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27Slider Bearings
27.1 IntroductionSlider Bearing Types • Compressible Lubrication • Compressible vs. Incompressible • Advantages and Disadvantages for Bearing Types
27.2 Self-acting Finite BearingsFixed-Geometry Thrust Bearings • Pivoted (Tilting) Pad Thrust Bearings • Journal Bearings
27.3 Failure ModesCavitation Erosion Damage • Wear Due to Contaminants
27.4 Slider Bearing MaterialsMaterials for Liquid-Film Applications • Bearing Materials for Gas-Film Applications
27.1 Introduction
The vast number of industrial slider bearing designs initially evolved from a desire to create a bearinghaving better load-carrying capacity and/or reduced friction and wear. Thus, a great deal of emphasiswas placed on the effectiveness of the bearing geometry to generate pressure (self-acting bearings) andthus increase load capacity.
To illustrate how geometry affects the pressure-generating mechanism in a bearing, first consider theone-dimensional inclined slider in Figure 27.1. If one assumes the “no slip” condition, fluid is draggedinto the converging wedge region by the moving runner. Since the exit is smaller than the entrance, apressure is created to open up the exit so as to balance the flow into and out of the slider. If the twosurfaces are restrained by a force (load), then pressure created within the bearing surfaces will resist theamount of fluid trying to enter (i.e., reverse flow) and will push more fluid out the exit so that the actualflow entering equals the flow exiting the slider.* For a finite bearing, one must take into account the fluidexiting along the sides as well (i.e., side-leakage). The slope of the inclined slider in Figure 27.1 is greatlyexaggerated for bearing applications. To put it in perspective, Fuller (1984) considers the extreme caseof a bearing pad having the length of a football field. The rise**, based upon a slope known for goodload capability (3 mils/ft), was calculated to be 0.9 in. (2.28 cm).
With respect to the slope of the inclined slider, another question arises: For the converging wedgegeometry, is there an optimum slope that provides a maximum load-carrying capacity? Pinkus andSternlicht (1961) calculated load capacity and friction, and plotted them against h1/h2 (see Figure 27.2).In the plot, Cp and Cf are functions of h1/h2, representing the dimensionless coefficients for load W andfriction F, respectively. That is:
*Hamrock (1994) provides a more detailed account of this process.**The difference in elevation between the entrance, h1, and exit, h2, of the inclined slider, i.e., h1 – h2 as viewed
in Figure 27.1.
David E. BreweNASA Glenn Research Center
(27.1)
and
(27.2)
where µ is the lubricant viscosity, U is the linear velocity, B is the breadth of the bearing (parallel to thedirection of motion), and L is the bearing length (normal to the direction of motion). They showed thatthe maximum load capacity is achieved if h1/h2 = 2.2, at which value the load coefficient Cp was calculatedto be 0.1602. Frene et al. (1997) plotted the dimensionless pressure profiles for three values of h1/h2 (seeFigure 27.3). The figure illustrates the pronounced effect that geometry has on the pressure developmentfor the one-dimensional inclined slider. Note that the profile producing the maximum pressure supportsthe optimization performed by Pinkus and Sternlicht. Note further from Equation 27.1 that aside fromgeometry, one can increase the load-carrying capacity of the bearing by increasing the fluid viscosity orthe relative velocity of the runner.
From Figures 27.2 and 27.3, one can see how the angle of inclination affects the one-dimensionalinclined slider bearing. However, Lord Rayleigh (1918) recognized that other bearing profiles were aseffective as or were more effective than the inclined slider in generating pressure. His analysis of severalbearing profiles revealed that the shape for maximum load capacity was simply two parallel surfaces —one having a rectangular cross-sectional dam. This geometry eventually became known as the Rayleighstep bearing, which is shown in Figure 27.4, along with the corresponding pressure profile. Pinkus and
FIGURE 27.1 Slider bearing configuration. (From Anderson, W.J. (1964), Hydrostatic lubrication, in AdvancedBearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, National Aeronautics and Space Adminis-tration, Washington, D.C.)
FIGURE 27.2 Load capacity and friction in plane sliders. (From Pinkus, O. and Sternlicht, B. (1961), Theory ofHydrodynamic Lubrication, McGraw-Hill, New York. With permission.)
Runner
Tapered land
tan-1m
h2h1
x2x1
B
B_
W
U
0.20
0.18
0.16
0.14
0.12
0.101 2 3 4 51.5 2.5 3.5 4.5 5.5
1.0
0.9
0.8
0.7
0.6
0.5
cf
cp
cp cf
a = h1/h2
WU L B
hCp= µ⋅ ⋅ ⋅ ⋅
2
22
FU B L
hC f= µ⋅ ⋅ ⋅ ⋅
2
Sternlicht (1961) calculated the load coefficient for the step bearing to be 0.2052. Using the calculus ofvariations, one can verify that the stepped bearing is the optimum geometry for a one-dimensional slider.Frene et al. (1997) plot dimensionless load vs. h1/h2 (Figure 27.5) for both the inclined slider and thestep bearing. Again, the plot supports the conclusion by Pinkus and Sternlicht (1961).
27.1.1 Slider Bearing Types
An overall view of industrial-type bearings can be presented expediently by first considering an assort-ment of possible one-dimensional configurations (e.g., Figure 27.6). Regardless of the specific geometry,the pressure-generating mechanism works basically in the same way as described previously for thesimplest case, as seen in Figure 27.6b. The geometry in Figure 27.6a is characteristic of a partial arcbearing and/or journal bearing in which the upper member represents the shaft and the lower memberthe housing. Here, the housing is shown as the moving surface although the application dictates themotion. In the case in which there exists only normal motion relative to the two members, the geometrywould be representative of a squeeze-film damper. Extending this geometry to three dimensions, in whichthe upper member is spherical and the lower member is a conforming cup-shaped surface, the geometrywould represent a spherical bearing.
The wedge-shaped configuration shown in Figure 27.6b is used in the classical Kingsbury (1950) andMichell (1905) thrust bearings, which will also be discussed in the context of tilting-pad thrust bearings
FIGURE 27.3 Pressure distribution for various ratios of a = h1/h2. (From Frene, J., Nicolas, D., Degueurce, B.,Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: Bearings and Thrust Bearings, Tribology Series 33,Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. With permission.)
FIGURE 27.4 Rayleigh step bearing and corresponding pressure profile, after Archibald (1950). (From Fuller, D.D.(1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
y y
h1
h2
xu
1 2
B1 B2
B
p Pmax
for region 1 for region 2
(Figure 27.7). The same geometry and variations thereof are employed in the “flying heads” used forcomputer hard drives. The heads are tilting-pad sliders that are supported above the spinning magneticdisk by a hydrodynamic air film. Fuller (1984), at that time, reported films on the order of 5.0 × 10–7 m(20 millionths of an inch) and less. According to Van der Stegen (1997), the development of the harddisk slider has enabled gas film spacing on the order of 25 nm (9.84 × 10–7 in.) and less. Bao and Li(1998) reported studies on liquid films an order of magnitude less, i.e., ~ 2.0 to 3.0 nm (7.87 × 10–8 to11.81 × 10–8 in.).
Figure 27.6 includes geometries [(c) through (h)] that Purday (1949) had analyzed for pressuregeneration. His conclusion was in agreement with Rayleigh’s; which was that one geometry was aboutas effective in generating pressure as the other, and that the step bearing geometry in Figure 27.6hgenerated the maximum peak pressure. Furthermore, friction forces were larger for a step bearing than
FIGURE 27.5 Dimensionless load vs. ratio h1/h2. (From Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet,M. (1997), Hydrodynamic Lubrication: Bearings and Thrust Bearings, Tribology Series 33, Dowson, D. (Ed.), ElsevierScience B.V., Amsterdam. With permission.)
FIGURE 27.6 Eight typical geometries that have been analyzed for the formation of hydrodynamic films. (From Fuller,D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
(a)
(c)
(e)
(g)
(b)
(d)
(f)
(h)
for a plane inclined slider, but the flow was smaller. Also, the moment of pressure (i.e., center of pressure)was independent of h1/h2. The idea of using the step bearing was advanced by Archibald (1950) when heapplied it to a sector-shaped thrust bearing and then later to a journal bearing. The stepped bearingdesign is easier to fabricate than the tapered land bearings shown in Figures 26.6e and f (Fuller, 1984).
Self-acting bearings sometimes required additional help (via external pressurization) to keep thebearing surfaces separated during start and stop conditions to avoid surface wear and reduce frictionalenergy loss. Thus, hybrid bearings were the result of occasionally combining the two pressure-generatingschemes to provide greater load-carrying capacity and/or a stiffer bearing to improve stability. Externallypressurized bearings without relative motion between the bearing surfaces are commonly referred to as“hydrostatic bearings.”* The consideration of industrial bearings herein is limited to those having relativemotion, that is “pure sliding,” “relative rotation,” and/or “normal motion” described by Szeri (2001) inself-acting and hybrid applications.
As industrial applications increased, it became apparent that the bearing designer often did not havethe option of choosing the lubricant. For example, launch vehicles and power generation systems arebetter suited for space exploration if one can eliminate conventional oil lubrication systems. This cutsdown on the size and weight and reduces the hazard of leakage which could result in a chemical/physicalinteraction of the working fluid with the oil. Furthermore, the design of the pump and/or power generatoris simplified by elimination of several seals normally required for conventional lubricants and bearings.
In the foregoing applications, hydrodynamic fluid-film-lubricated bearings were preferred to rollingelement bearings because of the flexibility in choosing materials compatible with many of the highlyreactive/corrosive working fluids (e.g., liquid-oxygen, liquid-hydrogen, and liquid-sodium). However,the extremely low absolute viscosity of cryogenic fluids (about one fifth that of water) used in launchvehicle applications severely limits the hydrodynamic load capacity of such bearings. For extended spacetravel, the bearings used for power generation operate under zero-gravity conditions and load capacityis not so much a concern as bearing instability. The bearing instability referred to here is the so-called“half-frequency whirl.” This is the tendency of the journal center to orbit about the bearing center at anangular velocity slightly less than or equal to one half the angular velocity of the journal around its owncenter. Various types of bearing designs are discussed with regard to their effectiveness in reducingtendencies for this type of instability.
FIGURE 27.7 Tilting-pad slider bearing and generated pressure distribution. (From Anon. (1983), Thrust BearingCalculations: Calculation Methods for Steadily Loaded, Off-Set Pivot, Tilting-Pad Thrust Bearings, Engineering SciencesData Unit, Item 83004, Institution of Mechanical Engineers, London, England.)
*The principles of hydrostatic bearings are treated in detail in Chapter 11 of this handbook by A. Szeri.
Motion of the runner
Padleading edge
Film-pressureprofile
Pivot
h
Runner
Wp
The study of gas bearings was noticeably accelerated following the Manhattan Project during WorldWar II. According to Fuller (1992), gaseous diffusion plants were used to provide an enriched fuel bypumping uranium hexafluoride gas through a cascade of successive diffusion stages. Several thousandstages in series were needed to achieve the required composition. The bearings and seals in the pumpscould not be oil-lubricated because of the high power losses and concerns for contamination of thelubricant. The natural choice became the working fluid (i.e., gaseous uranium hexafluoride) and aconcerted design effort helped contribute to the success of the project.
27.1.2 Compressible Lubrication
For a compressible lubricant, one needs to consider how the pressure depends on the density of the fluid,that is, the equation of state. For a perfect gas, the equation of state is:
(27.3)
where ρ is the density; ℜ, the gas content; T, the temperature; cp , the specific heat per unit weight forconstant pressure; cv , the specific heat for constant volume per unit weight; and g, the gravitationalconstant. Because temperature is a function of pressure, the conservation of energy equation has to belinked with the Reynolds equation to calculate pressure. Fortunately, most gas lubricating films are nearlyisothermal* due to the fact that bearing materials generally dissipate heat much faster than gases generateheat. Therefore, according to the ideal gas law (Equation 27.3), the pressure is directly proportional tothe density, so the energy equation can be bypassed.
Gas-lubricated bearings are used in a wide variety of applications (Fuller, 1992; van der Stegen, 1997):
1. High-speed grinding spindles2. A high-speed spindle for laser copiers and printers is shown in Figure 27.8. The figure reveals a
fixed shaft with straight grooves for the aerodynamic bearing, and a rotating hollow shaft, whichis driven by the rotor. The rotor is suspended vertically by magnetic thrust bearings and positionedhorizontally by the aerodynamic bearings. The mirror has ten flat surfaces for the reflection of alaser beam (Vliestra, 1987; cited in van der Stegen, 1997).
3. Sliding ways on machine tools, for avoiding stick-slip vibration4. Bearings for precise linear and rotational indexing metrology devices5. Hermetically sealed high-speed blowers and compressors that use the working fluid as the lubri-
cant. Typical applications include gas-cooled reactors, cryogenic and pyrogenic turbomachinerywhere great temperature extremes are encountered.
6. High-precision inertial guidance instruments such as gyroscopes and accelerometers7. Foil-type gas bearings for auxiliary power units in aircraft and power-generating components used
in space8. Computer peripheral devices, such as hard/floppy disk drives, consisting of slider-bearing read-
write heads. Figure 27.9 presents a rotating disk with an arm-slider assembly of a hard disk; andFigure 27.10 a video recording tape consisting of a rotating drum with heads and tape.
9. High-speed dental and orthopedic drills and cutters that operate with quiet, oil-free performance10. Membrane bearings, that are used to support and position large machine tools, heavy die blocks,
full-scale railroad cars, or a grandstand in a football stadium
*Although the literature contains many references to adiabatic gas lubricating films, a gas lubricating film that isnot virtually isothermal has not been shown to exist (Gross, 1962).
p T g c c Tp v= ⋅ℜ⋅ = −( )ρ ρ
27.1.3 Compressible vs. Incompressible*
The advantages of gas-lubricated bearings over liquid-lubricated fluid-film bearings are now well-under-stood. These include:
• Cleanliness: elimination of contamination caused by more traditional lubricants
• Reduction (often elimination) of the need for bearing seals
FIGURE 27.8 Spindle in a copier. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting GasLubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente,Enschede, The Netherlands. With permission.)
FIGURE 27.9 Computer hard disk with arm-slider assembly. (From van der Stegen, R.H.M. (1997), NumericalModeling of Self-Acting Gas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuig-bouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.)
*The list of advantages and disadvantages of gas bearings is given in Fuller (1992).
7
13
65
4
2
arm with slider
disk
• Lubricant stability: no vaporization, cavitation*, solidification, decomposition, or phase changeover extreme ranges of temperature, from cryogenic (–270°C or –450°F) up to approximately1650°C (3000°F). Operation at these extremes of temperature is a current research goal.
• Permits practical attainment of high speeds (700,000 rpm) at low friction** and heating, withlittle or no cooling generally required.
Disadvantages of gas-lubricated bearings are recognized as resulting from the relatively low viscosity***and damping of gas films. Thus,
• Gas-lubricated bearings have a reduced load-carrying capacity compared to liquid-lubricatedbearings, especially with self-acting or hydrodynamic bearings. Consequently, for a given load, gasbearings operate with thinner hydrodynamic films than their liquid-lubricated counterparts. Asthe films become thinner, the possibility of surface scoring, wear, and eventual bearing failure isa real concern. Tighter manufacturing tolerances and improved surface finishes are required. Inaddition, careful bearing alignment is necessary as well as consideration of possible loss of clearancedue to thermal effects. However, compliant surface bearings (i.e., foil bearings and membranebearings) are more forgiving and do not require the rigid specifications regarding design andmanufacture of the bearings. The membrane bearing, for example, operates very satisfactorilyover a typical factory floor.
• The gas film in a slider bearing behaves as a cushion of air providing very little damping. If acritical speed or instability is encountered, there may not be enough damping to suppress orcontrol it. This makes it necessary to carefully analyze the dynamics of the system so that by designone can preclude severe rubbing sand /or failure of the bearing.
FIGURE 27.10 Videotape with head. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-ActingGas Lubricated Bearings with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, UniversiteitTwente, Enschede, The Netherlands. With permission.)
*While cavitation causes damage in liquid-lubricated journal bearings, it can, on the other hand, be beneficialbecause cavitation stabilizes the behavior of liquid-lubricated journal bearings (van der Stegen, 1997). Calculationsby Brewe (1986) show that the occurrence of vapor cavitation in a journal bearing undergoing circular whirl canincrease load capacity by as much as 20%.
**Gross (1962) points out “… that both the load carrying capacity and the friction of a gas film must be muchless than that of a liquid film. Interestingly, though, the ratio of friction to load, the coefficient of friction, mustalways be greater for a self-acting gas film than for a similar liquid film.”
***Approximately 2 × 10–5 Pa s (2.9 × 10–9 lbf · sec/in.2) for air under room conditions compared with oil, approx-imately 2 × 10–2 Pa s (2.9 × 10–6 lbf · sec/in.2) (van der Stegen, 1997).
video tapedrum
head
• Pressure buildup in a slider bearing is limited by the gas compressibility. As the velocity of therunner is increased, the effectiveness to build pressure and carry load is decreased. Eventually, themost important parameter to generate pressure depends on the minimum to maximum filmthickness ratio (van der Stegen, 1997).
• Because of a lack of boundary lubricating properties, additional surface treatments are necessary.Otherwise, when there is not sufficient lift to keep the surfaces separated during starts and stops,damage can occur easily. Even after a sufficient film has formed, vibrations can cause the gas tocompress enough so that the surfaces touch (van der Stegen, 1997).
While this should be helpful if one is confronted with the choice of using a liquid or gaslubricant, the following section provides a more global viewpoint, which includes a broader classof bearings.
27.1.4 Advantages and Disadvantages for Bearing Types
Tables 27.1 and 27.2 from the Engineering Sciences Data Unit (1965, 1967) illustrate the advantages anddisadvantages of bearings (including rolling element bearings) for both thrust and journal (radial) bearingapplications.
27.2 Self-acting Finite Bearings
Self-acting bearings all operate on the principle that pressures are generated via relative motion betweenthe surfaces to produce load support. The mechanism in which pressures are generated is discussed inthe Introduction in the context of infinitely wide bearings (i.e., no side leakage) and in more detail byHamrock (1994). In designing finite bearings, side-leakage becomes an important issue. It determinesthe effectiveness of the bearing to generate pressure and thus carry loads. Consequently, one can increaseload capacity of a step bearing by including side-rails, hence shrouded-step bearings and pocket bearings.In the case of recording air bearing sliders used in computer hard disk drives, rails are designed to bethe load-bearing area.
27.2.1 Fixed-Geometry Thrust Bearings
Several configurations of fixed-geometry sliders are shown in Figure 27.11 as rectilinear and sector thrustbearings. However, these geometries are also suitable for journal bearing applications as well as conicaland spherical geometry bearings. Sector thrust bearings are used specifically to take loads in the axialdirection for rotating machinery. A typical thrust bearing arrangement illustrating the main componentsof a fixed-inclined-pad thrust bearing is shown in Figure 27.12. The upper configuration in Figure 27.13illustrates a side view of the wedge-shaped pad with land, along with the pressure distribution. Thebearing support plate contains several such pads distributed evenly around the axial plate, as shown inthe bottom half of the figure.
27.2.1.1 The Dynamics of Fixed-Geometry Thrust Bearings
Bearing instability is a problem peculiar to thrust bearings having a fixed-geometry. To understand theinstability of the fixed pads, refer back to Equation 27.1 and Figure 27.2, which illustrates the optimizationof the load coefficient (Pinkus and Sternlicht, 1961). The outlet (minimum) film thickness can be solvedfrom Equation 27.1; that is:
(27.4)h
B
U C
W LP2 = µ ⋅
TA
Enic
Hydrostatic Liquid Film
BearingsSelf-acting
Gas Bearings
Externally Pressurized
Gas Bearings
Hit
idation resistance of ssary
Excellent Excellent
Lot ions,
of
Lubricant may impose limitations
Excellent, thorough drying of gas necessary
Exv
Excellent Normally satisfactory
Excellent
Spr
ent but total space epends on the d system
Small radial extent
Small radial extent but total space requirement depends on the gas feed system
Dic
ation of lubricant is Sealing important
Satisfactory
Va Not normally applicable
Not applicable when vacuum has to be maintained
Wc
Satisfactory
Ra Excellent
BLE 27.1a Advantages and Limitations of Thrust Bearings
vironmental Conditions General Comments Rubbing Bearings
Oil-Impregnated Porous Metal
Bearings Rolling Bearings
HydrodynamLiquid Film
Bearings
gh emperature
Attention to differential expansions and their effect upon fits and clearances necessary
Normally satisfactory depending upon material
Attention to oxidation resistance of lubricant necessary
Up to 100°C (212°F) no limitations; from 100°C to 250°C (212 to 482°F), stabilized bearings and special lubrication procedures probably required
Attention to oxlubricant nece
w emperature
Attention to differential expansions and starting torques necessary
Lubricant may impose limitations, consideration of starting torque necessary
Below minus 30°C (–22°F) special lubricants required, consideration of starting torque necessary
Lubricant may impose limitatconsiderationsstarting torquenecessary
ternal ibration
Attention to the possibility of fretting damage necessary (except hydrostatic bearings)
Normally satisfactory except when peak of impact load exceeds load capacity
May impose limitations; consult manufacturer
Satisfactory
ace equirements
Small radial extent Bearings of many different proportions, small axial extent
Small radial extrequirement dlubrication fee
rty or dusty onditions
Normally satisfactory, scaling advantageous
Sealing important Satisfactory filtrimportant
cuum Excellent Lubricant may impose limitations
et and humid onditions
Attention to the possibility of metallic corrosion necessary
Normally satisfactory depending upon material
Normally satisfactory, sealing advantageous
Normally satisfactory, but special attention to sealing perhaps necessary
Satisfactory
diation Satisfactory Lubricant may impose limitations
TA
Rquid
Hydrostatic Liquid Film
BearingsSelf-acting Gas
Bearings
Externally Pressurized Gas
Bearings
Lowto
Excellent Satisfactory Excellent
Lowto
Excellent
Accra
Excellent Good Excellent
Life e, but n and nd
Theoretically infinite
Theoretically infinite, but affected by number of stops and starts
Theoretically infinite
Coaxloca
e provided to carry the axial loads
Sile Excellent, except for possible pump noise
Excellent Excellent, except for possible compressor noise
Simlu
blies ertain d and his, ssary
Auxiliary high-pressure pump necessary
Excellent Pressurized supply of dry clean gas necessary
Avast
Not available
Precoofansu
t where a process liquid Excellent
BLE 27.1b Advantages and Limitations of Thrust Bearings
equirements General Comments Rubbing Bearings
Oil-Impregnated Porous Metal
Bearings Rolling BearingsHydrodynamic Li
Film Bearings
starting rque
Not normally recommended
Satisfactory Good Satisfactory
running rque
Satisfactory
uracy of dial location
Poor Good
Finite, but predictable Theoretically infinitaffected by filtrationumber of stops astarts
mbination of ial and radial ad carrying pacity
A thrust face must be provided to carry the axial loads
Most types capable of dual duty
A thrust face must b
nt running Good for steady loading Excellent Usually satisfactory, consult manufacturer
Excellent
plicity of brication
Excellent Excellent with self-contained grease or oil lubrication
Self-contained assemcan be used with climits of load, speediameter. Beyond toil circulation nece
ilability of andard parts
Good to excellent depending upon type
Excellent Good
vention of ntamination the product d rroundings
Improved performance can be obtained by allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations
Normally satisfactory, but attention to sealing necessary, excepcan be used as a lubricant
Frequent stop-start
nt Good Excellent Poor Excellent
Frequent change of direction of notation
Generally good
Running costs Depends upon complexity of lubrication system
Cost of lubricant supply has to be considered
Nil Cost of gas supply has to be considered
From Anonymous (1965),
General
Sciences Data Unit, Item 67033, Institution of Mechanical Engineers, London, England.
TABLE 27.1b
(continued) Adv
Requirements General Commen g BearingsHydrodynamic Liquid
Film Bearings
Hydrostatic Liquid Film
BearingsSelf-acting Gas
Bearings
Externally Pressurized Gas
Bearings
Excellent Good Excelle
Generally good
Very low
Guide to the Choice of Thrust Bearing Type, Engineering
antages and Limitations of Thrust Bearings
ts Rubbing Bearings
Oil-Impregnated Porous Metal
Bearings Rollin
TA
EnC
ostatic d Film rings
Self-acting Gas Bearings
Externally Pressurized Gas
Bearings
Higte
nce of Excellent
Lowte
nt may e tions
Excellent, thorough drying of gas necessary
Extvi
nt Normally satisfactory Excellent
Spare
ace
Small axis extent Small axis extent but total space requirement depends on the gas feed system
Dirco
icant Sealing important Satisfactory
Vac Not normally applicable
Not applicable when vacuum has to be maintained
Weco
Ra Excellent
BLE 27.2a Advantages and Limitations of Journal Bearings
vironmental onditions General Comments Rubbing Bearings
Oil-Impregnated Porous Metal
Bearings Rolling Bearings
Hydrodynamic Liquid Film
Bearings
HydrLiqui
Bea
h mperature
Attention to differential expansions and their effect upon axial clearance necessary
Normally satisfactory depending upon material
Attention to oxidation resistance of lubricant necessary
Up to 100°C (212°F) no limitations; from 100°C to 250°C (212 to 482°F) stabilized bearings and special lubrication procedures probably required
Attention to oxidation resistalubricant necessary
mperature
Attention to differential expansions and starting torque necessary
Lubricant may impose limitations, consideration of starting torque necessary
Below minus 30°C (–22°F) special lubricants required, consideration of starting torque necessary
Lubricant may impose limitations, consideration of starting torque necessary
Lubricaimposlimita
ernal bration
Attention to the possibility of fretting damage necessary (except hydrostatic bearings)
Normally satisfactory except when peak of impact load exceeds load capacity
May impose limitations, consult manufacturer
Satisfactory Excelle
ce quirements
Small axial extent Bearings of many different proportions available
Small axis extent but total sprequirement depends on thelubrication feed system
ty or dusty nditions
Normally satisfactory, sealing advantageous
Sealing important Satisfactory, filtration of lubrimportant
uum Excellent Lubricant may impose limitations
t and cold nditions
Attention to the possibility of metallic corrosion necessary
Normally satisfactory depending upon material
Normally satisfactory, sealing advantageous
Normally satisfactory, but special attention to sealing perhaps necessary
Satisfactory
diation Satisfactory Lubricant may impose limitations
TABLE 27.2b
Advan
Requirements Genc Liquid ings
Hydrostatic Liquid Film
BearingsSelf-acting
Gas Bearings
Externally Pressurized
Gas Bearings
Low starting torque
Excellent Satisfactory Excellent
Low running torque
Excellent
Accuracy of axial location
Excellent Good Excellent
Life nite, but ation and ts and
Theoretically infinite
Theoretically infinite, but affected by number of starts and stops
Theoretically infinite
Combination of axial and radial load carrying capacity
g surface must be provided to carry the radial loads
Silent running Excellent except for possible pump noise
Excellent Excellent except for possible compressor noise
Simplicity of lubrication
ssemblies th certain peed, and d this, oil
essary
Auxiliary high pressure pump necessary
Pressurized supply of dry clean gas necessary
tages and Disadvantages of Journal Bearings
eral Comments Rubbing Bearings
Oil-Impregnated Porous Metal
Bearings Rolling BearingsHydrodynami
Film Bear
Not normally recommended
Satisfactory Good Satisfactory
Satisfactory
Good
Finite but can be estimated Theoretically infiaffected by filtrnumber of starstops
A journal bearing surface must be provided to carry the radial loads
Some types capable of dual duty
A journal bearin
Good for steady loading Excellent Usually, satisfactory; consult manufacturer
Excellent
Excellent Excellent with self-contained grease lubrication. With large sizes or high speeds, oil lubrication might be necessary
Self-contained acan be used wilimits of load, sdiameter. Beyoncirculation nec
Avs
Good Not available
Prcoas
ut attention to sealing necessary, except where a process liquid ant
Excellent
Tomai
factory Poor Satisfactory Poor Satisfactory
TyGood Excellent Excellent
SuitableSome type suitable Suitable Some types
suitableSuitable
Unsuitable UnsuitableRu Depends upon complexity
of lubrication systemCost of
lubricant supply has to be considered
Nil Cost of gas supply has to be considered
ing Sciences Data Unit, Item 65007, Institution of Mechanical Engineers, London, England.
ailability of tandard parts
Good to excellent depending upon type
Excellent
evention of ontamination f the product nd urroundings
Improved performance can be obtained by allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations
Normally satisfactory, bcan be used as a lubric
lerance to anufacturing
nd assembly naccuracies
Good Satis
pe of MotionFrequent
start-stopsExcellent
UnidirectionalBidirectional Suitable
Oscillatorynning costs Very low
From Anonymous (1965), General Guide to the Choice of Journal Bearing Type, Engineer
Using the fact that h2 is directly proportional to C1/2P , and h1/h2 is a function of CP, according to
Figure 27.2, one can account for the occurrence of a bearing instability. Further, the ratio h1/h2 is equalto (δ/h2 + 1), where δ is the rise of the slider (h1 – h2). For bearings with fixed inclination, the rise isestablished during manufacture.* If the bearing is operating so that the value of h1/h2 yields the maximumload coefficient, then any increase in load will cause a decrease in minimum film thickness. This will, inturn, cause CP to decrease because it is proportional to h2. However, according to Figure 27.2, as CP drops,the value of h1/h2 increases, causing h2 to decrease. Mathematically, the bearing is stable only when ∂CP /∂H≥ 0. Although this poses a serious limit to the stable operation of fixed-pad bearings, other concerns maybe more potently dangerous that affect competing type bearings as well. For example, temperature-viscosity effects may well be a greater concern when loads are increased because they can lead to anincrease in shear heating, raising the temperature of the lubricant and decreasing the viscosity. This wouldresult in a decreased minimum film thickness.
27.2.1.2 Tapered-land Slider
The tapered-land thrust bearing is shown in Figure 27.14, illustrating the lubricant flow between succes-sive pads. Here, the lubricant source is provided at the inside diameter of the pad support plate and is
FIGURE 27.11 Examples of self-acting thrust bearings. (From Ausman, J.S. (1964), Gas-lubricated bearings, inAdvanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, 109–138.)
FIGURE 27.12 View showing relative position of bearing components for an axial thrust bearing. (From Anon.(1982), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings,Engineering Sciences Data Unit, Item 82029, Institution of Mechanical Engineers, London, England.)
*Cameron (1966) points out that tilting-pad bearings have the most important feature (which fixed inclinationpads do not have): that the inlet and outlet gaps vary together, so that h1/h2 always remains constant.
U U U
Taper Taper-flat
Spiral groovePocket Herringbone
Step
Runner
DR
t
ds
W
Pad
Bearing support plate
expelled at the inner and the outer diameter. Referred to as an oil-bath or flood-feed system, a disad-vantage of this supply type is that oil is caught in the large space between pads and causes a drag (orchurning) loss. This loss can be considerable, especially for large bearings and high-speed applications.One means of reducing the power loss is by including an orifice between each pad to direct the lubricantinto the pad inlet as shown in Figure 27.15. In this way, the space between each pad does not have to beflooded to assure adequate lubrication in the inlet.
A land at the trailing edge of the taper provides load support upon starting and stopping. This canbe effective without any assistance from external pressure (hydrostatic jacking), provided the land pres-
FIGURE 27.13 Sectional view of thrust plate and layout of pads. (From Anon. (1982), Thrust Bearing Calculations:Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item82029, Institution of Mechanical Engineers, London, England.)
FIGURE 27.14 Flooded or oil-bath system of lubrication. (From Anon. (1982), Thrust Bearing Calculations: Cal-culation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029,Institution of Mechanical Engineers, London, England.)
MOTION Wp Runner
h
Pad
Typical pressure patterngenerated
Section through a thrust pad
Trailing edge
Outer side L
b
LandInner side
Leading edge
Individual pad
dmdm
Pad
β
d
D
MOTION
Side leakage
Pad
SideLeakage GrooveQf
Pad
Side leakage
Side leakage
Qi
sures remain less than 0.7 MN/m2 (Anon., 1982). Harrison (1913) optimized the one-dimensional taperedthrust bearing with regard to the extent of the land and the slope parameter δ/h2.
For optimum load capacity, the extent of the land was determined to be 20% of the breadth of thebearing with a value of δ/h2 = 1.25. For a pad having fixed inclination, this optimum condition can beachieved only at a single value of applied load (or minimum film thickness h2). The value of δ/h2 willchange as the value of applied load changes, as discussed in the section on dynamics. No significanterrors should arise for land lengths within the range of 10 to 30% (Anon., 1982). The use of rectangularpad data for the design and analysis of bearings with sector-shaped pads does not lead to errors ofpractical significance with sector angles up to 45°.
Tapered-land bearings have been used in large thrust bearings for hydroelectric turbines with somesuccess. Hall and de Guerin (1957) and Linn and Shepard (1938) described their performance (Cameron,1966).
27.2.1.3 Rayleigh Step Bearing
A typical axial Rayleigh step sector thrust bearing is shown in Figure 27.16. Even though Lord Rayleigh(1918) showed that the infinitely wide step bearing gave a 20% greater load capacity than infinitely widetilling-pad bearings, Kingsbury and Michell had captured the marketplace with the tilting-pad bearing,causing the step bearing to be neglected until about 1950. At that time, Archibald (1950) calculated theload capacity for a square step bearing, including side flow:
(27.5)
If one calculates the load capacity per unit width for the corresponding square tilting-pad bearing:
FIGURE 27.15 Individual pad feed system of lubrication. (From Anon. (1982), Thrust Bearing Calculations: Cal-culation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust Bearings, Engineering Sciences Data Unit, Item 82029,Institution of Mechanical Engineers, London, England.)
FIGURE 27.16 Rayleigh step sector thrust bearing.
MOTION
Side leakage
Side leakage
Side leakage
Pad
Groove
PadQf
Side leakage
Ql
WU B
h= ⋅µ ⋅ ⋅0 0725 2
22
., per unit width
h hs
σg
ro
ri
T
∆
(27.6)
The difference between the two bearings, including side flow, is now much smaller than before.Numerous studies have been performed to retard the side flow with shrouded designs in order to
maximize load capacity and/or stiffness. Johnston and Kettleborough (1956) conducted experimentsusing straight and shrouded steps. Wildmann et al. (1965) studied gas-lubricated step thrust bearingsextensively. In an earlier study, Ausman (1961) optimized sector-shaped pad geometries based uponmaximum load capacity for low compressibility numbers (near-incompressible lubrication). Hamrock(1972) extended the range of compressibility using a similar analysis for rectangular pads. In 1983, Bagciand Singh extensively analyzed the effects of side flow for finite bearings.
27.2.1.3.1 Semicircular Step BearingTypically, results from Cameron (1966) show that a bearing with a semicircular step of radius equal toB/2 and a ratio of h1/h2 of 1.7, had a load coefficient of 0.105 (see Figure 27.17a). Thus,
(27.7)
27.2.1.3.2 Triangular Step BearingA triangular step bearing (Figure 27.17b) with h1/h2 of 2.12 had a load coefficient of 0.121:
(27.8)
This represents a considerable increase in load capacity due to retardation of side flow.Note that in all of the above shrouded step bearings, the height of the step (h1 – h2), Figure 27.4, is
usually much less than 0.025 mm (0.001 in.). Such a small step height can be difficult to fabricate. Duringoperation, especially starts and stops where the runner is prone to touch the bearing, a small amount ofwear may wipe away the step.
In spite of the disadvantages listed, step bearings are widely used as gas bearings because they are lessexpensive to make than the attractive tilting-pad bearings.
27.2.1.3.3 Pocket Step BearingWilcock (1955) demonstrated that one could combine some of the advantages of hydrostatic-type pocketbearings with a hydrodynamic-type thrust bearing to achieve a thrust bearing having low power loss andhigh load-carrying capability without the disadvantage of maintaining an external high-pressure pump.The hydrodynamic pocket thrust bearing, as it was originally, conceived, is illustrated in Figure 27.18.
FIGURE 27.17 Shrouded step bearings. (a) Semicircular step bearing; (b) triangular step bearing. (From Cameron,A. (1966), The Principles of Lubrication, John Wiley & Sons, New York. With permission.)
WU B
h= ⋅µ ⋅ ⋅0 0704 2
22
., per unit width
WU B
h= ⋅µ ⋅ ⋅0 105 2
22
., per unit width
WU B
h= ⋅µ ⋅ ⋅0 121 2
22
., per unit width
The upper side-view in the figure shows oil being introduced at the inlet of an inclined pumping land(hydrodynamic slider bearing). The pumping action in this region provides lubricant to help fill thepocket and establish high pressure. Oil leakage out of the pocket and pump land occurs through theclearance between the rails and runner. The clearance height adjusts itself until the oil leakage out of thebearing is exactly equal to the flow into the bearing. At this point, the pocket pressure is sufficient tosupport the external load. Wilcock provided further analysis to show that for maximum film thicknessat a given load and speed the taper of the pumping land must be zero. In other words, a Rayleigh stepwith a pocket at the end of the step provides the best performance.
Wilcock and Booser (1957) compared the performance of a hydrodynamic-pocket-step thrust bearingwith the tapered-land and the tilting-pad thrust bearings. The results are shown in Table 27.3.
Some of the advantages indicated in the table are lower power loss for the same high load capacity.Consistent with lower power loss, the film temperature rise during operation is significantly less forroughly the same hydrodynamic oil flow. Disadvantages of the hydrodynamic pocket step-bearing are:(1) that it is sensitive to misalignment, (2) it can’t carry a heavy thrust load for low speed conditions,and (3) at high Reynolds number, turbulence in the pockets becomes a serious issue and was shown byWilcock (1955) to reverse the trend of decreasing power loss with increasing speed. To address themisalignment, Wilcock (1955) devised a frictionless pressurized ball seat mounting that was self-aligning.
FIGURE 27.18 Diagram of hydrodynamic-pocket thrust bearing. (From Wilcock, D.F. and Booser, E.R. (1957),Bearing Design and Application, McGraw-Hill, New York. With permission.)
TABLE 27.3 Comparison of the Pocket-Step Thrust Bearing with Two Hydrodynamic Thrust Bearings
Tapered Land Bearing Tilting Pad Bearing Pocket-Step Bearing
Load W 70,000 lbs 311.37 kN 70,000 lbs 311.37 kN 70,000 lbs 311.37 kNSize, D1/D2 7/15 7/15 7/15Nos. of pads 6 6 4Pad slope 0.00105a 0.00049 0Operating
viscosity18 cP 2.61 µReyns 18 cP 2.61 µReyns 18 cP 2.61 µReyns
Avg. unit load 555 psi 3.83 MPa 614 psi 4.23 MPa 565 psi 3.90 MPahmin 0.0015 in. 38.1 µm 0.0016 in. 40.6 µm 0.00185 in. 47.0 µmPower loss 76 hp 56.67 kW 86 hp 64.13 kW 45 hp 35.56 kWOil flow, Q 15.7 gpm 9.91 × 10–4 m3/s 23.9 gpm 15.1 × 10–4 m3/s 17.5 gpm 11.0 × 10–4 m3/sFilm temp.
rise, ∆T58°F 32.22°C 44°F 24.44°C 31°F 17.22°C
a Average of inner and outer slopes.
b
L
E B
b
b
OIL IN
Uhy
δ
x
And if high loads must be carried at low speed, high-pressure oil can be fed to the pocket so that it operatesas a hydrostatic bearing at low speeds. But the issue of turbulence in the pockets at high speed remains aconcern. Wilcock and Booser (1957) hypothesized that decreasing pocket depth might have a beneficialeffect but concluded there is virtually no advantage in reducing the pocket depth to avoid turbulence.
Kettleborough (1961) analyzed the pocket step bearing having the geometry shown in Figure 27.19.The distinguishing geometric features of this bearing over that studied by Wilcock (1955) and shown inFigure 27.18 are the shape of the side rails and the absence of a lubricant supply hole at the inlet. Thespeckled region (Figure 27.19) having film thickness h1 and length bB (i.e., pumping length) is the inletof the Rayleigh step. The step height is the difference between h1 and the minimum film thickness h2.Upon having chosen h1/h2 to be 1.76 and the angle of the inside rail wall relative to the outside wall θto be 18.5°, Kettleborough optimized this bearing based upon minimum friction and maximum loadcapacity for a wide range of pumping lengths (i.e., 0 ≤ b ≤ 1.0). The value of b that resulted in maximumdimensionless load
was b = 0.6 where W is load, U is the speed of the runner, and µ is the absolute viscosity, while theminimum dimensionless friction f/(h2/B) is 5.3 where b = 0.3 and f is the friction coefficient. Naturallythe choice of b depends upon the importance the designer places on minimum friction or maximumload. Giving them equal weight, a reasonable compromise would be to assign b = 1/2. Cameron (1966)points out that the dimensionless load
very nearly equals that of the optimum square tilting pad, just less than 0.1 (Figure 27.20).
27.2.1.4 Recurrent-Grooved Thrust Bearings
27.2.1.4.1 Spiral Grooved Thrust BearingAn annular plate, spiral grooved thrust bearing is shown in Figure 27.21. The operating principle of thespiral grooved thrust bearing is based on the fact that a viscous lubricant (oil, grease, or air) is draggedinto a slot or groove by a moving runner. If the flow is inhibited at the end of the groove by a dam orrestrictor, pressure builds up and the bearing is able to support a load. The direction of rotation
FIGURE 27.19 Pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley &Sons, New York. With permission.)
B
BbB
h2
h1
0.1B
θ
W B
U
h
Bµ⋅
2
2
W B
U
h
Bµ⋅
2
2
determines whether fluid is pumped inward to, or outward from the center of rotation. Muijderman(1966) describes how bearing performance can be improved by considering the relationship betweenpressure development and leakage as a consequence of the pumping action. Increasing the groove depthδ increases the pumping action and hence the lift as a result of the increase in pressure generation. If thegrooves are too deep, the leakage will become excessive. If the groove depth is reduced to zero, thepumping effect naturally ceases. Here, the groove depth can be optimized so as to continue to supportthe constant bearing load and/or the rotating disk. The shape of the spiral grooves should be optimizedto achieve the most effective pumping. This would result in a maximum pressure buildup. Muijdermancalculated the value of α required to produce maximum pressure for a basic element (see Figure 27.22).This can be done by ensuring that the angle α between the local velocity vector (
→ω × →r) and the tangent
to the groove at all times produces maximum pressure. Muijderman deduced that the shape of the grooveis a logarithmic spiral. In polar coordinates, the shape of the groove is defined as
FIGURE 27.20 Load and friction for pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York.)
FIGURE 27.21 Flat spiral grooved thrust bearing without transverse flow (no net flow from r1 to r2). (From Muij-derman, E.A. (1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands. With permission.)
0.12
0.10
0.08
0.06
0.04
0.02
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.000
2
4
6
8
10
12
W/L ηU
h o/L
h 02 L2
µFriction
Load
b
r2
r1
a2
h2hc
Wt
ho h1
a1
α
GrooveRidge
ω
(27.9)
as the lubricant. Cameron (1966) points out that bearing flatness is most important if air is used. Theflatness is checked by optical interference. It is found that, as the front (frictional) surface gets hot, thebearing “hogs” and so it is usually made initially slightly hollow to allow for this bifilar-type expansion.The grooves can be made by vapor blasting, sandblasting, or etching.
Pressure: The pressure above ambient at radius r1 (where pr2 = pambient) for the spiral groove thrust bearing
without transverse flow is derived by Muijderman (1966) as:
(27.10)
where λ = r1/r2, H = h2/h1, γ = α2/α1, k = number of grooves, µ = viscosity, and C1 is:
(27.11)
and g1 is:
(27.12)
Load-carrying capacity: Muijderman calculates the load-carrying capacity of the spiral groove bearingwithout transverse flow to be:
FIGURE 27.22 The logarithmic spiral, r = r1eθtanα. (From Muijderman, E.A. (1966), Spiral Groove Bearings, PhilipsTechnical Library, Eindhoven, The Netherlands.)
Radius vectorr =f (θ)
0
r
C
Ar1
θ
α
α
β
ω x rTangent
r re= ⋅1
θ αtan
pr
hg H C H kr1
312
2
22
21 1= −( )⋅ ( ) ( )µω λ α γ α γ λ, , , , , ,
C H ke e
k
H
H k
H
H
1
190
2
1
1
1 21
90
2
1
1
1
2
3
3
3
3
1α γ λ λ
λ
α αγ
γ α αγ
γ
, , , ,
tan tan
( ) = − ⋅−
− π −°
( ) +⋅ +
++ π −
°
( ) +⋅ +
+
g HH H H
H H H1
2 3
3 3 3 2 2
1 1
1 1α γ
γ α
γ γ α γ, ,
cot
cot( ) =
( ) −( ) −( )+( )⋅ +( ) + ( ) +( )
(27.13)
where
(27.14)
Frictional torque: In this case, the frictional torque from the inner chamber is neglected because hc � h2.Thus, for the case without transverse flow,
(27.15)
Coefficient of friction: The coefficient of friction for the inward pumping spiral grooved bearing withouttransverse flow is given as:
(27.16)
27.2.1.4.2 Herringbone Grooved Thrust BearingFigure 27.23 shows a herringbone annular thrust bearing configuration where the fluid is pumped intothe grooves from both outside edge and the inside edge. This bearing operates properly when the groovesare not closed off at the inner or outer diameter. However, this bearing can operate without transverseflow (no net flow across the inner and outer radius) if rh is chosen so that the inner and outer groovesbuild up equal pressures at a distance r = rh from the center.
Pressure: For the inner (r1 < r < rh) and outer (rh < r < r2) grooves, respectively, the pressure buildup wasdetermined by Muijderman to be:
(27.17)
and
(27.18)
In practice, the expression for rh is often approximated as:
(27.19)
Wr
hg H C H ktsgb. , , , , , ,= π −( )⋅ ( ) ( )3
212
4
22
41 2
µω λ α γ α γ λ
C H ke e
k
H
H k
H
H
2
21
90
2
1
1
1 4
21
90
2
1
1
1
4
3
3
3
3
1α γ λ λ
λ
α αγ
γ α αγ
γ
, , , ,
tan tan
( ) = − ⋅−
− π −°
( ) +⋅ +
++ π −
°
( ) +⋅ +
+
Mr
hg Htsgb. , ,= π −( )⋅ ( )µω λ α γ2
4
2
422
1
fh
r
g H
g H C H ktspg .
, ,
, , , , , ,= ⋅
( )( ) ( )
2
2
2
1 23
α γ
α γ α γ λ
ph
r r e g Hrk
H
H= − ⋅
⋅ ( )π ⋅ − °
°
⋅ ( ) +⋅ +
+3
22
212
190
2
1
1
11
3
3µω α γα α
γγ
tan
, ,
ph
r e r g Hrk
H
H= ⋅ −
⋅ ( )− π ⋅ − °
°
⋅ ( ) +⋅ +
+3
22 2
21
90
2
1
1
1 21
3
3µω α γα α
γγ
tan
, ,
r r rh ≈ ⋅ +( )1
2 12
22
Load-carrying capacity: Muijderman calculates the load-carrying capacity of the herringbone thrustbearing with no transverse flow to be
FIGURE 27.23 Herringbone spiral-grooved bearing, with no net flow between r2 and r1. (From Muijderman, E.A.(1966), Spiral Groove Bearings, Philips Technical Library, Eindhoven, The Netherlands. With permission.)
FIGURE 27.24 Diagram of a tilting-pad bearing (one shoe), showing the optimum pivot location and the resultantshoe inclination. (From Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGraw-Hill, New York.With permission.)
r1
h2
Wt
ho h1
a2 a1
rh
r2
groove
inner grooves
outer grooves
ridge
α
ω
PIV
OT
bD2
D1
B
hmin
1.45hmin
U
B0 58 B
(27.20)
Frictional torque: For the frictional torque, he obtained
(27.21)
Coefficient of friction:
(27.22)
27.2.2 Pivoted (Tilting) Pad Thrust Bearings
27.2.2.1 Basic Features*
The tilting-pad thrust bearing (Kingsbury-type bearing) differs from the tapered-land thrust bearing inthat each pad is an individual plate which is free to pivot. The pivot line is radial so that each pad canbe inclined in a circumferential direction in order to provide a tapered oil film. Figure 27.24 shows thegeometry of one tilting pad. Such bearings usually have three or more pads and are enclosed in a housing.Lubricating oil is normally fed to the center of the housing near the shaft and expelled at the outer edgebecause of the pumping action of the bearing. A large portion of the oil flowing through a tilting-padbearing does not flow over the working bearing surfaces, because of the spaces necessarily left free aroundeach pad. For this reason, oil flow is normally controlled by an orifice.
When the runner is stationary, the pads will lie with their surfaces parallel to the runner face. As thebearing is started and an oil film is created between the pad and runner, each pad will tilt to the anglethat will generate the proper distribution of film pressures (Figure 27.24).
In setting out to design a tilting-pad bearing, the designer will normally know the total load W to becarried, the shaft speed N, the shaft diameter D, the inlet-oil temperature T1, the desired oil-temperaturerise ∆T, and the oil-viscosity grade. In addition, a minimum film thickness, usually 0.001 in., is stipulated.The designer must then determine the number of pads and the size of each pad that will give the desiredvalues of temperature rise and minimum film thickness. Another variable to be determined is the locationof the pivot.** If rotation is always to be in one direction, the optimum pivot location is 58% of thedistance from the leading edge to the trailing edge of the pad. The design procedure given in this sectionis based on this pivot location. If the shaft is to rotate in either direction, the pivot location must be atthe mid-point, or 50% point. Experience has shown that there is usually enough crown to the pad asmanufactured to give pads pivoted at the mid-point an equivalent performance. This is discussed inmore detail in Wilcock and Booser (1957). Use of a 58% pivot point not only gives maximum loadcapacity and minimum friction, but also greatly simplifies the calculation procedures.
27.2.2.2 Michell and Kingsbury Bearings
Tilting-pad bearings were first introduced in 1905 by Michell and Kingsbury, almost simultaneously.Michell had been seeking an efficient thrust bearing that could withstand the demands of the newly
*This section is taken from Wilcock and Booser (1957).**A brief discussion of the basic equations can be found in Wilcock and Booser (1957); Chap. 7, Sec. 7-4,
pp. 195–197.
Wr
hg H C H ktherr . , , , , , ,= π −( )⋅ ( ) ( )3
412
4
22
21 1
2µω λ α γ α γ λ
Mr
hg Htherr . , ,= π −( )⋅ ( )µω λ α γ2
4
2
422
1
fh
r
g H
g H C H ktherr .
, ,
, , , , , ,= ⋅ +( )
−( ) ⋅( )
( ) ( )2
3
1
1
2
2
2
2
2
1 12
λ
λ
α γ
α γ α γ λ
emerging steam turbine applications. In 1897, ships were being powered by turbines and required thrustbearings that would take up the loading transmitted from the propellers to the ship’s hull.
A typical tilting-pad thrust bearing with several segmented pads is shown in Figure 27.25. The earlierKingsbury thrust bearings were operated in a bath of oil that was circulated by the pumping action ofthe rotating element. Kingsbury bearings commonly used three, six, or eight pads per bearing. Thenumber of segmented pads depended on the application. To obtain maximum load-carrying, each pad
FIGURE 27.25 Tilting-pad thrust bearing with multiple segmented pads mounted on pivots. (From Hamrock, B.J.(1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. With permission.)
FIGURE 27.26 Kingsbury pivoted pad thrust bearing incorporating load equalizer “leveling plates.” (From Michell,A.G.M. (1950), Lubrication: Its Principles and Practice, Blackie and Son Limited, London. With permission.)
FIGURE 27.27 Developed section of bearing showing the leveling plates to distribute the load equally among thesix shoes of the thrust bearing. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed.,John Wiley & Sons, New York. With permission.)
Collar
Base ring Joint in base ringLeveling plate
Shoe
should carry the same load. In actual practice, the bearings can expect to be subjected to a certain amountof misalignment, which causes uneven loading. The Kingsbury Machine Works addressed this problemby developing a system of “leveling plates.” This consisted of an annular series of equalizing levers onwhich the pads were supported. Figure 27.26 illustrates the Kingsbury thrust bearing with leveling plates.A section view is shown in Figure 27.27. The leveling plates leave each pad free to move up or down totake an equal share of the load regardless of the misalignment.
As mentioned above, the earlier designs ran submerged in a bath of oil. But, as pointed out in thediscussion on fixed-geometry sector thrust bearings, this leads to unnecessary churning of the oil andhigh power loss. By placing a groove at the leading edge of each pad, the bearing can run with lesslubricant between pads. This effectively reduces the power loss of the bearing. Further, cool oil isintroduced at the leading edge, displacing the hot-oil carryover, and thus providing a cooler load- bearingfilm. This enables the bearing to carry more load. Brockwell, Dmochowski, and DeCamillo (1994)reported a significant reduction in both power loss and oil flowrate compared to a conventional pivotedpad bearing. Figure 27.28 shows the flow path of the oil over the pad surface for a tilting-pad loadequalizer bearing with grooves at the leading edge of the bearing.
27.2.3 Journal Bearings
27.2.3.1 Plain Journal Bearings
A plain journal bearing, a true circular bearing without grooves, is shown in Figure 27.29. Applicationof a vertical load on the shaft displaces the shaft in the direction of the load. This creates a tapered wedgein the bearing, establishing a pressure on the inlet side so as to establish a flow balance into and out ofthe bearing. The hydrodynamic pressure also reacts to support the load. A moment is exerted on theinlet side of the shaft by the buildup in pressure that causes the shaft to be displaced in a direction normalto the load. When the applied load and the hydrodynamic forces balance each other, the measure of theeccentrically displaced shaft along the line of centers settles at an angle ψ from the load line. This isreferred to as the attitude angle of the bearing for a particular load, speed, and lubricant condition. Atypical pressure distribution around the circumference of the bearing is shown in Figure 27.29b. Alongthe axial direction, the pressure peaks at the center, thus creating a pressure flow to the ambient sides.The axial pressure distribution is shown in Figure 27.29c.
FIGURE 27.28 Kingsbury LEG® thrust bearing illustrating lubricant flow path. (Courtesy of the Kingsbury Bearing Co.)
In dynamically loaded bearings, the relative normal motion of the shaft to the bearing through theline of centers (Figure 27.30b) creates an additional contribution to the load capacity. The pressuresdepicted in this figure are a result of the squeezing action caused by the normal approach of shaft andbearing. Conversely, negative pressures are created if the shaft and the bearing are receding from eachother. If the negative pressure reaches the saturation pressure of the liquid, dissolved gases can be releasedfrom the liquid to form gaseous cavitation. If the pressure decreases to the vapor pressure of the fluidbefore the gases have time to be released, then vapor cavitation will occur.
FIGURE 27.29 Hydrodynamic journal bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C.(1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLE SP-37, Society ofTribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
27.2.3.1.1 Steady-state Pressure DistributionSteady-state operation occurs when the bearing and shaft centers remain fixed relative to each otherduring operation. To obtain the pressures, the film shape must first be defined and appropriate boundaryconditions applied upon integration of the Reynolds equation. From Figure 27.29, the film thickness, h,can be expressed as:
(27.23)
FIGURE 27.30 Dynamically loaded squeeze film bearing. (From Brewe, D.E., Fleming, D.P., Dimofte, F., andHendricks, R.C. (1997), Fluid film lubrication, in Tribology for Aerospace Applications, Zaretsky, E.V. (Ed.), STLESP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594. With permission.)
h c= ⋅ + ⋅( )1 ε θcos
Fluid
Fluid
W
W
(a) Plane surfaces.
Bearing
Housing
Cavitation
Journal
(b) Cylindrical journal bearing.
Time(c) Loading.
Load
, W
0
+
-
27.2.3.1.2 Flow Balance and Cavitated Flow CharacteristicsMaking a cut at the line of centers where the maximum film thickness occurs results in a plot of the filmthickness along the circumference of the unwrapped bearing (Figure 27.31). The film is convergent for0 < θ < π and divergent for π < 0 < 2π. As described earlier, pressure builds up in the convergent regionbecause fluid is being convected into a constricting space. This pressure buildup reaches a maximumnear the minimum film thickness and within the convergent region. As a result, a pressure flow awayfrom the peak pressure is created, leading to some side-flow leakage out of the bearing as well as someflow into the divergent region (see Figure 27.32). This extra pressure flow together with the convectiveflow into the divergent region helps fill the increasing available space until there is insufficient fluid tocomplete the film. The film ruptures and, depending on the load, speed, viscosity, and surface tensionat the bearing/journal surfaces, either (1) it breaks up into small filmlets similar to those shown inFigure 27.32, or (2) fluid is transported through the cavity in the form of a sheet having a free surfaceand attached to the faster moving surface. The latter condition occurs if the surfaces are sufficientlyseparated so as to preclude the possibility of fluid attaching itself to both surfaces. This is more apt tooccur for very light loads and/or higher (viscosity × speed) applications. Coyne and Elrod (1971)demonstrated the start of film striations and their sensitivity to load. In heavily loaded applications, thefilmlets extend to both surfaces and are separated by gas, vapor, and/or foam. The fluid within the filmletsis convected downstream either until it encounters a fresh supply from a groove or until pressure flowfrom the high-pressure region helps to reestablish a full film. For a submerged bearing, unless thepressures in the divergent region are subambient to draw fluid back into the bearing, the fluid would
FIGURE 27.31 Film thickness around the circumference of the bearing. (From Hamrock, B.J. (1994), Fundamentalsof Fluid Film Lubrication, McGraw-Hill, New York. With permission.)
FIGURE 27.32 Plan view of unwrapped bearing illustrating direction of fluid flow out of and into bearing. (FromBrewe, D.E., Fleming, D.P., Dimofte, F., and Hendricks, R.C. (1997), Fluid film lubrication, in Tribology for AerospaceApplications, Zaretsky, E.V. (Ed.), STLE SP-37, Society of Tribologists and Lubrication Engineers, Park Ridge, IL, 453–594.With permission.)
0
0
x:
¿:
h
rwb
prb 2prb
2pp
soon be pumped out from the high-pressure region, causing starvation and subsequent failure. Fluids,in particular oil, are known to sustain negative pressure (i.e., tensile stress) relative to atmospheric pressure(Sun et al., 1993). The extent to which oil can sustain tension depends on the availability of cavitationnucleation sites. These sites can consist of tiny gas bubbles and/or wear particles within the fluid. Inpractice, most lubricants contain an abundance of nucleation sites so that the fluid cavitates at either itsgas saturation pressure or vapor pressure. If the fluid is relatively free of gas, vapor cavitation can occurduring steady-state conditions. Under dynamic conditions, the content of the cavitation region shouldbe oil vapor rather than gas liberated from solution. Evaporation liberates dissolved gases much fasterthan does diffusion (Sun and Brewe, 1990), and the conditions that caused cavitation would havedisappeared before gases could be liberated from the fluid.
27.2.3.2 Lubricant Supply Arrangements
In the foregoing discussion of the submerged plain circular journal bearing, it was mentioned that unlessthe pressure along the sides of the bearing is greater than the cavitation pressure there wouldn’t be anatural mechanism to draw fluid into the bearing. Consequently, one either pressurizes the fluid at thesides of the bearing or replenishes the lubricant in the bearing with oil holes and/or grooves. Supplyholes and grooves are preferred because they improve the distribution of oil and are more effective incooling. In order to ensure an easy entrance for the lubricant to the bearing, the oil holes and groovesshould be well rounded or chamfered. They should not be placed in the loaded area of the bearing wherethey will tend to disrupt the formation of high fluid pressure. By providing an amount in excess of thatrequired to lubricate, the lubricant can provide additional cooling. Fuller (1984) discusses a variety oflubricant supply schemes; but only the simplest schemes will be discussed here. These include thehole/orifice-, the circumferential groove-, and the axial groove-supply. The ring bearing offers a differentmeans of bringing the lubricant to the journal bearing without requiring pressurization and is includedto illustrate its effectiveness.
27.2.3.2.1 Single Oil Supply HoleIn the case of a unidirectional loading, lubricant is commonly supplied through a hole or holes in thebearing housing. From the experiments of Boyd and Robertson (1948), it was found that in the case ofa single hole, the most desirable position to place the supply hole is opposite the area of load applicationwhere the pressure is least. For rotating loads, oil can be supplied through a hole in the journal. Thusthe source will rotate with the journal and is usually quite satisfactory. A case in point is the radial-enginecrankpin bearing discussed in Shaw and Macks (1949). The oil can be supplied through a hole in thecrankpin at a location that is always in the unloaded region. Although, in some engine bearings the loadvector periodically traverses the complete periphery of the journal and so the oil inlet hole cannot alwaysbe in the unloaded portion of the bearing. A circumferential groove is often used in this case.
27.2.3.2.2 Bearing with a Circumferential GrooveOne widely used practice is to place a circumferential groove at the center of the bearing. The oil is fedunder pressure to this groove. This method is very effective as far as cooling is concerned, but it doeshave the disadvantage that the groove interrupts the active length of the bearing and splits the bearingin half, each half having a much lower l/d ratio than the original bearing. Despite this disadvantage,however, such a groove generally lowers the oil temperature sufficiently to permit the bearing to carrymore load, even with the circumferential groove in place. Without such a groove, the bearing mightoverheat so badly that it could carry very little load. The circumferential groove configuration is shownin Figure 27.33.
27.2.3.2.3 Axial-Grooved BearingThe same rule that applies to positioning of a lubricant supply hole applies to the axial groove arrange-ment. The groove needs to be placed at a position that is least disruptive to oil pressure generation. A
good choice would be at the opposite area of load application where the pressure is the least. In the caseof a split bearing, location of the groove or grooves at the split line (which is assembled normal to theload line) is convenient and causes very little problem to pressure generation (Figure 27.34). The grooveshould extend across the major portion of the bearing as shown in the figure. In most applicationsadequate lubrication can be assured if the axial extent is nominally 80% of the bearing length, and acircumferential extent roughly 25% of the diameter. To avoid significant restriction of the inlet flow, thedepth of the grooves should not be less than 20 times the diametral clearance (Anon., 1984).
When axial grooves are indiscriminately placed in the bearing, the groove can act as a scraper andinterrupt the film. Figure 27.35 shows the effect of improper groove location on pressure generation forboth the axial and the circumferential groove. The dashed line represents the pressure generated withoutthe groove. The groove in that location bleeds off the hydrodynamic film that would have otherwise beenestablished there and the pressure falls to the value of the groove pressure. It wouldn’t be unusual forthe groove pressure to be an order of magnitude lower than the hydrodynamic film pressure.
FIGURE 27.33 Circumferential groove in journal bearing. (From Fuller, D.D. (1984), Theory and Practice ofLubrication for Engineers, 2nd ed., John Wiley & Sons, New York.)
FIGURE 27.34 Example of 2-axial groove bearing with load mid way between grooves. (From Neale, M.J. (1993),Steady load pressure fed journal bearings, in Bearings: A Tribology Handbook, Neale, M.J. (Ed.), Butterworth-Heinemann, Oxford. With permission.)
27.2.3.2.4 Ring BearingsOne important use of oil-ring bearings is to provide a fresh supply of lubricant to a rotating journal asshown in the schematic in Figure 27.35. The lubricant is supplied from the sump by the ring. The ringdrags against the top of the rotating journal. The imparted rotational motion to the ring enables it to pickup oil on its sides and underside of the ring from the sump. It is then carried to the top of the journalwhere it is distributed for lubrication. This is a case in which it is desirable to maintain high frictionbetween the ring/journal interface so that the ring will rotate at higher speed and deliver more oil to thebearing. A sectioned view of an oil-ring bearing for an industrial application is shown in Figure 27.36.
“At low ring speed, oil is delivered to the journal by the inside of the ring and by the sides of the ring.The oil adhering to the inner surface of the ring is the most important potential source of oil supply tothe journal. It is partly squeezed out on the shaft at the point of contact between the ring and the shaft.At low speeds, additional oil is supplied by gravity from the oil that adheres to the sides of the ring. Thus,at low speeds, the radial depth of the ring probably has more effect on ring oil delivery than the axialwidth of the ring. Figure 27.37a and b indicates in a general way this mechanism of oil delivery. At highring speeds the oil is thrown off by the rotational effect in the form of a spray. This spray should becollected in the crown of the bearing by collector scoops and directed back to the journal. Otherwise, itwill flow down the inside of the bearing housing, directly back into the oil sump. A typical curve of deliveryis shown in Figure 27.38. At high speeds, the transmission rate of oil from the ring is roughly proportionalto its width. Baildon (1937) indicates that the demarcation between high-speed and low-speed ring
FIGURE 27.35 Modification of hydrodynamic film pressure due to introduction of groove in load-carrying area.(From Shaw, M.C. and Macks, F.E. (1949), Analysis and Lubrication of Bearings, McGraw-Hill, New York. With permission.)
N
With groove
With groove
Without groove
Without groove
W
W
N
(a) Axial groove
Groove
Groove
(b) Circumferential groove
FIGURE 27.36 (a) Representation of oil-ring bearing; (b) detail of film formation between ring and shaft. (From Fuller,D.D. (1984), Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
FIGURE 27.37 Oil-ring journal bearing, in cross-section. (Courtesy of Mobil Oil Corp.) (From Fuller, D.D. (1984),Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
FIGURE 27.38 General mechanism of oil delivery. (From Fuller, D.D. (1984), Theory and Practice of Lubricationfor Engineers, 2nd ed., John Wiley & Sons, New York. With permission.)
Shaft
Ring
Oil
(a) (b)
Oil Oil
Oil Oil
Shaftlow
speed
Shafthigh
speed
(a) (b)
