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## Hydrostatic Bearing Systems

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**Hydrostatic Bearing Systems**Figure 13.1 Formation of fluid in hydrostatic bearing system. (a) Pump off; (b) pressure build up; (c) pressure times recess area equals normal applied load; (d) bearing operating; (e) increased load; (f) decreased load. [From Rippel (1963)].**Circular Step Pad & Pressure**Figure 13.2 Radial-flow hydrostatic thrust bearing with circular step pad. Figure 13.3 Pressure distribution in radial-flow hydrostatic thrust bearing.**Pad Coefficients**Load coefficient: Flow coefficient: Power coefficient: Figure 13.4 Chart for determining bearing pad coefficients for circular step thrust bearing. [From Rippel (1963)].**Annular Thrust Pad Bearing**Figure 13.5 Configurations of annular thrust pad bearing. [From Rippel (1963)].**Pad Coefficients**Load coefficient: Flow coefficient: Power coefficient: Figure 13.6 Chart for determining bearing pad coefficients for annular thrust pad bearings. [From Rippel (1963)].**Rectangular Hydrostatic Pad**Figure 13.7 Rectangular hydrostatic pad.**Pad Coefficients**Load coefficient: Flow coefficient: Power coefficient: Figure 13.8 Pad coefficients. (a) Square pad; (b) rectangular pad with B= 2L and b = l.**Compensated Hydrostatic Bearings**Figure 13.9 Capillary-compensated hydrostatic bearing. [From Rippel (1963)]. Figure 13.10 Orifice-compensated hydrostatic bearing. [From Rippel (1963)].**Flow-Valve Compensation**Figure 13.10 Constant-flow-valve compensation in hydrostatic bearing. [From Rippel (1963)].**Speed vs. Load**Figure 14.1 Effect of speed on load for self-acting, gas-lubricated bearings. [From Ausman (1961).]**Rectangular-Step Thrust Bearing**Figure 14.3 Transformation of rectangular slider bearing into circular sector bearing. Figure 14.2 Rectangular-step thrust bearing. [From Hamrock (1972).]**Optimum Step Parameters**Figure 14.4 Effect of dimensionless bearing number on optimum step parameters. (a) For maximum dimensionless load-carrying capacity; (b) for maximum dimensionless stiffness. [From Hamrock (1972).]**Load-Carrying Capacity & Stiffness**Figure 14.5 Effect of dimensionless bearing number on dimensionless load-carrying capacity and dimensionless stiffness. (a) For maximum dimensionless load-carrying capacity; (b) for maximum dimensionless stiffness. [From Hamrock (1972).]**Spiral-Groove Thrust Bearing**Figure 14.6 Spiral-groove thrust bearing. [From Malanoski and Pan (1965).]**Spiral-Groove Thrust Bearing Characteristics**Figure 14.7 Charts for determining characteristics of spiral-groove thrust bearings. (a) Groove factor; (b) load; (c) stiffness; (d) torque; (e) flow; (f) optimal groove geometry; (g) groove length factor. [From Reiger (1967).]**Pressure Perturbation Solution**Figure 15.1 Design chart for radially loaded, self-acting, gas-lubricated journal bearings (isothermal first-order perturbation solution.) [From Ausman (1959).]**Pivoted-Pad Bearings**Figure 15.3 Geometry of individual pivoted-pad bearing. [From Gunter et al. (1964)] Figure 15.4 Geometry of pivoted-pad journal bearing with three pads. [From Gunter et al. (1964)]**Herringbone-Groove Journal Bearing**Figure 15.6 Configuration of concentric herringbone-groove journal bearing.**Parameters for Herringbone Bearing**Figure 15.7 Charts for determining optimal herringbone-journal-bearing groove parameters for maximum radial load. Top plots are for grooved member rotating; bottom plots are for smooth member rotating. (a) Optimal film thickness ratio; (b) optimal groove width ratio. [From Hamrock and Fleming (1971)]**Parameters for Herringbone Bearing (cont.)**Figure 15.7 Concluded. (c) Optimal groove length ratio; (d) optimal groove angle.**Load-Carrying Capacity**Figure 15.8 Chart for determining maximum normal load-carrying capacity. (a) grooved member rotating; (b) smooth member rotating. [From Hamrock and Fleming (1971)]**Stability of Herringbone-Groove Bearings**Figure 15.9 Chart for determining maximum stability of herringbone-groove bearings. [From Fleming and Hamrock (1974).]**Foil Bearing**Figure 15.10 (a) Schematic illustration of a foil bearing; (b) free-body diagram of a section of foil.**Pressure in Foil Bearing**Figure 15.11 Pressure distribution and film thickness in a foil bearing. [From Bhushan (2002).]**Lubrication of Rigid Cylinder**Figure 16.1 Lubrication of a rigid cylinder near a plane. (a) Coordinates and surface velocities; (b) forces.**Cavitation Fingers**Figure 16.2 Cavitation fingers.**Effect of Leakage**Figure 16.3 Side-leakage effect on normal load component. Figure 16.4 Effect of leakage on tangential load component.**Contact Geometry**Figure 16.5 Contact geometry. (a) Two rigid solids separated by a lubricant film: (a-1) y=0 plane; (a-2) x=0 plane. (b) Equivalent system of a rigid solid near a plane separated by a lubricant film: (b-1) y=0 plane; (b-2) x=0 plane. [From Brewe et al. (1979)].**Boundary Conditions & Nodal Structure**Figure 16.6 Effect of boundary conditions. (a) Solution using full Sommerfeld boundary conditions; (b) solution using half Sommerfeld boundary condition; (c) solution using Reynolds boundary conditions. [From Brewe et al. (1970)]. Figure 16.7 Variable nodal structure used for numerical calculations. [From Brewe et al. (1979)].**Hydrodynamic Lift**Figure 16.8 Effect of radius ratio on reduced hydrodynamic lift. [From Brewe et al. (1979)].**Comparison of Fully Flooded and Starved Contact**Figure 16.11 Three-dimensional representation of pressure distributions for dimensionless minimum film thickness Hmin of 1.0 x 10-4. (a) Fully flooded condition; (b) starved condition. [From Brewe and Hamrock. (1982)].**Comparison of Fully Flooded and Starved Contact**Figure 16.11 Three-dimensional representation of pressure distributions for dimensionless minimum film thickness Hmin of 1.0 x 10-3. (a) Fully flooded condition; (b) starved condition. [From Brewe and Hamrock. (1982)].**Pressure Contours - Starved**Figure 16.13 Isobaric contour plots for three fluid inlet levels for dimensionless minimum film thickness Hmin of 1.0 x 10-4. (a) Fully flooded condition: dimensionless fluid inlet level Hin, 1.00; dimensionless pressure, where dP/dX=0, Pm, 1.20 x 106; dimensionless load-speed ratio W/U, 1153.6. (b) Starved condition; Hin, 0.004; Pm = 1.19 x 106; W/U = 862.6. (c) Starved condition: Hin =0.001; Pm = 1.13 x 106; W/U = 567.8. [From Brewe and Hamrock. (1982)].**Inlet Level Effect**Figure 16.14 Effect of fluid inlet level on film thickness reduction factor in flooded conjunctions. [From Brewe and Hamrock (1982)].**Lubricant Flow**Figure 16.15 Lubricant flow for a rolling-sliding contact and corresponding pressure buildup. [From Ghosh et al. (1985)].**Pressure Distributions vs. Normal Velocity Parameter**Figure 13.2 Radial-flow hydrostatic thrust bearing with circular step pad.**Performance Parameters**Figure 16.19 Effect of radius ratio on dynamic load ratio. Dimensionless central film thickness Hmin, 1.0 x 10-4; dimensionless fluid inlet level Hin, 0.035. [From Ghosh et al. (1985)].**Peak Pressure vs. Radius Ratio**Figure 16.20 Effect of radius ratio on dynamic peak pressure ratio. Dimensionless central film thickness Hmin, 1.0 x 10-4; dimensionless fluid inlet level Hin, 0.035. [From Ghosh et al. (1985)].**Contact Geometry**Figure 17.1 Geometry of contacting elastic solids. [From Hamrock and Dowson (1981).]**Radii of Curvature**Figure 17.2 Sign designations for radii of curvature of various machine elements. (a) Rolling elements; (b) ball bearing races; (c) rolling bearing races.**Pressure Distribution**Pressure: Maximum pressure: Figure 17.3 Pressure distribution in ellipsoidal contact.**Ellipticity Parameter and Elliptic Integrals**Figure 17.4 Variation of ellipticity parameter and elliptic integrals of first and second kinds as function of radius ratio. [From Hamrock and Brewe (1983).]**Hertz Contact Summary**Contact dimensions: Maximum elastic deformation: Effective elastic modulus: