hydrostatic bearing systems

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Fundamentals of Fluid Film Lubrication Hamrock, Schmid & Jacobson ISBN No. 0-8247-5371-2 Hydrosta tic 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)].

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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) ]. - PowerPoint PPT Presentation

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Page 1: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 2: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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.

Page 3: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pad Coefficients

Figure 13.4 Chart for determining bearing pad coefficients for circular step thrust bearing. [From Rippel (1963)].

Load coefficient:

Flow coefficient:

Power coefficient:

Page 4: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Annular Thrust Pad Bearing

Figure 13.5 Configurations of annular thrust pad bearing. [From Rippel (1963)].

Page 5: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pad Coefficients

Figure 13.6 Chart for determining bearing pad coefficients for annular thrust pad bearings. [From Rippel (1963)].

Load coefficient:

Flow coefficient:

Power coefficient:

Page 6: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Rectangular Hydrostatic Pad

Figure 13.7 Rectangular hydrostatic pad.

Page 7: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pad Coefficients

Figure 13.8 Pad coefficients. (a) Square pad; (b) rectangular pad with B= 2L and b = l.

Load coefficient:

Flow coefficient:

Power coefficient:

Page 8: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Compensated Hydrostatic Bearings

Figure 13.9 Capillary-compensated hydrostatic bearing. [From Rippel (1963)].

Figure 13.10 Orifice-compensated hydrostatic bearing. [From Rippel (1963)].

Page 9: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Flow-Valve Compensation

Figure 13.10 Constant-flow-valve compensation in hydrostatic bearing. [From Rippel (1963)].

Page 10: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Compensating Element Ranking

Page 11: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Speed vs. Load

Figure 14.1 Effect of speed on load for self-acting, gas-lubricated bearings. [From Ausman (1961).]

Page 12: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Rectangular-Step Thrust Bearing

Figure 14.2 Rectangular-step thrust bearing. [From Hamrock (1972).]

Figure 14.3 Transformation of rectangular slider bearing into circular sector bearing.

Page 13: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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).]

Page 14: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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).]

Page 15: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Spiral-Groove Thrust Bearing

Figure 14.6 Spiral-groove thrust bearing. [From Malanoski and Pan (1965).]

Page 16: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Spiral-Groove Thrust

Bearing Characteristic

s

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).]

Page 17: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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).]

Page 18: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Linearized ph Solution

Page 19: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)]

Page 20: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pivoted-Pad Perfor-mance Parameters

Page 21: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Herringbone-Groove Journal Bearing

Figure 15.6 Configuration of concentric herringbone-groove journal bearing.

Page 22: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)]

Page 23: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Parameters for Herringbone Bearing

(cont.)

Figure 15.7 Concluded. (c) Optimal groove length ratio; (d) optimal groove

angle.

Page 24: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)]

Page 25: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Stability of Herringbone-Groove Bearings

Figure 15.9 Chart for determining maximum stability of herringbone-groove

bearings. [From Fleming and Hamrock (1974).]

Page 26: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Foil Bearing

Figure 15.10 (a) Schematic illustration of a foil bearing; (b) free-body diagram of a section of foil.

Page 27: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure in Foil Bearing

Figure 15.11 Pressure distribution and film thickness in a foil bearing. [From Bhushan (2002).]

Page 28: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Lubrication of Rigid Cylinder

Figure 16.1 Lubrication of a rigid cylinder near a plane. (a) Coordinates and surface velocities; (b) forces.

Page 29: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Cavitation Fingers

Figure 16.2 Cavitation fingers.

Page 30: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Effect of Leakage

Figure 16.4 Effect of leakage on tangential load component.

Figure 16.3 Side-leakage effect on normal load component.

Page 31: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 32: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 33: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Hydrodynamic Lift

Figure 16.8 Effect of radius ratio on reduced hydrodynamic lift. [From Brewe et al. (1979)].

Page 34: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure for Two Radius

Ratios

Page 35: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure Contours

Page 36: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 37: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 38: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 39: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Inlet Level Effect

Figure 16.14 Effect of fluid inlet level on film thickness reduction factor in flooded conjunctions. [From Brewe and Hamrock (1982)].

Page 40: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Lubricant Flow

Figure 16.15 Lubricant flow for a rolling-sliding contact and corresponding pressure buildup. [From Ghosh et al. (1985)].

Page 41: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Effect of Velocity

Page 42: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure Distribution

s vs. Normal Velocity

Parameter

Figure 13.2 Radial-flow hydrostatic thrust bearing with circular step pad.

Page 43: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 44: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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)].

Page 45: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Contact Geometry

Figure 17.1 Geometry of contacting elastic solids. [From Hamrock and Dowson (1981).]

Page 46: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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.

Page 47: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure Distribution

Figure 17.3 Pressure distribution in ellipsoidal contact.

Pressure:

Maximum pressure:

Page 48: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

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).]

Page 49: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Hertz Contact SummaryContact dimensions:

Maximum elastic deformation:

Effective elastic modulus:

Page 50: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Elliptic Integrals

Page 51: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Effect of Radius Ratio on Subsurface Stress

Page 52: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Simplified Equations for Elliptic Integrals

Page 53: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Conformity

Figure 17.5 Three degrees of conformity. (a) Wheel on rail; (b) ball on plane; (c) ball-outer-race contact. [From Hamrock and Brewe (1983).]

Page 54: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Calculation of Elastic Deformation

Page 55: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Load Components

Figure 18.1 Sketch to illustrate calculations of Xr,end and N. [From Houpert and Hamrock (1986).]

Figure 18.2 Load components and shear forces. [From Hamrock and Jacobson (1984).]

Page 56: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Profiles at Early

Iterations

Figure 18.3 Pressure profiles and film shapes at iterations 0, 1, and 14 with

dimensionless speed, load, and material parameters fixed at U = 1.0 x 10-11, W’ =

2.045 x 10-5, and G=5007. [From Houpert and Hamrock (1986).]

Page 57: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure and Film Profiles

Figure 18.4 Dimensionless pressure profiles for isoviscous and viscous solutions. Compressibility effects were considered. [From Hamrock et al. (1988).]

Figure 18.5 Film thickness profiles for isoviscous and viscous solutions. Compressibility effects were considered. [From Hamrock et al. (1988).]

Page 58: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Detail of Spike Location

Figure 18.6 Pressure and film thickness profiles in region 0.9 ≤ Xr ≤ 1.0. (a) Dimensionless pressure; (b) dimensionless film thickness. [From Hamrock et al. (1988).]

Page 59: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Compressibility Effect

Figure 18.8 Dimensionless pressure and film thickness profiles for an incompressible fluid. Viscous effects were considered. [From Hamrock et al. (1988).]

Figure 18.9 Dimensionless pressure and film thickness profiles for a compressible fluid. Viscous effects were considered. [From Hamrock et al. (1988).]

Page 60: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Detail of Spike Location

Page 61: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Pressure as a Function of Load

Figure 18.11 Variation of dimensionless pressure in elastohydrodynamically lubricated conjunction for six dimensionless loads with dimensionless speed and materials parameters held fixed at U=1.0 x 10-11 and G=5007. [From Pan and Hamrock (1989).]

Page 62: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Speed Effects

Figure 18.12 Variation of dimensionless pressure in elastohydrodynamically

lubricated conjunction for three dimensionless speeds with

dimensionless load and materials parameters held fixed at W’ = 1.3 x 10-4 and G=5007. [From Pan and Hamrock

(1989).]

Page 63: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Spike Amplitude

Page 64: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Spike Location

Page 65: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Film Thickness

Page 66: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Variation in Film Shape

Figure 18.13 Variation of dimensionless film shape in

elastohydrodynamically lubricated conjunction for six dimensionless

loads with dimensionless speed and materials parameters held fixed at U=1.0 x 10-11 and G=5007. [From

Pan and Hamrock (1989).]

Page 67: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Central Film Thickness

Page 68: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Film Shape for Different Speeds

Figure 18.14 Variation of dimensionless film shape for three dimensionless

speeds with dimensionless load and materials parameters fixed at W’ = 1.3 x

10-4 and G=5007. [From Pan and Hamrock (1989).]

Page 69: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Location of Minimum Film Thickness

Page 70: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Center of Pressure

Page 71: Hydrostatic Bearing Systems

Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2

Mass Flow Rate