Handbook of Lubrication Episode 2 Part 5 ppt

Hence K = 9.5 × 1.01 × 10 5 = 9.6 × 10 5 lb/in. stiffness B = 11.3 × 1.01 × 10 5 /(2π × 30) = 6.05 × 10 3 lb 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 (e o = ⑀ o C′ = 0.01 × 0.0075 = 75 × 10 –6 in.). The likelihood of pad resonance can be calculated from the critical pad mass M crit = 1.12 lb sec 2 /in. as shown in the previous example. The power loss is found to be H = 1.45 × 10 5 lb in./sec (21.4 hp). Volume II 453 FIGURE 45. Effect of excitation frequency on bearing vertical stiffness (five 60° tilting pads, centrally pivoted, no preload, no pad inertia, laminar flow). 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 Pr = Prandtl number = v/α, dimensionless Q, Q in = Flow rate into bearing, in. 3 /sec Q s , Q s1 ,Q s2 , = Side flow flow, in. 3 /sec R = Journal radius, in. R 1 ,R 2 , = Sector pad inner radius, outer radius, in. R mean = (R 1 + R 2 )/2, in. R p = Pivot or center-of-pressure radial location, in. R e = Global Reynolds number = RωC/v, dimensionless R h = Local Reynolds number = Rωh/v, dimensionless Re p = Slider bearing Reynolds number = Uh p /v, dimensionless S = Bearing characteristic number = (R/C) 2 (μN/P), dimensionless T = Temperature, °F T _ = Mean (turbulent) value of T,°F T i ,T o ,T s = Temperature at inlet, outlet, side, °F T max = Maximum bearing temperature, °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). Copyright © 1983 CRC Press LLC ΔT = Temperature rise, °F Ta = Taylor number = (C/R) (RωC/v 2 ), dimensionless U,U a = Linear velocity, average value, in./sec U 1 ,U 2 = Tangential velocities, in./sec V o = Normal velocity, in./sec W = Load, lb c f = Coefficient of wall stress = 8τ w /ρU 2 2 , dimensionless c = Specific heat, in. 2 /sec 2 °F e = Eccentricity or displacement of journal with re- spect to pad or partial arc, in. e ° = Eccentricity (displacement) of journal with respect to bearing (O b O j ), in. e ° max = Maximum possible eccentricity, in. f = Coefficient of friction = F/W, dimensionless h,h a = Film thickness, average value, in. h _ = Dimensionless film thickness = h/C Volume II 457 FIGURE 49. Effect of preload on four-pad bearing (vertical rotor with slight radial load giving ε o = 0.01, laminar flow, no pad inertia). 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 ⑀ ° max = ⑀ ° max /C′ = 1.2361 (For five-pad bearing, Figure 40), dimensionless ⑀ ° ′ = e o /e ° max = ⑀ ° /⑀ ° max = ⑀ ° /1.2361 = Normalized bearing eccentricity ratio (for five-pad tilting pad journal bearing only), dimensionless φ = Attitude angle, deg µ = Absolute viscosity, lb-sec/in. 2 ␯ = Kinematic viscosity, in. 2 /sec ρ = Density, lb-sec 2 /in. 4 τ w = Wall stress, lb/in. 2 θ p = Pivot or center-of-pressure location, measured from trailing edge, rad δ = Crown, in. γ r ,γ θ = Radial, tangential slope of pad, rad ω = 2πN = Rotation speed, rad/séc ξ = 2(R/C) 3 μNL, lb/in. ( ) i = Quantity evaluated at inlet 460CRC 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). Copyright © 1983 CRC Press LLC REFERENCES 1. 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. Volume II 461 Copyright © 1983 CRC Press LLC [...]... elemental metals on high-speed sliding contact with steel, Trans ASME, 78, 1 659 , 1 956 5 Crankshaw, E., Mechanical features of sfeel backed bearings, in Sleeve Bearing Materials, American Society for Metals, Metals Park, Ohio, 1949, 150 6 Roach, A E., and Goodzeit, C L., Why bearings seize, Gen Motors Eng J., 2( 5) , 25 , 1 955 Copyright © 1983 CRC Press LLC ... percentages of lead than the leaded bronzes, these have the best score resistance and embedability of the copper-based bearing materials Lead content of this group may go as high as 51 % (SAE 4 85) Copper-lead alloys SAE 48, 49, 480, and 481 have minimum amounts of tin and arc somewhat subject to oil corrosion SAE 4 82, 484, and 4 85 have 3 to 5% tin The steel-backed, copper-lead bearing was developed about 1 923 ... Europe for highly loaded diesel bearings Copyright © 1983 CRC Press LLC 463-476 4/6/06 7:17 PM 4 72 Page 4 72 CRC Handbook of Lubrication Special techniques were found to increase the tin content of tin aluminum A 20 % tinaluminum material was developed in Great Britain in 1 958 The composition is nominally 20 % tin and 1% copper, with special cold-working and heat-treating to provide a reticular tin-aluminum... Page 476 CRC Handbook of Lubrication REFERENCES 1 Anon., Sliding-Bearing Materials, Mach.Design, 53 (14) 148, 1981 2 Booser, E R., Bearing materials, in Encyclopedia of Chemical Technology, Vol 3, 3rd ed., John Wiley & Sons, New York, 1978, 670 3 Pratt, G C., Materials for plain bearings Int Metall Rev., 18, 62, 1973 4 Roach, A E., Goodzeit, C L., and Hunnicutt, R P., Scoring characteristics of thirty-eight...4 62 CRC Handbook of Lubrication 34 Boyd, J and Raimondi, A A., Clearance considerations in pivoted pad journal bearings, ASLE Trans., 5, 418, 19 62 35 Lund, J W., Spring and damping coefficients for the tilting-pad journal bearing ASLE Trans., 7, 3 42, 1964 Copyright © 1983 CRC Press LLC 463-476 4/6/06 7:17 PM Page 463 Volume... 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... basic requirement 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 compositions is given in Figure 2 One method of improving the effective compressive strength of weaker materials is by using... 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... babbitt that was mixed into the aluminum bearing materials by a novel casting process to develop a lead gradient across the thickness of the aluminum alloy The nominal composition of the bearing material of the surface was 10% lead, 11 /2% tin, 2% silicon, 1% cadmium, 1% copper, 1 /2% magnesium, with the balance aluminum This alloy, bonded to a steel back, was developed to fill the gap between the babbitts... 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 . McGraw-Hill, New York, 1 957 . 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, 1 959 . 30. Raimondi, A for Metals, Metals Park, Ohio, 1949, 150 . 6. Roach, A. E., and Goodzeit, C. L., Why bearings seize, Gen. Motors Eng. J., 2( 5) , 25 , 1 955 . 476 CRC Handbook of Lubrication 463-476 4/6/06 7:17 PM Page. Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. R. Soc, Ser, A, 22 3, 28 9, 1 923 . 4. Coles, D., Transition in circular couette flow, J. Fluid Mech., 21 , 3 85, 19 65. 5.