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Abstract

This paper presents a numerical approach to analyze the performance of aerostatic thrust bearings based on the differential quadrature method. The Reynolds equation of aerostatic thrust bearings is firstly discretized as a series of algebraic equations by the differential quadrature method and the pressure distribution is calculated with the discretized equations invoking the boundary conditions. Analytical approximation of Heaviside step function and a multi-domain technique are then introduced to resolve the discontinuous problem of grooved aerostatic bearings. Numerical solutions are obtained for two types of aerostatic thrust bearings. The mass flow rate, load capacity, and stiffness predicted by these solutions are further compared with corresponding analytical, finite difference method and computational fluid dynamics solutions. It is demonstrated that the differential quadrature method has high efficiency and accuracy for the solution of aerostatic thrust bearings.

Keywords

Aerostatic thrust bearing differential quadrature method performance analysis Reynolds equation groove

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References

Powell

. Design of aerostatic bearings, London: Machinery Publishing, 1970.

Al-Bender

Van Brussel

. Symmetric radial laminar channel flow with particular reference to aerostatic bearings. J Tribol 1992; 114: 630–636.

Ding

. A simplified calculation method on the performance analysis of aerostatic thrust bearing with multiple pocketed orifice-type restrictors. Tribol Int 2012; 56: 66–71.

Kogure

Kaneko

Ohtani

. A Study on characteristics of surface-restriction compensated gas bearing with T-shaped grooves. Bull JSME 1982; 25: 2039–2045.

Nakamura

Yoshimoto

. Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors. Tribol Int 1996; 29: 145–152.

Bonneau

Huitric

Tournerie

. Finite element analysis of grooved gas thrust bearings and grooved gas face seals. ASME Trans J Tribol 1993; 115: 348–354.

Belforte G, Raparelli T, Trivella A, et al. Numerical analysis on the supply hole discharge coefficient in aerostatic bearings. In: Proceedings of international conference on tribology AITC-AIT, Parma, Italy, 20–22 September 2006, CD ROM.

Ding

. Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice-type restrictor on its performance. Tribol Int 2007; 40: 1120–1126.

Gero

McC

. An evaluation of finite difference and finite element methods for the solution of the Reynolds equation. ASLE Trans 1986; 29: 166–172.

10.

Wang

Chang

S-H

Huang

H-C

. Comparison of iterative methods for the solution of compressible-fluid reynolds equation. J Tribol 2011; 133: 021702–021702.

11.

Bellman

Casti

. Differential quadrature and long-term integration. J Math Anal Appl 1971; 34: 235–238.

12.

Bellman

Kashef

Casti

. Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 1972; 10: 40–52.

13.

Shu

Chew

. On the equivalence of generalized differential quadrature and highest order finite difference scheme. Comput Meth Appl Mech Eng 1998; 155: 249–260.

14.

Quan

Chang

. New insights in solving distributed system equations by the quadrature method—I. Analysis. Comput Chem Eng 1989; 13: 779–788.

15.

Shu C. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD Thesis, University of Glasgow, Glasgow, 1991.

16.

Bert

Malik

. Differential quadrature method in computational mechanics: a review. Appl Mech Rev 1996; 49: 1–27.

17.

Shu

. Differential quadrature and its application in engineering, London: Springer-Verlag, 2000.

18.

Miyatake

Yoshimoto

. Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes. Tribol Int 2010; 43: 1353–1359.

19.

Yang

Cao

Chung

T-S

. Applied numerical methods using MATLAB, Hoboken, NJ: Wiley-Interscience, 2005.

20.

Constantinescu

Wehe

. Gas lubrication, New York: American Society of Mechanical Engineers, 1969.

On the analysis of aerostatic thrust bearings with the differential quadrature method

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