal conduc-tivity, compared with most otheralloying elements. Copper-tinbearing alloys, traditionally calledtin bronzes, also exhibit low fric-tion coefficients against steel. Thecombination of these propertiescauses the surface temperatures ofthe tin bronzes to tend to remainlower than other bearing alloys.Since heat adversely affects allbearings, this is seen as a distinctadvantage.
All of the alloys in this seriescontain more than 5% tin andcontain the hard intermetalliccompound Cu31Sn8 in theirmicrostructure. The more tin(C90300 < C90500 < C90700), the
greater the proportion of Cu31Sn8
will be present. The hard inter-metallic compound imparts highwear resistance, but it also causesthe alloys to be somewhat abrasive,and as a result, the tin bronzesshould be used against hardenedsteel shafts (minimum hardness300-400 HB). The addition of zincto tin bronzes displaces some ofthe tin and increases the presenceof a strong delta phase. Zinc istherefore added as a strengtheningagent, as in alloys C90300 andC90500.
The tin bronzes are hard andstrong, and have good corrosionresistance, especially against sea-water. They are wear resistant andwithstand pounding well. The tinbronzes can be classified as beingonly moderately machinable.They can be turned, bored andreamed, but are difficult to broach.
The alloys work well withgrease lubricants. They can func-tion as boundary-type bearingsdue to their ability to form polarcompounds with small traces oflubricants, thus stabilizing (holdingon to) extremely thin organiclayers and thereby reducing thechance for metal-to-metal contact.Lacking lead, however, the tinbronzes require adequate andreliable lubrication.
Leaded Tin BronzesThis group of tin bronzes
contains between one and two per-cent lead, chiefly to improve theirmachinability. Their lead content istoo small to materially affect theirbearing properties, and they can bethought of as free-cutting versionsof the tin bronzes described above.It therefore follows that they areused in applications similar totheir lead-free counterparts and are
especially advantageous wherehigh-speed volume productionand/or complex shapes demanda relatively large amount ofmachining.
High-Leaded Tin BronzesThis class of alloys consists of
the most commonly used bearingmaterials. They rank somewhatlower than the unleaded or leadedcopper-tin alloys described abovein load-carrying capacity, howeverthey adequately satisfy require-ments for bearings operating undermoderate loads and medium-to-high speeds—the bulk of bearingapplications.
Lead has very low solubility inliquid copper and is almost entirelyinsoluble in solid copper or its alloys.Further, lead melts at a relativelylow temperature (327 C, 621 F),and when bearings are cast, thelead in the alloy freezes last, form-ing irregular globules betweenboundaries of the copper-tin alloy.The lead content in these alloys,nominally between 7% and 15%,is sufficiently high to improve theirbearing properties. The islands offree lead tend to smear over thebearing and shaft surfaces acting,in effect, like a built-in lubricant;this can prevent seizing in theevent of an interruption in thelubricant supply. These alloys aretherefore especially recommendedfor boundary-lubricated andmixed-film applications. Thealloys can be run against unhard-ened shafts. Like the lower-leadedbronzes described above, thesealloys are free-cutting.
Since lead is not in solid solu-tion, its effect on thermal conduc-tivity is much lower than its highproportion of the microstructurewould suggest. High-leaded tin
19
bronzes therefore retain much ofthe favorable thermal conductivityof their unleaded counterparts.Lead does, however, reduce thealloys' strength and ductility, there-fore alloys with very high leadcontents (C93800 and C94300 atnominally 15% and 25% lead,respectively) should be used atlower operating stresses and insituations in which there is littlechance of impact or shock loading.
In a boundary-type bearing,one rule of thumb advises thatdesigners choose the softest (low-est strength) alloy able to supportthe applied load. The advantageoffered by this method of alloyselection lies in the fact that softalloys such as high-leaded tinbronzes are better able to conformto shaft misalignment or deflection,and can accommodate (embed) dirtparticles carried in the lubricantstream, be it oil or grease. Somedesigners follow this rule to thepoint of lengthening the bearing toreduce the applied stress, therebyenabling the use of softer materials.
Alloy C93200 (SAE Alloy660) is generally considered to bethe workhorse alloy of this series.Originally developed as a low-tincomposition during World War II,the alloy remains in wide usetoday. Major areas of applicationinclude light to moderate dutygeneral purpose bearings.
Alloy C93600 can be thoughtof as a modified version of AlloyC93200; it contains about one-third as much zinc and almosttwice as much lead as the SAE 660alloy. As a result of the alloy's highlead content, its machinability andanti-seizing properties are consid-erably improved. Reduced zinccontent improves corrosion resis-tance somewhat. High hardnessand strength impart the alloy with
good pounding resistance.Alloy C93700 exhibits good
corrosion resistance against sulfuricacid (in limited concentrations),acid mine waters, mineral watersand paper-mill sulfite liquors. Ithas excellent wear resistance athigh speed and heavy pressureand, among alloys in this family,tolerates shock and vibration well.
Alloy C93800 can be charac-terized as having fair strength,good corrosion resistance to sulfu-ric acid and sour mine waters. Ithas fair wear resistance but excel-lent antifriction properties. It isnon-seizing, readily machinableand can be used where lubricationis doubtful.
Alloy C94100 has moderateload carrying capacity but, like theother members of this family, itexhibits excellent antifriction prop-erties. It is especially good for useunder boundary and mixed-filmconditions.
High-Strength BrassesThe high-strength brasses
(sometimes improperly referred toas manganese bronzes) are modifi-cations of the familiar 60% Cu-40% Zn yellow brass known asMuntz Metal. Alloy C86300 con-tains manganese, aluminum andiron, which raise its tensile strengthto well over 800 MPa (115 ksi).Alloy C86400 is somewhat lowerin strength, but it contains onepercent lead to improve itsmachinability. Despite their hightensile strength, the alloys' fatigueresistance can only be rated asmoderate. These high-tensile brassescan operate under very high loadsand at moderately high speeds;however, they require hardened,well aligned shafts and reliablelubrication. Being relatively hard,
they have little capacity to embedtrapped particles and therefore donot tolerate dirty lubricants.
Aluminum BronzesAluminum bronzes are the
highest-strength standard copper-based bearing alloys. Aluminumis a potent strengthener in thesealloys; in general, the higher thealloys' aluminum content, the high-er their strength. Alloys with alu-minum contents higher than about9.5% can be heat treated, and thisis noted in the designation "HT"following the alloys' UNS numbers.Alloy C95500HT, for example,can attain tensile strengths inexcess of 800 MPa (115 ksi).
One interesting feature of thealuminum bronzes is their highelevated temperature strength. Thecompressive strength of C95400 at260 C (500 F) is the same as thatof tin bronzes at room temperature.The aluminum bronzes have thehighest fatigue strength of allbronze bearing materials, and theycan resist repeated and severeimpact loads very well. Oneimportant disadvantage is their rel-atively poor machinability. Theycan be turned, bored and reamed,but like the tin bronzes, they aredifficult to broach.
Like the high tensile brasses,most of the aluminum bronzesmust be used against steel shaftshardened to greater than 500 HB.Alloy C95200 is somewhat moreforgiving in this respect. As aclass, aluminum bronzes requirereliable full-film lubrication toprevent metal-to-metal contact andpossible scoring. Both bearing andshaft should be machined to surfacefinishes finer than 0.4-0.5 µm (15-20 µinch) rms. The alloys do notembed dirt well, and generally
20
require good shaft alignment.Their thermal conductivity is onlyslightly lower than some of thelower strength alloys, and as aresult, they can be used at moderatespeeds if shaft hardness, shaftalignment and lubrication are allwell controlled.
Silicon BrassesSilicon imparts good castability
to copper-zinc alloys, and alsoadds significantly to the alloys'strength. Silicon brasses are notamong the most common bearingalloys, but they do have good bear-ing characteristics at moderatelyhigh speeds. They are quite readilymachinable, considering theycontain no lead and are higher instrength than standard tin bearingalloys. Silicon brasses require reli-able, clean lubrication (dirt embed-ding ability in these relatively hardalloys is only rated as fair). Thealloys should be used againsthardened shafts.
Copper Beryllium AlloysCopper beryllium alloys can
be heat treated to attain higherstrengths than any other copperalloy. Heat treatment is fairlystraightforward: solution annealingat 780-800 C (1450-1500 F) isfollowed by water quenching andaging at 340 C (650 F). This heattreatment, in alloy C82800,produces tensile strengths at orhigher than 1,100 MPa (165 ksi).Other copper beryllium alloyshave similar or slightly lowerstrengths.
Copper beryllium alloys havegood bearing properties. Whenfully hardened, they withstandextremely high stresses. Heat treat-ment can be adjusted to produce arange of mechanical properties,
and the alloys can be used in lessdemanding applications. Copperberyllium alloys are, however,quite expensive and their use istherefore usually reserved forapplications in which their strengthcan be fully exploited.
The bearings require very hardshafts, machined to close tolerancesand very precise alignment. Theyrequire reliable lubrication. Dirtembedding properties are poor.Although very strong, the alloyshave fair to poor impact resistance,therefore bearings should besupported as required by suitablehousings.
Lead-Free Bearing BronzeBismuth may be substituted
for lead in the cast bronze bearingmaterials. Lead-free bronzes areformulated to mimic the propertiesof the leaded alloys but without thesafety concerns of lead. Friction,yield and tensile strength andcorrosion resistance are all compa-rable to leaded bearing bronzes.Alloy C89320 is thus very similarin performance to C93200.
Effect of Other Alloying ElementsThe compositions of the bearing
alloys described above have beenstandardized and can be orderedaccording to their UNS designa-tion or applicable standard specifi-cations. As in most cast alloys,allowable compositions are givenin ranges to accommodate foundrypractice. Except in the case ofcopper beryllium alloys and alu-minum bronzes, minor deviationsfrom set compositions have onlyminor effects, if any, on mechani-cal property.
Modifications to standardcompositions are always possible,of course. These may be called for
to accommodate special or severeservice conditions. For example,manganese, aluminum and phos-phorus can be added in smallamounts to enhance the propertiesimparted by one or more of themajor alloying elements; tin, zinc,and in some cases, silicon.Manganese increases strength butmoderately decreases ductility. Itdoes, however improve an alloy'shigh-temperature working proper-ties. Aluminum, a potent strength-ener in its own right, tends to raisethe strength of copper-zinc andcopper-tin alloys when added insmall amounts. Phosphorus is adeoxidizer and potent strengthener.It also improves fluidity duringcasting. When used to excess,phosphorus can give rise to local-ized hard spots, a condition whichobviously should be avoided.
Summary of Cast BronzeCharacteristics and Usage
A distillation of the majorbearing characteristics and usageof the different cast bronze materi-als is shown in Table 2.2. Thistable may be used for an initialscan for potential materials orwhen searching for an improvedmaterial.
Selection Procedure forBearing Materials
The selection of a suitablebearing material for a given appli-cation is a rather difficult taskbecause, unlike the theoreticalcalculations used for film thicknessdeterminations, a large number ofvariables are involved. In practicethough, we seldom design a com-pletely new bearing system. Oftenthere is a similar design, or anextension of a given design that wecan glean some information fromfor the start of a material selection.
21
Alloy
Leaded Red Brass
Tin Bronzes
Leaded Tin Bronzes
High-Leaded Tin Bronzes
High-Strength Brasses
Aluminum Bronzes
Silicon Brasses
Copper Beryllium Alloys
Leaded Copper
Lead-Free Bronzes
Characteristics and Uses
Reasonable strength, excellent thermal conductivity, reasonable corrosion resistance to sea-water andbrine, and good machining and casting properties. Lead content ensures pressure tightness. LeadedRed Brass is used as a low-cost bearing material when low loads and low speeds are encountered.Requires good, reliable lubrication and a moderately hard shaft.
Hard, strong alloys with good corrosion resistance, especially against seawater. Moderatelymachinable. As bearing materials, they are wear resistant and resist pounding well. Best for highloads, low speeds. Require good, reliable lubrication and a moderately hard shaft. Higher tinconcentrations improve strength, but at the expense of conformability and embeddability.
Lead improves machinability in these tin bronzes but does not materially affect mechanicalproperties. The alloys are essentially free-cutting versions of the tin bronzes, above, and have similarproperties and uses.
Most commonly used bearing alloys, found in bearings operating at moderate loads andmoderate-to-high speeds. Excellent for boundary-lubricated situations or where lubrication isuncertain. Since lead is insoluble in the solid phases, it is dispersed in the matrix as small isolatedglobules, acting as small reservoirs of lubricant. Increasing lead concentrations increaseconformability and scoring resistance, but at the expense of reduced strength and poundingresistance.Alloy C93200 is considered the workhorse alloy of the series. Alloy C93600 has improvedmachining and anti-seizing properties. C93800 is noted for its good corrosion resistance againstconcentrations of sulfuric acid below 78%. Alloy C94100 is especially good under boundary-lubricated conditions.
Alloys with high mechanical strength, good corrosion resistance and favorable castability, and of lowrelative cost. Can be machined but, with the exception of C86400 and C86700, are less readilymachined than leaded compositions.Brasses have typically poor tribological properties, and hence as a bearing material tend to be usedin non-critical applications. When used for high-strength bearings, alloys C86300 and C86400require hardened shafts and reliable lubricant supplies.
The aluminum bronzes are characterized by high strength and excellent corrosion resistance. Somecan be heat treated ("HT"). Physical properties remain good at elevated temperatures.Excellent heavy duty bearing alloys with very good abrasion resistance and excellent resistance torepeated, severe impacts.Poor anti-seizure properties, relatively poor conformability and embeddability, hence require goodreliable lubrication, hard shafts and proper shaft alignment, with both shaft and bearing machined tofine surface finishes.
Moderate-to-high strength alloys with good corrosion resistance and favorable casting properties.Used for mechanical products and pump components where combination of strength and corrosionresistance is important.
Relatively high-strength materials with good electrical and thermal conductivity. Used wherebearings and bushings with a good combination of strength and conductivity are needed. Excellentheavy duty bearing alloys, but do not tolerate misalignment or dirty lubricants and generally shouldbe used against hardened steel shafts, with both shaft and bearing machined to fine surface finish.
Ultrahigh-lead alloys for special purpose bearings. Alloys have relatively low strength and poorimpact properties and generally require reinforcement. Excellent for boundary-lubricated situations,or where lubrication is uncertain.
Formulated to mimic the properties of the leaded alloys but without the safety concerns of lead.Friction, yield and tensile strength and corrosion resistance are all comparable to leaded bearingbronzes.
Table 2.2. Summary of Cast Bronze Characteristics.
22
Initial Selection of CandidateMaterials Based on Past Usage
To know what has been usedfor a specific application is a verypowerful way to start with a givenmaterial selection. Even if theapplication is not quite the same aswhat you are working on, it willmost likely form a good startingpoint. Table 2.3 is a compilationof different bearing applicationsusing cast bronze alloys. SeeRippel9. It is suggested that youselect several materials from thislist; do not be too restrictive in thetype of application. Again, thisshould not be taken as the lastword on materials selection,but rather the starting point.Knowledge of how well previousdesigns fared can be an invaluablehelp in such cases.
Another way to make aninitial materials selection is byconsidering that a leaded-tinbronze such as C93200 is the mostcommonly used material. We maythen examine this choice in lightof some other considerationsgiven next.
Additional Materials SelectionConsiderations
After we have made someinitial materials selection we canapply some additional criteria. Forall the different choices of bearingmaterials there are two criticalconditions that must be met.These are:
■ the material must be strongenough to withstand the peakapplied bearing stresses, and
■ it must have sufficienttemperature capacity.
agricultural machinery
air compressor wrist pin bushingsaircraft accessory drives
aircraft control bushings
aircraft landing gear bushings
aircraft-carburetor bearingsautomotive spindle bushings
automotive transmission thrust washers
backs for lined bearingsbearings for earth moving machines
boring bar guide bushings
brass and copper rolling-mill neck bearings
bridge bearings
cam bearings
cam bushings for diesel engines
cam bushings for farm equipmentcam bushings for mechanical devices
clutch pilot bushingsconnecting-rod bushings for farm equipment
cornpicker snapping roll bushings
cranes and hoist bearings
crankshaft bushings for farm equipmentcrankshaft main bearings
deep-well pump-line shaft bearingsdeep-well pump-bowl bushings
drum bushings for cranesdrum bushings on earthmoving machinery
earthmoving equipment bushings
electric-motor bushings
elevatorsfire-pump bushings
freight and streetcar bearings
fuel and water-pump bushings
garden tractors
gas, gasoline and diesel engine bearingsgasoline pump bearingsgear bushings for farm equipment reducers
gear bushings for motorcyclesgenerator and distributor bushings
guide bushings for piston rods
guide bushings for rams
guide bushings for valves
guide post bushingsheavy earthmoving equipment bushings
C94100
C90300
C90700
C93700
C90300C94300
C92700
C83600
C93800, C93700, C93600C92700
Al Bronzes
C93800
C90700, C90300Al bronzes
C93700, C93200, C93600
C93700
C93700
C90500
C93700, C92700C83600
C94100
C93700
C93600, C93700
C83600, C89320C93800, C93600
C93800
C93800Al bronzes
C93700, C93200,C94100, C93600
C94100
C94300
C93800
C93700
C93700
C93800C93800
C93700, C92700
C93700C93200
C93200, C89320, C93600
C93200, C89320, C93600C93200, C89320, C93600Al bronzes
Al bronzes
Table 2.3. Candidate Bearing Bronzes Based on Past Usage. (cont. p. 24)
23
High levels of applied bearingstress may cause plastic flow of thebearing material. This should beavoided because it will otherwisecause severe dimensional changes.Similarly, high operating tempera-tures will cause a reduction in thebearing strength and higher poten-tial for wear and seizing.
To obtain exact values ofmaximum recommended stressand temperatures for the differentalloys is very difficult and dependsa lot on the nature of the bearingdesign. Typical values may befound in the literature of, for exam-ple: Rippel9, CDA7, and DIN10.Table 2.4 lists typical maximumbearing pressures and operatingtemperatures that can be used withcareful bearing design practice.The range of temperatures andpressures within each alloy classresults from the variouslevels of soft phase present.Materials with higher soft phasecontent (more lead) tend towardsthe lower temperature andpressure levels.
These numbers should be usedas guidelines only. Also, we typicallyselect a material that is just strongenough for the job. Allowanceshould be made for possible over-load conditions.
Other tribological characteris-tics to consider are the propensityto seizure and the resistanceto wear. These are indicated inTable 1.1 on a relative basis.This table should be consulted forfurther refinement of the materialsselection. The relative wearresistance of a bearing materialmay also be judged from theidentation hardness. It is wellknown that hardness plays amajor role in preventing wear. Itshould be realized however thatincreasing hardness levels will
hydraulic glands seals
hydraulic pump bushings
king pin bushings for off-highway equipment
lathe bearingslinkage bushings for machine tools and presses
locomotive bearing parts
low-pressure valve bearings
machine tool bearings
main bearings for presses
main bearings for refrigeration compressors
manifold bushings for earthmoving machinery
marine equipment
mechanical linkage bushings for farm andmaterial handling equipment
mechanical linkage for farm equipmentand packaging machinery
motorcycle-engine bearings
outboard motor crankshaft bearings
piston pin bushings
piston pins for packaging equipment
power lawnmower bushings
power shovel bushings
propeller bushings
pump sleeves
rail and heavy equipment trunnion bearings
railroad car wheel bearings
reduction-gear pinion bearings
C93800, C89320
C94300
C93800
C93700C90500, C93700
C94300, C92700, C93600
C83600, C89320
C94100,C90700,Al bronzes, C90300
C93200
C94300
C83600
C90700C93200, C93600, C89320
C92700
C93200
C93700
C90500, C93600,C93700 (diesels)
C93700
C93700
Al bronzes
C83600
C83600, C89320
C93700
C93700, C93800, C94300
C94100
Table 2.3. (cont.) Candidate Bearing Bronzes Based on Past Usage. (cont. p. 25)
Bearing AlloyLeaded Red Brass
Tin Bronze andLeaded Tin Bronze
High-LeadedTin Bronzes
Aluminum Bronze
High Strength Brass
Copper Beryllium Alloys
Leaded Copper
Max. RecommendedOperating Temp.
°C, °F180-230 356-446
170 338
170 338
300 572
200 392
>200 >392
160 320
Range of Max. RecommendedOperating Pressure,
MPa psi20-30 2900-4350
25-35
15-25
50-70
30-50
50-200
10-15
3625-5075
2175-3625
7250-10155
4350-7250
7250-29010
1450-2175
Table 2.4. Maximum Recommended Operating Temperatures and Pressures.
24
rod bushings
rod bushings for refrigeration compressors
roll bushings
roll neck bearings in rolling mills
roller bushings for conveyors
rolling mill bearings
seals
sleeve bushings for cranes and draglines
spacer bushings and bearings for pumps.
speed reducers bearings
spindle bushings for farm equipment and trucks
spindles and connecting rods in farm equipment
spring bushings for farm andautomotive equipment
spring-shackle bushings
starter motor bushings
steel mill equipment
steering-knuckle bushings
supercharger bushings
textile machinery bushings
thrust washers and components for chemicalprocess equipment
torque-tube bushings
track-roller bushings for crawler tractors
trolley wheel bushings
trunnion bearings
turbocharger spindle bushings (floating type)
turntable bushings
valve guides
valve rocker arm bushings
valve stem nuts
water-lubricated bushings
wristpin bushings
C93800, C93600
C94300
C90500
C93700, Al bronzes
C93200
C90500, C93800, C93700
C93800, C89320
C93200, C93600
C93800, C89320, C93600
C93700
C93700, C93200
C93700
C83600
C93200
C93200
C90700, C93600
C93700
C94100
C94100
C93600
C93200
C93700, C93200
C90300
C90300, C92700, C93700
C94100,C89320
Al bronzes
C90500
C93700
Al bronzes
C94300
C93700, C93600, C89320
Table 2.3. (cont.) Candidate Bearing Bronzes Based on Past Usage.
reduce the resistance to seizure,and also reduce the conformabilityand embeddability. Typical hardnessvalues are indicated in Table 2.4.The values are indicated as Brinnellhardness. This is a hardness test
using a fairly large indenter, andthus, averages the hardness readingover a fairly large domain. Theindicated hardness values do notnecessarily reflect the hardestpossible phase in the alloy.
Physical Properties of BearingMaterials
Other properties such as thermalconductivity, thermal expansioncoefficients and density are alsoimportant tribological parameters,especially so when high bearingtemperatures are expected. Table 2.5list values for the most commonlyused physical properties.
This data is from DIN10; CDA7;and Rippel9. The values listed inthis table should only be used as aguideline. More specific informa-tion should be obtained once amore definitive material selectionhas been made. A range of valuessuggests that slightly differentresults were reported by the refer-ences. The range for the hardnessvalues may also reflect the differ-ent heat treatment conditions forthe alloy.
Compatibility with WorkingFluids
While for the most part wedesign sliding bearings usinggrease or oil as the lubricant, wedo not need to restrict ourselves tothese lubricants. In fact the use ofsliding bearings can be turned toenormous advantage when using agiven process fluid as the lubricant.The use of seals, always a weaklink in the design, can then be avoidedaltogether. Typical process fluidssuch as water, gasoline, kerosene,creosote, paints, and even foodproducts such as ketchup andmolasses are used as lubricants.Even highly corrosive fluids suchas hydrochloric and muratic acidscan be used as liquid lubricants forsliding bearings.
It is also important that thebearing and shafting materials to
25
Table 2.5. Physical Properties of Bearing Materials.
be used are compatible with theprocess fluid. Extensive corrosion
resistance ratings for various castbronzes as a function of different
process media is given in CDA'sCopper Casting Alloys8.
26
Leaded Red BrassC83600 CuSn5Pb5Zn5 55-60 80-100 11.6-14.5 95 14 19 11 72 42 8.90 0.322
Tin BronzesC90300 70 145 21.0 96 14 18 10 75 43 8.80 0.318C90500 75 150 21.8 103 15 20 11 75 43 8.72 0.315C90700 80 150 21.8 103 15 18 10 71 41 8.77 0.317
Leaded Tin BronzesC92200 65 130 18.9 96 14 18 10 70 40 8.64 0.312C92300 70 140 20.3 96 14 18 10 75 43 8.77 0.317C92700 77 145 21.0 110 16 18 10 47 27 8.78 0.317
High-Leaded Tin BronzesC93200 CuSn7Pb7Zn3 65-70 100-120 14.5-17.4 100 14.5 18 10 59 34 8.80 0.318C93400 60 110 16.0 76 11 18 10 58 34 8.87 0.320C93500 60 110 16.0 100 14.5 18 10 70 40 8.87 0.320C93600 65-70 135(0.5%) 19.6 77 11 18.5 10 49 28 9.05 0.327C93700 CuPbl0Snl0 60-70 80-110 11.6-14.5 76-90 11-13 18 10 47 27 9.00 0.325C93800 55 110-140 11.6-20.3 72 10 18.5 10 52 30 9.25 0.334C94300 AMS 4840 48 105 15.2 72 10 18 10 63 36 9.30 0.336C94100 approx. CuPb20Sn5 45-50 60-80 8.7-11.6 75 10.9 19 11 59 34 9.30 0.336
High-Strength BrassesC86300 215 400-450 58.0-65.3 98 14 22 12 35 20 7.83 0.283C86400 90 170 24.7 96 14 20 11 28 16 8.33 0.301C86800 approx. CuZn37Mn2A12Si 150-170 280-350 40.6-50.8 100 14.5 19 11 65 38 8.10 0.293
Aluminum BronzesC95300 140-170 — — 110 16 16 9 63 36 7.53 0.272C95400 170-195 — — 107 16 16 9 59 34 7.45 0.269C95500 195-230 — — 110 16 16 9 42 24 7.53 0.272C95800 160 240(0.5%) 34.8 114 17 16 9 36 21 7.64 0.276C95520 approx. CuA110Fe5Ni5 140-150 250-280 36.3-40.6 120 17 16 9 60 38 7.60 0.275C95800 approx. CuA19Fe4Ni4 180-220 480-530 69.6-76.9 118 17 16 9 27 16 7.60 0.275
Silicon BrassesC87200 80 150-200 21.8-29.0 100 14.5 17 9 28 16 8.36 0.302C87600 135 220 31.9 — — — — 28 16 8.30 0.300
Copper Beryllium AlloysC82800 180-380 500 72.5 130 18.9 22 12 123 71 8.30 0.300Leaded Copper
C98820 30-45 65 9.4 75 10.9 16 9 80 46 — —Lead-Free Bronze
C89320 70 120(0.5%) 17.4 98 14.2 18 10 56 32 8.80 0.318
NOTES:
27
Design of Boundary LubricatedBronze Bearings
DESIGN OF BOUNDARY LUBRICATED BRONZE BEARINGS
Boundary lubrication occurswith sliding interfaces wherethe transmitted load is carriedcompletely by the contactingasperities. While a liquid lubricantmay be present, an insignificantportion of the load is supportedby it. Wear occurs with boundarylubrication. The wear rate is depen-dent upon the design parameters(materials, load, sliding distance) andthe ability of the lubricant to formprotective, sacrificial chemical com-pounds to avoid direct metal-to-metal contact. When significantchemical action takes place, therole of temperature is very important.System temperatures may resultfrom some ambient condition, orthey may be self-generated due tosliding under friction conditions.The level of friction will of coursedepend on the nature of the asperityboundary interaction and the filmsthat may form here due to thechemical kinetics.
The whole aspect of boundarylubrication is thus a complex phe-nomena of chemical, thermal andmechanical interactions. It is veryhard to predict what may happenfor a given situation, but we cansay a few things about what bringson the boundary lubrication mode.
The accompanying program,Bound, is based on the experimentaldata and the modeling presented inthis chapter.
Conditions Leading toBoundary Lubrication
While the nature of the interac-tions that take place between asper-ities during sliding conditions areimpossible to predict (as of today),there are several macro parametersthat force a lubricated tribologicalsystem to operate in the asperity orboundary mode of load bearing.These conditions are;
■ High load■ Low speed■ Low lubricant viscosity■ Starting and stopping■ Rough surfaces■ Irregular surfaces■ Lack of suitable or adequate
film formation mechanisms■ Inadequate clearance■ Misalignment
The above list indicates thatalmost every tribo-system willoperate at one point or another inthe lubricated wear regime. There-fore, correct design considerationsand criteria must be kept in mind inthe design stage of every system.
Boundary LubricatedWear Data for CastBronze Bearings
As mentioned under the mate-rials selection of the various castbronzes, the superior boundarylubrication aspects of copper basedalloys are second to none. These
characteristics are even furtherenhanced when lubricants such asgreases are introduced into theinterface. Friction and wear nowdecrease dramatically, and verylong lives may be obtained fromgrease-lubricated bronze bearings.
To determine the boundarylubrication performance of severalcommonly used cast bronze bearingalloys, the International CopperResearch Association sponsoredextensive research that producedinvaluable data for use in the designof such bearings. This research alsofurthered the understanding of theunderlying phenomena that set thelimits of operation. Glaeser et al11,conducted an extensive set of lubri-cated journal bearing wear experi-ments on the followingbearing bronzes;
C93200 Leaded BronzeC90500 Tin BronzeC95400 Aluminum BronzeC94500 High-Leaded Bronze.It was found that the bearing
performance could be presented ona plot of sliding velocity versus themean bearing stress, or a so-calledlubricated wear map, Figure 3.1.
This lubricated wear map fora journal bearing shows three areasof wear identified as follows:
Region of Moderate Wear,(K = 3xl0 -7)Region of High Wear,( K = l xl0-6)Region of High Temperature.
29
Figure 3 .1 . Lubricated Wear Map for a Journal Bearing.
The high-wear limit occurs ata temperature of about 150 C (302 F).At temperatures above this, severewear develops and failure takesplace. This temperature limit willdepend on the nature of the materialsand lubricant and is thus very sys-tem specific.
The experimental results showthat wear and bearing distressbecomes unacceptable at bearingstress levels from 24-28 MPa(3500-4000 psi). In many grease-lubricated continuous rotationbearing installations, 3.5 MPa(500 psi) is accepted as a maxi-mum. Therefore, boundary lubri-cated bearings are seldom operatedat bearing stress levels much above28 MPa (4000 psi). Some high-strength bronzes, such as alu-minum bronze, are operated atbearing pressures on the order of70 MPa (10,000 psi) in oscillatingmotion applications (airframebearings, for instance).
Lubricated Wear Limitsfor Bearing Bronzes
The maximum load-speedlimit at which moderate lubricated
wear might be expected to takeplace is critical in the design ofbearings. This limit was determinedby Glaeser11 and is summarized inFigure 3.2 for the four alloys.Unlike the original publication byGlaeser11, which averaged datafrom four separate tests to obtainthe wear transition limit, here thelowest pressure limit at which atransition occurred for any onespeed is taken as the upper stresslimit. Original comments byGlaeser on the behavior of thematerials follow:
Alloy C95400 (aluminumbronze) shows the most consistentand highest load-capacity resultsover the speed range studied. Atspeeds of 0.10 m/s (0.33 ft/s) and0.15 m/s (0.49 ft/s), the maximumallowable operating stress is sharplylimited because of excessive tem-peratures from frictional heating.Up to the maximum allowablestresses at these speeds, the coeffi-cient of friction is typically 0.01 orless. Exceeding the maximumresults in an abrupt increase in thecoefficient of friction to valuesaround 0.1. This, coupled with thehigher applied load, causes a thermal
runaway with rapidly increasingtemperatures. Such behavior isindicative of at least partial hydro-dynamic films separating the slidingsurfaces at the lower stresses. How-ever, electrical continuity measure-ments always showed metal-to-metalcontact or the absence of a completelubricant film. At the lower speeds of0.025 m/s (0.08 ft/s) and 0.05 m/s(0.16 ft/s), the coefficient of frictionis typically 0.1 at all bearing stress-es. The maximum allowable stresswas determined by frictional heat-ing, but no abrupt transition to run-away temperatures occurred.
Alloy C90500 (tin bronze)shows similar behavior to AlloyC95400, but has a distinctly lowerload capacity at 0.10 m/s (0.33 ft/s).The reduction in load capacity isdirectly related to the stress atwhich the transition from lowfriction coefficients (0.01) to highcoefficients (0.1) occurs.
Alloy C93200 (leaded bronze)is similar to alloy C90500 atspeeds of 0.10 m/s (0.33 ft/s) and0.15 m/s (0.49 ft/s), but shows thelowest load capacity of all fouralloys at 0.025 m/s (0.08 ft/s) and0.05 m/s (0.16 ft/s). Reduced loadcapacity at the lower speeds resultsfrom higher coefficients of frictionof up to 0.18, which cause a corre-spondingly higher thermal inputfrom friction.
Alloy C94500 (high-leadedbronze) shows the most inconsis-tent performance of the four alloys,which results from variability inthe transition from low friction tohigh friction as load is increased.This alloy also produces low coef-ficients of friction (0.01 to 0.02)at the lower speeds as well. As aresult, the transition from accept-able to unacceptable stress levelswas fairly sharply defined at0.05 m/s (0.16 ft/s).
30
Lubricated Wear Ratesfor Bearing Bronzes
The wear rates of four bearingalloys were measured by Glaeser at7 MPa bearing pressure and 0.10m/s sliding speed. The results areplotted in Figure 3.3 as the averageof three bearings for each material.The four alloys are clearly dividedin their extent of wear under identi-cal running conditions.
Alloy C95400 was the mostwear resistant, followed closely byalloy C90500. Alloy C93200 hadan intermediate wear resistance,while alloy C94500 experienced alarge amount of wear. All fouralloys showed the classic high ini-tial wear rate ("break-in") followedby a leveling off to a more con-stant, lower value.
Predictions of the amount ofdiametral wear encountered over agiven time period for the differentmaterials may be made by fittingthe data to a wear model. For thelubricated wear data, an equationthat follows the typical Archard-Holm12 works well, see AppendixA for further details on this model.The predicted amount of diametralwear is given by:
where;d = diametral wearK = wear coefficientP = nominal bearing stress
Fn/B•DFn = applied radial loadD, B = bearing diameter and widthH = hardnessts = total sliding timeU = sliding velocity
To account for the high wearrate in the initial break-in, twodifferent wear coefficients are need-ed for this model. These are incor-porated in the Bound program.
Figure 3.2. Load-Speed Limits for the Different Bronze Materials.
Figure 3.3. Lubricated Wear Behavior for Four Bronze Materials.
Bearing TemperaturesThe energy loss, W, in the
bearing may be calculated fromthe product of frictional force andsliding velocity, viz:
W = fFnU
The coefficient of friction, f,here should be chosen carefully. Itdepends very much on the lubrica-tion conditions. For the grease-lubricated bearings we will assumethat the friction coefficient is 0.1.This will be an overestimate inmost cases, but it will give us aconservative estimate for the bearing
temperature, and it is in keepingwith the experimental findings.
The dissipated energy will giverise to a bearing temperatureincrease. For boundary lubricatedbearings, the heat generated isremoved by air cooling of someform. This may be natural convec-tion or, in some cases, forcedconvection. It is a very complexmechanism that involves manydifficult to estimate variables. Tomake the model workable from anengineering point of view, wesimplify it to the following:
31
where:heat flow to ambientheat transfer coefficientto ambientouter surface area ofbearing housingbearing temperatureambient temperature
Typical values for the heattransfer coefficient are calculatedby a method detailed in Appendix B.By equating the heat generated tothat convected away to the envi-ronment, we get a heat balance asfollows:
Hence at the point of equilib-rium we obtain:
Note, this expression suggeststhat constant temperature lines onthe lubricated wear map should behyperbolas, assuming the frictionand heat transfer coefficients stayconstant. The limit of operationregion where high wear takes placehas the general shape of a hyperbola.This limit on the bearing tempera-ture was found to be about 150 C(302 F) for the four materialsevaluated.
Bearing PV FactorsExamination of the wear
equation and the bearing tempera-ture equation shows that both usethe product of pressure and velocity.This is sometimes referred to as the"PV" factor of a bearing. Somedesign manuals use this as a generalrule for boundary lubricated bearingdesign. As we see from the abovetwo expressions, this could either
reflect a temperature limit, or awear limit. Also, strict reciprocitybetween pressure and speed cannotbe used, as is apparent from thebearing temperature equation.
Design ConsiderationsThere are several critical
considerations for the design of asuccessful boundary lubricatedbronze bearing. Adherence to thesedesign considerations make it morelikely that the bearing performancewill be satisfactory.
Bearing diameter is usuallydictated by shaft stiffness consider-ations and is thus not somethingwe can truly select at random.Bearing width is normally chosenso as to keep the width-to-diameterratio close to unity, though this willbe dictated somewhat by the meanprojected bearing stress levels forthe application. Other importantconsiderations are discussed next.
Maximum Allowable BearingTemperatures
Glaeser found that rapidincreases in bearing wear occurwhen the bearing temperaturesexceed about 150 C (302 F). Thisis often accompanied by suddenincreases in friction coefficientsfrom low numbers like 0.01-0.03to high values like 0.10-0.15. Weshould thus calculate the theoreticaltemperature rise based on thehigher friction coefficient.
The 150 C (302 F) temperaturelimit is well below the capability of
the various bronzes used in theinvestigation. Glaeser suggests it ismore indicative of the grease limit,rather than the bearing materialsper se. Accepting the fact that theexperimental limit is in fact more agrease limit, we may make somerecommendations for the maximumsafe temperatures in a bearing fromthe known temperature limits fordifferent types of greases, seeTable 3.2.
Besides the type of filler usedfor the grease, the base lubricantwill also significantly affect perfor-mance. Overall however, the tem-peratures shown in Table 3.2 maybe used as guidelines.
Additional information on theselection and application of greasesmay be found in NLGI13.
Maximum Allowable BearingStress
The maximum allowablebearing stress depends on the typeof material used for the bearingand the form of lubrication used.For grease-lubricated bearingsoperating in the boundary lubrica-tion mode, the maximum bearingstress is normally kept below 3.5-5 MPa (508-725 psi). From the testdata by Glaeser11, it is clear thatsome of the materials are capableof much higher stress levels.However, it is recommendedto use only these higher levelsunder special design circumstanceswhen space is critical.
Grease TypeLithium soap based
Calcium soap
Clay-based
Maximum Temperature, °C,14060
160-200
284140
320-392
°F CommentsGeneral purposeRelatively cheap
Wide temperature range
Table 3 .1 . Recommendation for Grease/Bearing Temperature Limits.
32
Normally the projected bearing area is selected such that the recommended stress levels are not exceeded.
Clearance Clearance values for boundary
lubricated sleeve bearings should be larger than for hydrodynamic lubrication. This is because the bearing has to operate in the pres-ence of wear debris and any other adventitious debris that would normally be flushed out by a flow-ing lubrication system. In addition, sufficient clearance space is needed to allow injection of fresh grease into the bearing periodically.
Recommended clearance values range from 0.2% to 0.5% of the journal diameter. Sufficient clear-ance should also be allowed for possible reduction in clearance
due to different thermal expansion coefficients. Figure 3.4 shows the recommended diametral bearing clearances as suggested by Bartz14.
Shafting The hardness and surface fin-
ish of steel shafting is an important consideration in the design of
boundary lubricated bearings. The shaft plays a major role in the wear-in process and subsequent performance is directly influenced by wear-in. For the leaded bronzes, cold-rolled steel, finished to 0.5-0.7 µm (20-28 µin.) Ra (arithmetical average of roughness), can be used. However, steel shafting, AISI 1045, hardened to HRC 30 minimum, ground and polished (or comparable steel), is a better choice and certainly should be used with tin bronzes containing no lead.
Harder shafting is appropriate as long as it has the fracture tough-ness and fatigue strength required for the application. When using harder shafting, it is important to keep the surface roughness levels low to prevent abrasive wear of the bearing by the shaft.
Surface Finish In boundary lubricated bronze
bearings, the shaft surface finish is important. Since the shaft should always be harder than the bearing material, steel asperities will tend to plow the bronze bearing surface, producing an abrasive type wear.
The original surface finish of the bearing material will change during the "wear-in" period early in the life of the bearing. Some wear of the shaft will also occur owing to the hard intermetallics in the bronze microstructure. A shaft surface finish of between 0.25-0.7 µm (10-28 µin.) Ra is recommended.
Wall Thickness and Flange Dimensions
Bronze sleeve bearings are normally contained within a housing or shell. A reasonable criteria for wall thickness is that the bearing, when installed in its housing, should provide adequate strength to support the imposed loads without elastic or thermal distortions which would destroy the "built-in" geometry of the bearing.
In general, increasing wall thick-ness is required for increasing bore diameter. Thin bearing walls and heavy housings provide more strength than the opposite arrange-ment, but heat transfer from the bearing may be impeded. If severe wear of bearing material is permis-sible and expected, adequate mater-ial thickness should be provided. Anticipated temperature rise is another consideration when wall thickness is specified. Large varia-tions in temperature, and different coefficients of thermal expansion for bearing and housing materials, combine to produce expansion and contraction forces that make bear-ing dimensions and fits difficult to maintain. Varying clearances with-in the bearing can result.
To locate a bearing axially in a housing bore, a shoulder flange as shown in Figure 3.5 may be provid-ed. This can be used as a marginal thrust surface as well.
33
Figure 3.4. Recommended Clearance for Grease-Lubricated Bearings.
When a bearing is pressed or shrunk in its housing, unequal expansions can also cause stressing of both members. If the bearing material yields, cooling may change the original interference fit and result in a loose bearing. However, these difficulties may be minimized by proper design. A final requirement is that wall thick-ness should be at least three times the depth of any grooving.
Solid bushing minimum and maximum wall thicknesses and recommended flange sizes according to ISO-4379 are shown in Figure 3.6. For flanged bushings, it is recom-mended that the flange height, hflange, is at least equal to the bushing wall thickness, twall. Also the flange thickness, tflange, is made the same as the wall thickness. Maximum wall thickness and flange dimensions may be desirable for high load applications where a lot of interference fit is required. This will reduce the possibility of buckling.
Methods of Retaining Bearings Many different techniques are
used to ensure that a bronze bear-ing stays put within its housing. The method used depends upon the particular application, but it is important to ensure that the unit lends itself to convenient assembly and disassembly. One goal to keep in mind is that the bearing wall should be uniformly thick to prevent introduction of weak points in the construction which might lead to elastic or thermal distortion.
Press or Shrink Fit The most common and satis-
factory technique for retaining the
Figure 3.5. Dimensions for Straight and Flanged Bushings.
bearing is to press or shrink the bearing in the housing with an interference fit. Uniform wall thickness over the entire bearing is easily maintained by either of these processes.
Standard stock bushings with finished inside and outside diameters are available in sizes up to approximately 125 mm (4.92 in.) bore size. Stock bushings are commonly provided with slightly over nominal OD sizes. Since these tolerances are built into standard bushings, the amount of press fit is controlled
Figure 3.6. Recommended Wall Thickness and Flange Dimensions for Solid Cast Bronze Bushings.
34
by housing bore. Recommended fits for general applications with cast bronze bushings in cast iron or steel housings are H8/p7 according to ISO-1101. For aluminum hous-ings, the interference may have to be increased by as much as 0.001 D to provide satisfactory tightness.
For high-temperature work, the recommended interference fits may need to be adjusted to allow for expansion differences between bearing and housing and to avoid yielding of the bearing material.
Thin walled housings require somewhat lighter press fits. For fabricated bearings, tolerances of both bearing OD and housing bore should be specified to produce the recommended interference fits.
As a result of a press or shrink fit, the bore of the bearing material "closes in" by some amount. In general, this diameter decrease is approximately 70% to 105% of the interference fit. Any attempt to accurately predict the amount of close-in, in an effort to avoid final clearance machining, should be avoided.
Shrink fits may be accom-plished by chilling the bearing in dry-ice and alcohol or in liquid nitrogen. These methods are easier than heating the housing and are preferred. Dry ice in alcohol has a temperature of -78 C (-108 F) and liquid nitrogen boils at -196 C (-321 F). The use of a hollow mandrill filled with liquid nitrogen will greatly extend the useful working time to install bushings
into machine bores. Lubricants should not be used when employing shrink-fits as this may lead to hydraulic blister formation between the bearing and the housing bore.
When a bearing is pressed into the housing, the driving force should be uniformly applied to the end of the bearing to avoid upsetting of the bearing. A steady pressing force is preferred. An insertion arbor should always be used. Also important are the mating surfaces, which must be clean, smoothly finished and free of machining imperfections.
Keying Methods Many different ways are used
to fix the position of the bearing with respect to its housing by "keying" the two together. Possible keying methods are:
■ Set screws ■ Woodruff keys ■ Bolted bearing flanges ■ Threaded bearing OD
■ Dowel pins ■ Housing caps
These methods may be easier than a press or shrink fit, but they are much less satisfactory as they do not result in a very solid con-nection. They should only be used for light duty applications and cer-tainly not when dynamic loads are applied to the bearing.
Grease Grooving Patterns Because grease will only go
where it is pushed or dragged, it will not distribute itself in a bearing like a liquid lubricant will. Therefore, grooving is generally cut into the inner surface of a bush-ing. There are many grooving designs used. Some of the more common designs are shown in Figure 3.7, where the bushing has been unfolded along an imaginary line opposite the grease feed hole. Most of these configurations are easily cut with special tools.
Figure 3.7. Various Grease Redistribution and Supply Groove Patterns: (a) straight axial, (b) circular, (c) axial and circular, (d) butterfly groove, (e) single loop, (f) double loop, (g) figure eight, (h) double figure eight, (i) chain-link, (j) ladder.
35
Straight Axial Supply GrooveWhere the applied load is
predominantly in one direction andcontinuous rotation exists, then theoptimum design is to use one ormore axial feed grooves, seeFigure 3.7a. The axial slot shouldbe oriented so it is in the unloadedarea of the bearing. In addition todistributing the grease, the groovealso provides a reservoir for thegrease and a trap to collect weardebris. Axial lubricant grooves mayhave an angular extent of as muchas 30°. If one groove is specifiedthis should be positioned between90° and 120° upstream of thedirection of applied load. If twogrooves are used, they should bediametrically opposite at 90° to theapplied load. Axial groove lengthshould be approximately 0.8 timesthe bearing width.
Circumferential GroovesIf the applied load varies
considerably in direction, then thechoice of a central circumferentialgroove is preferred, see Figures 3.7band c. Such a design has, however,a lower load capacity than an axialgroove bearing of equivalent size.Typically the width of the circum-ferential groove is approximately20% of the total bearing width.When using this groove pattern foroscillating bearings, it is preferredthat the axial groove spacing isabout the same as the sweep duringa given oscillatory move. This is toensure that the entire shaft is relu-bricated for each cycle. If rotationalmotion is very limited, then theladder-groove as shown in Figure 3.7jshould be used.
Recirculating ConfigurationsOne difficulty with grease
lubrication is to keep the grease inthe bearing without affecting theload capacity greatly. Configu-rations such as those shown inFigures 3.7f, g, h and i, and to lesserextent in e achieve this. Theseconfigurations also tend to bepreferred for longer bearings. Theside grooves recapture the lubri-cant and bring it back to the greasesupply location for redistribution.Dirt and debris are however alsobrought back into the load zoneand this may lead to abrasive wearin the bearing. The grease applica-tion hole is typically placed oppo-site the point of load applicationwith these configurations.
Configurations such as shownin Figures 3.7f and h reduce theload capacity by virtue of interrupt-ing the load bearing area. Thisreduction is less for g and i. Both gand i are also very efficient inrecapturing the grease. Tests con-ducted by Bethmann and reportedby Spiegel15 show the benefit inrecirculation of grease for these
types of groove patterns, seeFigure 3.8. At a bearing stress of3 MPa (435 psi), the chain-linktype groove consumes about 20times less grease than the straightaxial groove.
Groove GeometryThe grooves should not extend
out to the ends of the bearing andshould not take up too much ofbearing area providing load support.Conventional design calls for thegrooves to be machined to withinabout 10% of the ends of the bear-ing so the lubricant is kept withinthe bearing area. However, underheavy load conditions where bear-ing temperature is high and debrisaccumulation becomes a problem,it is better to have the grooves exitat the ends of the bearing so peri-odic flushing of the bearing withfresh grease will remove the debrisand lubricant decompositionproducts collected in the grooves.Experiments with "non-recirculat-ing" grooves indicate lower wearthan with recirculating grooves.
Figure 3.8. Experimental Grease Consumption for Different Groove Patterns(Sliding speed is 1 m/s, bearing diameter is 80mm).
36
There are many differentcross-sectional groove geometries.The most commonly used areshown in Figure 3.9.
It is very important that thegroove edges are all properlyrounded. Sharp edges tend to act asa grease scraper and thus removegrease from the shaft rather thanapply it.
Recommendations for groovedepth and width for grease lubrica-tion are given by Rippel9, and areshown in Figure 3.10.
Grease ConsumptionLow wear rates can be main-
tained only over long periods oftime when grease is present in thebearing and can perform its intendedfunction. Because grease is lostfrom the bearing due to side leak-age, and also somewhat consumeddue to chemical action, we have tomake provisions for its replace-ment. This may be done on a con-tinual basis or as is more common,on a periodic basis. Certainly amajor advantage of grease-lubricat-ed cast bronze bearings is that theyare not overly critical for a continualgrease supply, and can thus be usedfor periodic relubrication.
Grease consumption for grease-lubricated bearings is a very com-plex phenomenon, and thus far hasbeen treated on an empirical basisonly. It clearly must be a functionof the bearing size, and practicalexperience indicates that it liessomewhere between:
Vf = (40-1000) Aj, where Aj isthe inside bearing area (πBD).
This expression shows a verywide range of possible greaseconsumption, and can only beused as a starting point.
Figure 3.9. Common Forms of Grease Grooving. From Rippel9.
Besides bearing size, we mustalso expect that it is a function ofbearing speed, bearing loading,operating temperature and groovepatterns. These effects were incor-porated in an empirical expressionby Henningsmeyer as reportedby Bartz14 that may be used fora more refined estimate.Henningsmeyer gives the followingexpression for the grease consump-tion rate:
and where;B = bearing width,U = sliding velocity,Λ = loading factor, andG= environmental factor.
This expression does not takethe groove pattern into account,and we will thus need experimentalrefinement to get better estimates.This can easily be done throughvery careful monitoring of thebearing temperature. Rapidlyincreasing temperatures suggestmore grease is needed.
Figure 3.10. Recommended Groove Dimensions for Grease Lubrication.
37
The bearing loading factor, Λ,is a function of the bearing loadand the bearing operating tempera-ture. The following expression issuggested:
P = bearing stress,2B = bearing temperature.
When using this expressioncare should be taken that Λ>1.The environmental factor maybe estimated from the conditionssurrounding the bearing. Values aresuggested in Table 3.2.
Regreasinq IntervalsAssuming that grease leaks
from a bearing at a constant rateduring operation, we may estimatea regreasing interval. This intervalis based on the assumption that themaximum allowable grease deple-tion is 25% of the total greasevolume in the bearing (excludingthe supply and redistributiongrooves). The total grease volumein the bearing is given by;
Thus, the regreasing intervalmay be estimated from;
When using this estimate, itshould be realized that the estimateis for the actual operating time andnot clock time. Also grease quanti-ties smaller than about 0.04 cm3
(.002 in.3) are difficult to deliver.
Likely ingression of dirt or dustLikely ingression of waterLikely ingression of dirt and water
G = 0.01G = 0.02G = 0.03
Table 3.2. Values for Estimating the Environmental Factor of ConditionsSurrounding the Bearing.
38
where:B = bearing width,D = journal diameter,
CD = diametral clearance.
NOTES:
39
Hydrodynamic JournalBearing Design
HYDRODYNAMIC JOURNAL BEARING DESIGN
When the load on a bearing isfully supported by hydraulic pres-sure in a lubricant film, there willbe a finite separation between thebearing and shaft. The two compo-nents do not contact each other andwear is nonexistent or very low. Ifthis separating lubricant film issolely caused by the motion of thejournal surface relative to the bear-ing, we speak of hydrodynamiclubrication.
In a hydrodynamic journalbearing, the part that moves is gen-erally the journal (as with the shaftof a motor), sometimes the bearing(for example, the wheel of aConestoga wagon), and sometimesboth parts (such as a connectingrod that joins a piston and thecrankshaft in an automobile engine).
Since many motors, enginesand other machines incorporatehydrodynamic journal bearings, theannual production of hydrodynamicjournal bearings is in the billions.Not only is the hydrodynamicjournal bearing very common, it issuperior to rolling-element bearingsfor many purposes because it cancarry heavier loads, operate athigher speeds, is less expensive,is more reliable, and can lastindefinitely when designed well.
A typical hydrodynamic jour-nal bearing is shown in Figure 4.1.Because the hydrodynamicoperation is dependent on thepresence of lubricant, we typicallyrequire a constant supply. Severalways of achieving this are com-
Figure 4 .1 . Basic Journal Bearing Component Designation.
monly used. The lubricant to ajournal bearing may be supplied bya non-pressurized lubricant feedsuch as an oil ring, a wick or othermeans. It may also be supplied bypressure. Pressure-fed systems mayinclude supply and return lines forthe oil, a storage tank, filter, andtemperature and pressure regula-tors. Similar to grease-lubricatedbearings, grooves may be used tospread the oil along the bearing.
Load Capacity ofHydrodynamic JournalBearings
The key to hydrodynamiclubrication is the formation of alubricant film that separates theshaft from the bearing. Pressure inthis film, when integrated over thebearing area, will support the load
applied to the journal. Because thisfilm consists of lubricant, it maybe sheared as much as necessarywithout any permanent damageto the bearing.
Pressure in the lubricant filmdevelops when we drag lubricantinto a converging space, A, shownin Figure 4.2a. This drag is impart-ed on the fluid because fluids liketo adhere to surfaces. As the lubri-cant is drawn around into the con-verging space, a certain amount ofthe fluid is forced out against theviscous action, B. This results in alocal pressure. As the gap con-verges, the sideways squeezingbecomes more and more difficultand higher pressures develop. Inthe end, only a small but finiteamount goes through the smallestgap in the bearing. After the small-est gap is passed, C, the space
41
Figure 4.2a. Lubricant Flow in aJournal Bearing.
opens up again, and the pressurerapidly drops to ambient.
The resulting pressure distribu-tion around the bearing looks thussomething like that shown inFigure 4.2b. Note, this pressure isgenerated by the action of thelubricant film in the bearing,and not by the supply pressure.Integrating this generated pressureover the bearing area results in theapplied load.
The beauty of a journal bear-ing is that we can get this hydrody-namic action almost for free. Theonly special provisions we need tomake are to ensure a suitable clear-ance exists between the shaft andthe bearing surface and sufficientlubricant is supplied at all times.The clearance is easy to achieve,simply by making the shaft some-what smaller than the bearing bore.The rest of the action takes placeby itself. The thickness of the gap,for example, adjusts itself to theload that is applied. If this load is
Figure 4.2b. Pressure DistributionResulting from theLubricant Flow.
small, then a fairly large gap at C ispossible because not much pressureis needed to support the load. Forhigh loads, this gap will be smallbecause higher pressures are needed.
Full-film formation occursas long as the smallest gap in thebearing is greater than the com-bined roughness on the journal andbearing. The smallest gap in thebearing occurs along the line ofcenters in the vicinity of the load.The line of centers makes an angle,φ, with this load line. The actualvalue of the minimum film thick-ness is given as hmin. From thedisplacement of the journal centerrelative to the bearing center, seeFigure 4.1, and the radial clear-ance between the journal and thebearing, we calculate this gap as;
where C = radial clearance(Db-Dj)/2, and
e = bearing eccentricity.
From the foregoing discussionof action in a hydrodynamic journalwe might expect that the loadsupported by the film would bea function of the viscosity, speed,journal area, and radial clearance.These variables are often combinedinto a convenient dimensionlessvariable called the Sommerfeldnumber, in honor of the work doneby Sommerfeld in finding a closedform solution to load capacity.Hence the Sommerfeld number isgiven as:
This number contains all theessentials required to find the loada given bearing can support. It is afunction of the bearing eccentricityand the bearing width-to-diameterratio, as shown in Figure 4.3. InFigure 4.3 the independent vari-able is given as the eccentricityratio. This ratio is defined as:
and forms yet another convenientdimensionless group to use. Wemay use the eccentricity ratio tocalculate the minimum filmthickness in the bearing by;
The calculation of Sommerfeldnumbers has been studied andresearched at great length eversince Osborne Reynolds formulatedthe differential equations to solvefor this problem. For in depthdetails of the mathematicsinvolved, the reader is referred to
42
Cameron16, Constantinescu17, Szeri18, Hamrock19, and others. Tables prepared by CD A20 contain some of the earliest calculated data by Raimondi21.
Besides the load capacity we also need data on the required oil flow and the friction generated by the bearing. These data may be found in CDA20. The data from these tables were incorporated into the Hydro program for bearing calculation purposes.
Thermal Effects Heat generated by lubricant
shear in a bearing is of major importance in practical applica-tions, mostly because it causes an increase in lubricant temperature. For most lubricants, the viscosity decreases with increasing tempera-ture. This directly affects the load capacity of a bearing as may be seen from the Sommerfeld number. Lower viscosities mean lower load capacity for a fixed Sommerfeld number.
A second effect of increasing bearing temperatures is the increase or decrease in bearing clearance. If materials with different thermal expansion coefficients are used, the resulting clearance increase can result in a significant loss of load capacity. Both the viscosity-temperature and thermal expansion effects are incorporated into Hydro.
Frictional heat can be removed by conduction through the bearing components or by oil flow. In some cases, sources external to the bear-ing bring additional heat into the system so that the lubricant and bearing then act as a cooling system as well.
Cast bronzes are excellent choices as bearing materials because of their very high heat transfer coefficients. Hence struc-tural cooling of the bearing is quite feasible for a moderately loaded hydrodynamic bearing.
Heat removal by a continuous supply of cooler lubricant is also a very effective way to cool the bear-ing. Both structural and lubricant cooling of the bearing are incorpo-rated in the Hydro program.
Additional cooling of the bear-ing may be obtained by supplying lubricant at higher than required flow rates through the bearing. In fact automotive engine bearings are cooled this way. The current version of Hydro does not have this feature. It is expected that a future release will have this option, together with some additional lubricant supply methods.
Transition to Hydrodynamic Lubrication
For a given journal bearing with a fixed R/C ratio, the coeffi-cient of friction may be plotted as a function of the hydrodynamic parameter, ηN/P. This friction is due to the viscous shear of the lubricant only. In real bearings however the surfaces have a definite roughness, and it may be expected that at high values of the eccentricity, i.e., when the film thickness is small, some interaction of asperities on opposing surfaces occurs. When the eccentricity goes to unity, the friction coefficient plot needs to be modified to include the boundary layer friction, see Figure 4.4.
Minimum friction occurs at an eccentricity of ε ≈ 1- hc/C. The transition takes place where the film thickness is equal to the convection heat transfer coefficient, hc.
43
Figure 4.3. Sommerfeld Number as a Function of the Eccentricity Ratio for Bearings of Different Width.
For any practical application, wealways operate to the right of thispoint. This region is known as thehydrodynamic friction region, andthe slope reflects the operatingviscosity. The point at which theaction is mostly hydrodynamic iscalled the transition point. Noticethat viscosity has an impact onthis transition.
During start-up from cold con-ditions, the viscosity is typicallyhigh. Hence a lower transitionspeed is required to get hydrody-namic action. When the bearingcomes to a halt after extensiveoperation at higher temperatures,viscosity is much lower, and thedanger of scuffing is higher. If thetransition occurs at a higher speed,more heat is produced at this point.Critical in the prevention of scuff-ing is the choice of bearing materi-als. Here the cast bearing bronzesexcel because of their very goodboundary friction characteristics.(See Chapter III.)
The transition journal speed,NT may be calculated from theminimum recommended safe filmthickness and the Sommerfeldnumber. Consider the criticaleccentricity ratio as follows;
We extract the critical speedfrom this as:
This speed can now be used in theboundary lubrication calculations
Figure 4.4. Modified Bearing Friction due to Boundary Lubrication.
to make sure the bearing will notsuffer a scuffing failure. It may berequired to adjust the surfaceroughness, viscosity or bearing sizeto make possible a reliable transi-tion-to-boundary lubrication.
Design Criteria for JournalBearings
Having considered some of thetheoretical aspects of hydrodynamiclubrication, we now have come tothe hardest part of all. By whatcriteria do we judge a bearingdesign to be satisfactory?
We need to define severaldesign criteria. For example: whatis the minimum safe film thicknessfor operation? What are the factorsfor safety? What are the allowabletemperatures? In some cases, youmay have internal guidelines to fol-low based on previous experience.It may also be very worthwhile touse Hydro and reverse engineer acouple of designs that you know togive satisfactory performance.
Bearing SizeThe design of a hydrodynamic
bearing is aimed at avoiding exten-sive metal-to-metal contact when
components are under load. Basedon this aim, it would seem that weshould try to make the separationbetween the two bearing membersas large as possible. This howeverwould take a lot of power, since ahydrodynamic bearing system isnothing more than a viscous pump,and a very leaky one at that.
To arrive at some reasonablechoices about the separation, wetend to make the bearing size assmall as necessary, and at the sametime have a reasonably safe separa-tion. Because bearings of largelength tend to suffer more fromedge contact due to shaft deflec-tions and misalignment, we sel-domly use B/D ratios larger than 1.Also we will try to maximize thesafe temperature increase in thebearing, within the limits as speci-fied. A design that follows theseguidelines will be safe and, at thesame time, not waste unnecessaryenergy.
Minimum Recommended FilmThickness
From the above discussion, itis quite clear we need to establishsome criteria for the separation of
44
the two surfaces. This suggestedseparation will depend on a num-ber of judgmental variables thatshould be carefully consideredbefore making a final choice.Consideration should be given tothe following:
■ size of the bearing (largerbearings require larger separa-tion just due to manufacturingtolerances),
■ applied loads during runningand during starting periods,
■ bearing deflections and framedistortions,
■ consequences of a bearingfailure, loss of life, etc.With these considerations in
mind, we now must choose a mini-mum acceptable film thickness forthe bearing. Below are some guide-lines based on empirical informa-tion and with a solid experimentalbasis. They should help to mini-mize the probability of any trouble.
■ Minimum recommended filmthickness h2min. In most cases,this is a function of machinesize and surface roughness. Inthe absence of any internalcompany guidelines, Figure4.5 may be used. These dataare based on marine bearingdesign practice, and usuallyhave some form of loadsharing, see Hill22.
The DIN10 guidelines for theminimum allowable film thicknesstake the operating speed intoaccount. This is a more refinedmethod.
Comparison between the valuesin Figure 4.5, and those in Table 4.1indicates they are roughly in linewith each other.
■ Eccentricity ratios of less than0.7 should be avoided becauseof possible dynamic instabilities.
Figure 4.5. Minimum Recommended Film Thickness for Journal Bearings.
Table 4.1. DINx Guidelines for Minimum Allowable Film Thickness forJournal Bearings, μm.
Design ClearancesEqually important in journal
bearings is the correct choice ofbearing clearance. We have seenthat small bearing clearances resultin high operating temperatures.On the other hand, large clearancesresult in loss of performance.The right clearance is thusvery important.
■ Clearance ratios: for smallbearings use a clearance ratio500 ≤ R/C ≤1000, with thelarger clearances for highspeed application. For larger
bearings, use the values asgiven in Figure 4.6.
■ Seizure concerns: When thebearing and journal materialshave different thermal expan-sion coefficients we mustmake sure this effect isconsidered. Also we need tocheck and see if the chosenclearances can result in bearingseizure at temperatureextremes. This may be thecase at either end of thetemperature spectrum. If atall possible, the thermal
45
Figure 4.6. Minimum Recommended Diametral Clearances for Journal Bearings.
expansion coefficients of thebearing should always beequal to or greater than thejournal material. Thisrequirement is automaticallysatisfied for most commonconfigurations of steel jour-nals and cast bronze bearings.It is also possible to get start-up seizures when very quickheating of the shaft allows itto grow more rapidly thanthe bearing. Seizures of thistype typically occur very fast(within 10 seconds of start-up).To check for possible seizure
conditions, perform a layout calcu-lation as shown in Figure 4.7. Thetolerance range on the nominalbearing and shaft size is taken intoconsideration.
Maximum Temperatures andTemperature Rises
■ Maximum permissible
lubricant temperature θ m a x
This is calculated at the cavita-
tion point in the bearing. This
46
criteria is mostly for oil oxida-tion life. This gets rapidlyshorter as the operatingtemperature exceeds 80 C(176 F). There are two differ-ent cases that are considered;
• Bearings with oil circulation:θ m a x is 100-125 C (212-257 F).
• Self-contained bearings (aircooling): θ m a x is 90 C (194 F).When synthetic lubricants areused we add 30-40 C (86-104 F).
■ Permissible lubricant tempera-
ture rise, Δθ (from lubricantinlet to exit), is from 30-50 C(86-122 F), depending on thematerials used. It is restrictedto keep thermal gradients andsubsequent distortions to rea-sonable levels. Because of thehigh thermal conductivity ofcast bronze materials we canuse the upper limit.
Bearing Stresses and Materials■ Satisfactory boundary
lubrication must be providedfor start-up purposes. Thistranslates into a maximumbearing pressure of aboutF/LB < 2.5-3 MPa (362-435 psi)at start-up. When running, thismay be considerably higher. Ifthe start-up load results inpressures higher than thoserecommended we shouldprovide a hydrostatic assist.
■ Maximum recommendedbearing pressure calculatedover the projected areadepends on the bearingmaterials chosen. For castbronze bearings, we willfollow the guidelines asindicated in Table 2.3, page 24.
Figure 4.7. Clearance Variation with Temperature for a Bearing with a HigherThermal Expansion Coefficient than the Journal
Safety FactorsOne has to be very careful with
the use of safety factors in hydro-dynamic bearing design. Liberaluse of large safety factors will leadto very inefficient bearing design,and in some cases, may even leadto design failures.
■ Safety factor on load. Inpractice, a safety factor of 1.2to 2.0 on load is used dependingon how well the load is known.Under no circumstances shoulda factor greater than 2.0 be used.
■ Safety factors on oil supplyshould be about 1.5 to 2.0.
Lubricants and Filtration■ In modern designs the viscosity
grade does not exceed ISOVG100 (lighter oils areoften used).
■ Adequate filtration must beprovided. Typical filtrationlevels should be for particlesgreater than 50% of the mini-mum operating film thickness.Filtration below 10 μm mayrequire special filters. Thefilter must be sized for full-flow filtration, and should con-sider the effects of loading-up.
Geometry Considerations■ Oil inlet may be anywhere in
the low pressure region, but issafest in the region betweenthe angle of eccentricity andopposite the line of the normalload (as in Figure 4.2b).
■ Bearing wall thickness shouldbe about 30-40% of the largestsurface dimension to avoidload based deflections thatmight affect performance.
■ Shaft and housing deflectionsshould be kept to levels lessthat half of the minimum filmthickness in the bearing. In
some cases it may be necessaryto provide special construc-tional modifications to reduceeffects of distortions.
Lubricant GroovingGrooves may be machined into
the bearing surfaces to promote thedistribution of lubricant. The appli-cation and precautions are similarto grease grooving, see page 35.For oil-lubricated bearing grooves,use only about 60% of the suggestedgrease groove width.
Machining Considerations■ Cylindricality and waviness
errors should be less than 50%of the smallest expected filmthickness for the operation ofthe bearing, thus:waviness error < 0.5 x h2 m i n
■ The maximum surface rough-
ness should be less that 25to 40 times the minimumseparation, or:
rms surface roughness<h2min/(25 to 40)
This is for the harder of thetwo bearing components, normallythe shaft.
A word of wisdom aboutsurface roughness. Experience hastaught us that bearing surfacesshould be as smooth as possible,yet as rough as necessary.
A certain amount of roughnessacts in a beneficial way. Smallpockets that retain lubricant cansignificantly improve load capacityduring start-up times.
Other Journal BearingDetails
The analysis in Hydro is forthe journal bearing with the journalrotating and the bearing stationary.What if the bearing rotates and the
journal is fixed? What if the loadrotates relative to the bearing? Wewill provide some simple rules forthis in the next section. We willalso provide some simple guide-lines on easy ways to avoid severeedge-loading problems.
Bearing and Load RotationSo far the load capacity and
friction analysis for journal bear-ings has dealt with the simple caseof journal rotation. In many practicalapplications we also have bearingrotation, load rotation, or combina-tions of all three. It is quite simpleto extend the foregoing analysis toinclude these additional possiblerotations by using an equivalentjournal speed. Note that all rota-tions are referenced to the loadvector. The general case of journal,bearing and load rotations may beanalyzed by considering journaland bearing rotations independentfrom load rotations, see Figure 4.8.
In the first case, the equivalentspeed results from the addition ofjournal and bearing speeds. Thesecond case derives from arrestingthe load rotation through the back-ward rotation of the entire bearingsystem. This imparts a speed of-NF on both the journal and bearing,hence the equivalent journal speedis -2 NF. The final case is the mostgeneral and derives from the addi-tion of the two cases above. Thuswe convert journal, load and bear-ing rotations into a single journalrotation by:
Ne = Nj + Nb - 2 NF
where:
Ne = equivalent journal rotation
Nj = original journal rotation
Nb = bearing rotation
NF = load vector rotation.
47
Figure 4.8. Equivalent Journal Rotations for Different Journal, Load andBearing Rotations.
As might be apparent by now,the sense of the rotations should bekept in mind. We have used clock-wise here as positive. (Note: Someof these bearings will require a ringgroove supply in order to functioncorrectly.)
Geometries to Mitigate EdgeLoading due to Shaft Bending
Edge loading due to shaftbending is a serious problem, andcan significantly reduce loadcapacity. In Figure 4.9 are severalsimple ideas that can reduce theseverity of the problem (fromBartz14).
The last column in Figure 4.9shows some very simple construc-tions that often can easily be incor-porated in a new design. Oftenthese 'silent' features introducea significant robustness intothe design.
Mating SurfacesThe choice and properties of
the mating surface in a bearingsystem are just as important as theselection of the bearing material.Specifically, the material type, thesurface roughness and preparationmethods, and the hardness of themating bearing surface are
extremely important. In the follow-ing discussion of each of thesetopics we will refer to the matingsurface as the shaft. This is onlyout of convenience, and the detailsof the discussion apply equally wellto the mating surface of a thrustbearing, a spherical bearing or anyother form of bearing surface.
Shafting MaterialsThe predominant number of
bearing applications involve steelas one of the members. The pre-dominant shafting material is steel,either a carbon steel, tool steel,gray or nodular cast iron. Stainlesssteel shafting may be used, but caremust be taken in selecting gradesthat have high seizure resistancewhen used with certain bearingalloys. Fatigue strength of the shaftis important if cyclic loading isanticipated on the bearing.
The use of the case-hardenedshafts in many machine elements isvery common. Hardened steel isvery resistant to both adhesive andabrasive wear. This wear resistanceincreases with hardness. From apractical standpoint, the maximumobtainable hardness on carbon steelcomponents is about 65 HRC. Atthis level of hardness, the ductilityof the steel is very low, and failureby brittle fracture can occur veryrapidly if the shafts are overloaded.To avoid this problem we use case-hardening techniques.
In case-hardening, the surfaceof the material is hardened to maxi-mize wear resistance, while the coreis kept soft to avoid brittle fractureof the part. This hardened case maybe achieved on shafts by suitableinduction heat treating of moderateto high carbon steels or by carbur-izing of a low-carbon based metal.
48
Figure 4.9. Methods to Avoid Edge-Loading Problems.
The latter method is used mostcommonly for mass productiontechniques and is less subjectto error.
Surface PreparationThe most common method of
surface preparation is grinding.This may be done by centerlessgrinding or by conventional methods.The control of surface roughnessand waviness levels, surface layand fuzz generation are veryimportant in the satisfactoryoperation of a bearing.
To keep circumferential wavi-ness, out-of-round and grindingchatter under control, it is suggestedthat roughness and waviness tracesbe made periodically. Chatter shouldbe kept to a minimum, and lobingeffects of grinding must be withinthe circumferential waviness limits.The presence of 3 to 7 definite lobe
patterns on the shaft is highlyundesirable.
Surface Roughness LevelsThe best levels of roughness
on the bearings and shaft are oftena compromise between the cost toproduce these levels of roughness,and the amount of run-in wear thatcan be tolerated. Wear of the bearingand shaft will lead to larger clear-ances, and thus part of the wear lifeof a bearing system may be con-sumed simply by not producing theoptimum roughness on the newcomponents.
Wear in a bearing system cantake the form of adhesive wear,abrasive wear or a combination ofboth. We control adhesive wearthrough a proper materials selec-tion, while abrasive wear can becontrolled through roughness. Toavoid two-body abrasion of the
softer bearing material by the shaft,its roughness should be low. Typicalnominal Ra values are around 0.2-0.3 μm (8-12μin.) for the shaft anddouble this value for bearings.
If the differential hardnessbetween bearing and shaftingmaterials exceeds 150-200 HV, theshaft roughness should be madecorrespondingly lower. Also, as thehardness of the bearing materialincreases, its roughness and theshaft roughness should be madecorrespondingly lower to avoidtwo-body abrasion by the bearingmaterial on the shaft and by theshaft on the bearing.
Hardness of ShaftsThe surface hardness of the
shaft should be high to resist wearby the bearing and to resist wear bythe ever-present abrasives such assilica. In most cases, the shaft isthe expensive, difficult-to-changemember which increases theimportance of minimizing wearon the shaft.
Tin bronzes require hardersteel shafting and a good finish.The hard constituents in tinbronzes will tend to wear in thesteel surface and improve its finish.Aluminum bronzes require a hard-ened steel shaft or chromiumplating on the shafting. Copperberyllium alloys also require ahardened shaft material—prefer-ably a tool steel.
As a good starting point, weshould aim to make the shaft atleast 150-200 HV points harderthan the hardest constituent in abearing material. This will ensurethat almost all the wear in a bearingsystem will take place on the softercomponent. If the hardness differ-ential is greater than this, careshould be taken to lower the levelsof roughness for the shaft. We tend
49
Figure 4.10. Common Design Problems with Bearings.
to rely on a certain amount ofpolishing of the shaft by the bear-ing material. This becomes moreand more difficult as the shaftgets harder.
Other IssuesDesigning a good bearing can
be helped immeasurably by knowingthe pitfalls of bad design. Figure 4.10shows some of the common designerrors presented by Pesek23 to be
avoided in order that satisfactorybearing life may be realized.
The index numbers shown onthe figure are explained as follows:
1. Shaft ending within thebushing allows journal towear a matching ridge in therelatively soft bearing mater-ial. This restricts free flow ofthe lubricant across theheavily loaded area, causesedge loading and results in
high temperatures, excesswear debris in the bearingand eventual seizure.
2. Grooved shaft producessame conditions as 1.
3. Bearing thrust face largerthan mating surface producessame conditions as 1.
4. Opposing oil inlet holeswithin one bearing bushingprevent proper oil flowacross bearing surface. Thepressure gradient producedresults in high temperature,excessive wear and eventualseizure.
5. Dead end acts as a reservoiruntil filled and then preventsproper oil flow across bearingsurface, resulting in hightemperatures and excessivewear. (A point to rememberis that it is just as critical in abushing application to getthe oil out as it is to get theoil in.)
6. Fillet ride also prevents oilflow.
7. Two precision bushings inone short hole can result inmisalignment due to accu-mulated manufacturingtolerances. This forces theshaft out of line and resultsin edge loading. Do not usecoaxial flats on shaft if theycan be avoided.
50
NOTES:
51
Computer Programs
COMPUTER PROGRAMS
The CDA computer programsBound and Hydro provide a meansfor the design of either boundaryor hydrodynamic lubricated jour-nal bearings. These programs canbe used on either IBM PC compat-ible computers or Macintosh. Theywill accept units in both English(IPS) or Metric (SI).
The hydrodynamic programHydro develops a table of filmthickness, eccentricity ratio, powerabsorption, bearing oil temperatureand oil flow rate for a given rangeof radial clearances and at a fixedload. The designer inputs the load,speed (rpm), bearing size, inlettemperature and selects a lubricant.The program stores a database ofproperties for various types of oilsand inserts these data as needed.
The boundary lubricated bear-ing design program Bound is forheavily loaded, slow speed grease-lubricated bearings. It develops atable that includes estimated wear,maximum operating bearing tem-perature (with or without air cooling)and adsorbed horsepower for fourclasses of bronze bearing alloys.The program also sets bounds foracceptable operating temperatures.
Both programs cover a widerange of bearing operating condi-tions, from high bearing pressuresand low speed (25 MPa, 5 cm/s(3500 psi, 10 fpm)) to fully hydro-dynamic conditions (14 MPa, 5 m/s(2000 psi, 1000 fpm)). Bothprograms overlap in the range ofoperating conditions as shown inFigure 5.1.
In Figure 5.1 maximumallowable bearing pressure (loaddivided by the projected bearingarea) is plotted versus journalspeed in rpm, for a 25 mm (1 in.)diameter bearing. In the hydrody-namic portion, the maximum oper-ating bearing pressures are shownfor two different grades of oil. Inthe boundary lubrication zone,maximum bearing pressures areshown for two different frictioncoefficients
The boundary lubrication pro-gram is based on grease lubricationonly. The criterion for maximumbearing pressure is grease thermalinstability. Boundary lubricatedbearings wear continuously duringservice, and bronze bearing alloyshave maximum allowable com-pressive loads. Thus it is possibleto consider grease-lubricated oper-ation for a hydrodynamic designedjournal bearing that is clearly over-
loaded at, say, 10 MPa, 10 cm/s(1500 psi, 20 fpm) or to investigatelow friction hydrodynamic designfor a relatively slow speed, lightlyloaded bearing, say, 3.5 MPa,15 cm/s (500 psi, 30 fpm) thathad been originally considered aboundary lubricated bearing.
Background to the ProgramsThe hydrodynamic bearing
program is based on the materialpresented in the previous chapter.The bearing performance charts ofRaimondi and Boyd21, developedfrom solutions to Reynold's equa-tions have been computerized. Theprogram automatically iterates theconverging estimates for oil tem-perature. This is essentially a great-ly expanded computerized versionof the Rippel9 manual.
The boundary lubricationprogram is based on empirical data
Figure 5.1. Maximum Bearing Stress Operating Range for a 25 mm (1 in.)Journal Bearing for Both Boundary and Hydrodynamic Lubrication.
53
for grease-lubricated bearings andheat-transfer equations with themaximum operating temperatureas a criterion for design, seeChapter III.
The user should be aware thatboth programs have certain limita-tions. Specific assumptions andlimitations are:
■ Programs are for steady stateloading only,
■ Program are for full 360°bearings only,
■ Oil is supplied at a single oilsupply hole located oppositethe applied load,
■ The effect of oil oversupply isnot considered in the coolingor performance of the bearing,
■ The designer should ensuresuitable alignment to avoidedge loading of the bearing,
■ The heat transfer model forboth Hydro and Boundassume certain boundaryconditions (See Appendix Bfor more details.),
■ Installed clearances are atroom temperature, 20 °C (68 F),
■ Clearances indicated areradial clearances,
■ The included viscosity data onSAE oils is for high viscosityindex oils.(See Appendix Cfor details.)The two programs are intended
to provide quick estimates forbearing performance for the designengineer. Special effects such asthe influence of grooving, edgeloading or non-circularity of thecomponents is not taken into accountby these programs. Nevertheless,they do provide a good first cutestimate of bearing performance.
For such exceptional runningconditions as turbulent flow orbearing instability (whirl), otheranalytical approaches should beused. In any instance, it is best torun bearing tests to verify thedesign before freezing the design.
Graphical presentation of thehydrodynamic program output isan option. For IBM DOS compatiblesystems this requires a VGA orhigher level monitor. Hard-copiesof the graphs can be obtained ondot matrix printers that are Epsoncompatible, or on laser printers thatare HP Laserjet compatible.
Graphics can be viewed, saved,and printed on all Macintoshsystems.
Using the HydrodynamicProgram
Insert the floppy disk and,depending on the system you areusing, follow the instructions inFigure 5.2.NOTE: The programs may also be
MacintoshOn the desktop:Double click on floppy disk iconDouble click on file "HYDRO"
IBM PC DOSAt the DOS prompt:Type "HYDRO"Press RETURN/ENTER
Figure 5.2. Opening the Program.
moved to a directory on your hard-drive. Make sure you also copy theLUBE.TRU file to the same directory.All the input and output files willthen show up on this directory.
Something like the messagein Figure 5.3 should appear.
Answer the query. If you knowof a file on the current disk thatrelates to this program enter it. Ifyou want to start afresh, answer N,or simply press RETURN becausethe default value is (N)o.
The screen display shown inFigure 5.4 will appear.
This table allows you to inputbearing load, speed, size, ambienttemperature, bearing thermal prop-erties, lubricant and lubricant inlettemperature.
The table appears with the val-ues inserted from a default set orthe last run. Some of the values aredefault values such as thermal con-ductivity and expansion (valuesassumed for steel and bronze).
CDA HYDRODYNAMIC LUBRICATED BEARING CALCULATION
Rev= 16.2 Date 930722 Time 12:13:43 Project: Journall Units: IPS
Do you want to get an input file from disc? Y/N (N)
Figure 5.3. Opening Screen.
54
*****
Rev=
*****
ITEM
ABCD
LU
FGHIJKLMN0PQ
U
Enter
******************************************
CDA HYDRODYNAMIC LUBRICATED BEARING
16.2 Date 930722 Time 12:13:43 Project:
******************************************
# NAME
Bearing Radial Load
Shaft Speed
Bearing Inside Diameter
Effective Bearing Width
Total Shaft Length
Housing Outside Diameter
Housing Width
Shaft Thermal Conductivity
Housing Thermal Conductivity
Ambient Air Temperature
Air Velocity
Shaft Therm. Exp. Coeff.
Bearing Therm Exp. Coeff.
Lubricant Name
Lubricant Supply Temperature
Heat Remvl by lube (On/Off)
Heat Remvl by amb.air (On/Off)
Toggle the Unit system
Letter for Item # or Y(es) to accept ? ()
************
CALCULATION
Journal 1
************
UNITS
(lbf)
(rpm)(inch)
(inch)
(inch)
(inch)
(inch)
(Btu/h ft F)
(Btu/h ft F)
(F)(fpm)(mu-in/in F)
(mu-in/in F)
SAE 30
(F)OnOff
**********
Units: IPS
**********
VALUE
500
3500
1.1.4.3.1.
29.28.83
.6.
10.
83
*
*
000000000000000000
03020
Figure 5.4. Input Table.Initially, the program assumes yoursystem uses an oil supply that thebearing pumps through its clear-ance, removing the bearing heat.NOTE: Clearance values in thisprogram are radial.
Entering Bearing DataThe input values shown above
can be changed by selecting theiritem number (such as B or b forshaft speed) and then entering theappropriate values. If the systemuses a drip feed or oil vapor sys-tem, air cooling can be assumed byselecting line Q and toggling line P
(heat removal by air) on. In addi-tion the air velocity may be supplied(line K) if forced air cooling isanticipated. Appendix A has moredetails on the assumptions made inthe thermal modeling and some ofthe different ways that control canbe exercised over the heat transfermechanisms.
The bearing and shaft materialthermal properties (thermal expan-sion and thermal conductivity) areparameters used in the program.These values in the default table(File Journal 1) are for C93200bronze and AISI 1040 carbon steel.Since thermal expansion is a
significant process in bearingperformance, it is essential that thecorrect conductivity and expansionvalues are entered in the programfor materials selected for a givendesign. Therefore items H,I, L andM should be adjusted for materials.
Lubricant SelectionTo select a different lubricant,
press N and a table of lubricantnames will appear. When youselect a lubricant, its temperature-viscosity properties are enteredinto the program. Note that whenyou select the lubricant, the
55
program displays the lubricant nameand asks if it is correct. If you answerY(es), you are returned to the inputtable.
The default data in the data fileis based upon high viscosity index(HVI) lubricants. It should be real-ized that there may be a significantvariation in viscosity-temperaturebehavior from one nominally samelubricant to another. Hence it isalways best to enter your own mea-sured viscosity data for the specificlubricant you intend to use.
Additional lubricant data maybe added to the data file as shownin Appendix C.
Entering Data in Alternate UnitSystems
You may use IPS (inch, lb-force, seconds) units or SI (meters,Newtons, seconds) units in yourdesign. The unit system can bechanged at any time during datainput by toggling between the twowhen pressing U. You can mixyour units as they are entered. Forinstance, if you have entered load,shaft speed and bearing dimensionsin IPS units (lbf, rpm, inches) andyou have the shaft and bearingthermal expansion in SI units(µm/m °C), you can toggle to SIunits by pressing U and Return.The table converts to all SI units.You can then enter your thermalexpansion values. If you wish tohave results in IPS, press U andReturn. The table is then in IPS units.
Calculating BearingPerformance
When the correct values areentered into the table, the programcan be asked to compute the bearingperformance values by answeringY(es) to the inquiry. The input canbe saved in a file as instructed bythe program.
However, if you do not save asa file, the same input values willcome up again when you activatethe input table. While the programis computing, a series of messagesshow the percentage of completionand information related to the bear-ing design. The results then appearas a table. See Figure 5.5.NOTE: On some systems you maybe asked to press Return half waythrough the output.
The output reiterates the inputvalues, including the lubricantselected and its properties. The tableof calculated data below the inputtable shows a number of perfor-mance values for 10 different radi-al clearances.
(NOTE: If you are using diame-tral clearances in your design, ratherthan radial clearance, multiply theclearance values in the table by 2.)
The output table providespower loss in the bearing, minimumoil flow rate, mean oil film temper-ature, minimum oil film thickness,eccentricity ratio and a rating forthe reliability of the calculations(confidence). It also prints out theminimum recommended filmthickness and clearance in twostatements below the table.
After the bearing calculationresults are displayed, the programgives choices for G(raphic) displayof performance characteristics orsending the output to a F(ile).Graphics provides a valuable chart-ing of bearing behavior over arange of clearances and showlimitations such as recommendedminimum film thickness and bear-ing instability threshold. If a D(ot)matrix or a L(aser) printer is online, you may choose to print outthe graphics. Otherwise it may bedisplayed on the screen. (NOTE:For IBM PC systems this requiresVGA graphics and EPSON dot
matrix or HP Laserjet compatibilityof your hardware.)
Two plots are available: mini-mum film thickness versus radialload for all the clearance valuesdisplayed in the output table andminimum film thickness versusmean film temperature for all theclearances. Both plots show theselected operating load, recom-mended minimum film thicknessand whirl instability threshold.Examples of the graphics areshown in the Figures 5.6 and 5.7.
Figure 5.6 shows minimumfilm thickness versus radial loadfor 10 different clearances. Thedesign load is shown as the appliedload line. A vertical dot-dash lineshows recommended minimumfilm thickness limit. A dashed lineshows the limit for reduced load or"whirl limit." This limit representsa condition where the journal posi-tion has come close to the bearingaxis. This can lead to instability(vibration) or shaft whirl.
Figure 5.6 shows another oper-ating characteristic for a hydrody-namic bearing: shearing of thelubricant film in the bearing gener-ates heat. The program estimatesthe bearing temperature expectedfor the input parameters. It is wiseto operate at as low a bearingtemperature as possible to minimizethermal breakdown of the lubricant.Note that temperatures decreasewith increasing clearance andincrease with increasing film thick-ness. Thus with a given clearance,a fluctuating load will result invariable bearing temperature as thefilm thickness varies with load.
Instinctively, one would like tochoose design parameters thatresult in the largest value of mini-mum film thickness. However,other factors must be considered.
56
CDA HYDRODYNAMIC LUBRICATED BEARING CALCULATIONRev= 16.2 Date 930722 Time 12:13:43 Project: Journall Units: IPS
INPUT DATA:Bearing Radial LoadShaft SpeedBearing Inside DiameterEffective Bearing WidthTotal Shaft LengthHousing Outside DiameterHousing WidthShaft Thermal ConductivityHousing Thermal ConductivityAmbient Air TemperatureAir VelocityShaft Therm. Exp. Coeff. (muBearing Therm Exp. Coeff. (muLubricant NameLubricant Supply TemperatureHeat Remvl by lube (On/Off)Heat Remvl by amb.air (On/Off)
(lbf)(Rpm)(inch)(inch)(inch)(inch)(inch)
(Btu/h ft F)(Btu/h ft F)
(F)(fpm)
-in/in F)-in/in F)
SAE 30(F)OnOff
5003500
1.00001.00004.003.001.0029.0028.0083
.06.3010.20
83
LUBRICANT DATA Name = SAE 30Dynamic ViscosityDynamic ViscosityDynamic ViscositySpecific HeatLubricant Density
1.200e+l Pa.s at - 18 C9.000e-2 Pa.s at 40 C9.500e-3 Pa.s at 99 C1.850e+3 Joules/kg C at 20 C8.850e+2 kg/mA3 at 20 C
CALCULATED DATA:PREDICTED HYDRODYNAMIC PERFORMANCE FOR DIFFERENT CLEARANCES:
Rad Clear.(mu-in)
2666.672133.331706.671365.331092.27873.81699.05559.24447.39357.91
Load(Ibf)
500.0500.0500.0500.0500.0500.0500.0500.0500.0500.0
Pwr Loss(hp)
.181
.181
.178
.172
.165
.156
.147
.138
.130
.123
Oil Flow(Gpm)
.077
.058
.044
.033
.026
.020
.016
.013
.011
.009
Minimum recommended Film thicknessMinimum recommended Radial Clearance
Oil Temp(F)
98103109117125134143153162171
210.01051.5
hmin(mu-in)
687.67671.69635.74586.85532.61478.89429.45385.95349.27318.88
(mu-in)(mu-in)
Ecc. Confdnc
.748
.695
.644
.598
.557
.522
.492
.467
.447
.429
GoodGoodGoodGoodGoodGoodGoodGoodGoodGood
Figure 5.5. Calculation Screen. 57
Figure 5.6. Diagram of Bearing Operating Characteristics Showing Minimum FilmThickness Limit. (Data points are clearances, µinches)
ClearanceThe dotted lines in Figure 5.7
are radial clearances that may betoo small for safe operation.Selecting the optimum clearancefor a journal bearing requiresconsideration of several options.Referring to Figure 5.7, it can beseen that bearing stiffness (springrate) increases with decreasingclearance.
Keep in mind, manufacturingpractices limit the precision possi-ble in producing a bearing. Thisincludes bearing I.D. and journalO.D. tolerances, geometry (out ofround condition), misalignment,and thermal gradients existing
during start-up.The latter condition, thermal
gradient, becomes quite significantas bearing sizes and speedsincrease. During start-up, thefrictional heating causes the journalto expand while the bearing mayexpand inward until the bearinghousing equilibrates in temperature.Thus the clearance closes downduring this initial phase of opera-tion. If the clearance is too small,the bearing clamps down on thejournal and seizure occurs.
Therefore clearance must belarge enough to get through thisinitial critical start-up period. Inaddition, one can determine theeffect of manufacturing tolerances
on bearing performance by deter-mining minimum film thicknessesfor the maximum and minimumclearance resulting from dimen-sional tolerances.
A good approach to clearanceselection involves picking thesmallest clearance on the basis ofthe above considerations so that asthe bearing wears during its life(during start-up and shutdown), theincrease in clearance will stay atthe lower end of the recommendedvalues. So one might select a radialclearance of 1092 (µinch (28 µm)from Figures 5.6 and 5.7.
If one should choose to use thelower clearance values included asdotted lines in the figure, one mustmake sure to prescribe the neededprecision in manufacture and thefine surface finish values for reli-able operation. The recommendedclearance range in the programoutput is based on several investi-gators findings, from journal bearingtests. See Fuller24.
Air-Cooled DesignIf the bearing under considera-
tion is expected to operate underlimited lubrication flow (such asdrip feed, vapor lubrication, orhydrodynamic grease lubrication),the design process should be modi-fied for air-cooling only. To changethe program to air-cooling mode,press P and answer the instructionby typing "off, then press Q andenter "on". When the input tableshows "Heat removal by lube... off"and "Heat removal by amb. air...on",press K to input the cooling airvelocity selected for your design.
The output shown below willhave different values from theoutput for oil-cooled design.Generally, when air-cooling is
58
used, bearing load capacity willbe reduced as compared with oil-cooling mode. To illustrate thedifference in bearing operatingcharacteristics for air-cooled andoil-cooled operation, two bearingdesigns will be examined. Thegraphic results for the two condi-tions are shown in Figures 5.4 and.7.
Applying the HydrodynamicProgram Results
The bearing design and lubri-cant selection is aimed at long lifeand reliable operation. These con-cerns are of great importance whenreviewing the program output. Letus refer to the graphics, Figures 5.6and 5.7. Figure 5.2, showing mini-mum film thickness curves for tenclearances and a large load range,is probably the most useful chart.
First of all, where the load linecrosses the recommended mini-mum film thickness line, it can beseen that the design is within safeoperating limits for all clearancesshown.
Looking at the family ofcurves, it can be seen that as clear-ance increases, the slope of theload-film thickness curve decreases.This means that the smaller theclearance, the stiffer the bearing,i.e., if the load increases, the jour-nal center will move a smalleramount away from the bearingcenter. In addition, the smaller theclearance, the closer to the recom-mended minimum film thicknessthe bearing will operate. Owing toprecision limits in manufacturing,a minimum clearance should bespecified. Also, a maximum clear-ance should also be specified toinsure a reasonably stiff bearing.
Figure 5.7. Mean Film Temperature versus Minimum Film Thickness.(Data points are clearances, µinches)
Referring to the output table, it isalso evident that the larger clear-ances lead to higher oil flow andhigher power losses in the bearing.
As bearings wear in service,the original clearance will open up.Therefore it is best to base thedesign on the minimum clearanceor the left side of the "recommend-ed design envelope" shown inFigure 5.6.
For the usual surface finishachieved in manufacturing, theclearance should be set at between0.10% and 0.15% of the journaldiameter. This limit is shown inFigure 5.6. Thus the "safe" operat-ing limits of the bearing are con-tained within the box outlined in
Figure 5.6. An operating bearingmay be subjected to periods of loadchanges, increased temperaturesand speed changes. The designmust be able to operate within thatset of operating conditions and stillbe within the safe operating limits.
Referring to Figure 5.7, notethat with increasing clearance, themean film temperature of the bear-ing decreases. Heat is detrimentalto oil since extended exposure toelevated temperatures causes dete-rioration. Therefore, it is wise totry to set the design for minimumoperating temperature. Higherclearance limits might thus beadvisable in a design that appearsto involve elevated temperatures.
59
Figure 5.8. Operating Characteristics for Air-Cooled Conditions.(Data points are clearances, µinches)
Using the BoundaryLubrication Program
NOTE: This program isbased on the use of grease asthe lubricant.
The Bound program isbasically for slow moving, heavilyloaded grease-lubricated bronzebearings. To initiate the program,insert the CDA floppy disk and,depending on the computer systemyou are using, follow the instruc-tions in Figure 5.10.
MacintoshOn the desktop:Double click on floppy disk iconDouble click on file "BOUND"
IBM PC DOSAt the DOS prompt:Type "BOUND"Press RETURN/ENTER
Figure 5.10. Opening the Program.
The message shown in Figure5.11 should appear:
Answer the query. If you know
of a file on the current disk thatrelates to this program enter the filename. If you wish to start afresh,answer N(o) and press return. Theinput table in Figure 5.12 of theappears on the opposite page.
Entering Bearing DataThe above table shown in
Figure 5.12 allows you to inputbearing load, speed, size, ambienttemperature, bearing thermal prop-erties and bearing friction coeffi-cient. The table appears with thevalues inserted from a defaultset of the last run. The programassumes that frictional heat is dissi-pated by convection, conductionand radiation. Other coolingaccepted is forced air movedover the bearing housing. The pro-gram allows one to input coolingair velocity.
FrictionThe default friction coefficient
is 0.10. This is a maximum leveldetermined in the bearing perfor-mance experiments. It is also con-sidered a likely starting value fornewly installed bearings. As thebearings wear in, the friction levelcan decrease. The lower end of thefriction range is assumed to be0.05. Friction coefficient levelstend toward the maximum at high-loads, low-velocity conditions.
UnitsThe input can be in IPS or SI
units. Inputting U will toggle fromone units system to the other.
CDA BOUNDARY LUBRICATED BEARING PERFORMANCE PROGRAMRev= 6.2 Date 930725 Time 16:06:22 Project: None Units: IPS******************************************************************************
Do you want to get an input file from disc? Y/N (N)
Figure 5.11. Opening Screen.
60
Figure 5.9. Operating Characteristics for Oil-Cooled Operation.(Data points are clearances, µinches)
The unit system can be changedduring data input. For instance ifyou have input load in lbf, speed inrpm and bearing size in inches andyou have thermal conductivity datain W/m °C, press U and RETURNand all entries in the input tablewill be changed to SI units. Youmay then enter your conductivityvalue. If you want your results inIPS, toggle your table back to IPSby pressing U and Return.
Calculating BearingPerformance
When the correct values havebeen entered into the table, the pro-gram can be asked to compute theestimated operating temperatureand wear by answering Y(es) to theinquiry. In boundary lubricatedbearings, some metal-to-metal con-tact occurs, and the bearing willwear continuously during its oper-ating life. Heat developed fromfriction in the bearing is not dissi-pated by lubricant flow. Therefore,bearing temperature is the critical
Rev =
ITEM #
A
B
C
D
E
F
G
H
I
J
K
L
M
U
Enter
CDA BOUNDARY LUBRICATED BEARING PERFORMANCE
6.2 Date 930725 Time 16:06:22 Project:
NAME
Bearing Radial Load
Shaft Speed
Required Operational Life
Bearing Inside Diameter
Shaft Length
Effective Bearing Width
Shaft Thermal Conductivity
Housing Outside Diameter
Housing Width
Housing Conductivity
Ambient Air Temperature
Air Velocity
Bearing Friction Coefficient
Change the Unit system
Letter for Item # or Y(es) to accept ? ()
None
UNITS
(lbf)
(rpm)
(hr)
(inch)
(inch)
(inch)
(Btu/h
(inch)
(inch)
(Btu/h
(F)
(fpm)
(-)
PROGRAM
Units: IPS
VALUE
225
300
1000
1.000
4.00
1.000
ft F) 29.00
3 .00
1.00
ft F) 28.00
75
300.0
. 10
Figure 5.12. Input Table. 61
parameter for judging performance.The program assumes that a bearingtemperature above 300 F (150 C)will cause unacceptable lubricantdeterioration for conventionalmineral oil-based greases.
The results shown in Figure 5.13will appear when the query isanswered and Return is pressed.The output provides values forsliding velocity, bearing stress (load/projected area) and horsepowerabsorbed by the bearing. It alsoshows estimated bearing tempera-ture with or without forced-air con-vection cooling. Finally it showsa table of estimated increase in
diametral clearance caused by wearfor four different grades of bronzebearing materials. The wear is relat-ed to the total number of hours ofoperational life. Note that the wearvalues differ among the four bronzes.This may influence your selectionof material. For instance, the leadedbronze materials (C93200 andC94500) tend to operate at a lowerfriction coefficient than the non-leaded bronzes. Thus one mightwant to compromise on wear lifefor a lower operating temperature.
The default coefficient of fric-tion (0.10) is conservative for leadedbronzes. Thus, if one selects one of
the leaded bronzes, it would beappropriate to select a lower coeffi-cient, say, 0.08. With that change ininput and the program recalculated,the results shown in Figure 5.13are obtained.
Note that the estimated bearingtemperature now is 43 F lower(289 F-246 F). This would insurelonger lubricant life. The wear ofleaded bronze remains the same. Ifthe bearing temperature for naturalconvection exceeds 150 C (300 F)and the value for forced convectionstays below that temperature, thefollowing message will be addedto the output:
CDA BOUNDARY LUBRICATED BEARING PERFORMANCE PROGRAMRev= 6.2 Date 930725 Time 16:06:22 Project: None Units: IPS
INPUT DATA:Bearing Radial LoadShaft SpeedRequired Operational LifeBearing Inside DiameterShaft LengthEffective Bearing WidthShaft Thermal ConductivityHousing Outside DiameterHousing WidthHousing ConductivityAmbient Air TemperatureAir VelocityBearing Friction Coefficient
CALCULATED DATA:Sliding Speed = 78.54 (fpm)Bearing Stress = 225 (psi)Power Loss = .054 (hp)
Bearing Temperature due to Natural ConvectionBearing Temperature due to Forced Convection
PREDICTED DIAMETRAL WEAR FOR DIFFERENT MATERIALS:Diametral
(Ibf)(rpm)(hr)(inch)(inch)(inch)
(Btu/h ft F)(inch)(inch)
(Btu/h ft F)(F)(fpm)
(-)
2253001000
1.0004.001.00029.003.001.0028.0075300.0
.10
289199
(F)(F)
MATERIALC93200 (Bronze 660)C90500 (Bronze 62)C95400 (AL. Bronze)C94500 (Bronze 520)
Wear (inch).0458.0114.0034.0567
Figure 5.13. Results Screen.62
"The bearing temperature exceedsthe recommended value for usewith simple natural convectioncooling. You must use the forcedconvection cooling."
If both the natural convectionand forced convection cooling
results in temperatures above 150 C(300 F), the following messagewill appear:"The bearing temperature exceedsthe recommended value. It can bereduced by increasing the forcedconvection cooling."
Of course, other means canbe taken to reduce the operatingtemperature. One can increase thehousing surface area (increase thehousing diameter) and/or the bear-ing length. Bearing load or bearingrpm can be reduced also, if thedesign permits.
CDA BOUNDARY LUBRICATED BEARING PERFORMANCE PROGRAM
Rev= 6.2 Date 930725 Time 17:30:41 Project: None
INPUT DATA:
Units: IPS
Bearing Radial LoadShaft Speed
Required Operational Life
Bearing Inside Diameter
Shaft Length
Effective Bearing Width
Shaft Thermal Conductivity
Housing Outside Diameter
Housing Width
Housing Conductivity
Ambient Air Temperature
Air Velocity
Bearing Friction Coefficient
(Ibf)(rpm)(hr)(inch)(inch)(inch)
(Btu/h ft F)(inch)(inch)
(Btu/h ft F)(F)(fpm)(-)
2253001000
1.0004.001.00029.003.001.0028.0075300.0
.08
CALCULATED DATA:
Sliding Speed =
Bearing Stress =
Power Loss =
78.54 (fpm)
225 (psi)
.043 (hp)
Bearing Temperature due to Natural Convection
Bearing Temperature due to Forced Convection
PREDICTED DIAMETRAL WEAR FOR DIFFERENT MATERIALS:
246174
(F)(F)
C93200
C90500
C95400
C94500
MATERIAL
(Bronze 660)(Bronze 62)(AL. Bronze)(Bronze 520)
DiametralWear (inch)
.0458
.0114
.0034
.0567
Figure 5.14. Results Screen.63
References and Appendices
REFERENCES AND APPENDICES
References
1. Snow Snow, Richard F., "Bearing up Nobly," American Heritage of Invention and Technology, Vol 4, Number 1, 1988.
2. Cameron Beauchamp Tower Centenary Lecture, Proceedings of the Institute of Mechanical Engineers, 1979, Vol 193, No 25.
3. Rabinowicz Rabinowicz, Ernest., Friction and Wear of Materials., John Wiley & Sons, Second edition, 1995.
4. Lansdown Lansdown, A.R, and Price, A.L., Materials to resist Wear., Pergamon Press, 1986.
5. Pratt Pratt, G.C., "Materials for Plain Bearings," International Metallurgical Reviews, 1973, Vol 18, pp 62-88.
6. Glaeser Glaeser, William A., Materials for Tribology, Tribology Series 20, Elsevier, 1992.
7. CDA Copper Alloy Bearing Materials, Design and Application Guide, CDA TN-45, 1991.
8. CDA Copper Casting Alloys, Copper Development Association, 1994.
9. Rippel Rippel, H. C, "Cast Bronze Bearing Design Manual," Cast Bronze Bearing Institute, Inc, Chicago, 1959.
10. DIN DIN-Taschenbuch 198, "Gleitlager 2,Werkstoffe, Prüfung, Berechnung, Begriffe," BeuthVerlag, 1991.
11. Glaeser Glaeser, W.A., Dufrane, K.A. & Buchnor, W.R., Final Report on Evaluation of Load Capacity of Cast Bronze Bearings, International Copper Research Association, Inc., 1976.
12. Archard Archard, J.F., Contact and Rubbing of Flat Surfaces, J. Appl. Phys., Vol 24, 1953, p 981.
13. NLGI NLGI Lubricating Grease Guide. Second edition. National Grease Lubricating Institute, Kansas City, Mo., 1989.
14. Bartz Bartz, W J., Gleitlagertechnik Teil 2. Band 163, Expert Verlag, 1986.
15. Spiegel Spiegel, K., Fricke, J., Meis, K.R., and Sonntag, F., Zur Verbesserung der Berechnungsmoeglichkeiten fuer fettgeschmierte Radialgleitlager., Tribology und Schmierungstechnik, Vol 6, 1995.
16. Cameron Cameron, A. Basic Lubrication Theory, Longman, 1971.
17. Constantinescu Constantinescu, Virgiliu., et al, Sliding Bearings, Allerton Press, New York, 1985.
18. Szeri Szeri, A. Z., Tribology. Friction Lubrication, and Wear, McGraw Hill., 1980.
19. Hamrock Hamrock, B.J., Fundamentals of Fluid Film Lubrication, NASA Reference Publication 1255, 1991.
20. CDA Cast Bronze Hydrodynamic Sleeve Bearing Performance Tables, Copper Development Association, 1969.
21. Raimondi Raimondi, A.A., & Boyd, J., "A Solution for the Finite Journal Bearing and its Application to Analysis and Design III," ASLE Trans. Vol l, No l, 1958.
65
22. Hill Hill, A., "Modern Bearing Design and Practice," Transactions from the Institute of Marine Engineers, Vol 88, 1976.
23. Pesek Pesek, Laddie, and Smith, Walter, "Sleeve Bearing and Thrust Washer Design Trends," SAE Transactions 680426, 1968.
24. Fuller Fuller, Dudley D., Theory and Practice of lubrication for engi-neers, Second Edition, John Wiley & Sons, 1984, pp 285-287.
25. Holm Holm, R., Electric Contacts Handbook, Springer-Verlag, Berlin, 1946.
26. Herschel (1919) Herschel, W. H.: Standardization of the Saybolt Universal Viscometer. Bur. Standards, Technical Paper 112, (1919).
For Further Reading
Gunther Gunter, Edgar J., Dynamic Stability of Rotor-bearing Systems, NASA SP-113, 1966, U.S. Government Printing Office, Washington D.C. 20402.
Lang Lang, O.R., and Steinhilper, W, Gleitlager, Springer Verlag, 1978.
Moes Moes & Bosma, "Design Charts for Optimum Bearing Configurations", Trans. ASME April 1971, JOLT, pp. 302-305.
Pinkus Pinkus and Sternlicht, Theory of Hydrodynamic Lubrication, McGraw-Hill, 1961.
Welsh Welsh, R.J., Plain Bearing Design Handbook, Butterworths, London, 1983.
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Appendix A. QuantifyingLubricated Wear
Wear in the presence of a lubri-cant occurs commonly in mecha-nisms and is a primary cause ofdeteriorated performance and fail-ure. The extent of wear occurringdepends upon the lubricationregime encountered. In someapplications that are specificallydesigned to develop a hydrodynamicfilm, the lubricated wear phase isshort and transitional during run-ning-in and during start-stop cyclesonly. When conditions of fullhydrodynamic film generation can-not be established, it is the mainmode of lubrication. It should bepointed out here that even subtlesurface features such as machiningwaviness can contribute significanthydrodynamic action in whatappears to be an otherwise non-hydrodynamic application.
The extremely complicatednature of wear virtually precludesaccurate quantitative relationshipsto predict wear. However, for engi-neering purposes, relationshipsexist for assessing the general wearregime and the likely effect ofchanging one of the variables onthe resulting wear rate.
Archard-Holm EquationFrom very simple basic argu-
ments, it may be expected that theremoval of material between twosurfaces in contact is proportionalto their real area of contact. Alsomaterial removal may be expectedto be proportional to the total dis-tance through which the surfacesmove. Thus it is perfectly reason-able to expect that wear is:
where,V = volume of material wornAr = real area of contact
L = total sliding distanceα = thermal expansion coefficient
It is also well known that thereal area of contact between twosurfaces is directly proportional tothe applied load. This is regardlessof whether the asperity contact waselastic or plastic. If the contacts arepredominantly plastic then we findthat the real area of contact isinversely proportional to the hard-ness of the softer of the two bodiesin contact. Material removal fromthe surface is thus expected to beproportional to the applied load,and inversely proportional to hard-ness. Hence the relationshipbetween wear volume V anddistance L, load Fn, and hardnessH is expected to be:
where,V = wear volumeFn = normal load
L = sliding distanceH = hardness
If the contact conditions at theasperities stays the same whilematerial is removed, then we mayintroduce a constant of proportion-ality K, and the wear equation nowreads:
where,K = wear coefficient
The above wear equation wasdeveloped by Archard12, drawingon Holm's25 theory of wear. Theconstant, K, is often called thewear coefficient. It is extremelyimportant to realize the nature ofthe assumptions that have goneinto the derivation of this equation.If we in anyway alter the contactconditions during asperity interac-tions, we generally expect that toalter the removal rate of material.Hence the wear coefficient is verydependent on the particular condi-tions that prevail at the asperities.Of particular importance are thefollowing:
• Adhesion conditions of thematerials. This in turn depends on:
• Local temperatures (depen-dent upon ambient tempera-ture, friction and slidingvelocity)
• Local cleanliness conditions• The solubilities of the two
materials• Asperity contact conditions:
• Load and geometry result inelastic or plastic contact stress
• What portion of the appliedload is carried by the asperities.
Hence the above wear equationwith a constant, K, is only validover a range of loads and distancewhen asperity conditions stay thesame. Experience verifies this.
The lubricated wear dataobtained by Glaeser" was observedto behave according to the Archardmodel. The experimental wearcoefficients are as indicated inFigure 3.1. Because the bearingswere grease-lubricated, the wearmechanism remained the same dur-ing the tests, with the exception ofthe initial wear due to running-in.
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The experimental data fitted tothis model is used in the Boundprogram.
Other Forms of the ArchardEquation
It is often convenient to writethe wear equation in a somewhatdifferent form. Sometimes weprefer to express wear as a lineardimension change. For example,we may be more interested in achange of bearing clearance overtime. Such an expression may bederived from the above, if we con-sider the wear volume V to be theproduct of the apparent area ofcontact A and the depth of wear.This allows us to derive an expres-sion for the depth of wear simplyby dividing by the apparent area ofcontact, or:
where,A = apparent area of contactd = depth of wearP = nominal contact pressure
bearing stress
The nominal contact pressurein a bearing is thus simply the radialload divided by the projected bear-ing area. This is taken to be D*B.
To calculate the time t to reacha critical wear depth d*, when slid-ing takes place at constant velocityU, can be done by letting L = U t.Rearranging gives:
KPUwhere,
U = constant sliding velocity,d* = critical depth of wear
We may also calculate thewear depth when the bearingoperates at constant speed for agiven time t as:
Lubricated Wear under VariableLoading Conditions.
In many applications, the load-ing on a bearing may be variable,and the speed may change, or thedirection of rotation may evenreverse. To predict wear in suchinstances, we need to apply cumu-lative damage models. Fortunatelythis is fairly simple for bearingwear calculations, provided that thewear mode stays the same over thelife prediction period. With grease-and oil-lubricated cast bronze bear-ings, this is expected to be the case.
To apply cumulative damagemethods for lubricated wear calcu-lations, we simply make a summa-tion of the product of load andsliding distance over the predictionlifetime. Hence the wear depthequation becomes:
We have here used the absolutevalue of the product of pressureand velocity because wear is essen-tially path dependent. For situa-tions where the load and slidingvelocities are essentially constantover long periods of time, andwhere a distinct finite number ofthese constant usage periods exists,we may write:
The cumulative damage con-cept may also be used to calculatean equivalent wear period for anapplication with variable loadingand speed. The time to reach thesame wear depth may be foundfrom manipulation of the aboveequation as:
is average pressure, and
is the average speed.
This simple model will bevery useful when using the Boundprogram for applications withvariable loading.
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Appendix B. ThermalModeling of the Bearing
In the performance analysis ofjournal bearings, the operatingtemperature plays an importantrole. For the boundary lubricationmechanism, the peak temperatureat the interface is the key to deter-mine the life and suitability of theconstruction. For hydrodynamicallylubricated bearings, it is the strongtemperature dependence of viscosityfor lubricating fluids that interactswith the load capacity. Hence it isessential that reasonably accurateprediction of the bearing tempera-ture be performed. This prediction,however, has to be in keeping withthe requirements of the solution.
Computer programs have beendeveloped which are capable ofobtaining a thermo-hydrodynamicsolution to the energy and Reynold'sequation for a given bearing con-figuration. The difficulty whichoften remains here is what bound-ary values to use for the variouscomponent temperatures. Thermalanalysis of the entire bearing con-struction for different boundaryconditions is then required.
An alternate solution, and theone used here, is one whereby areasonably simple empirical modelis used for the heat loss from abearing configuration, and then touse the resulting temperatures as away to calculate an effective vis-cosity in the bearing. This methodessentially is a film energy balance,whereby the frictional heat gener-ated is carried away by conductiveand convective mechanisms. Thesimplicity of the model, however,necessitates some restrictions inthe applicability of the model.These restrictions are explained inthe next section.
General Heat Transfer ModelA general heat transfer model
of the bearing is shown in FigureB.1. This model allows for the gen-eration of heat within the bearing,and for dissipation of this heat byconvective, conductive and radia-tive heat transfer. This model isessentially implemented in bothprograms with the followingrestrictions:
1. Shaft diameters are the sameon both sides and are thesame as the bearing insidediameter.
2. Both sides of the shaft havean equal length of exposure.
3. The ambient air temperatureis the same for the shaft andthe bearing.
4. The effective length of theshaft is at such a locationwhere the shaft temperatureis ambient. This meansthere is no heat flux in theshaft at that location.
5. The radiative emmissivitycoefficients for the shaft andbearing housing have beenfixed at 0.8 and 0.7,respectively.
6. The model assumes that theshaft is solid.
With these assumptions andrestrictions in mind, the programcalculates the heat transfer fromthe bearing by conductive, convec-tive and radiative mechanisms. Allof this heat has to be absorbed bythe ambient air. Additional heattransfer from the bearing isallowed for by the convectivemechanism in the lubricant flow.
The important dimensionsrequired by the program for theheat transfer calculations areshown in Figure B.2.
Control of Heat TransferMechanisms
In designing a bearing applica-tion it is often required that thebearing performance be checked
Figure B.1. General Model of the Various Heat Transfer Modes from aJournal Bearing.
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Figure B.2. Definition of Bearing Dimensions for the Heat Transfer Model.
under a number of different condi-tions. This is especially importantfor bearings where the heat transferconditions are not well known. Thebearing design programs Hydroand Bound have a number of con-trols that can be exercisedby the user to determine theirinfluence.These are:
■ Heat removed by theambient air. For Hydro, this maybe turned "On" or "Off." When
turned "Off," only convection bythe lubricant is permitted. ForBound, it cannot be changed.
■ Heat removed by the lubri-cant. Can be switched "On" or"Off " in Hydro. When it isswitched "Off," it simulates theheat transfer from a grease-lubri-cated bearing operating in thehydrodynamic mode.
■ Control of the air velocity.Heat transfer from the bearing andshafts is based upon both natural
and forced-air convection. Bychanging the "air velocity," we canalter the degree of forced convec-tion. When the "air velocity" is setto 0, only natural convection andradiative heat transfer from thehousing take place. The heat trans-fer from the shaft is, however,based on the forced convectionmode due to shaft rotation.
Because bearings must have amechanism whereby viscous/fric-tional heat is removed, a number ofsafeguards have been implement-ed. Thus it is not possible to setboth "heat removal by lubricant"and ambient air to "Off." The pro-grams will reset the value for"heat removal by lubricant" to"On." For the Bound program, theheat transfer mechanism by thelubricant does not exist and is thusnot provided as an option.
It is recommended that theuser implement a cautious approachto the heat management of bear-ings, i.e., always estimate on theconservative side.
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Appendix C. Fluid ViscosityDatabase
The Hydro program as sup-plied comes with a limited fluidsdatabase. The current fluids in thedatabase are:
■ ISO VG32■ SAE 10W■ ISO VG46■ SAE 10■ SAE 20■ ISO VG68■ SAE 30■ ISO VG100■ SAE 40■ ISO VG150■ SAE 50■ ISO VG220■ SAE 60■ Di-2 Ethylhexyl Sebacate■ TetraChloroDiphenyl■ Polydimethyl Siloxane■ Glycerol■ Tolulene■ Castor Oil■ Methanol■ Ethanol■ Water
The database contains thetemperature-related properties ofthese fluids. Because the standardsfor both the ISO VG and the SAEgrades DO NOT specify the tem-perature viscosity behavior of thesespecific grades, certain assumptionswere made in selecting data forthese lubricants. The user should beaware of and consider the following:
■ The default data for mineraloil-based lubricant is basedupon high viscosity index(HVI) lubricants;
■ There may be a significantvariation in viscosity-tempera-ture behavior from one nomi-nally-the-same lubricant toanother;
■ It is always best to enter your
own measured viscosity datafor the specific lubricant youintend to use;
■ It is imperative that the userverifies the assumed tempera-ture-viscosity and the actualtemperature viscosity behaviorof the fluid he selects.
Adding Additional Fluids to theDatabase
Additional fluids may beadded to the database by using anyword processing program. The dataare contained in an ASCII text filecalled LUBE.TRU. This file mustbe called up as an ASCII text fileand saved as an ASCII text file. Beaware that some word processingprograms add special characters toa file if you do not save it as ASCII.The data essential to the hydrody-namic program are the following:
■ Fluid name,■ 3 temperature-viscosity points,■ Fluid density data point, and■ Fluid specific heat data point.
This information needs to beentered on a single line in commaseparated value (CSV) format. Atypical entry, for example, forGlycerol is given below. Details ofeach entry are given next.
Glycerol, 0,12.1, 100,0.013,200, 0.00022, 1260, 2350
■ Fluid name. Any name up to15 characters long thatdescribes the fluid. (Glycerol);
■ Temperature-viscosity points:These points are used to inter-polate the fluid viscosity atdifferent temperature forms.The values must be given inthe Temp 1, Vis 1, Temp 2,Vis 2, Temp 3, Vis 3 order. Tryto use the maximum spread intemperatures for best results. Itis also recommended that youenter the data in increasing
temperature order. Thetemperatures need to beexpressed in °C, and theviscosity needs to be expressedin the dynamic units of Pa·s(a section dealing with viscosityconversion factors is givenlater);
Temperature, °C0
100200
DynamicViscosity, Pa·s
12.10.0130.00022
■ Fluid density data point. Onedata point on the fluid densityin kg/ms at 20°C is required.(1260kg/m3);
■ Specific heat capacity datapoint. One data point for thespecific heat capacity at constantvolume (Cv) in Joule/kg•°K at293 K is required. (2350Joule/kg•°K).
Viscosity ConversionsTraditionally viscosity was
measured by noting the timerequired for a given amount offluid to be drained by gravitythrough a small orifice. The SayboltUniversal Seconds (SUS), theRedwood Seconds (RS), and theDegree Engler (E) are all based onthis method. The information thusobtained is a measure of the kine-matic viscosity. This measuredtime in seconds may be convertedto proper kinematic viscosityby the following formula due toHerschel26:
where,n = kinematic viscosity in
centistokes (cSt)t = measured runout time.
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The constants A and B depend on the type of instrument used and aregiven below.
NOTES:
Type of ViscometerSaybolt (SUS)Redwood (RS)
Engler (E)
A0.220.260.147
B180171374
The units of kinematic viscosity in SI units are m2/s. Formerly the kine-matic viscosity was quoted in Stokes or Centistokes. Conversion factorsfrom other units of kinematic viscosity are:
Kinematic Viscosity Unit
1 Stoke (St)
1 Centistoke (cSt)
1 square foot per hour
1 square foot per second
1 square inch per hour
1 square inch per second
Conversion Factor
10-4 m2/s
10-6
0.258 x l0 -4
929.03 x l0-4 m2/s
0.179 x l0 -6 m2/s
6.452 x 10-4 m2/s
Temperature changes affect the oil kinematic viscosity in two ways: bychanging the flow resistance or dynamic viscosity and by changing thedensity. For hydrodynamic lubrication, we only require the change in flowresistance and therefore the dynamic viscosity. In the SI system of units,the dynamic viscosity has units of:
The dynamic viscosity of a lubricant is obtained by multiplying thekinematic viscosity by the density of that fluid. Note that the density needsto be expressed in kg/m3 and the kinematic viscosity in m2/s for this calcu-lation. (Units are: m2 s-1 x kg m-3 = kg m-1 s-1 = N s m-2 = Pa·s)
Conversion factors from other dynamic viscosity units are:
Viscosity Unit
1 poise (P)
1 centipoise (cP)
1 poundforce second per square inch (Reyn)
1 poundforce second per square foot
1 poundal second per square foot
1 pound per foot-second
1 slug per foot-second
Conversion Factor
0.1 Pa ·s
0.001 Pa·s
6896 Pa·s
47.88 Pa·s
1.488 Pa·s
1.488 Pa·s
47.88 Pa·s
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