Air bearings : theory, design and applications /
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, NJ :
John Wiley & Sons, Inc.,
2021.
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| Series: | Tribology series.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- List of contributors ; List of Tables ; List of Figures ; Preface ; Nomenclature ; 1. Introduction ; 1.1 Gas lubrication in perspective ; 1.1.1 Short history ; 1.2 Capabilities and limitations of gas lubrication ; 1.3 When is the use of air bearings pertinent ; 1.4 Situation of the present work ; 1.5 Classification of air bearings for analysis purposes ; 1.6 Structure of the book 1 ; References ; 2 .General Formulation and Modelling ; 2.1 Introduction ; 2.1.1 Qualitative description of the flow ; 2.2 Basic equations of the flow ; 2.2.1 Continuity equation ; 2.2.2 Navier-Stokes momentum equation ; 2.2.3 The (thermodynamic) Energy equation ; 2.2.4 Equation of State ; 2.2.5 Auxiliary conditions ; 2.2.6 Comment on the solution of the flow problem ; 2.3 Simplification of the flow equations ; 2.3.1 Fluid properties and body forces ; 2.3.2 Truncation of the flow equations ; 2.3.3 Film flow (or channel flow) ; 2.4 Formulation of bearing flow and pressure models ; 2.4.1 The quasi-static flow model for axisymmetric EP bearing ; 2.4.2 The Reynolds plus restrictor model ; 2.5 The basic bearing characteristics ; 2.5.1 The load carrying capacity ; 2.5.2 The axial stiffness ; 2.5.3 The feed mass flow rate ; 2.5.4 The mass flow rate in the viscous region ; 2.5.5 The tangential resistive, "friction" force ; 2.6 Normalization and similitude ; 2.6.1 The axisymmetric flow problem ; 2.6.2 Geometry ; 2.6.3 Dimensionless parameters and similitude ; 2.6.4 The Reynolds equation ; 2.6.5 The bearing characteristics ; 2.6.6 Static similarity of two bearings ; 2.7 Methods of solution ; 2.7.1 Analytic methods ; 2.7.2 Semi-analytic Methods ; 2.7.3 Purely numerical methods ; 2.8 Summary ; References ; 3. Flow into the bearing gap ; 3.1 Introduction ; 3.2 Entrance to a parallel channel (gap) with stationary, parallel walls ; 3.2.1 Analysis of flow development ; 3.3 Results and discussion ; 3.3.1 Limiting cases ; 3.3.2 Method of solution ; 3.3.3 Determination of the entrance length into a plane channel ; 3.4 The case of radial flow of a polytropically compressible fluid between nominally parallel plates ; 3.4.1 Conclusions on pressure-fed entrance ; 3.5 Narrow channel entrance by shear-induced flow ; 3.5.1 Stability of viscous laminar flow at the entrance ; 3.5.2 Development of the flow upstream of a slider bearing ; 3.5.3 Development of the flow downstream of the gap entrance ; 3.5.4 Method of solution ; 3.5.5 Conclusions regarding shear-induced entrance flow ; 3.6 Summary ; References ; 4. Reynolds Equation: Derivation, forms and interpretations ; 4.1 Introduction ; 4.2 The Reynolds equation ; 4.3 The Reynolds Equation for various film/bearing arrangements and coordinate systems ; 4.3.1 Cartesian coordinates (x; y) ; 4.3.2 Plain polar coordinates (r; -) ; 4.3.3 Cylinderical coordinates (z; -) with constant R ; 4.3.4 Conical coordinates (r; -) (- =
- = constant) ; 4.3.5 Spherical coordinates (-; -) (r = R = constant) ; 4.4 Interpretation of the Reynolds Equation when both surfaces are moving and not flat ; 4.4.1 Stationary inclined upper surface, sliding lower member ; 4.4.2 Pure surface motion ; 4.4.3 Inclined moving upper surface with features ; 4.4.4 Moving periodic feature on one or both surfaces ; 4.5 Neglected flow effects ; 4.6 Wall smoothness effects ; 4.6.1 Effect of surface roughness ; 4.7 Slip at the walls ; 4.8 Turbulence ; 4.8.1 Formulation ; 4.9 Approximate methods for incorporating the convective terms in integral flow formulations and the modified Reynolds Equation ; 4.9.1 Introduction ; 4.9.2 Analysis ; 4.9.3 Limiting solution: the Reynolds equation ; 4.9.4 Approximate solutions to steady channel entrance problems ; 4.9.5 Approximation of convective terms by averaging: the modified Reynolds Equation ; 4.9.6 Approximation of convective terms by averaging in turbulent flow ; 4.9.7 summary ; 4.10 Closure ; References ; 5. Modelling of Radial Flow in Externally Pressurised Bearings ; 5.1 Introduction ; 5.2 Radial flow in the gap and its modelling ; 5.3 Lumped parameter models ; 5.3.1 The orifice/nozzle formula ; 5.3.2 Vohr's correlation formula ; 5.4 Short review of other methods ; 5.4.1 Approximation of the inertia (or convective) terms ; 5.4.2 The momentum integral method ; 5.4.3 Series expansion ; 5.4.4 Pure numerical solutions ; 5.5 Application of the method of "separation of variables" ; 5.5.1 Boundary conditions on I ; 5.5.2 Flow from stagnation to gap entrance ; 5.5.3 The density function in the gap ; 5.5.4 Solution procedure ; 5.6 Results and discussion ; 5.6.1 Qualitative trends ; 5.6.2 Comparison with experiments ; 5.7 Other comparisons ; 5.8 Formulation of a lumped-parameter inherent compensator model ; 5.8.1 The entrance coefficient of discharge ; 5.8.2 Calculation of Cd ; 5.8.3 The normalized inlet flow rate ; 5.8.4 Solution of the static axisymmetric bearing problem by the Reynolds/compensator model ; 5.9 Summary ; References ; 6. Basic Characteristics of Circular Centrally Fed Aerostatic Bearings ; 6.1 Introduction ; 6.2 Axial characteristics: Load, stiffness and flow ; 6.2.1 Determination of the pressure distribution ; 6.2.2 Typical results ; 6.2.3 Characteristics with given supply pressure ; 6.2.4 Conclusions on axial characteristics ; 6.3 Tilt and misalignment characteristics (Al-Bender 1992; Al-Bender and ; Van Brussel 1992) ; 6.3.1 Analysis ; 6.3.2 Theoretical results ; 6.3.3 Experimental investigation ; 6.3.4 Results, comparison and discussion ; 6.3.5 Conclusions on tilt ; 6.4 The influence of relative sliding velocity on aerostatic bearing characteristics ; (Al-Bender 1992) ; 6.4.1 Formulation of the problem ; 6.4.2 Qualitative considerations of the influence of relative velocity ; 6.4.3 Solution method ; 6.4.4 Results and discussion ; 6.4.5 Conclusions on relative sliding ; 6.5 Summary ; References ; 7. Dynamic Characteristics of Circular Centrally Fed Aerostatic Bearing Films, and the Problem of Pneumatic Stability ; 7.1 Introduction ; 7.1.1 Pneumatic instability ; 7.1.2 Squeeze film ; 7.1.3 Active compensation ; 7.1.4 Objeetives and layout of this study ; 7.2 Review of past treatments ; 7.2.1 Models and theory ; 7.2.2 System analysis tools and stability criteria ; 7.2.3 Methods of stabilization ; 7.2.4 Discussion and evaluation ; 7.3 Formulation of the linearized model ; 7.3.1 Basic assumptions ; 7.3.2 Basic equations ; 7.3.3 The perturbation procedure ; 7.3.4 Range of validity of the proposed model ; 7.3.5 Special and limiting cases ; 7.4 Solution ; 7.4.1 Integration of the linearized Reynolds Equation ; 7.4.2 Bearing dynamic characteristics ; 7.5 Results and discussion ; 7.5.1 General characteristics and Similitude ; 7.5.2 The supply pressure response Kp ; 7.5.3 Comparison with experiment ; 7.6 Summary ; References ; 8. Aerodynamic action: Self-acting bearing principles and configurations ; 8.1 Introduction ; 8.2 The aerodynamic action and the effect of compressibility ; 8.3 Self-acting or EP Bearings? ; 8.3.1 Energy