Stability of Full journal Bearings The stability characteristics of a rotor carried on full journal bearings (ruptured film, Type 2BC) supported on a rigid foundation can be estimated from Figure 35. The full journal bearing (unruptured continuous film, Type 1 BC) is inherently unstable over its entire operating range. External damping in the system must be present to yield stable operation. More stable fixed-type bearing and the influence of bearing support flexibility can be found in References 32 and 33. Example:determine the oil film-rotor stability given the following for a horizontal rotor: From Figure 35: P = W/(DL) = 1/2 × 5000/(5 × 2.5) = 200 psi; S = 0.225 with S(L/ D) 2 = .0563, (C/W)K S = 10, and (C/W)Mω 2 = (0.005/2500) × 13.0 × (2 π × 90) 2 = 8.28. Since coordinate point S(L/D) 2 = 0.0563, (C/W)Mω 2 = 8.28 lies below the curve for (C/W)K S = 10, the rotor is free of oil whip instability. PIVOTED-PAD JOURNALBEARINGS Tilting-pad journal bearings consist of a number of individually pivoted pads or shoes. This pivoting capability enables relatively high loading in applications where shaft deflection or misalignment is a factor. Another advantage is their inherent stability since the load component from each pad passes through the journal center. Afurther advantage is that clearance can be closely controlled by making the pivots adjustable radially, thus enabling Volume II 443 FIGURE 34. Film damping for full journal bearing with ruptured oil film (laminar flow, Re < 1000). D = 2R = 5 in. N = 90 r/sec (5400 rpm) L = 2.5 in. K S = 5 × 10 6 lb/in. (rotor stiffness) C = 0.005 in. Rotor weight = 5000 lb (M = 5000/386 = 13.0 lb sec 2 /in.) μ = 2 × 10 −6 lb sec/in. 2 Copyright © 1983 CRC Press LLC imbalance, misalignment, etc.) and thus operate nearly concentric (⑀ o ~ 0) with the journal. This is often undesirable because of the low-radial stiffness and possible spragging. There- fore, vertical machines often resort to preloaded guide bearings. Preload is measured by preload coefficient m = (C – C′)/C which represents the fraction of the radial clearance C “used up” by moving the pad radially. Avalue of m = 1 means that the pad has been moved inward a distance C to touch the shaft (C′ = 0); m = 0 represents a pad which is radially at its machined position (C′ = C, no preload). While each pad pivot is usually displaced inward the same amount, only the top (normally unloaded) pads are sometimes preloaded to prevent spragging in horizontal machines. If the pad pivot were moved radiallyoutward,the pad will have negative preload, an undesirable situation. Fitted pads machined to the journal contour (C = 0) result in (infinite) negative preload when assembled with a bearing clearance C′. Their use is suspect. Spragging Spragging usually causes no difficulty in ordinary applications. With high speeds and low-viscosity fluids like water, liquid metals, and gases, however, an unloaded or lightly loaded pad may become tipped forward with its leading edge pulled in toward the shaft. 34 Adivergent film is momentarily created which sucks the loading edge of the pad tighter against the journal. With a very lightly loaded journal, this decrease in pressure at one pad will change the load on the other pads and cause the journal to shift its position in the bearing. This sometimes results in a persistent spragging of each pad in succession as the journal migrates through the clearance space. Spragging can be controlled by: 1. Stops or springs to prevent improper tipping of the pads. 2. Aclearance ratio which permits the pads to realign automatically (preloading). 3. Relieving the leading edge of the pads. Pad Inertia Apad supported on a rigid pivot (Figure 37) will track journal vibration by rocking (pitching) about the pivot. The influence of pad inertia on dynamic spring and damping coefficients is negligible except when approaching pad resonance when the phase angle between a zero-inertia pad and a pad with a finite inertia becomes 90°, implying that journal Volume II445 FIGURE 36.Preloading of a pad. (1) As machined and (2) preloaded; O b = bearing (pivot circle) center. O j = journal center, O p = pad center, r b = bearing (pivot circle) radius, r p = pad radius, and R = journal radius. Copyright © 1983 CRC Press LLC in Figure 37 by taking t 1 /r p = t/r p = 0. Design data accounting for pad inertia near resonance can be found in Reference 35. Excitation Frequency Unlike fixed-arc bearings, dynamic spring and damping coefficients of tilting pad journal bearings are dependent upon the frequency Ωof the excitation force. These coefficients are usually presented for the common case of unbalance excitation (Ω/ω = 1.0). Following presentation of a variety of performance data for five-pad bearings in Figures 38 to 44, the effect of excitation frequency is provided in Figures 45 to 48 for a five-pad bearing. Influence of preload on the stability of vertical (essentially unloaded) guide bearings employing four, five, six, and eight pads is given in Figures 49 to 52. Example:(horizontal rotor): find the performance of a five-pad bearing given: β = 1.05 rad (60°)W = 2500 lb D = 5 in. μ = 2 × 10 -6 lb sec/in. 2 (ISO VG 32 oil L = 2.5 in. (L/D = 0.5)at 135 F avg. temp., T S , Figure 1) C = C′ = 0.005 in. (no preload) ρ = 7.77 × 10 -5 1b sec 2 /in. 4 N = 60 r/sec = μ / ρ = 2.57 × 10 -2 in. 2 /sec Volume II 447 FIGURE 39. Total power loss (five 60° tilting pads, centrally pivoted, no preload, L/D = 0.5). Copyright © 1983 CRC Press LLC Calculating the Reynolds and bearing characteristic numbers: Minimumfilmthickness— Because Re is below 1000, flow is laminar and Re = 1.0, curve in Figure 38 gives: h n /C = 0.26 h n = 0.26 × 0.005 = 0.0013 in. Powerloss— From Figure 39, H/(2πWNC) = 3.9 from which H = 1.84 × 10 4 lb- in./sec (2.78 hp). Normalizedbearingeccentricityratio— Entering Figure 40 with h n /C = 0.26 gives ⑀′ o = ⑀ o /1.2361 = 0.67. This value will be used to enter the charts to obtain the dynamic stiffness and damping coefficients. As a matter of interest, the journal displacement (ec- centricity) is e o = ⑀ o C′ = 0.67 × 1.2361 × 0.005 = 0.0041 in. Dynamicperformance— (Ω/ω = 1,unbalance excitation). Entering Figures 41 to 43 with ⑀′ o = 0.67 gives (C/W)K xx = 4.9 from which K xx = 4.9(W/C) = 4.9(2500/0.005) = 2.5 × 10 6 lb/in. 448CRC Handbook of Lubrication FIGURE 40. Normalized bearing eccentricity ratio (five 60° tilting pads, centrally pivoted, no preload, L/D = 0.5). Copyright © 1983 CRC Press LLC If the excitation frequency ratio were different from Ω/ω = 1.0, say 2.0, the stiffness and damping coefficients could be obtained directly by entering Figures 45 to 48 with ⑀ o ′ = 0.67, as in the above example, and Ω/ω = 2.0. Figures 45 to 48, although valid only for laminar flow, can also be used for turbulent flow (Re у1000) to approximate the stiffness and damping coefficients since they are not strongly dependent on Reynolds number. To do this, ⑀ o ′should first be obtained as shown in the above example through Figures 38 and 40 using the appropriate curve for the actual value of Re. Criticalmass— From Figure 44, the critical pad mass parameter is 450CRC Handbook of Lubrication FIGURE 42.Bearing horizontal stiffness (five 60° tilting pads, centrally pivoted, no preload, (Ω/ω = 1.0, no pad inertia, L/D = 0.5). Copyright © 1983 CRC Press LLC NOMENCLATURE B = Slider bearing width (in direction of motion), in. B, B xx , B xy , B yx , B yy = Lubricant film damping coefficient, lb-sec/in. B′ = r p β, Pad arc length (tilting pad journal bearing), in. C = r p – R = Pad or partial arc radial clearance, in. C′ = r b – R = Tilting pad journal bearing (pivot cir- cle) radial clearance, in. C W, L C H,L ;C Qin,L ; C Qs,L ; C ho,L = Laminar flow performance factors for load, power loss, inlet flow, side flow, and minimum film thickness, respectively, dimensionless C W, T ; C H,T ;C Qin,T ; C Qs,T ; C ho,T = Turbulent flow correction factors for load, power loss, inlet flow, side flow, and minimum film thickness, respectively, dimensionless D = 2R = Journal diameter, in. 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). Copyright © 1983 CRC Press LLC D xx , D xy , D yx , D yy = Lubricant film acceleration coefficients, lb-sec 2 /in. F = Friction force or excitation force, lb F = Thermohydrodynamic (THD) turbulence function, dimensionless F x , F y = Dynamic lubricant film force components, lb H = Power loss, lb-in./sec I p = Mass moment of inertia of pad around axial axis (Figure 37), lb-in sec 2 K, K xx , K xy , K yx , K yy = Lubricant film stiffness coefficient, lb/in. K s = Rotor stiffness (Figure 35), lb/in. L = Length (perpendicular to motion), in. M = I p /r 2 p = Equivalent pad mass, lb-sec 2 /in. M crit = Value of M giving resonance, lb-sec 2 /in. NSpeed, rev/sec P = Unit load, W/DL(journal bearing), = W/BL(sli- der bearing), lb/in. 2 Pe = Peclet number =ρcωC 2 /k, dimensionless Volume II 455 FIGURE 47. Effect of excitation frequency on bearing vertical damping (five 60° tilting pads, centrally pivoted, no preload, no pad inertia, laminar flow). Copyright © 1983 CRC Press LLC h e = Film thickness at geometric center of sector pad, in. h p = Film thickness at pivot location, in. h o = Minimum film thickness (crowned pad), in. h min = Minimum film thickness (sector pad), in. h 2 = Outlet film thickness (crowned pad), minimum film thickness (slider bearing, Figure 8), in. h n = Minimum film thickness (journal bearing), in. k,k b = Heat conductivity of oil, bearing, lb/sec °F k x ,k z = Turbulence functions, dimensionless m = Mass, lb-sec 2 /in. m = (C – C′)/C = Preload coefficient, dimensionless m r = Radial slope parameter = R 1 γ/h c , dimensionless m θ = Tangential slope parameter = R 1 γ θ /h c , dimensionless n = Number of pads, dimensionless p = Lubricant film pressure, lb/in. 2 p cav , p atm = Cavitation, atmospheric pressure, lb/in. 2 458CRC 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). Copyright © 1983 CRC Press LLC p _ = Mean (turbulent) pressure, lb/in. 2 r b = Tilting pad journal bearing (pivot circle) radius, in. r p = Pad or partial arc radius, in. t = Time, sec t _ = Dimensionless time = tω t′ = Fluctuating component of T,°F x _ ,y,z = Rectangular Cartesian coordinates, in. x = Pivot or center-of-pressure location, measured from leading edge, in. Ω = Excitation speed, rad/sec Λ = Dissipation number = μω(R/C) 2 /ρcT, dimensionless α = Diffusitivity = k/ρc, in. 2 /sec β = Angular extent of pad, sector, or partial-arc, rad ⑀ = e/c = Pad, or partial-arc eccentricity ratio, dimensionless Volume II 459 FIGURE 51. Effect of preload on six-pad bearing (vertical rotor with slight radial load giving ⑀ o = 0.01, laminar flow, no pad inertia). Copyright © 1983 CRC Press LLC [...]... of the surfaces; and the removal of fused metal particles cause the surfaces to be rough The rough surfaces produce further wear by mechanical abrasion An additional consequence of sparking is deterioration of the lubricant and possible contamination of the lubricant and the lubricating system by spark debris In extreme cases, the passage of current can cause an increase in the temperature of the parts... removal of material from the bearing and/or the journal surfaces Mechanical, electrical, or thermal phenomena, or combinations of these phenomena can cause wear Mechanical Wear Mechanical wear results from the abrasive action of debris which enters the bearing with the lubricant This debris often results from the processes used in the manufacture of the Copyright © 1983 CRC Press LLC 480 CRC Handbook of Lubrication. .. 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,... 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 Copyright © 1983 CRC Press LLC 462 CRC Handbook of Lubrication 34 Boyd, J and Raimondi,... additional layer is added, most often composed of a thin electroplated surface of lead and tin or lead, tin, and copper This thin layer can substantially increase the score resistance, embedability, and conformability of the basic bi-metal construction Addition of copper reportedly increases strength of the overplate and reduces the wear rate Many overplates use a nickel barrier layer of approximately 1-µm thickness... lead babbitts were at least equivalent of tin in thin linings, but in thicker linings the tin may be superior Additions of tin and antimony have been found generally to correct the inadequate corrosion resistance with some of the wartime lead babbitts Today, most high-performance bearings use some type of plated lead babbitt of nominally 10% tin, with about 3% copper often used to confer additional hardness... 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... 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... 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,... are often used both dry and lubricated in applications where speeds, loads, and temperatures are low They are inexpensive and generally compatible with steel surfaces The least expensive bushing for minor bearing requirements is molded of nylon or polyacetal While these materials can operate without lubricant, their durability is much increased with some type of lubrication Service applications of plastic . 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. R 1 γ θ /h c , dimensionless n = Number of pads, dimensionless p = Lubricant film pressure, lb/in. 2 p cav , p atm = Cavitation, atmospheric pressure, lb/in. 2 458CRC Handbook of Lubrication FIGURE 50. Effect of preload. film thickness, respectively, dimensionless D = 2R = Journal diameter, in. 454 CRC Handbook of Lubrication FIGURE 46. Effect of excitation frequency on bearing horizontal stiffness (five 60° tilting pads,