Effect of excitation frequency on bearing vertical stiffness five 60° tilting pads, centrally pivoted, no preload, no pad inertia, laminar flow... Effect of excitation frequency on beari
Trang 2K = 9.5 × 1.01 × 105= 9.6 × 105lb/in stiffness
B = 11.3 × 1.01 × 105/(2π × 30) = 6.05 × 103lb sec/in damping These are the dynamic stiffness and damping coefficients for calculating rotor response to
an unbalance excitation
A load W = ξC/14.6 = 104 lb is required to produce a very small static displacement
(eo = oC′ = 0.01 × 0.0075 = 75 × 10–6 in.) The likelihood of pad resonance can be calculated from the critical pad mass Mcrit = 1.12 lb sec2/in as shown in the previous example The power loss is found to be H = 1.45 × 105lb in./sec (21.4 hp)
FIGURE 45 Effect of excitation frequency on bearing vertical stiffness (five 60° tilting pads, centrally pivoted,
no preload, no pad inertia, laminar flow).
Trang 3B = Slider bearing width (in direction of motion), in
B, Bxx, Bxy, Byx, Byy = Lubricant film damping coefficient, lb-sec/in B′ = rpβ, Pad arc length (tilting pad journal bearing),
in
C = rp– R = Pad or partial arc radial clearance, in C′ = rb– R = Tilting pad journal bearing (pivot
cir-cle) radial clearance, in
CW,LCH,L;CQin,L; CQs,L; Cho,L = Laminar flow performance factors for load, power
loss, inlet flow, side flow, and minimum film thickness, respectively, dimensionless
CW,T; CH,T;CQin,T; CQs,T; Cho,T = Turbulent flow correction factors for load, power
loss, inlet flow, side flow, and minimum film thickness, respectively, dimensionless
454 CRC Handbook of Lubrication
FIGURE 46 Effect of excitation frequency on bearing horizontal stiffness (five 60° tilting pads, centrally pivoted,
no preload, no pad inertia, laminar flow).
Trang 4Dxx, Dxy, Dyx, Dyy = Lubricant film acceleration coefficients, lb-sec2/in.
F = Friction force or excitation force, lb
F = Thermohydrodynamic (THD) turbulence function,
dimensionless
Fx, Fy = Dynamic lubricant film force components, lb
H = Power loss, lb-in./sec
(Figure 37), lb-in.-sec2
K, Kxx, Kxy, Kyx, Kyy = Lubricant film stiffness coefficient, lb/in
L = Length (perpendicular to motion), in
p= Equivalent pad mass, lb-sec2/in
Mcrit = Value of M giving resonance, lb-sec2/in
P = Unit load, W/DL (journal bearing), = W/BL
(sli-der bearing), lb/in.2
FIGURE 47 Effect of excitation frequency on bearing vertical damping (five 60° tilting pads, centrally pivoted,
no preload, no pad inertia, laminar flow).
Trang 5Pr = Prandtl number = v/α, dimensionless
Q, Qin = Flow rate into bearing, in.3/sec
Qs, Qs1,Qs2, = Side flow flow, in.3/sec
R1,R2, = Sector pad inner radius, outer radius, in
Rp = Pivot or center-of-pressure radial location, in
Rep = Slider bearing Reynolds number = Uhp/v,
dimensionless
S = Bearing characteristic number = (R/C)2(μN/P),
dimensionless
T
_
= Mean (turbulent) value of T,°F
Ti,To,Ts = Temperature at inlet, outlet, side, °F
456 CRC Handbook of Lubrication
FIGURE 48 Effect of excitation frequency on bearing horizontal damping (five 60° tilting pads, centrally pivoted, no preload, no pad inertia, laminar flow).
Trang 6ΔT = Temperature rise, °F
Ta = Taylor number = (C/R) (RωC/v2), dimensionless U,Ua = Linear velocity, average value, in./sec
U1,U2 = Tangential velocities, in./sec
cf = Coefficient of wall stress = 8τw/ρU22,
dimensionless
e = Eccentricity or displacement of journal with
re-spect to pad or partial arc, in
e° = Eccentricity (displacement) of journal with respect
to bearing (ObOj), in
h
_
= Dimensionless film thickness = h/C FIGURE 49 Effect of preload on four-pad bearing (vertical rotor with slight radial load giving εo = 0.01, laminar flow, no pad inertia).
Trang 7he = Film thickness at geometric center of sector pad,
in
hmin = Minimum film thickness (sector pad), in
film thickness (slider bearing, Figure 8), in
hn = Minimum film thickness (journal bearing), in k,kb = Heat conductivity of oil, bearing, lb/sec °F
kx,kz = Turbulence functions, dimensionless
m = (C – C′)/C = Preload coefficient, dimensionless
mr = Radial slope parameter = R1γ/hc, dimensionless
mθ = Tangential slope parameter = R1γθ/hc,
dimensionless
n = Number of pads, dimensionless
pcav, patm = Cavitation, atmospheric pressure, lb/in.2
458 CRC Handbook of Lubrication
FIGURE 50 Effect of preload on five-pad bearing (vertical rotor with slight radial load giving o , = 0.01 laminar flow, no pad inertia).
Trang 8_
= Mean (turbulent) pressure, lb/in.2
rb = Tilting pad journal bearing (pivot circle) radius,
in
t
_
= Dimensionless time = tω
x
_
from leading edge, in
dimensionless
β = Angular extent of pad, sector, or partial-arc, rad
= e/c = Pad, or partial-arc eccentricity ratio,
dimensionless
FIGURE 51. Effect of preload on six-pad bearing (vertical rotor with slight radial load giving o = 0.01, laminar flow, no pad inertia).
Trang 9°max = °max/C′ = 1.2361 (For five-pad bearing, Figure
40), dimensionless
°′ = eo/e°max = °/°max = °/1.2361 = Normalized
bearing eccentricity ratio (for five-pad tilting pad journal bearing only), dimensionless
φ = Attitude angle, deg
θp = Pivot or center-of-pressure location, measured
from trailing edge, rad
δ = Crown, in
γr,γθ = Radial, tangential slope of pad, rad
ω = 2πN = Rotation speed, rad/séc
460 CRC Handbook of Lubrication
FIGURE 52 Effect of preload on eight-pad bearing (vertical rotor with slight radial load giving o , = 0.01, laminar flow, no pad inertia).
Trang 101 Kaufman, H N., Szeri, A Z., and Raimondi, A A., Performance of a centrifugal disk-lubricated
bearing, Trans ASLE, 21, 315, 1978.
2 Szeri, A Z., Ed., Tribology: Friction, Lubrication and Wear, Hemisphere Publishing, Washington, D.C.,
1980.
3 Taylor, G I., Stability of a viscous liquid contained between two rotating cylinders, Phil Trans R Soc,
Ser, A, 223, 289, 1923.
4 Coles, D., Transition in circular couette flow, J Fluid Mech., 21, 385, 1965.
5 DiPrima, R C., A note on the stability of flow in loaded journal bearings, Trans ASLE, 6, 249, 1963.
6 Li, C H., The effect of thermal diffusion on flow stability between two rotating cylinders, Trans ASME
Ser F, 99, 318, 1977.
7 Li, C H., The influence of variable density and viscosity on flow transition between two concentric rotating
cylinders, Trans ASME Ser F, 100, 260, 1978.
8 Gardner, W W and Ulschmid, J G., Turbulence effects in two journal bearing applications, Trans.
ASME Ser F, 96, 15, 1974.
9 Abramovitz, S., Turbulence in a tilting-pad thrust bearing, Trans ASME, 78, 7, 1956.
10 Gregory, R S., Performance of thrust bearings at high operating speeds, Trans ASME Ser F, 96, 7,
1974.
11 Ng, C W and Pan, C H T., A linearized turbulent lubrication theory, Trans ASME Ser, D, 87, 675,
1965.
12 Suganami, T and Szeri, A Z., A thermohydrodynatnic analysis of journal bearings, Trans ASME Ser.
F, 101, 21, 1979.
13 Suganami, T and Szeri, A Z., A parametric study of journal bearing performance: the 80 degree partial
arc bearing, Trans ASME Ser F, 486, 1979.
14 Constantinescu, V N., On the influence of inertia forces in turbulent and laminar self-acting films, Trans.
ASME Ser F, 92, 473, 1970.
15 Szeri, A Z., Raimondi, A A., and Giron, A., Linear force coefficients for squeeze-film damper, Trans.
ASME Ser F, in press.
16 Alford, J S., Protecting turbomachinery from self-excited rotor whirl, ASME J Eng Power Ser A, 87,
333, 1965.
17 Hagg, A C., Influence of oil-film journal bearings on the stability of rotating machines, J Appl Mech.,
Trans ASME, 68, A211, 1946.
18 DenHartog, J P., Mechanical Vibrations, 4th ed., McGraw-Hill, New York, 1956.
19 Raimondi, A A and Boyd, J., Applying bearing theory to the analysis and design of pad-type bearings,
Trans ASME, 77, 287, 1955.
20 Johnston, R C R and Kettleborough, C.F., An experimental investigation into stepped thrust bearings,
Proc Inst, Mech Eng., 170, 511, 1956.
21 Wilcock, D F., The hydrodynamic pocket bearing, Trans ASME, 77, 311, 1955.
22 Raimondi, A A., Adiabatic solution for the finite slider bearing, ASLE Trans., 9, 283, 1966.
23 Gross, W A., Matsch, L A., Castelli, V., Eshel, A., Vohr, J H., and Wildmann, M., Fluid Film
Lubrication, John Wiley & Sons, New York, 1980.
24 Baudry, R A., Kuhn E C., and Wise, W W., Influence of load and thermal distortion on the design
of large thrust bearings, Trans ASME, 80, 807, 1958.
25 Raimondi, A A., The influence of longitudinal and transverse profile on the load capacity of pivoted pad
bearings, ASLE Trans., 3, 265, 1960.
26 Malinowski, S B., Rerate tilting-pad thrust bearings, Mach Design, 45, 100, 1973.
27 Vohr, J H., Prediction of the operating temperature of thrust bearings, Trans ASME J Lubr TechnoL.,
103, 97, 1981.
28 Wilcock, D F and Booser, E R., Bearing Design and Application, McGraw-Hill, New York, 1957.
29 Raimondi, A A., A theoretical study of the effect of offset loads on the performance of a 120° partial
journal bearing, ASLE Trans., 2, 147, 1959.
30 Raimondi, A A., Boyd, J., and Kaufman, H N., Analysis and design of sliding bearings, in Standard
Handbook of Lubrication Engineering, McGraw-Hill, New York, 1968, chap 5.
31 DuBois, G B and Ocvirk, F W., Analytical Derivation and Experimental Evaluation of Short-Bearing
Approximation for Full Journal Bearings, NASA TR1157 and TN2808, National Aeronautics and Space Administration, Washington, D.C., 1952.
32 Allaire, P E., Design of journal bearings for high speed rotating machinery, in Fundamentals of the Design
of Fluid Film Bearings, American Society of Mechanical Engineers, New York, 1979, 45.
33 Warner, R E and Soler, A I., Stability of rotor-bearing systems with generalized support flexibility
and damping and aerodynamic cross-coupling, ASME J Lubr Technol., 7F, 461, 1975.
Trang 1134 Boyd, J and Raimondi, A A., Clearance considerations in pivoted pad journal bearings, ASLE Trans.,
5, 418, 1962.
35 Lund, J W., Spring and damping coefficients for the tilting-pad journal bearing ASLE Trans., 7, 342,
1964.
462 CRC Handbook of Lubrication
Trang 12SLIDING BEARING MATERIALS
A O DeHart
BEARING MATERIAL PROPERTIES
Selection of materials for sliding surface bearings is a multifunctional optimizational problem: no one material is best for all applications Commonly considered material prop-erties include score resistance, conformability, embedability, compressive strength, fatigue, corrosion, thermal properties, wear resistance, and cost Unfortunately, a selection based upon the best value for one of these properties may be improper when all factors are considered
In spite of the difficulty, bearing materials are selected for many different applications every day If we consider each of the required properties separately, a rational basis should develop to aid in making the best compromise in finding the right material for the job at hand.1-3
Score Resistance
Score resistance, also termed antiweld and antigalling, is the vital ability of the bearing material to resist welding to the journal under what can be highly distressful conditions Many engineering tests have been run to assess the ability of bearing materials to resist welding to the steel or cast iron commonly employed for journals Roach et al.4 showed that the only elemental metals that have satisfactory score resistance against steel are in the
B subgroup of the periodic table and are either insoluble with iron or form weak intermetallic compounds Relative score resistance for various elements is given in Table 1 Although bearing alloys and mixtures are much more complicated, the performance of elements can
be used as a guideline For example, adding more of a good material (e.g., lead) to a bronze will generally improve score resistance, while the addition of a poor metal (e.g., zinc) will degrade the score resistance
Strength
Several bearing properties have a relationship to material strength — compressive strength, fatigue strength, embedability, and conformability Compressive strength, a basic require-ment for support of the applied load without cracking or extruding, is closely related to normally reported physical properties But the effect of temperature should be reecognized when choosing a particular babbitt (Figure 1) Ultimate strength for typical babbitt com-positions is given in Figure 2
One method of improving the effective compressive strength of weaker materials is by using a thin layer on a strong substrate such as steel Providing the bond is adequate, a thin layer of soft bearing material tends to adopt the stiffness and strength of the substrate
Fatigue Strength
Fatigue strength is important in bearings subjected to load reversals such as are encountered with connecting rod and main engine bearings Not only is the fatigue problem due to the dynamic nature of the load, but also to the attendant flexing of the support structure While fatigue strength varies with temperature and application Table 2 gives an approximate guide for various materials It is clear that fatigue ratings are opposite of conformability ratings Fatigue strength is enhanced by bonding a thin layer of bearing material to a steel back to form the bimetal bearing, particularly when the bearing material thickness is less than 0.1
mm (Figure 3)
Copyright © 1983 CRC Press LLC
Trang 13Matching thermal expansion of the bearing to that of the journal is important to maintain
the correct clearance This clearance is readily controlled with bimetal or trimetal bearings with steel back construction But solid wall bearings, where one material is used for the entire bearing, can cause problems Poor heat transfer and high expansion rates are major concerns that have prevented the adoption of plastic bearings in high-speed applications Even solid bronze bearings must be used carefully to prevent loss of clearance or retention Such bearings must be mechanically located in their housings, because press fits cannot be relied upon for retention As noted previously, material strength, and therefore load capacity, generally decrease with increasing temperature
Wear
Bearing wear is many faceted It can take the form of adhesion, abrasion, corrosion, and fatigue as well as any combination of these Adhesive wear is associated with score resistance
If the bearing material welds to the journal surface, the material with the weaker bond is torn away and wear results Abrasive wear is a more mechanical process where the harder material abrades or machines a softer material Corrosive wear is related, of course, to the corrosion resistance Shearing of oil and journal sliding action tend to remove any passivating films that may form on the bearing surface, so that materials deficient in corrosion resistance can suffer very rapid wear in corrosive environments Fatigue wear of bearings can occur
in the large scale already described or on a micro basis at small surface peaks or stress sites Score resistance, conformability, compressive strength, fatigue, corrosion, thermal prop-erties, wear resistance, and cost: in general, these performance requirements cannot be met with a single material A modern-day, high-performance automotive bearing might have several layers of mixtures and alloys — each engineered to meet a particular set of per-formance parameters
METALLIC BEARING MATERIALS
Basically, modern materials fall into five classes: babbitts, copper-based bearings, alu-minum-based bearings, silver bearings, and porous metal bearings Representative properties
of the various classes are given in Table 3.2
Babbitt
Babbitt, named after Issac Babbitt who obtained the first American patent on a special bearing material in 1839, is used today to describe a number of soft lead- and tin-based bearing materials bonded to a harder and stronger shell While bronzes have been widely used for the backing material, current practice commonly makes use of steel Where babbitts have sufficient strength, they are good materials for most applications They have superior embedability and conformability and excellent antiscore qualities Unfortunately, their strength
is limited by temperature
Effective strength of babbitts can be improved by reducing thickness The highest strength babbitts are obtained by electrodeposition of lead and tin or lead, tin, and copper onto a bearing substrate On the other hand, in large electrical machinery or in some marine applications, babbitts as heavy as 10-mm thick are cast onto steel or cast iron supporting structures and are often mechanically keyed into place Typically, these bearing systems are designed for very low unit loads (on the order of 1.4 mPa) with life expectancies of over
20 years Table 4 gives nominal compositions for tin- and lead-based babbitts
Tin Babbitt
Tin-base babbitts are the material of choice for corrosive conditions where the increased cost can be justified Tin-base babbitts are composed of up to 90% tin with copper and
463-476 4/6/06 7:17 PM Page 467
Copyright © 1983 CRC Press LLC