Friction, Lubrication, and Wear Technology (1997) Part 9 ppsx

Fig. 22 Bushing insert for pivoted-pad hydrostatic journal bearing. Source: Ref 21 Three-Sector Journal Bearing This journal bearing, with three equally spaced axial grooves, has shown some degree of stability against self-excited whirl. Castelli and Pirvics (Ref 26) have presented comprehensive numerically computed performance characteristics for three- and four-axial grooved gas-lubricated journal bearings. Angular extent of each groove is considered to be 5°. Thus for a three-sector bearing, the arc length of a sector would be 120 - 5 = 115°. Figure 23 lists results in terms of the dimensionless load capacity parameter W' = W/p a rl plotted against the bearing compressibility number . Note that the value of used here is actually the same as in Eq 1. The applied load is directed toward the center of one sector. Evaluating W' and will determine the eccentricity ratio and thus the minimum film thickness. Fig. 23 Load function W' versus for three-groove journal bearing. Source: Ref 26 Information on many other sizes, load directions, and attitude angles can be found in Ref 26 and 27. Helical-Grooved Journal Bearings The helical grooving in this type of journal bearing enhances stability by reducing the attitude angle below that obtained from a plain cylindrical journal bearing. These bearings are known for their stability and are often used as a possible substitute for tilting-pad journal bearings. Castelli and Vohr (Ref 28) solved the appropriate equations numerically for load capacity and attitude angle for the case of l/d = 1.0, with various values of . Figure 24 lists the geometric parameters for the spiral-grooved bearing as used in Ref 28. Figure 25 lists the results showing the load parameter W' = Wp a as a function of with the eccentricity ratio as the third variable. Malanoski (Ref 29) shows good comparison between the theoretical predictions of Castelli and Vohr and his own measured results for helical-grooved journal bearings. Fig. 24 Geometry of spiral-groove bearing, using notation of Castelli and Vohr (Ref 28) Fig. 25 Load capacity of spiral- groove journal bearing as a function of bearing number and eccentricity ratio. Source: Ref 28 Hydrostatic Gas-Lubricated Bearings The many advantages of externally pressurized bearings are well known (Ref 9). With gas they have the added benefit of extreme cleanliness, and the use of gas enables them to operate over a wide range of temperatures. However, analytical and design complications arise because of the compressibility of the gas. At low supply pressures (gage) equal to or less than ambient pressure (absolute), the system can be very simple; for example, supply pressure 70 kPa (10 psig) with an ambient pressure of 100 kPa (14.7 psia). With high feed pressure, the gas flow in the entrance section is extremely complicated and may involve choked flow, shock waves, vortex formation, and boundary layer growth. Many comprehensive studies have been made of supersonic pressure depression in the feeding region of externally pressurized bearings (Ref 30, 31, 32, 33, 34). These bearings do not involve a constant volume of flow as is the case with many liquid-lubricated hydrostatic bearings. Therefore, in order to achieve stiffness, they must have some kind of upstream restrictor in the feed line (Fig. 26). The flow restrictor can be an orifice or a capillary, and the bearing is then described as being restrictor compensated; the orifice restrictor area is equal to (Fig. 26). Fig. 26 Flow-restricted hydrostatic gas-lubricated bearing Sometimes, the resistance to flow at the entrance to the film itself may dominate. In that case the bearing is identified as having inherent compensation. Many bearings are of this type. The inherent restrictor area would then be the circumferential annulus r 0 h at the entrance to the film (Fig. 26). A typical pressure profile is shown in Fig. 27 for a simple circular thrust bearing with a central feed source. With a supply pressure of 480 kPa (70 psig) and a film thickness on the "sill" of h = 0.05 mm (0.002 in.), the effect of sonic velocity is seen. The minimum pressure measured on the sill (p s ) is 76 kPa (11.01 psia), indicating a partial vacuum. The maximum recovery pressure on the sill is 101 kPa (14.6 psig). Fig. 27 Experimental pressure profiles for simple area 2 r 0 h externally pressurized thrust bearing However, notice in Fig. 27 that the radial distances are measured in mils (0.001 in. = 0.025 mm), so that all of this "micro-aerodynamic" activity has taken place within a radius of 120 mils, or about 3.2 mm. The remainder of the bearing area can thus be treated as laminar isothermal gas flow and analyzed accordingly. The dashed line in Fig. 27 shows the pressure profile when the bearing feed pressure was 70 kPa (10 psig). There is no sonic flow. Allowing for the pressure drop in the restrictor, either external or inherent, the bearing characteristics can be obtained in a relatively simple manner. Figure 28 is a sample of the excellent program conducted by Laub (Ref 35) on thrust bearings and journal bearings intended for metrology applications. The pressure profiles show no indication of significant flow restriction and localized pressure loss because of bearing geometry and low pressure levels that were used. Flow evaluation, however, must include compressibility effects. Fig. 28 Pressure profiles in gas-lubricated hydrostatic bearing: Source: Ref 35 As an example of the need to include the compressibility effect in flow prediction, consider the hydrostatic step bearing shown in Fig. 29. For liquids (incompressible), the supply pressure, P 0 and the ambient pressure, P 1 , are gage pressures, R 0 is the radius of the recess, and R is the radius of the shaft. The derivation for the flow of lubricant in such a bearing is given in Ref 9 as: (Eq 8) Fig. 29 Schematic diagram of a step bearing However, when compressibility effects are included, the equation for flow volume becomes (Ref 9): (Eq 9) where P 0 and P 1 are in this case absolute pressures, and V 0 is the flow volume at the supply pressure P 0 . Pneumatic Hammer The most troublesome characteristic of the externally pressurized air bearing is instability. During test programs, the phenomenon of self-excited vibration is often encountered, characterized violent fluctuations of pressure in the recess and amplitudes of vibration many times greater than the gap width at the equilibrium point. This phenomenon is often called pneumatic hammer. Licht, Fuller, and Sternlicht (Ref 36) used a simplified lumped-parameter analysis to examine this problem. The gas film density in an oscillating thrust bearing is time dependent, and, in general, the mass inflow does not equal the mass outflow. As a consequence of film compressibility, energy from the film may be periodically added to the system in phase with the motion so that instability develops. The vibration is independent of system resonances. The general stability analysis reveals the following: • For a constant supply pressure, p s , stability is enhanced by increasing the recess pressure p 0 that is, minimizing the pressure drop through the supply restrictor so that p s - p 0 is a minimum. This of course reduces the stiffness of the bearing • A recess depth comparable to the film thickness would be the ideal • Maximizing the size of the inlet supply orifice wil l increase stability because capillary restriction is more likely to be unstable than orifice restriction • Incompressible films are always stable Multiple-Pressure Sources To avoid pneumatic instability, it is clear that the high-pressure recess should be very shallow. The limit would be a recess of zero depth or no recess at all. However, that would reduce the load capacity of the bearing. A frequently used alternative is a ring or other appropriate pattern of multiple supply orifices that acts to develop an equivalent high- pressure area with the same depth as the film itself. Figure 30 shows a simple thrust bearing modified in this manner. Fig. 30 Multiple-source feed for thrust bearing In this bearing, the orifices are located on a circle of radius r 0 . All orifices feed air to the interface at the same pressure P 0 . Because there is no pressure gradient between the orifices, there is no flow between the orifices, and the entire circle of radius r 0 acts as a high-pressure recess. The same concept has also been successfully applied to journal bearings by Laub (Ref 35). Porous Bearings An alternate means for reducing the size and depth of a pressurized recess, other than using a finite number of multiple orifices as just described, is to feed the bearing through a section of porous material. Gas is admitted to the bearing interface through the pores of the material, resulting in a very large number of feeding restrictors in parallel. Again, the recess has been eliminated and stability enhanced. Many porous bearings have been made in both flat thrust and cylindrical journal bearing configurations. Sneck (Ref 37) provides an excellent survey of the many applications that have been made of this type of bearing, plus a very complete list of references. Figure 31 is typical of a circular thrust bearing with pressurization through a porous annulus.Frequently, a porous carbon graphite is used so that antiscuff protection is provided by the material when in solid contact. A reasonable range of permeability is available in these commercial products, and they have proven to be satisfactory. Clean air is essential to keep the pores from clogging with dust. Fig. 31 Typical configurations for externally pressurized porous gas-lubricated thrust bearings. Source: Ref 9 Typically, pressurized porous bearings can be used anywhere classical orifice-compensated bearings are used. Design charts have been prepared by Gargiulo and Gilmour (Ref 38) to assist in a more exact analysis of these bearings. However, it must be expected that the actual permeability of the material will be subject to some variation, even when cut from the same block. Vohr (Ref 4) discusses many additional design details involved in the use of porous materials in externally pressurized gas-lubricated bearings. These bearings can be extremely useful and are an attractive option for applications that call for a hydrostatic gas bearing. Compliant-Surface Bearings Compliant-surface bearings have been mentioned before in this article. They can use elastomers as the bearing material; in this form they have remarkable low-speed fluid-film capabilities. Foil bearings fall into this category as well. Compliant-surface bearings can be used as flexible membrane bearings. The advantages of compliant-surface bearings include: • Freedom from precision machining and maintenance of close tolerances • Ability to accept misalignment • Tolerance of dirt and particulates • Accommodation of surface roughness with low surface speeds The foil bearing (Fig. 32) is the most widely used form of compliant-surface bearing. It was first introduced, in simple form, by Blok and Van Rossum (Ref 39). Fig. 32 Schematic diagram of a foil bearing. Source: Ref 27 The bearing can consist of a thin strip of flexible material (such as a plastic tape or thin metallic foil) partially wrapped around simple journal like the saddle belly band on a horse. As the journal spins, a reasonably large force can be supported by the self-acting hydrodynamic film in the contact area between the tape and the journal. The simple foil bearing was further analyzed by Patel and Cameron (Ref 40) in 1957. It was utilized in the United States as an air bearing for applying load to a rotating shaft as early as 1956 by Fischer, Cherubim, and Fuller (Ref 27). By far, the greatest value of this simple concept is in tape transport for high-speed magnetic tape recorders. In this application, the journal is stationary and contains the recording head for the read-out components, while the tape glides past. Foil bearing analysis and design are reviewed extensively in Ref 4 and 41. Developments of the original foil bearing concept of Blok and Van Rossum have now reached the stage of commercial application. Their advantages are many. If a metallic foil is used, the bearing can operate at high temperatures, especially when lubricated with air or some other gas. There is no problem with the possible loss of clearance due to differential thermal expansion between shaft and bearing, as is often the case with rigid surface units. The foil bearing establishes its own operating film thickness at all times. It can also tolerate misalignment. In manufacturing, the foil bearing greatly reduces the need for holding expensive dimensional tolerances. An additional benefit is its stability in conjunction with high-speed rotor applications. The foil bearing is often used just for this reason, because it effectively reduces the possibility of self-excited fractional-frequency whirl (Ref 42). Three distinct commercial varieties of foil bearings are available: • Tension-dominated foil bearings (Fig. 33a) • Bending-dominated segmented foil bearings (Fig. 33b) • Bending-dominated continuous foil bearings (Fig. 33c) [...]... 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Jan 196 9, p 171-180 50 T.G Lewis, "Hydrostatic Gas Bearings and Metrology in Ultra-Precision Machining," 196 5 ASME Spring Lubrication Symposium, American Society of Mechanical Engineers, June 196 5 51 E.L Hemingway, Surface Finish Key to Bearing Life, Mach Des., Jan 194 5, p 168, 170 52 J.T Burwell, Jr., Teaching Lubrication and Bearing Design, Part V, Mach Des Manuf Bull., Vol XV (No 6), March 194 9 53... 15 H.G Elrod and S.B Malanoski, "Theory and Design Data for Continuous-Film, Self-Acting Journal Bearings of Finite Length," Report I-A 20 49- 13, Franklin Institute Laboratories for Research and Development, Nov 196 0 16 H.G Elrod and S.B Malanoski, "Theory and Design Data for Continuous-Film, Self-Acting Journal Bearing of Finite Length," (Supplement to Report I-A 10 49- 13), Report I-A 20 49- 17, Franklin... 131-155 19 A.C Hagg, The Influence of Oil-Film Journal Bearings on the Stability of Rotating Machines, J Appl Mech (Trans ASME), Vol 68, 194 6, p A211-A220 Discussion, Vol 69, Mar 194 7, p A77-A78 20 V Castelli and H.G Elrod, Solution for the Stability Problem for 360 Degree, Self-Acting Gas-Lubricated Bearings, J Basic Eng (Trans ASME), Vol 87, Mar 196 5, p 199 -212 21 E.J Gunter, J.G Hinkle, and D.D Fuller,... nitride, tungsten carbide, and chromium oxide Ceramics and cermets exhibit superior wear resistance Cermets are ceramics that have been bonded with metals to improve their ability to handle impact and shock loading The results, of course, vary with the ceramic and its bonding material Cobalt is often used as a binder Hinkle and Fuller (Ref 54) conducted a study of the friction and wear of various materials... forces (static and dynamic) Gear tooth material and surface characteristics (physical and chemical) Lubricant characteristics (physical and chemical) Environmental characteristics (physical and chemical) Note: Originally published in Lubrication Engineering, Jan-April, 199 0 Reprinted by permission of the Society of Tribologists and Lubrication Engineers All rights reserved Advantages and Disadvantages... 196 7 25 J.H Dunn, "Inspection of Two Brayton Rotating Units after Extensive Endurance Testing," Report TM X735 69, Lewis Research Center, National Aeronautics and Space Administration, 197 6 26 V Castelli and J Pirvics, Equilibrium Characteristics of Axial-Groove Gas-Lubricated Bearings, J Lubr Technol (Trans ASME), Vol 85, p 177- 195 27 G.K Fischer, J.L Cherubim, and D.D Fuller, "Some Instabilities and. .. I, 1886, p 157-234 9 D.D Fuller, Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, 198 4 10 W.A Gross, A Gas Film Lubrication Study; Part I: Some Theoretical Analyses of Slider Bearings, IBM J Res Dev., Vol 3, July 195 9, p 248 11 S Abramovitz, Theory for a Slider Bearing with a Convex Pad Surface; Side Flow Neglected, J Franklin Inst., Vol 2 59 (No 3), Mar 195 5, p 221-233 12 . Apr 196 7, p 24-1 to 24-34 55. W. Winer and M. Peterson, Ed., Wear Control Handbook, ASME Research Committee on Lubrication, American Society of Mechanical Engineers, 198 0 Friction, Lubrication,. (No. 6), March 194 9 53. R. Poppinga, Wear and Lubrication of Piston Rings and Cylinders, Society of Tribologists an d Lubrication Engineers (ASLE), 194 8 54. J.G. Hinkle and D.D. Fuller,. ASME), 196 8, p 810-817 39. H. Blok and J.J. van Rossum, Foil Bearing New Departure in Hydrodynamic Lubrication, Lubr. Eng., Vol 9, 195 3, p 316-320 40. B.J. Patel and A. Cameron, The Foil