Volume 18 - Friction, Lubrication, and Wear Technology Part 14 potx

25 Load capacity of spiral-groove journal bearing as a function of bearing number and eccentricity ratio.. Hydrostatic Journal Bearings Externally pressurized journal bearings may be us

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/pa 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' = Wpa 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 r0 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 (ps) 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 r0 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, P0 and the ambient pressure, P1, are gage pressures,

R0 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):

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, ps, stability is enhanced by increasing the recess pressure p0 that is,

minimizing the pressure drop through the supply restrictor so that ps - p0 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 will 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 r0 All orifices feed air to the interface at the same pressure P0 Because there is no pressure gradient between the orifices, there is no flow between the orifices, and the entire circle of

radius r0 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)

Fig 33 Foil bearing designs (a) Tension-dominated foil bearing (b) Bending-dominated segmented foil

bearing Source: Ref 9 (c) Bending-dominated continuous foil bearing Source: Ref 9

Tension-dominated foil bearings (Fig 33a) have been used in data-processing equipment, where they provide

support for magnetic tape traveling over guides, heads, and vacuum columns in tape transport Recent developments have concentrated on adapting these bearings to the support of high-speed rotors for turbomachinery (Ref 43)

Bending-dominated segmented foil bearings of the type shown in Fig 33(b) are widely used in both commercial

and military aircraft applications One example is the air-cycle refrigeration compressor used on many commercial transports for cabin cooling Operating speeds can easily be 100,000 rpm, yet the compressor exhibits a high degree of reliability and freedom from rotor whirl instabilities These bearings are being developed for cryogenic compressors at working temperatures near absolute zero

A great deal of research and development work is being devoted to extending these bearings to high-temperature applications With support from the Air Force Aero Propulsion Center and the Naval Air Propulsion Center, research programs are underway to develop a foil bearing capable of operating at high speed in a 650 °C (1200 °F) ambient The potential application is for high-temperature gas turbines (Ref 44) Thrust bearing configurations are also used

Bending Dominated Continuous Foil Bearings This configuration has a single top foil strip that is restrained at

one end and supported by a resilient corrugated foil strip called the bump foil strip (Fig 33c) This piece elastically supports the top foil and controls the stiffness of the bearing The deflection of the bump foil tolerates load fluctuations, and its elastic behavior provides resilience Friction damping is also introduced with its beneficial stabilizing effects on the dynamics of the rotor

Significant accomplishments have been recorded for bending-dominated continuous foil bearings, including:

• Three years of operation in automotive-type gas turbines at 60,000 rpm and 260 °C (500 °F)

Modified Bending-Dominated Continuous Foil Bearings This type of bearing is a modification of the design

shown in Fig 33(c) Although only limited applications have been made, it does appear to have excellent performance characteristics

Design Analysis There is no significant design analysis available, in the public domain, for the foil bearings described

above The design procedures are essentially proprietary However, if a proposed application involves light starting loads ( 7 to 14 kPa, or 1 to 2 psi) and when up to speed (>20,000 rpm) the unit loads do not exceed 70 to 100 kPa (10 to 15 psi), it appears that some type of foil bearing would be an excellent choice

Pressurized-membrane bearings are bearings with a flexible membrane pressurized from the center through port

holes (Fig 34) At equilibrium conditions, the air escapes from under the inflated membrane through the minimum air gap Levy and Coogan (Ref 45) first developed the analysis for such a device

Fig 34 Compliant-surface membrane bearing Source: Ref 45

These bearings find wide use in areas where large loads must be lifted and transported over surfaces that may not be perfectly smooth, such as the floors in warehouses and factories The flexibility of the membrane accommodates itself to the undulations that may exist, and motion proceeds smoothly with almost no friction When the desired location or position is attained, the air supply is shut off and the object is set down These devices are now available commercially

A spectacular application of this type of hydrostatic membrane bearing is the Mile High Stadium in Denver, Colorado The stadium was designed so that it would be suitable for both football and baseball Accordingly, the entire side section

of the grandstand, weighing 4080 Mg (4500 tons) and including 21,000 seats, is mounted at 46 points on water-lubricated hydrostatic rubber pads Each pad is 1.2 m (4 ft) in diameter and made of fabric-reinforced synthetic rubber

When pressurized, the entire section of the grandstand floats on a film of water and is moved back a distance of 44 m (145 ft) with very little effort It is then set down in place, producing an arena suitable for playing baseball (Fig 35) Although water was the pressurized lubricant of choice in this application, air could have been used

Fig 35 Use of pressurized membrane bearings in Denver Mile High Stadium

It is surprising how little pressure is needed to support a large load An available circular commercial unit 430 mm (17 in.) in diameter, with a pressure of about 21 kPa (3 psig) can carry a load of 270 kg (600 lb) with a flow of about 57 L/min (2 standard ft3/min) The same unit at only 70 kPa (10 psig) can carry 900 kg (2000 lb) with, of course, a greater flow

A novel application was made recently by a company in England that refurbishes full-size passenger railroad cars A cradle platform was built to hold the four-wheel trucks at each end of the car Then the platforms were floated on air-pressurized membrane bearings Once this was done, the railroad car could be easily moved to any location on the factory floor without being encumbered by rails

A few years ago, this type of hydrostatic compliant pad was offered as an option on a well-known brand of domestic refrigerator By reversing the hose connection on a standard vacuum cleaner, the discharge pressure could be directed to the pads under the refrigerator and cause it to float in a film of air It could then be moved very easily away from the wall, even when fully loaded, to allow for cleaning and maintenance

Hydrostatic Journal Bearings

Externally pressurized journal bearings may be used when it is necessary to maintain a precise shaft position, with negligible friction, when rotational speed is insufficient to establish a hydrodynamic film External pressurization is also used in combination with a hydrodynamic-type bearing to increase film stiffness, reduce the attitude angle, and raise the threshold of instability The combination of these two actions produces what is known as a "hybrid bearing" (Fig 36)

Fig 36 Typical hybrid journal bearing designs Source: Ref 9

The mutual contribution of each type of lubrication is of course of design decision The rotor may be started or stopped without solid contact Bearings for high-speed dental drills (500,000 rpm) are of the hybrid variety (Ref 46)

Externally pressurized journal bearings are affected by a great many combinations of parameters, so their design is relatively complex Lund (Ref 47) has combined first-order self-acting and externally pressurized perturbation solutions for small eccentricity ratios The results are found to be satisfactory and in good agreement with experimental results for small eccentricity ratios

As with thrust bearings, the recesses must be kept as small as possible to avoid pneumatic instability Multiple feed orifices or porous sections may be an answer to the problem With multiple feeds, the assumption is usually made that the discrete points be considered as a continuous line source of pressure

Comprehensive design charts for externally pressurized journal bearings are presented in Ref 48 Shapiro (Ref 49) has evaluated a three-sector hybrid journal bearing for both steady-state and dynamic behavior He has published the results for this gas bearing, which uses orifice compensation, in tabular and graphical forms

Many applications of externally pressurized gas bearings have been made to instruments, with remarkable increases in precision Wunch, in Ref 45, describes the revolution that gas bearings have produced in the field of metrology The surprising conclusion is that even though the components of the air bearing have been produced with normal manufacturing tolerances on dimensions and surface finishes, the rotational accuracy of the final instrument itself is of the order 0.075 to 0.125 m The explanation assumes the pressurized film has an averaging effect, and the small surface undulations of the bushing (surface roughness) are not transmitted to the shaft This is similar to the smooth motion of a row boat on the surface of a pond; the boat is not influenced by the roughness of the bottom of the pond

In machine tool applications, Lewis (Ref 50) has shown that grinder spindles, shapers, and gear cutters will actually show run-outs measured in microinches using externally pressurized journal bearings

Materials for Gas-Lubricated Bearings

Engineers have been forced to search for materials that, when operated under extremely adverse conditions, will deliver acceptable life expectancy and reasonably low friction These adverse conditions may be associated with high

temperature, with the use of lubricants with low viscosity and little or no natural oiliness (like gas), or with dry operation where no lubricants are present at all

Experimentation has led in the direction of harder and harder materials, such as refractory materials and ceramics (Ref 51,

52, 53) These materials are usually brittle, so impact must be avoided When they are used as rigid bearings with gas lubrication, the geometry must be precise and true because there is little possibility of conformability with such materials (as there could be with tin or lead-based babbitt, for example) Rigid designs, relatively light loads, and elimination of thermal or elastic deformations are necessary

Investigations of gas-lubricated rigid thrust bearings and journal bearings operating under high temperature and speed conditions have shown favorable performance with the use of hard ceramic materials Materials that might be considered for such applications include boron carbide, chromium carbide, silicon carbide, titanium carbide, alumina, silicon nitride, tungsten carbide, and chromium oxide

high-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 for gas-lubricated rigid journal bearings under conditions of start-stop and high-speed whirl-induced rubbing The tests were performed with a variety of imposed loads, temperatures, and ambient atmospheric conditions Of the 36 combinations of materials investigated, by far the best performance was exhibited by aluminum oxide (alumina) against itself The best specimens showed no visible evidence of wear even after extended testing

Surprisingly, of the four different types of aluminum oxide used, one was far superior to the other three The binder, the density, and the grain size are apparently strong variables It might be advisable to get guarantees of friction and wear characteristics from a prospective vendor before selecting a particular grade of aluminum oxide

Ceramics do provide low wear, but they also have relatively high friction This may be a problem in some applications In instrument gyroscopes, the electric motor drive is very small and light and has a low starting torque Consequently, unless the friction of the bearing material is low enough, the motor will stall and not start Much current research in gyro bearings is directed toward the reduction of friction in ceramic bearings through the introduction of some form of boundary lubrication

Research carried out at the University of Rhode Island has determined that if final grinding of the ceramic is done in a bath of a prescribed boundary lubricant, a surface modification is achieved that provides lower friction For silicon nitride, octadecanoic armide is recommended For glass ceramics such as Pyroceram, the use of dioctedecyl disulfide is indicated

In England, the British Royal Navy Scientific Service frequently uses silicon nitride against silicon nitride for gyro air bearings They have been successful with small built-in graphite brushes that spread a thin film of solid graphite on the running surfaces This technique not only reduces wear and lowers friction, but it also burnishes the surfaces to a high gloss while running An alternative technique is burnishing the surfaces before installation with either molybdenum disulfide (MoS2) or Teflon Reducing friction with ceramics is an active research field

Surface Coatings High-density ultrahard coatings can be applied to the surfaces of ordinary commercial machine

elements and provide them with a highly wear-resistant capability Typical applications include parts for use in jet aircraft and in the chemical, textile, steel, and data processing industries New coating technologies for tribological applications are described in Ref 55 Many different techniques can be used in making these surface depositions, depending on the end results desired

Surface coating is a specialized field in which dramatic developments have been made within the last decade For example, the metallic foil compliant-surface bearings, described earlier, have been coated with wear- and friction-resistant materials for use in various applications Commercially bonded MoS2, aluminum oxide, chromium oxide, and a three-component commercial blend of aluminum oxide, silicon oxide, and chromium oxide have all been used successfully for coating these bearings

References

1 H.D Smyth, Atomic Energy for Military Purposes, Princeton University Press, 1946

2 D.D Fuller, Ed., Proceedings, First International Symposium on Gas-Lubricated Bearings (Washington,

D.C.), ACR-49, 26-28 Oct 1959

3 Proceedings, Second International Symposium on Gas Lubrication (Las Vegas), 17-20 June 1968,

American Society of Mechanical Engineers

4 W.A Gross, Ed., Fluid Film Lubrication , John Wiley & Sons, 1980

5 A.S Raimondi, A Numerical Solution for the Gas-Lubricated, Full Journal Bearing of Finite Length, Trans ASME, Apr 1961, p 131-155

6 W.A Gross, A Gas Film Lubrication Study; Part I: Some Theoretical Analyses of Slider Bearings, IBM J Res Dev., Vol 3, July 1959, p 237-255

7 G.W.K Ford, D.M Harris, and D Pantall, Principles and Applications of Hydrodynamic-Type Gas

Bearings, Proc Inst Mech Eng., Vol 171, 1957, p 93-113, discussion, p 113-128

8 O Reynolds, On the Theory of Lubrication and Its Application to Mr Beauchamp Towser's Experiments,

Including an Experimental Determination of the Viscosity of Olive Oil, Philos Trans R Soc (London) A,

Vol 177, Part I, 1886, p 157-234

9 D.D Fuller, Theory and Practice of Lubrication for Engineers, 2nd ed., John Wiley & Sons, 1984

10 W.A Gross, A Gas Film Lubrication Study; Part I: Some Theoretical Analyses of Slider Bearings, IBM J Res Dev., Vol 3, July 1959, p 248

11 S Abramovitz, Theory for a Slider Bearing with a Convex Pad Surface; Side Flow Neglected, J Franklin Inst., Vol 259 (No 3), Mar 1955, p 221-233

12 R.K Brunner, J.M Harker, K.E Haughton, and A.G Osterlund, A Gas Film Lubrication Study; Part III:

Experimental Investigation of Pivoted Slider Bearing, IBM J Res Dev., No 3, 1959, p 260-274

13 A Kingsbury, Experiments with an Air Lubricated Journal, J Am Soc Naval Eng., Vol 9, 1897, p 267-292

14 H.F Brubach, Some Laboratory Applications for the Low Friction Properties of the Dry Hypodermic

Syringe, Rev Sci Instrum., Vol 18, May 1947, p 363-366

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 2049-13, Franklin Institute Laboratories for Research and Development, Nov 1960

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 1049-13), Report I-A 2049-17, Franklin Institute Laboratories for Research and Development, June 1962

17 H.G Elrod and A Burgdorfer, Refinements of the Theory of the Infinitely Long, Self-Acting,

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U.S Government Printing Office, Oct 1959, p 93-118

18 A.S Raimondi, A Numerical Solution for the Gas-Lubricated, Full Journal Bearing of Finite Length, Trans ASME, Apr 1961, p 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, 1946, p A211-A220 Discussion, Vol 69, Mar 1947, 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 1965, p 199-212

21 E.J Gunter, J.G Hinkle, and D.D Fuller, "Design Guide for Gas-Lubricated, Tilting-Pad Journal and Thrust Bearings with Special Reference to High-Speed Rotors," NYO-2512-1, U.S Atomic Energy Commission, Eng Development Branch, I-A 2393-3-1, Contract AT 30-1-2512, Nov 1964

22 E.J Gunter, J.G Hinkle, and D.D Fuller, The Effects of Speed, Load, and Film Thickness on the

Performance of Gas-Lubricated Tilting-Pad Journal Bearings, Trans ASLE, Vol 7, 1964, p 353-365

23 J Corniglion, G Kilmister, H Woodley and A.D Richards, Theoretical Design and Practical Performance

of Tilting-Pad Gas Bearings, Paper No 19, Gas Bearing Symposium Proceedings, University of

Southampton, United Kingdom, Apr 1967

24 C Mech, Some Practical Performance Aspects of the Design of Gas-Bearing Blowers and Some

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X-73569, Lewis Research Center, National Aeronautics and Space Administration, 1976

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27 G.K Fischer, J.L Cherubim, and D.D Fuller, "Some Instabilities and Operating Characteristics of Speed Gas-Lubricated Journal Bearings," Paper No 58-A-231, American Society of Mechanical Engineers

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Circular Thrust Bearings, Paper 17, Proceedings of Fourth Gas Bearing Symposium, Vol 1, University of

Southampton, United Kingdom

32 P.S Moller, Radial Flow without Swirl between Parallel Disks Having Both Supersonic and Subsonic

Regions, J Basic Eng (Trans ASME), Vol 88, 1966, p 147-154

33 J.H Vohr, A Study of Inherent Restriction Characteristics for Hydrostatic Gas Bearings, Paper 30,

Proceedings of Fourth Gas Bearing Symposium, Vol 2, University of Southampton, United Kingdom

34 H Mori, A Theoretical Investigation of Pressure Depression in Externally Pressurized Gas-Lubricated

Circular Thrust Bearings, J Basic Eng (Trans ASME), Vol 83, 1961, p 201-208

35 J.H Laub, Evaluation of Externally-Pressurized Gas Pivot Bearings for Instruments, Proceedings, First International Symposium on Gas-Lubricated Bearings, ACR-49, U.S Government Printing Office, Oct

38 E.P Gargiulo and P.W Gilmour, A Numerical Solution for the Design of Externally Pressurized Porous

Gas Bearings: Thrust Bearings, J Lubr Technol (Trans ASME), 1968, p 810-817

39 H Blok and J.J van Rossum, Foil Bearing New Departure in Hydrodynamic Lubrication, Lubr Eng., Vol

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40 B.J Patel and A Cameron, The Foil Bearing, Paper 73, Proceedings, Conference on Lubrication and Wear,

Institute of Mechanical Engineers (London), Oct 1957, p 219-223

41 W.A Gross, Analysis and Design of Foil Bearings, Paper No 23, Proceedings, Gas Bearing Symposium,

University of Southampton, United Kingdom, Apr 1967

42 F.J Suriano, R.D Dayton, and F.G Woessner, "Test Experience with Turbine-End Foil-Bearing-Equipped Gas Turbine Engines," Paper 83-GT-73, American Society of Mechanical Engineers, 1983

43 L Licht, The Dynamic Characteristics of a Turborotor Simulator on Gas-Lubricated Foil Bearings, J Lubr Technol (Trans ASME), Vol 94, 1972, p 211-222

44 "Gas Lubricated Foil Bearing Development for Advanced Turbomachines," Report AF APL-TR-76-114, Vol I and II, Air Force Aero Propulsion Laboratory, 1977

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Vol 90, 1968, p 184-190

46 N.S Grassam and J.W Powell, Gas Lubricated Bearings, Butterworths, London, 1964

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50 T.G Lewis, "Hydrostatic Gas Bearings and Metrology in Ultra-Precision Machining," 1965 ASME Spring Lubrication Symposium, American Society of Mechanical Engineers, June 1965

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Friction, Lubrication, and Wear of Gears

Robert Errichello, GEARTECH

Introduction

BECAUSE GEARS are such common machine components, they may be taken for granted It is not generally appreciated that they are complex systems requiring knowledge from all the engineering disciplines for their successful design Gear design is a process of synthesis in which gear geometry, materials, heat treatment, manufacturing methods, and lubrication are selected to meet the requirements of a given application The designer must design the gearset with adequate strength, wear resistance, and scuffing resistance To do this, he or she must consider gear tribology The choice

of lubricant and its application method is as important as the choice of steel alloy and heat treatment The interrelationship

of the following factors must be considered:

• Gear tooth geometry

• Gear tooth motion (kinematics)

• Gear tooth 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, 1990 Reprinted by permission of the Society of

Tribologists and Lubrication Engineers All rights reserved

Advantages and Disadvantages

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

• Stability of lubricant No vaporization, cavitation, solidification, decomposition, or phase change over extreme ranges of temperature, from cryogenic (-270 °C, or -450 °F) up to approximately 1650 °C (3000 °F) Operation at these extremes of temperature is a current research goal

• Low friction and heating with little or no cooling generally required Permits practical attainment of high speeds (700,000 rpm)

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 For acceptable application, therefore, the bearings are necessarily larger and operate with thinner hydrodynamic films than their liquid-lubricated counterparts

Thinner films demand closer control of manufacturing tolerances, surface finishes, and possible thermal and elastic distortions and alignments, to prevent rubbing contact With compliant surface bearings, as with foil bearings and membrane bearings, rigid specifications regarding design and manufacture can be dramatically relaxed The membrane bearing, for example, operates very satisfactorily over a typical factory floor

The low damping of the gas film makes it necessary to carefully analyze the dynamic characteristics of the mechanical system employing the gas bearing, since if a critical speed or instability is encountered, there may not be enough damping

to suppress it or control it With liquid-lubricated bearings these instabilities might not have been suppressed or passed over unnoticed because of the greater damping action that inherently exists with liquids Much recent research has been devoted to the dynamics of gas bearings and their associated mechanical systems

Gas-lubricated bearings have been characterized as being less forgiving than oil-lubricated bearings This is certainly true for self-acting or hydrodynamic bearings They are less forgiving of errors in estimating loads, of deviations from specifications during manufacture and installation, and of distortions and dirt that may afflict the rotor

Compressibility Numbers

Gas is, of course, compressible and this effect must be included in the derivations for various forms of bearings whether hydrodynamic (self-acting) or hydrostatic (externally pressurized) The extent of compressibility (represented by the compressibility number, ) is determined by a dimensionless group of parameters that actually evolves from the mathematical analysis It takes on several forms depending on the geometry of the bearing

For journal bearings (Fig 1), the value of is:

(Eq 1)

where c is the machined-in radial clearance, pa is the absolute ambient pressure, is the angular velocity of the journal

(rad/s), is the absolute viscosity, and r is the radius of the shaft

Fig 1 Journal in full 360° bearing

For a tilting-pad thrust bearing (Fig 2), the value of is:

(Eq 2)

where l is the length of the pad in the direction of sliding (sometimes designated as L), and h2 is the minimum film

thickness (sometimes referred to as h0), and u is the velocity of the runner past the shoe

Fig 2 Representation of pivoted shoe

For a Rayleigh step bearing (Fig 3), the value of is:

(Eq 3)

where l is the length of the pad in the direction of sliding, U is the velocity of the runner past the pad, and h2 is the minimum film thickness

Fig 3 Effect of bearing number on isothermal load for square-step slider bearings with film thickness ratios

h1/h2 = 2 and 3 Source: Ref 4

When approaches 0, operation of the gas-lubricated bearing approaches that of the liquid-lubricated (incompressible) case As a gets larger, as with lower ambient pressure or higher speed, the compressibility effects become very significant and must be included For example, with journal bearings it can be shown that the equations for determining the load-carrying capacity for liquids and gases are essentially the same up to a value of = 1 (Fig 4) For tilting-pad bearings, the identity remain up to a value of about 15 (Fig 5)

Fig 4 Discrepancy in load capacity between results based on incompressible and compressible lubricants

Source: Ref 5

Fig 5 Effect of bearing number on isothermal and adiabatic load for plane slider bearing operating in air with

film thickness ratio h1/h2 = 2 Length-to-breadth ratio l/b = 1 Source: Ref 6

An interesting experimental demonstration is illustrated in Fig 6, which shows the relationship between load-carrying

capacity, W, and for a hydrodynamic gas-lubricated journal bearing Speed, viscosity, and eccentricity ratio were held constant while the ambient pressure was reduced, thus producing higher values of Notice that when the ambient pressure was reduced to 9% of atmospheric, the load-carrying capacity was lowered by 40%

Fig 6 Example of relationship between load-carrying capacity, W, and for self-acting gas-lubricated journal

bearing Speed, viscosity, and eccentricity ratio held constant Ambient pressure varied Source: Ref 7

Definitions of Eccentricity Ratio and Clearance Modulus

In Fig 1, O represents the center of the bearing and O' the center of the shaft The distance O-O' is also designated as a; for light loads and high operating speeds, the center of the shaft and bearing coincide, and a approaches zero The ratio of the distance a for any given operating condition to the machined-in radial clearance c of the bearing is called the

eccentricity ratio,

For heavy loads or extremes of operation, such as low speed or very low viscosity, the journal becomes more eccentric in

the bearing and the distance a increases The limit is where the journal just begins to make solid contact with the bearing,

or the distance a equals the radial clearance The eccentricity ratio is then 1 The radial clearance in the journal bearing is often designated as mr, where m is the clearance modulus of the bearing and r is the radius of the shaft or journal The value of m will usually range between 0.0005 and 0.003 mm/mm, with typical industrial-type bearings running between

0.001 and 0.0025 mm/mm

In the analysis of fluid-film bearings using incompressible lubricants, the continuity relationship was satisfied by saying that the volume of lubricant leaving the bearing was the same as the volume entering With gas, of course, the volume changes, so that continuity must be based on equality of mass Thus the mass of lubricant leaving equals the mass entering

The basic Reynolds equation then becomes (Ref 8):

(Eq 4)

where is the mass density, x is the coordinate along the film in the direction of motion, z is the coordinate along the bearing dimension perpendicular to the direction of motion (sometimes called the length of the bearing, l, or the width of the bearing, b), p is the differential pressure, and h is the local differential film thickness

Except for a few restricted solutions with no side flow in the z direction, solutions are only possible through extended

iterative computer solutions The order of magnitude of the solutions, however, can often be checked by reference to results for incompressible lubricants, especially for cases of low (Ref 9)

Tilting-Pad Bearings

Some marked differences in behavior exist between tilting-pad gas-lubricated bearings (Fig 2) and liquid-lubricated bearings The expected pressure is somewhat modified, as shown comparatively in Fig 7 The peak pressure is shifted toward the trailing edge of the shoe This means that the pivot position for a gas-lubricated bearing is not the same as for a liquid-lubricated bearing Figure 8 shows quantitative values for a tilting-pad gas-lubricated bearing for various values of (Eq 2) In this case, was reduced by lowering the ambient pressure

Fig 7 Comparative pressure distribution for compressible and incompressible lubrication Source: Ref 6

Fig 8 Gas pressure distribution in flat tilting-pad bearing Note open circles (data points) for theoretical liquid

case Source: Ref 7

Notice that for high values of , the center of pressure moves toward the trailing edge or the back of the pad For each designated operating condition, the pivot should be located at the center of pressure Thus, if the ambient pressure, the speed, or the load is subject to change, a fixed pivot position will be optimum for only one set of operating conditions This is a disadvantage

In contrast, with incompressible lubricants, the tilting pad will react to a change in load or speed so that the ratio of to-outlet film thickness remains constant, even with the minimum film thickness getting smaller with increasing load Thus, with liquid lubricants, once the pivot position is chosen, it will remain optimized for all changes of load, speed, or viscosity

inlet-With gas-lubricated tilting-pad bearings, yet another complication arises As the load increases, the minimum film thickness decreases, but since the pivot location is fixed, the pad angle of inclination begins to get smaller and eventually becomes parallel to the runner An unstable condition will result, and the bearing will be unable to support the load and will collapse completely

Collapse of the gas film will not occur for a convex curved surface on a tilting pad (Fig 9) Because of the geometry, neglecting the influence of surface roughness asperities, a wedge must always be developed no matter how thin the film

An experimental study by Brunner et al (Ref 12) shows that for a pad 19 mm ( in.) wide by about 13 mm ( in.) long

in the direction of motion, even a crown height, , of as little as 0.25 m will prevent collapse of the film and produce a load-carrying characteristic that continues to rise as the film reduces Experience has shown that crown heights for optimum load-carrying capacity are approximately equal to the minimum film thickness, or about 7.5 to 10 m

Fig 9 Nomenclature for crowned tilting-pad bearing Source: Ref 11

A thorough analysis of optimum crown heights and pivot positions can be found in Ref 4 Experimental verification of the theory has been especially good Figure 10 shows values of the dimensionless load-carrying function as a function of the compressibility number for shoes having cylindrical crowns The pivot position is not identified, but a value of about 0.6

is typical That means, in Fig 2, c is 0.6 of the length in the direction of motion and a is 0.4 of the length The pivot is

always between the midpoint and the trailing edge

Fig 10 Effect of bearing number on isothermal load for cylindrically crowned slider bearing, b/l = 1, h1/hm = 2,

and Hc/h0 = 0.1 and 0.5 Source: Ref 4

Effect of Mean Free Path

When gas films become very thin, as for example, when operating in a partial vacuum, the gas may no longer be considered as a continuous fluid, having the bulk viscosity of that fluid Effects take place that can no longer be explained

by continuous theory Slip occurs at the boundary between the bearing surface and the gas and must be introduced into the calculation

The measure of this slip condition is determined by the Knudsen number (Kn) This is the ratio of the mean free path of

the gas ( ) to the film thickness in the bearing (h) Thus, Kn = /h When Kn is less than 0.01, the gas flow can be treated

as a continuum and slip flow ignored When Kn is in the range of 0.01 to 1.5, slip flow increases and should be

considered When Kn is greater than 1.5, slip flow becomes significant and fully developed molecular flow results

Typical values of mean free path at atmospheric conditions are:

Typical mean free path value

Many tilting-pad-type thrust bearings with air lubrication are used in magnetic storage devices for computers, where they

"fly" at film thicknesses of about 0.5 m (20 in.) At these very small film thicknesses, surface roughness can become a significant factor because no surfaces are perfectly smooth This effect can be analyzed and included in predicting load-carrying capacity

Rayleigh Step Bearings

This type of bearing is shown in Fig 3 Analytical results for a square-step bearing (width equals length) are shown in

Fig 11 for lubrication with gas A dimensionless load function W' is plotted against the compressibility number

established for step bearings (see Eq 3)

Fig 11 Effect of bearing number on isothermal load for square-step slider bearings with film thickness ratios

h1/h2 = 2 and 3 Source: Ref 4

Journal Bearings

This was the geometry first used to demonstrate true load-bearing ability by Kingsbury in 1897 (Ref 13) The same concept was used by Brubach (Ref 14) in utilizing inexpensive hypodermic syringes as air bearings These are precision-made plungers in closely fitting barrels that perform remarkably well as hydrodynamic journal bearings

Brubach has used these syringes as bearings for small centrifugal blowers running at 6000 rpm (Fig 12) Perhaps his most important application has been in the measurement of gas leaks at very low pressures Figure 13 shows the apparatus used for this purpose The plunger of the syringe is caused to rotate by air impinging on the Scotch tape vanes Due to this rotation, the plunger acts as an air bearing and is separated from the barrel by a hydrodynamic air film Because the surfaces are separated from the barrel by a thin air film, the force required to move the plunger along the axis of the barrel actually approaches zero

Fig 12 Centrifugal blower using hypodermic syringe as air-lubricant bearing Source: Ref 14

Fig 13 Sensitive pressure-measuring apparatus using hypodermic syringe as air-lubricated bearing Source:

Ref 14

As an illustration of the sensitivity of this apparatus, it was connected to a tank of 100 L (26 gal) capacity Then 0.1 mL (0.06 in.3) of air was introduced into the tank Immediately the plunger moved a corresponding 0.1 mL (0.06 in.3) The theoretical pressure increase resulting from the injection of 0.1 mL (0.06 in.3) into 100 L (26 gal) is about 0.01 mm (0.0004 in.) of water, and yet the low friction of the rotating plunger permitted it to respond instantly to this exceedingly small pressure differential

Journal bearings are also influenced by compressibility of the gaseous lubricant The value of was given in Eq 1 Ford,

Harris, and Pantall (Ref 7) show experimental correlation of the load-carrying parameter W' plotted against (Fig 14) For values of greater than 1, the relationship is no longer linear The deviation from a straight line indicates the point at which the compressibility effects make their influence felt

Fig 14 Load parameter W' evaluated in terms of and Source: Ref 7

Another important variable in journal bearing analysis, especially stability analysis, is the attitude angle In Fig 1 this angle is shown as the angle, , between the line of load action, W, and the line of centers of the bearing, O-O' The

attitude angle will vary with load, speed, and other operating conditions, and also will depend on the geometrical configuration of the bearing itself In general, if the attitude angle is small, the bearing is more stable against self-excited whirl If the attitude is large, the bearing will be less stable against self-excited whirl

For load-carrying capacity, the accumulated results of Gross (Ref 4), Elrod and Malanoski (Ref 15, 16), Elrod and Burgdorfer (Ref 17), and Raimondi (Ref 18) can be used as a general design approach for complete (360°) journal bearings Figures 15, 16, and 17 show typical results from these analytical evaluations

Fig 15 Theoretical load-carrying parameter versus compressibility number for full journal bearing with l/d =

Fig 16 Theoretical load-carrying parameter versus compressibility number for full journal bearing with l/d = 1

Fig 17 Theoretical load-carrying parameter versus compressibility number for full journal bearing with l/d =

Friction in Gas-Lubricated Journal Bearings

Of interest in some design applications is the power loss in the bearing due to friction resulting from viscous drag effects

of the gas Raimondi (Ref 18) has graphs of friction factors applicable to four l/d ratios, namely , 2, 1, and for values

Fig 18 Friction factor for full bearing of infinite length Source: Ref 16

It can be seen from Fig 18 that the friction loss is quite independent of up to values of about 0.5 This means that for many bearings with low , values of friction can be reasonably estimated by using only simple Newtonian viscous shear That would be shown by:

to pass through this resonant condition when approaching bearing speed

Synchronous whirl can take the form of a translatory whirl, where the center line of the shaft describes the locus of a cylinder, or synchronous whirl can be conical The conical mode form would resemble a bow tie, where there is no displacement at the center, only at the ends of the rotor The displacement at the ends of the rotor would be out phase with each other

If the bearing housing itself is elastically supported, it may also be capable of vibrating in either translatory or conical modes of vibration These phenomena are analyzed in considerable detail in Ref 9

A generally satisfactory approach is to estimate the quasi-static stiffness of the bearing film and then, in conjunction with the mass of the rotor, evaluate the natural frequency of vibration It is a method that has proven its value over dozens of applications; Ref 9 provides examples of analyses that demonstrate the procedure

Half-Frequency Whirl

One of the most serious forms of instability encountered in journal bearing operation is known as half-frequency whirl This phenomenon is one of self-excited vibration and is characterized by having the center of the shaft orbit around the

center of the bearing (within the clearance circle) at a frequency of one-half of the spinning or rotational speed of the shaft (the speed may be little less than one-half in some applications)

Under these conditions, Hagg (Ref 19) has shown that the capacity of the bearing to support radial loads falls to zero The shaft system may be stable as the speed is increased until this threshold is reached Crossing this threshold with further increase in speed will bring the system into a region of instability Unlike an ordinary critical speed, the shaft cannot pass through this one and attain a region of stability on the other side at a higher speed as with synchronous resonant whirl

A typical instance would be a bearing running smoothly without any difficulty at 40,000 rpm, but seizing and falling completely at 43,000 rpm Failure in most instances is instantaneous and complete as the amplitude of vibration becomes equal to the radial clearance in the bearing This is especially true of rigid gas-lubricated bearings because of their inherent low damping

This type of instability is not specific to gas bearings, but is a serious and continuing problem with high-speed, lightly loaded, rigid, liquid-lubricated bearings as well (Ref 9)

The compressibility of the gas has significant impact on the threshold of instability in gas-lubricated bearings, and must of course be included in the analysis One of the more convenient procedures is due to Castelli and Elrod (Ref 20) and deals with translatory half-frequency shaft whirl in infinitely long, cylindrical bearings

Although the procedure applies particularly to bearings of infinite length, it appears to have adequate accuracy in

predicting the stability threshold for shaft in very long bearings for example, where l/d values are 2.5, 3, or greater

It also appears to be conservative for all 360° bearings of finite length, provided that the eccentricity ratio for static loads,

0, is calculated for an equivalent bearing of infinite length This can be done using Fig 15, with a unit load on the bearing (lb/in.) corresponding to that of the finite length bearing of interest

The procedure is to use Fig 19 from Ref 20, showing the relationship between *1, and for several values of 0 These curves represent the threshold of instability for the bearing of interest The value of 0 is computed on a static load basis:

(Eq 7)

where is the shaft speed (rad/s), c is the radial clearance (in.), M1 is mass per unit length (lb · s2/in.2), and w is load per

unit of length (lb/in.) Individual curves are drawn for 0, the value of eccentricity ratio for a bearing of infinite length but with the same unit loading (lb/in.) as the bearing being examined

Fig 19 Plot of half-frequency whirl threshold for infinite-length 360° journal bearing Source: Ref 20

If the intersection of *1 and falls to the left of the curve for the operating value of 0, the bearing should be stable If

it falls to the right, the bearing should be unstable

Tilting-Pad Journal Bearings

One favored bearing design to achieve rotor stability is to use tilting-pad journal bearings Considerable analytical and experimental work has been devoted to these bearings, both in the liquid- and gas-lubricated forms These bearings also offer circumferential and axial misalignment capabilities

Placing a resilient support (like a spring) under one pad of a three-pad bearing permits accommodation of centrifugal growth of the shaft at high speed or thermal or elastic dimensional changes in both shaft and bearing housing When properly designed, this bearing is very forgiving Many succesful applications have been made

When using gas as the lubricant, some designs will include an auxiliary hydrostatic lift for starting (Fig 20), which will reduce initial solid contact friction and protect the surfaces The complete design is quite complex and an area of great specialization Design guides for gas-lubricated journal and thrust bearings can be found in Ref 21, 22, 23, 24, and 25

Fig 20 Cross-sectional view of a spring-mounted pivot assembly Source: Ref 21

A few fundamental concepts are critical in the design of a tilting-pad journal bearing Of primary importance are yaw stability, pivot circle clearance, and pivot design Other design features such as film stiffness of combined bearing, minimization of bearing friction, the effect of clearance on minimum film thickness, shoe pitching frequency, and rotor critical speeds are examined in the referenced design manual (Ref 21)

Yaw Stability A pivoted shoe (or pad) has three degrees of freedom It can pitch and roll like a ship, and it can yaw To

yaw is to act like a boat rotating about a vertical axis through its center of gravity Any such rotation will lead to film rupture at the outer corners of th pad, with resulting solid contact To provide for yaw stiffness in the bearing pad, the angle of wrap of the shoes should be no less than 90° of circumferential arc With shorter arcs, the pad rapidly loses its ability to provide a resisting moment

Pivot Circle Clearance One of the crucial parameters governing the operation of the bearing is the setting of the pivot

circle clearance (C' in Fig 21) If the shaft always remained in the central concentric position, then C' could equal the actual clearance in the bearing, designated by C That is to say, the radius of curvature of the shoe equals the radius of curvature of the shaft, R, plus the clearance C The radius of curvature of the shoe is thus greater than the radius of

curvature of the shaft This produces the same phenomenon as having a crowned tilting pad The load-carrying film cannot collapse even if the film becomes very thin

Fig 21 Pivoted-pad journal bearing with three shoes Source: Ref 21

However, with the journal bearing under load, and with low speeds, the eccentricity of the shaft can become great enough

so that it moves away from the top (unloaded) tilting pad, so that the pad will lose its converging wedge and become

unstable To avoid this possibility, the shaft is preloaded by squeezing the pads radially inward, making C' less than C The measure of this is the ratio C'/C, which should be less than 1 This is a design parameter and depends on the expected

range of eccentricity ratios to be encountered

Pivot Design The third important concept is the design of the actual pivot A ball and socket joint will not be

satisfactory because of the frictional resistance to sliding As the pad assumes its equilibrium position, its righting capacity goes to zero Any residual friction in the pivot will prevent the pad from ever reaching its equilibrium design inclination Figure 22 shows a recommended configuration utilizing rolling friction rather than sliding friction Incidentally, the surfaces should be smooth and very hard to prevent fretting corrosion

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/pa 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' = Wpa 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)