Slider Bearings Introduction. David E. Brewe

Transcription

1 7 Slider David E. Brewe NASA Glenn Research Center 7.1 Introduction Slider Bearing Types Compressible Lubrication Compressible vs. Incompressible Advantages and Disadvantages for Bearing Types 7. Self-acting Finite Fixed-Geometry Thrust Pivoted (Tilting) Pad Thrust Journal 7.3 Failure Modes Cavitation Erosion Damage Wear Due to Contaminants 7.4 Slider Bearing Materials Materials for Liquid-Film Applications Bearing Materials for Gas-Film Applications 7.1 Introduction The vast number of industrial slider bearing designs initially evolved from a desire to create a bearing having better load-carrying capacity and/or reduced friction and wear. Thus, a great deal of emphasis was placed on the effectiveness of the bearing geometry to generate pressure (self-acting bearings) and thus increase load capacity. To illustrate how geometry affects the pressure-generating mechanism in a bearing, first consider the one-dimensional inclined slider in Figure 7.1. If one assumes the no slip condition, fluid is dragged into the converging wedge region by the moving runner. Since the exit is smaller than the entrance, a pressure is created to open up the exit so as to balance the flow into and out of the slider. If the two surfaces are restrained by a force (load), then pressure created within the bearing surfaces will resist the amount of fluid trying to enter (i.e., reverse flow) and will push more fluid out the exit so that the actual flow entering equals the flow exiting the slider.* For a finite bearing, one must take into account the fluid exiting along the sides as well (i.e., side-leakage). The slope of the inclined slider in Figure 7.1 is greatly exaggerated for bearing applications. To put it in perspective, Fuller (1984) considers the extreme case of a bearing pad having the length of a football field. The rise**, based upon a slope known for good load capability (3 mils/ft), was calculated to be 0.9 in. (.8 cm). With respect to the slope of the inclined slider, another question arises: For the converging wedge geometry, is there an optimum slope that provides a maximum load-carrying capacity? Pinkus and Sternlicht (1961) calculated load capacity and friction, and plotted them against h 1 /h (see Figure 7.). In the plot, C p and C f are functions of h 1 /h, representing the dimensionless coefficients for load W and friction F, respectively. That is: *Hamrock (1994) provides a more detailed account of this process. **The difference in elevation between the entrance, h 1, and exit, h, of the inclined slider, i.e., h 1 h as viewed in Figure 7.1.

2 Runner U x 1 x h h 1 tan -1 m Tapered land W B B _ FIGURE 7.1 Slider bearing configuration. (From Anderson, W.J. (1964), Hydrostatic lubrication, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, National Aeronautics and Space Administration, Washington, D.C.) cp c f cp c f a = h 1 /h FIGURE 7. Load capacity and friction in plane sliders. (From Pinkus, O. and Sternlicht, B. (1961), Theory of Hydrodynamic Lubrication, McGraw-Hill, New York. With permission.) and U L B W = µ h U B L F = µ h C p C f (7.1) (7.) where µ is the lubricant viscosity, U is the linear velocity, B is the breadth of the bearing (parallel to the direction of motion), and L is the bearing length (normal to the direction of motion). They showed that the maximum load capacity is achieved if h 1 /h =., at which value the load coefficient C p was calculated to be Frene et al. (1997) plotted the dimensionless pressure profiles for three values of h 1 /h (see Figure 7.3). The figure illustrates the pronounced effect that geometry has on the pressure development for the one-dimensional inclined slider. Note that the profile producing the maximum pressure supports the optimization performed by Pinkus and Sternlicht. Note further from Equation 7.1 that aside from geometry, one can increase the load-carrying capacity of the bearing by increasing the fluid viscosity or the relative velocity of the runner. From Figures 7. and 7.3, one can see how the angle of inclination affects the one-dimensional inclined slider bearing. However, Lord Rayleigh (1918) recognized that other bearing profiles were as effective as or were more effective than the inclined slider in generating pressure. His analysis of several bearing 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 Rayleigh step bearing, which is shown in Figure 7.4, along with the corresponding pressure profile. Pinkus and

3 FIGURE 7.3 Pressure distribution for various ratios of a = h 1 /h. (From Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: and Thrust, Tribology Series 33, Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. With permission.) y for region 1 y for region 1 h 1 h u B 1 B B x p Pmax FIGURE 7.4 Rayleigh step bearing and corresponding pressure profile, after Archibald (1950). (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, nd ed., John Wiley & Sons, New York. With permission.) Sternlicht (1961) calculated the load coefficient for the step bearing to be Using the calculus of variations, one can verify that the stepped bearing is the optimum geometry for a one-dimensional slider. Frene et al. (1997) plot dimensionless load vs. h 1 /h (Figure 7.5) for both the inclined slider and the step bearing. Again, the plot supports the conclusion by Pinkus and Sternlicht (1961) Slider Bearing Types An overall view of industrial-type bearings can be presented expediently by first considering an assortment of possible one-dimensional configurations (e.g., Figure 7.6). Regardless of the specific geometry, the pressure-generating mechanism works basically in the same way as described previously for the simplest case, as seen in Figure 7.6b. The geometry in Figure 7.6a is characteristic of a partial arc bearing and/or journal bearing in which the upper member represents the shaft and the lower member the housing. Here, the housing is shown as the moving surface although the application dictates the motion. In the case in which there exists only normal motion relative to the two members, the geometry would be representative of a squeeze-film damper. Extending this geometry to three dimensions, in which the upper member is spherical and the lower member is a conforming cup-shaped surface, the geometry would represent a spherical bearing. The wedge-shaped configuration shown in Figure 7.6b is used in the classical Kingsbury (1950) and Michell (1905) thrust bearings, which will also be discussed in the context of tilting-pad thrust bearings

4 FIGURE 7.5 Dimensionless load vs. ratio h 1 /h. (From Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. (1997), Hydrodynamic Lubrication: and Thrust, Tribology Series 33, Dowson, D. (Ed.), Elsevier Science B.V., Amsterdam. With permission.) (a) (b) (c) (d) (e) (f) (g) (h) FIGURE 7.6 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, nd ed., John Wiley & Sons, New York. With permission.) (Figure 7.7). The same geometry and variations thereof are employed in the flying heads used for computer hard drives. The heads are tilting-pad sliders that are supported above the spinning magnetic disk by a hydrodynamic air film. Fuller (1984), at that time, reported films on the order of m (0 millionths of an inch) and less. According to Van der Stegen (1997), the development of the hard disk slider has enabled gas film spacing on the order of 5 nm ( in.) and less. Bao and Li (1998) reported studies on liquid films an order of magnitude less, i.e., ~.0 to 3.0 nm ( to in.). Figure 7.6 includes geometries [(c) through (h)] that Purday (1949) had analyzed for pressure generation. His conclusion was in agreement with Rayleigh s; which was that one geometry was about as effective in generating pressure as the other, and that the step bearing geometry in Figure 7.6h generated the maximum peak pressure. Furthermore, friction forces were larger for a step bearing than

5 Motion of the runner W p Runner Pad leading edge h Pivot Film-pressure profile FIGURE 7.7 Tilting-pad slider bearing and generated pressure distribution. (From Anon. (1983), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded, Off-Set Pivot, Tilting-Pad Thrust, Engineering Sciences Data Unit, Item 83004, Institution of Mechanical Engineers, London, England.) for a plane inclined slider, but the flow was smaller. Also, the moment of pressure (i.e., center of pressure) was independent of h 1 /h. The idea of using the step bearing was advanced by Archibald (1950) when he applied it to a sector-shaped thrust bearing and then later to a journal bearing. The stepped bearing design is easier to fabricate than the tapered land bearings shown in Figures 6.6e and f (Fuller, 1984). Self-acting bearings sometimes required additional help (via external pressurization) to keep the bearing surfaces separated during start and stop conditions to avoid surface wear and reduce frictional energy loss. Thus, hybrid bearings were the result of occasionally combining the two pressure-generating schemes to provide greater load-carrying capacity and/or a stiffer bearing to improve stability. Externally pressurized 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 relative motion, that is pure sliding, relative rotation, and/or normal motion described by Szeri (001) in self-acting and hybrid applications. As industrial applications increased, it became apparent that the bearing designer often did not have the option of choosing the lubricant. For example, launch vehicles and power generation systems are better suited for space exploration if one can eliminate conventional oil lubrication systems. This cuts down on the size and weight and reduces the hazard of leakage which could result in a chemical/physical interaction of the working fluid with the oil. Furthermore, the design of the pump and/or power generator is 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 rolling element bearings because of the flexibility in choosing materials compatible with many of the highly reactive/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 launch vehicle applications severely limits the hydrodynamic load capacity of such bearings. For extended space travel, the bearings used for power generation operate under zero-gravity conditions and load capacity is 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 an angular velocity slightly less than or equal to one half the angular velocity of the journal around its own center. Various types of bearing designs are discussed with regard to their effectiveness in reducing tendencies for this type of instability. *The principles of hydrostatic bearings are treated in detail in Chapter 11 of this handbook by A. Szeri.

6 The study of gas bearings was noticeably accelerated following the Manhattan Project during World War II. According to Fuller (199), gaseous diffusion plants were used to provide an enriched fuel by pumping uranium hexafluoride gas through a cascade of successive diffusion stages. Several thousand stages in series were needed to achieve the required composition. The bearings and seals in the pumps could not be oil-lubricated because of the high power losses and concerns for contamination of the lubricant. The natural choice became the working fluid (i.e., gaseous uranium hexafluoride) and a concerted design effort helped contribute to the success of the project 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: ( p v) p= ρ R T = ρg c c T (7.3) where ρ is the density; R, the gas content; T, the temperature; c p, the specific heat per unit weight for constant pressure; c v, the specific heat for constant volume per unit weight; and g, the gravitational constant. Because temperature is a function of pressure, the conservation of energy equation has to be linked with the Reynolds equation to calculate pressure. Fortunately, most gas lubricating films are nearly isothermal* due to the fact that bearing materials generally dissipate heat much faster than gases generate heat. Therefore, according to the ideal gas law (Equation 7.3), the pressure is directly proportional to the density, so the energy equation can be bypassed. Gas-lubricated bearings are used in a wide variety of applications (Fuller, 199; van der Stegen, 1997): 1. High-speed grinding spindles. A high-speed spindle for laser copiers and printers is shown in Figure 7.8. The figure reveals a fixed shaft with straight grooves for the aerodynamic bearing, and a rotating hollow shaft, which is driven by the rotor. The rotor is suspended vertically by magnetic thrust bearings and positioned horizontally by the aerodynamic bearings. The mirror has ten flat surfaces for the reflection of a laser beam (Vliestra, 1987; cited in van der Stegen, 1997). 3. Sliding ways on machine tools, for avoiding stick-slip vibration 4. for precise linear and rotational indexing metrology devices 5. Hermetically sealed high-speed blowers and compressors that use the working fluid as the lubricant. Typical applications include gas-cooled reactors, cryogenic and pyrogenic turbomachinery where great temperature extremes are encountered. 6. High-precision inertial guidance instruments such as gyroscopes and accelerometers 7. Foil-type gas bearings for auxiliary power units in aircraft and power-generating components used in space 8. Computer peripheral devices, such as hard/floppy disk drives, consisting of slider-bearing readwrite heads. Figure 7.9 presents a rotating disk with an arm-slider assembly of a hard disk; and Figure 7.10 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 performance 10. 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 is not virtually isothermal has not been shown to exist (Gross, 196).

7 FIGURE 7.8 Spindle in a copier. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.) arm with slider disk FIGURE 7.9 Computer hard disk with arm-slider assembly. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.) Compressible vs. Incompressible* The advantages of gas-lubricated bearings over liquid-lubricated fluid-film bearings are now well-understood. These include: Cleanliness: elimination of contamination caused by more traditional lubricants Reduction (often elimination) of the need for bearing seals *The list of advantages and disadvantages of gas bearings is given in Fuller (199).

8 video tape drum head FIGURE 7.10 Videotape with head. (From van der Stegen, R.H.M. (1997), Numerical Modeling of Self-Acting Gas Lubricated with Experimental Verification, Ph.D. thesis, Faculteit Werktuigbouwkunde, Universiteit Twente, Enschede, The Netherlands. With permission.) Lubricant stability: no vaporization, cavitation*, solidification, decomposition, or phase change over extreme ranges of temperature, from cryogenic ( 70 C or 450 F) up to approximately 1650 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, with little 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-lubricated bearings, especially with self-acting or hydrodynamic bearings. Consequently, for a given load, gas bearings operate with thinner hydrodynamic films than their liquid-lubricated counterparts. As the films become thinner, the possibility of surface scoring, wear, and eventual bearing failure is a real concern. Tighter manufacturing tolerances and improved surface finishes are required. In addition, careful bearing alignment is necessary as well as consideration of possible loss of clearance due to thermal effects. However, compliant surface bearings (i.e., foil bearings and membrane bearings) are more forgiving and do not require the rigid specifications regarding design and manufacture of the bearings. The membrane bearing, for example, operates very satisfactorily over a typical factory floor. The gas film in a slider bearing behaves as a cushion of air providing very little damping. If a critical speed or instability is encountered, there may not be enough damping to suppress or control it. This makes it necessary to carefully analyze the dynamics of the system so that by design one can preclude severe rubbing sand /or failure of the bearing. *While cavitation causes damage in liquid-lubricated journal bearings, it can, on the other hand, be beneficial because cavitation stabilizes the behavior of liquid-lubricated journal bearings (van der Stegen, 1997). Calculations by Brewe (1986) show that the occurrence of vapor cavitation in a journal bearing undergoing circular whirl can increase load capacity by as much as 0%. **Gross (196) points out that both the load carrying capacity and the friction of a gas film must be much less than that of a liquid film. Interestingly, though, the ratio of friction to load, the coefficient of friction, must always be greater for a self-acting gas film than for a similar liquid film. ***Approximately 10 5 Pa s ( lb f sec/in. ) for air under room conditions compared with oil, approximately 10 Pa s ( lb f sec/in. ) (van der Stegen, 1997).

9 Pressure buildup in a slider bearing is limited by the gas compressibility. As the velocity of the runner is increased, the effectiveness to build pressure and carry load is decreased. Eventually, the most important parameter to generate pressure depends on the minimum to maximum film thickness 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 to compress 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 gas lubricant, the following section provides a more global viewpoint, which includes a broader class of bearings Advantages and Disadvantages for Bearing Types Tables 7.1 and 7. from the Engineering Sciences Data Unit (1965, 1967) illustrate the advantages and disadvantages of bearings (including rolling element bearings) for both thrust and journal (radial) bearing applications. 7. Self-acting Finite Self-acting bearings all operate on the principle that pressures are generated via relative motion between the surfaces to produce load support. The mechanism in which pressures are generated is discussed in the Introduction in the context of infinitely wide bearings (i.e., no side leakage) and in more detail by Hamrock (1994). In designing finite bearings, side-leakage becomes an important issue. It determines the effectiveness of the bearing to generate pressure and thus carry loads. Consequently, one can increase load 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 be the load-bearing area Fixed-Geometry Thrust Several configurations of fixed-geometry sliders are shown in Figure 7.11 as rectilinear and sector thrust bearings. However, these geometries are also suitable for journal bearing applications as well as conical and spherical geometry bearings. Sector thrust bearings are used specifically to take loads in the axial direction for rotating machinery. A typical thrust bearing arrangement illustrating the main components of a fixed-inclined-pad thrust bearing is shown in Figure 7.1. The upper configuration in Figure 7.13 illustrates a side view of the wedge-shaped pad with land, along with the pressure distribution. The bearing support plate contains several such pads distributed evenly around the axial plate, as shown in the bottom half of the figure The Dynamics of Fixed-Geometry Thrust Bearing instability is a problem peculiar to thrust bearings having a fixed-geometry. To understand the instability of the fixed pads, refer back to Equation 7.1 and Figure 7., which illustrates the optimization of the load coefficient (Pinkus and Sternlicht, 1961). The outlet (minimum) film thickness can be solved from Equation 7.1; that is: h U C = µ B W L P (7.4)

10 TABLE 7.1a Advantages and Limitations of Thrust Environmental Conditions General Comments Rubbing Oil-Impregnated Porous Metal Rolling Hydrodynamic Liquid Film Hydrostatic Liquid Film Self-acting Gas Externally Pressurized Gas High temperature Low temperature External vibration Space requirements Dirty or dusty conditions Attention to differential expansions and their effect upon fits and clearances necessary Attention to differential expansions and starting torques necessary Attention to the possibility of fretting damage necessary (except hydrostatic bearings) Normally satisfactory depending upon material Attention to oxidation resistance of lubricant necessary Lubricant may impose limitations, consideration of starting torque necessary Normally satisfactory except when peak of impact load exceeds load capacity Small radial extent Normally satisfactory, scaling advantageous Sealing important Up to 100 C (1 F) no limitations; from 100 C to 50 C (1 to 48 F), stabilized bearings and special lubrication procedures probably required Below minus 30 C ( F) special lubricants required, consideration of starting torque necessary May impose limitations; consult manufacturer of many different proportions, small axial extent Attention to oxidation resistance of lubricant necessary Lubricant may impose limitations, considerations of starting torque necessary Lubricant may impose limitations Excellent Satisfactory Excellent Normally satisfactory Small radial extent but total space requirement depends on the lubrication feed system Satisfactory filtration of lubricant is important Excellent Excellent, thorough drying of gas necessary Small radial extent Sealing important Vacuum Excellent Lubricant may impose limitations Not normally applicable Wet and humid conditions 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 Satisfactory Radiation Satisfactory Lubricant may impose limitations Excellent Excellent Small radial extent but total space requirement depends on the gas feed system Satisfactory Not applicable when vacuum has to be maintained

11 TABLE 7.1b Advantages and Limitations of Thrust Requirements General Comments Rubbing Oil-Impregnated Porous Metal Rolling Hydrodynamic Liquid Film Hydrostatic Liquid Film Self-acting Gas Externally Pressurized Gas Low starting torque Not normally recommended Low running Satisfactory torque Accuracy of radial location Life Finite, but predictable Theoretically infinite, but affected by filtration and number of stops and starts Combination of axial and radial load carrying capacity Satisfactory Good Satisfactory Excellent Satisfactory Excellent Excellent Poor Good Excellent Good Excellent A thrust face must be provided to carry the axial loads Most types capable of dual duty Silent running Good for steady loading Excellent Usually satisfactory, consult manufacturer Simplicity of lubrication Availability of standard parts Prevention of contamination of the product and surroundings Excellent Excellent with selfcontained grease or oil lubrication Theoretically infinite Theoretically infinite, but affected by number of stops and starts A thrust face must be provided to carry the axial loads Excellent Self-contained assemblies can be used with certain limits of load, speed and diameter. Beyond this, oil circulation necessary Excellent, except for possible pump noise Auxiliary highpressure pump necessary Excellent Excellent Good to excellent depending upon type Excellent Good Not available Improved performance Normally satisfactory, but attention to sealing necessary, except where a process liquid Excellent can be obtained by can be used as a lubricant allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations Theoretically infinite Excellent, except for possible compressor noise Pressurized supply of dry clean gas necessary

12 TABLE 7.1b (continued) Advantages and Limitations of Thrust Requirements General Comments Rubbing Oil-Impregnated Porous Metal Rolling Hydrodynamic Liquid Film Hydrostatic Liquid Film Self-acting Gas Externally Pressurized Gas Frequent stopstart Excellent Good Excellent Good Excellent Poor Excellent Frequent change Generally good Generally good of direction of notation Running costs Very low 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 Guide to the Choice of Thrust Bearing Type, Engineering Sciences Data Unit, Item 67033, Institution of Mechanical Engineers, London, England.

13 TABLE 7.a Advantages and Limitations of Journal Environmental Conditions General Comments Rubbing Oil-Impregnated Porous Metal Rolling Hydrodynamic Liquid Film Hydrostatic Liquid Film Self-acting Gas Externally Pressurized Gas High temperature Low temperature External vibration Space requirements Attention to differential expansions and their effect upon axial clearance necessary Attention to differential expansions and starting torque necessary Attention to the possibility of fretting damage necessary (except hydrostatic bearings) Normally satisfactory depending upon material Attention to oxidation resistance of lubricant necessary Lubricant may impose limitations, consideration of starting torque necessary Normally satisfactory except when peak of impact load exceeds load capacity Small axial extent Up to 100 C (1 F) no limitations; from 100 C to 50 C (1 to 48 F) stabilized bearings and special lubrication procedures probably required Below minus 30 C ( F) special lubricants required, consideration of starting torque necessary May impose limitations, consult manufacturer of many different proportions available Attention to oxidation resistance of lubricant necessary Lubricant may impose limitations, consideration of starting torque necessary Lubricant may impose limitations Excellent Excellent, thorough drying of gas necessary Satisfactory Excellent Normally satisfactory Excellent Small axis extent but total space requirement depends on the lubrication feed system Small axis extent Dirty or dusty conditions Normally satisfactory, sealing advantageous Sealing important Satisfactory, filtration of lubricant important Sealing important Vacuum Excellent Lubricant may impose limitations Not normally applicable Wet and cold conditions 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 Radiation Satisfactory Lubricant may impose limitations Excellent Small axis extent but total space requirement depends on the gas feed system Satisfactory Not applicable when vacuum has to be maintained

14 TABLE 7.b Advantages and Disadvantages of Journal Requirements General Comments Rubbing Oil-Impregnated Porous Metal Rolling Hydrodynamic Liquid Film Hydrostatic Liquid Film Self-acting Gas Externally Pressurized Gas Low starting torque Not normally recommended Low running Satisfactory torque Accuracy of axial location Life Finite but can be estimated Theoretically infinite, but affected by filtration and number of starts and stops Combination of axial and radial load carrying capacity Satisfactory Good Satisfactory Excellent Satisfactory Excellent Excellent Good Excellent Good Excellent A journal bearing surface must be provided to carry the radial loads Some types capable of dual duty Silent running Good for steady loading Excellent Usually, satisfactory; consult manufacturer Simplicity of lubrication Excellent Excellent with selfcontained grease lubrication. With large sizes or high speeds, oil lubrication might be necessary Theoretically infinite Theoretically infinite, but affected by number of starts and stops Theoretically infinite A journal bearing surface must be provided to carry the radial loads Excellent Self-contained assemblies can be used with certain limits of load, speed, and diameter. Beyond this, oil circulation necessary Excellent except for possible pump noise Auxiliary high pressure pump necessary Excellent Excellent except for possible compressor noise Pressurized supply of dry clean gas necessary

15 Availability of standard parts Prevention of contamination of the product and surroundings Tolerance to manufacturing and assembly inaccuracies Type of Motion Frequent start-stops Unidirectional Good to excellent depending upon type Excellent Good Not available Improved performance Normally satisfactory, but attention to sealing necessary, except where a process liquid Excellent can be obtained by can be used as a lubricant allowing a process liquid to lubricate and cool the bearing, but wear debris may impose limitations Good Satisfactory Poor Satisfactory Poor Satisfactory Excellent Good Excellent Excellent Suitable Bidirectional Suitable Some type suitable Suitable Some types suitable Oscillatory Unsuitable Unsuitable Running costs Very low Depends upon complexity Nil of lubrication system Cost of lubricant supply has to be considered Suitable Cost of gas supply has to be considered From Anonymous (1965), General Guide to the Choice of Journal Bearing Type, Engineering Sciences Data Unit, Item 65007, Institution of Mechanical Engineers, London, England.

16 U U U Taper Taper-flat Step Pocket Spiral groove Herringbone FIGURE 7.11 Examples of self-acting thrust bearings. (From Ausman, J.S. (1964), Gas-lubricated bearings, in Advanced Bearing Technology, Bisson, E.E. and Anderson, W.J. (Eds.), NASA SP-38, ) W D R t Runner Pad d s Bearing support plate FIGURE 7.1 View showing relative position of bearing components for an axial thrust bearing. (From Anon. (198), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust, Engineering Sciences Data Unit, Item 809, Institution of Mechanical Engineers, London, England.) Using the fact that h is directly proportional to C 1/ P, and h 1 /h is a function of C P, according to Figure 7., one can account for the occurrence of a bearing instability. Further, the ratio h 1 /h is equal to (δ/h + 1), where δ is the rise of the slider (h 1 h ). For bearings with fixed inclination, the rise is established during manufacture.* If the bearing is operating so that the value of h 1 /h yields the maximum load coefficient, then any increase in load will cause a decrease in minimum film thickness. This will, in turn, cause C P to decrease because it is proportional to h. However, according to Figure 7., as C P drops, the value of h 1 /h increases, causing h to decrease. Mathematically, the bearing is stable only when C P / H 0. Although this poses a serious limit to the stable operation of fixed-pad bearings, other concerns may be more potently dangerous that affect competing type bearings as well. For example, temperatureviscosity effects may well be a greater concern when loads are increased because they can lead to an increase in shear heating, raising the temperature of the lubricant and decreasing the viscosity. This would result in a decreased minimum film thickness Tapered-land Slider The tapered-land thrust bearing is shown in Figure 7.14, illustrating the lubricant flow between successive pads. Here, the lubricant source is provided at the inside diameter of the pad support plate and is *Cameron (1966) points out that tilting-pad bearings have the most important feature (which fixed inclination pads do not have): that the inlet and outlet gaps vary together, so that h 1 /h always remains constant.

17 MOTION W p Runner β h Pad Typical pressure pattern generated Section through a thrust pad Pad Trailing edge Outer side L b d d m D d m Individual pad Land Inner side Leading edge FIGURE 7.13 Sectional view of thrust plate and layout of pads. (From Anon. (198), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust, Engineering Sciences Data Unit, Item 809, Institution of Mechanical Engineers, London, England.) MOTION Side leakage Side leakage Q i Pad Pad Side Leakage Q f Groove Side leakage FIGURE 7.14 Flooded or oil-bath system of lubrication. (From Anon. (198), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust, Engineering Sciences Data Unit, Item 809, Institution of Mechanical Engineers, London, England.) expelled at the inner and the outer diameter. Referred to as an oil-bath or flood-feed system, a disadvantage of this supply type is that oil is caught in the large space between pads and causes a drag (or churning) 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 lubricant into the pad inlet as shown in Figure In this way, the space between each pad does not have to be flooded to assure adequate lubrication in the inlet. A land at the trailing edge of the taper provides load support upon starting and stopping. This can be effective without any assistance from external pressure (hydrostatic jacking), provided the land pres-

18 MOTION Side leakage Side leakage Q l Pad Q f Side leakage Pad Groove Side leakage FIGURE 7.15 Individual pad feed system of lubrication. (From Anon. (198), Thrust Bearing Calculations: Calculation Methods for Steadily Loaded Fixed-Inclined-Pad Thrust, Engineering Sciences Data Unit, Item 809, Institution of Mechanical Engineers, London, England.) sures remain less than 0.7 MN/m (Anon., 198). Harrison (1913) optimized the one-dimensional tapered thrust bearing with regard to the extent of the land and the slope parameter δ/h. For optimum load capacity, the extent of the land was determined to be 0% of the breadth of the bearing with a value of δ/h = 1.5. For a pad having fixed inclination, this optimum condition can be achieved only at a single value of applied load (or minimum film thickness h ). The value of δ/h will change as the value of applied load changes, as discussed in the section on dynamics. No significant errors should arise for land lengths within the range of 10 to 30% (Anon., 198). The use of rectangular pad data for the design and analysis of bearings with sector-shaped pads does not lead to errors of practical significance with sector angles up to 45. Tapered-land bearings have been used in large thrust bearings for hydroelectric turbines with some success. Hall and de Guerin (1957) and Linn and Shepard (1938) described their performance (Cameron, 1966) Rayleigh Step Bearing A typical axial Rayleigh step sector thrust bearing is shown in Figure Even though Lord Rayleigh (1918) showed that the infinitely wide step bearing gave a 0% greater load capacity than infinitely wide tilling-pad bearings, Kingsbury and Michell had captured the marketplace with the tilting-pad bearing, causing the step bearing to be neglected until about At that time, Archibald (1950) calculated the load capacity for a square step bearing, including side flow: µ U B W =, per unit width h (7.5) If one calculates the load capacity per unit width for the corresponding square tilting-pad bearing: r i r o T σg h hs FIGURE 7.16 Rayleigh step sector thrust bearing.

19 FIGURE 7.17 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.) µ U B W =, per unit width h (7.6) 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 experiments using straight and shrouded steps. Wildmann et al. (1965) studied gas-lubricated step thrust bearings extensively. In an earlier study, Ausman (1961) optimized sector-shaped pad geometries based upon maximum load capacity for low compressibility numbers (near-incompressible lubrication). Hamrock (197) extended the range of compressibility using a similar analysis for rectangular pads. In 1983, Bagci and Singh extensively analyzed the effects of side flow for finite bearings Semicircular Step Bearing Typically, results from Cameron (1966) show that a bearing with a semicircular step of radius equal to B/ and a ratio of h 1 /h of 1.7, had a load coefficient of (see Figure 7.17a). Thus, µ U B W =, per unit width h (7.7) Triangular Step Bearing A triangular step bearing (Figure 7.17b) with h 1 /h of.1 had a load coefficient of 0.11: µ U B W =, per unit width h (7.8) 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 (h 1 h ), Figure 7.4, is usually much less than 0.05 mm (0.001 in.). Such a small step height can be difficult to fabricate. During operation, especially starts and stops where the runner is prone to touch the bearing, a small amount of wear may wipe away the step. In spite of the disadvantages listed, step bearings are widely used as gas bearings because they are less expensive to make than the attractive tilting-pad bearings Pocket Step Bearing Wilcock (1955) demonstrated that one could combine some of the advantages of hydrostatic-type pocket bearings with a hydrodynamic-type thrust bearing to achieve a thrust bearing having low power loss and high 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 7.18.

20 h U δ y x OIL IN b L b E B b FIGURE 7.18 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.) 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 the pocket and establish high pressure. Oil leakage out of the pocket and pump land occurs through the clearance between the rails and runner. The clearance height adjusts itself until the oil leakage out of the bearing is exactly equal to the flow into the bearing. At this point, the pocket pressure is sufficient to support the external load. Wilcock provided further analysis to show that for maximum film thickness at a given load and speed the taper of the pumping land must be zero. In other words, a Rayleigh step with 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 bearing with the tapered-land and the tilting-pad thrust bearings. The results are shown in Table 7.3. TABLE 7.3 Comparison of the Pocket-Step Thrust Bearing with Two Hydrodynamic Thrust Tapered Land Bearing Tilting Pad Bearing Pocket-Step Bearing Load W 70,000 lbs kn 70,000 lbs kn 70,000 lbs kn Size, D 1 /D 7/15 7/15 7/15 Nos. of pads Pad slope a Operating 18 cp.61 µreyns 18 cp.61 µreyns 18 cp.61 µreyns viscosity Avg. unit load 555 psi 3.83 MPa 614 psi 4.3 MPa 565 psi 3.90 MPa h min in µm in µm in µm Power loss 76 hp kw 86 hp kw 45 hp kw Oil flow, Q 15.7 gpm m 3 /s 3.9 gpm m 3 /s 17.5 gpm m 3 /s Film temp. rise, T 58 F 3. C 44 F 4.44 C 31 F 17. C a Average of inner and outer slopes. 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 for roughly the same hydrodynamic oil flow. Disadvantages of the hydrodynamic pocket step-bearing are: (1) that it is sensitive to misalignment, () 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 by Wilcock (1955) to reverse the trend of decreasing power loss with increasing speed. To address the misalignment, Wilcock (1955) devised a frictionless pressurized ball seat mounting that was self-aligning.

21 B θ h h 1 bb Pocket B 0.1B FIGURE 7.19 Pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York. With permission.) And if high loads must be carried at low speed, high-pressure oil can be fed to the pocket so that it operates as a hydrostatic bearing at low speeds. But the issue of turbulence in the pockets at high speed remains a concern. Wilcock and Booser (1957) hypothesized that decreasing pocket depth might have a beneficial effect 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 The distinguishing geometric features of this bearing over that studied by Wilcock (1955) and shown in Figure 7.18 are the shape of the side rails and the absence of a lubricant supply hole at the inlet. The speckled region (Figure 7.19) having film thickness h 1 and length bb (i.e., pumping length) is the inlet of the Rayleigh step. The step height is the difference between h 1 and the minimum film thickness h. Upon having chosen h 1 /h to be 1.76 and the angle of the inside rail wall relative to the outside wall θ to be 18.5, Kettleborough optimized this bearing based upon minimum friction and maximum load capacity for a wide range of pumping lengths (i.e., 0 b 1.0). The value of b that resulted in maximum dimensionless load W B h µ U B was b = 0.6 where W is load, U is the speed of the runner, and µ is the absolute viscosity, while the minimum dimensionless friction f/(h /B) is 5.3 where b = 0.3 and f is the friction coefficient. Naturally the choice of b depends upon the importance the designer places on minimum friction or maximum load. Giving them equal weight, a reasonable compromise would be to assign b = 1 /. Cameron (1966) points out that the dimensionless load W B h µ U B very nearly equals that of the optimum square tilting pad, just less than 0.1 (Figure 7.0) Recurrent-Grooved Thrust Spiral Grooved Thrust Bearing An annular plate, spiral grooved thrust bearing is shown in Figure 7.1. The operating principle of the spiral grooved thrust bearing is based on the fact that a viscous lubricant (oil, grease, or air) is dragged into a slot or groove by a moving runner. If the flow is inhibited at the end of the groove by a dam or restrictor, pressure builds up and the bearing is able to support a load. The direction of rotation

22 Load 10 h 0 L W/L ηu 0.06 Friction 6 µ L ho/ b FIGURE 7.0 Load and friction for pocket step thrust bearing. (From Cameron, A. (1966), The Principles of Lubrication, John Wiley & Sons, New York.) Wt ω h c h h o h 1 a a 1 Groove Ridge r 1 r α FIGURE 7.1 Flat spiral grooved thrust bearing without transverse flow (no net flow from r 1 to r ). (From Muijderman, E.A. (1966), Spiral Groove, Philips Technical Library, Eindhoven, The Netherlands. With permission.) 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 between pressure development and leakage as a consequence of the pumping action. Increasing the groove depth δ increases the pumping action and hence the lift as a result of the increase in pressure generation. If the grooves are too deep, the leakage will become excessive. If the groove depth is reduced to zero, the pumping effect naturally ceases. Here, the groove depth can be optimized so as to continue to support the constant bearing load and/or the rotating disk. The shape of the spiral grooves should be optimized to achieve the most effective pumping. This would result in a maximum pressure buildup. Muijderman calculated the value of α required to produce maximum pressure for a basic element (see Figure 7.). 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 groove is a logarithmic spiral. In polar coordinates, the shape of the groove is defined as

23 ω x r α Tangent r α β C Radius vector θ r =f (θ) 0 r 1 A FIGURE 7. The logarithmic spiral, r = r 1 e θtanα. (From Muijderman, E.A. (1966), Spiral Groove, Philips Technical Library, Eindhoven, The Netherlands.) r = re θ tanα 1 (7.9) as the lubricant. Cameron (1966) points out that bearing flatness is most important if air is used. The flatness is checked by optical interference. It is found that, as the front (frictional) surface gets hot, the bearing 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 r 1 (where p r = p ambient ) for the spiral groove thrust bearing without transverse flow is derived by Muijderman (1966) as: p µωr = 1 λ g1 α H γ C1 α H γ λ k h,,,,,, r 1 3 ( ) ( ) ( ) (7.10) where λ = r 1 /r, H = h /h 1, γ = α /α 1, k = number of grooves, µ = viscosity, and C 1 is: e C1( α, H, γ, λ, k)= α π 1 tan α k 90 1 γ ( ) γh 3 1+ H λ e 1 λ α + π 1 tan α k 90 1 γ ( ) γh 3 1+ H (7.11) and g 1 is: g 1 ( α, H, γ)= 3 γh ( cot α) ( 1 H) ( 1 H ) ( ) ( + ) + ( ) + ( ) γh γ H H cot α 1 γ (7.1) Load-carrying capacity: Muijderman calculates the load-carrying capacity of the spiral groove bearing without transverse flow to be:

24 ( ) ( ) ( ) 3 r Wtsgb. = π µω 4 1 λ g1 α, H, γ C α, H, γ, λ, k h 4 (7.13) where e C ( α, H, γ, λ, k)= α π 1 tan α k 90 1 γ ( ) γh 3 1+ H 4 λ e 4 1 λ α + π 1 tan α k 90 1 γ ( ) γh H (7.14) Frictional torque: In this case, the frictional torque from the inner chamber is neglected because h c h. Thus, for the case without transverse flow, ( ) ( ) r Mtsgb. = π µω 4 1 λ g α, H, γ h 4 (7.15) Coefficient of friction: The coefficient of friction for the inward pumping spiral grooved bearing without transverse flow is given as: f tspg. ( ) ( ) ( ) h g, H, α γ = 3r g α, H, γ C α, H, γ, λ, k 1 (7.16) Herringbone Grooved Thrust Bearing Figure 7.3 shows a herringbone annular thrust bearing configuration where the fluid is pumped into the grooves from both outside edge and the inside edge. This bearing operates properly when the grooves are not closed off at the inner or outer diameter. However, this bearing can operate without transverse flow (no net flow across the inner and outer radius) if r h is chosen so that the inner and outer grooves build up equal pressures at a distance r = r h from the center. Pressure: For the inner (r 1 < r < r h ) and outer (r h < r < r ) grooves, respectively, the pressure buildup was determined by Muijderman to be: p r 3 π α 1 + γh ( ) 3 k + + H = r r e g H h 1 1 tan α µω 90 1 γ α,, γ ( ) (7.17) and p r H π 3 α 1 + γ 1 ( tan α) 3µω k γ 3 1+ H = r e r g H h 1 α,, γ ( ) (7.18) In practice, the expression for r h is often approximated as: ( ) r 1 h r + 1 r (7.19)

25 W t ω h h o h 1 groove ridge a a 1 α r r 1 r h inner grooves outer grooves FIGURE 7.3 Herringbone spiral-grooved bearing, with no net flow between r and r 1. (From Muijderman, E.A. (1966), Spiral Groove, Philips Technical Library, Eindhoven, The Netherlands. With permission.) U 1.45h min h min 0 58 B B D b B PIVOT D 1 FIGURE 7.4 Diagram of a tilting-pad bearing (one shoe), showing the optimum pivot location and the resultant shoe inclination. (From Wilcock, D.F. and Booser, E.R. (1957), Bearing Design and Application, McGraw-Hill, New York. With permission.) Load-carrying capacity: Muijderman calculates the load-carrying capacity of the herringbone thrust bearing with no transverse flow to be

26 ( ) ( ) ( ) 3 r Wtherr. = π µω 1 λ g1 α, H, γ C1 α, H, γ, λ, k 4h 4 (7.0) Frictional torque: For the frictional torque, he obtained ( ) ( ) r Mtherr. = π µω 4 1 λ g α, H, γ h 4 (7.1) Coefficient of friction: f therr. ( ) h g, H, = 1+ λ r ( ) ( α γ) 3 1 λ g1 α, H, γ C1 α, H, γ, λ, k ( ) ( ) (7.) 7.. Pivoted (Tilting) Pad Thrust Basic Features* The tilting-pad thrust bearing (Kingsbury-type bearing) differs from the tapered-land thrust bearing in that each pad is an individual plate which is free to pivot. The pivot line is radial so that each pad can be inclined in a circumferential direction in order to provide a tapered oil film. Figure 7.4 shows the geometry 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 edge because of the pumping action of the bearing. A large portion of the oil flowing through a tilting-pad bearing does not flow over the working bearing surfaces, because of the spaces necessarily left free around each 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 the bearing is started and an oil film is created between the pad and runner, each pad will tilt to the angle that will generate the proper distribution of film pressures (Figure 7.4). In setting out to design a tilting-pad bearing, the designer will normally know the total load W to be carried, the shaft speed N, the shaft diameter D, the inlet-oil temperature T 1, the desired oil-temperature rise T, and the oil-viscosity grade. In addition, a minimum film thickness, usually in., is stipulated. The designer must then determine the number of pads and the size of each pad that will give the desired values of temperature rise and minimum film thickness. Another variable to be determined is the location of the pivot.** If rotation is always to be in one direction, the optimum pivot location is 58% of the distance from the leading edge to the trailing edge of the pad. The design procedure given in this section is based on this pivot location. If the shaft is to rotate in either direction, the pivot location must be at the mid-point, or 50% point. Experience has shown that there is usually enough crown to the pad as manufactured to give pads pivoted at the mid-point an equivalent performance. This is discussed in more detail in Wilcock and Booser (1957). Use of a 58% pivot point not only gives maximum load capacity and minimum friction, but also greatly simplifies the calculation procedures Michell and Kingsbury 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

27 FIGURE 7.5 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 7.6 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.) Collar Shoe Leveling plate Base ring Joint in base ring FIGURE 7.7 Developed section of bearing showing the leveling plates to distribute the load equally among the six shoes of the thrust bearing. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, nd ed., John Wiley & Sons, New York. With permission.) emerging steam turbine applications. In 1897, ships were being powered by turbines and required thrust bearings 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 7.5. The earlier Kingsbury thrust bearings were operated in a bath of oil that was circulated by the pumping action of the rotating element. Kingsbury bearings commonly used three, six, or eight pads per bearing. The number of segmented pads depended on the application. To obtain maximum load-carrying, each pad

28 FIGURE 7.8 Kingsbury LEG thrust bearing illustrating lubricant flow path. (Courtesy of the Kingsbury Bearing Co.) should carry the same load. In actual practice, the bearings can expect to be subjected to a certain amount of misalignment, which causes uneven loading. The Kingsbury Machine Works addressed this problem by developing a system of leveling plates. This consisted of an annular series of equalizing levers on which the pads were supported. Figure 7.6 illustrates the Kingsbury thrust bearing with leveling plates. A section view is shown in Figure 7.7. The leveling plates leave each pad free to move up or down to take 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 the discussion on fixed-geometry sector thrust bearings, this leads to unnecessary churning of the oil and high power loss. By placing a groove at the leading edge of each pad, the bearing can run with less lubricant between pads. This effectively reduces the power loss of the bearing. Further, cool oil is introduced at the leading edge, displacing the hot-oil carryover, and thus providing a cooler load- bearing film. 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 pivoted pad bearing. Figure 7.8 shows the flow path of the oil over the pad surface for a tilting-pad load equalizer bearing with grooves at the leading edge of the bearing Journal Plain Journal A plain journal bearing, a true circular bearing without grooves, is shown in Figure 7.9. Application of a vertical load on the shaft displaces the shaft in the direction of the load. This creates a tapered wedge in the bearing, establishing a pressure on the inlet side so as to establish a flow balance into and out of the bearing. The hydrodynamic pressure also reacts to support the load. A moment is exerted on the inlet side of the shaft by the buildup in pressure that causes the shaft to be displaced in a direction normal to the load. When the applied load and the hydrodynamic forces balance each other, the measure of the eccentrically displaced shaft along the line of centers settles at an angle ψ from the load line. This is referred to as the attitude angle of the bearing for a particular load, speed, and lubricant condition. A typical pressure distribution around the circumference of the bearing is shown in Figure 7.9b. Along the 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 7.9c.

29 FIGURE 7.9 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 of Tribologists and Lubrication Engineers, Park Ridge, IL, With permission.) In dynamically loaded bearings, the relative normal motion of the shaft to the bearing through the line of centers (Figure 7.30b) creates an additional contribution to the load capacity. The pressures depicted in this figure are a result of the squeezing action caused by the normal approach of shaft and bearing. Conversely, negative pressures are created if the shaft and the bearing are receding from each other. If the negative pressure reaches the saturation pressure of the liquid, dissolved gases can be released from the liquid to form gaseous cavitation. If the pressure decreases to the vapor pressure of the fluid before the gases have time to be released, then vapor cavitation will occur.

30 W Fluid (a) Plane surfaces. Bearing Cavitation Journal Fluid W Housing (b) Cylindrical journal bearing. + Load, W 0 - Time (c) Loading. FIGURE 7.30 Dynamically loaded squeeze film 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 of Tribologists and Lubrication Engineers, Park Ridge, IL, With permission.) Steady-state Pressure Distribution Steady-state operation occurs when the bearing and shaft centers remain fixed relative to each other during operation. To obtain the pressures, the film shape must first be defined and appropriate boundary conditions applied upon integration of the Reynolds equation. From Figure 7.9, the film thickness, h, can be expressed as: ( ) h= c 1+ ε cos θ (7.3)

31 x: 0 prb prb : 0 p rw b p h FIGURE 7.31 Film thickness around the circumference of the bearing. (From Hamrock, B.J. (1994), Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. With permission.) Flow Balance and Cavitated Flow Characteristics Making a cut at the line of centers where the maximum film thickness occurs results in a plot of the film thickness along the circumference of the unwrapped bearing (Figure 7.31). The film is convergent for 0 < θ < π and divergent for π < 0 < π. As described earlier, pressure builds up in the convergent region because fluid is being convected into a constricting space. This pressure buildup reaches a maximum near the minimum film thickness and within the convergent region. As a result, a pressure flow away from the peak pressure is created, leading to some side-flow leakage out of the bearing as well as some flow into the divergent region (see Figure 7.3). This extra pressure flow together with the convective flow into the divergent region helps fill the increasing available space until there is insufficient fluid to complete the film. The film ruptures and, depending on the load, speed, viscosity, and surface tension at the bearing/journal surfaces, either (1) it breaks up into small filmlets similar to those shown in Figure 7.3, or () fluid is transported through the cavity in the form of a sheet having a free surface and attached to the faster moving surface. The latter condition occurs if the surfaces are sufficiently separated so as to preclude the possibility of fluid attaching itself to both surfaces. This is more apt to occur 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, the filmlets extend to both surfaces and are separated by gas, vapor, and/or foam. The fluid within the filmlets is convected downstream either until it encounters a fresh supply from a groove or until pressure flow from the high-pressure region helps to reestablish a full film. For a submerged bearing, unless the pressures in the divergent region are subambient to draw fluid back into the bearing, the fluid would FIGURE 7.3 Plan view of unwrapped bearing illustrating direction of fluid flow out of and into 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 of Tribologists and Lubrication Engineers, Park Ridge, IL, With permission.)

32 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 cavitation nucleation sites. These sites can consist of tiny gas bubbles and/or wear particles within the fluid. In practice, most lubricants contain an abundance of nucleation sites so that the fluid cavitates at either its gas saturation pressure or vapor pressure. If the fluid is relatively free of gas, vapor cavitation can occur during steady-state conditions. Under dynamic conditions, the content of the cavitation region should be oil vapor rather than gas liberated from solution. Evaporation liberates dissolved gases much faster than does diffusion (Sun and Brewe, 1990), and the conditions that caused cavitation would have disappeared before gases could be liberated from the fluid Lubricant Supply Arrangements In the foregoing discussion of the submerged plain circular journal bearing, it was mentioned that unless the pressure along the sides of the bearing is greater than the cavitation pressure there wouldn t be a natural mechanism to draw fluid into the bearing. Consequently, one either pressurizes the fluid at the sides of the bearing or replenishes the lubricant in the bearing with oil holes and/or grooves. Supply holes and grooves are preferred because they improve the distribution of oil and are more effective in cooling. In order to ensure an easy entrance for the lubricant to the bearing, the oil holes and grooves should be well rounded or chamfered. They should not be placed in the loaded area of the bearing where they will tend to disrupt the formation of high fluid pressure. By providing an amount in excess of that required to lubricate, the lubricant can provide additional cooling. Fuller (1984) discusses a variety of lubricant supply schemes; but only the simplest schemes will be discussed here. These include the hole/orifice-, the circumferential groove-, and the axial groove-supply. The ring bearing offers a different means of bringing the lubricant to the journal bearing without requiring pressurization and is included to illustrate its effectiveness Single Oil Supply Hole In the case of a unidirectional loading, lubricant is commonly supplied through a hole or holes in the bearing housing. From the experiments of Boyd and Robertson (1948), it was found that in the case of a single hole, the most desirable position to place the supply hole is opposite the area of load application where the pressure is least. For rotating loads, oil can be supplied through a hole in the journal. Thus the source will rotate with the journal and is usually quite satisfactory. A case in point is the radial-engine crankpin bearing discussed in Shaw and Macks (1949). The oil can be supplied through a hole in the crankpin at a location that is always in the unloaded region. Although, in some engine bearings the load vector periodically traverses the complete periphery of the journal and so the oil inlet hole cannot always be in the unloaded portion of the bearing. A circumferential groove is often used in this case Bearing with a Circumferential Groove One widely used practice is to place a circumferential groove at the center of the bearing. The oil is fed under pressure to this groove. This method is very effective as far as cooling is concerned, but it does have the disadvantage that the groove interrupts the active length of the bearing and splits the bearing in 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 carry more load, even with the circumferential groove in place. Without such a groove, the bearing might overheat so badly that it could carry very little load. The circumferential groove configuration is shown in Figure Axial-Grooved Bearing The same rule that applies to positioning of a lubricant supply hole applies to the axial groove arrangement. The groove needs to be placed at a position that is least disruptive to oil pressure generation. A

33 FIGURE 7.33 Circumferential groove in journal bearing. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, nd ed., John Wiley & Sons, New York.) good choice would be at the opposite area of load application where the pressure is the least. In the case of a split bearing, location of the groove or grooves at the split line (which is assembled normal to the load line) is convenient and causes very little problem to pressure generation (Figure 7.34). The groove should extend across the major portion of the bearing as shown in the figure. In most applications adequate lubrication can be assured if the axial extent is nominally 80% of the bearing length, and a circumferential extent roughly 5% of the diameter. To avoid significant restriction of the inlet flow, the depth of the grooves should not be less than 0 times the diametral clearance (Anon., 1984). When axial grooves are indiscriminately placed in the bearing, the groove can act as a scraper and interrupt the film. Figure 7.35 shows the effect of improper groove location on pressure generation for both the axial and the circumferential groove. The dashed line represents the pressure generated without the groove. The groove in that location bleeds off the hydrodynamic film that would have otherwise been established there and the pressure falls to the value of the groove pressure. It wouldn t be unusual for the groove pressure to be an order of magnitude lower than the hydrodynamic film pressure. FIGURE 7.34 Example of -axial groove bearing with load mid way between grooves. (From Neale, M.J. (1993), Steady load pressure fed journal bearings, in : A Tribology Handbook, Neale, M.J. (Ed.), Butterworth- Heinemann, Oxford. With permission.)

34 W N With groove Without groove W Groove (a) Axial groove N Groove Without groove With groove (b) Circumferential groove FIGURE 7.35 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, McGraw-Hill, New York. With permission.) Ring One important use of oil-ring bearings is to provide a fresh supply of lubricant to a rotating journal as shown in the schematic in Figure The lubricant is supplied from the sump by the ring. The ring drags against the top of the rotating journal. The imparted rotational motion to the ring enables it to pick up oil on its sides and underside of the ring from the sump. It is then carried to the top of the journal where it is distributed for lubrication. This is a case in which it is desirable to maintain high friction between the ring/journal interface so that the ring will rotate at higher speed and deliver more oil to the bearing. A sectioned view of an oil-ring bearing for an industrial application is shown in Figure 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 to the 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 axial width of the ring. Figure 7.37a and b indicates in a general way this mechanism of oil delivery. At high ring speeds the oil is thrown off by the rotational effect in the form of a spray. This spray should be collected in the crown of the bearing by collector scoops and directed back to the journal. Otherwise, it will flow down the inside of the bearing housing, directly back into the oil sump. A typical curve of delivery is shown in Figure At high speeds, the transmission rate of oil from the ring is roughly proportional to its width. Baildon (1937) indicates that the demarcation between high-speed and low-speed ring

35 (b) (a) Ring Shaft Oil FIGURE 7.36 (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, nd ed., John Wiley & Sons, New York. With permission.) FIGURE 7.37 Oil-ring journal bearing, in cross-section. (Courtesy of Mobil Oil Corp.) (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, nd ed., John Wiley & Sons, New York. With permission.) Oil Oil Oil Oil Shaft low speed Shaft high speed (a) (b) FIGURE 7.38 General mechanism of oil delivery. (From Fuller, D.D. (1984), Theory and Practice of Lubrication for Engineers, nd ed., John Wiley & Sons, New York. With permission.) 001 by CRC Press LLC