Finite Element Solution of the Steady-State Compressible Lubrication Problem

Reddi, M. M.; Chu, T. Y.

doi:10.1115/1.3451453

Cited by 63 publications

(8 citation statements)

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“…Taking (7) into consideration term div(u) in Equation (37) of thermal conductivity may be written in the following form:…”

Section: Consideration Of Cavitationmentioning

confidence: 99%

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Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

Szávai

2020

Processes

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Many calculating methods have been already developed for solving contact problems of parts such as gears, cams, and followers under fluid film lubrication conditions considering the temperature and pressure dependence. Similarly, the determination of the elasto-hydrodynamic pressure distribution the processes taking place in the lubricant and the contacting bodies, as well as in their environment, have to be dealt with simultaneously for the determination of the temperature field. A system of equation for the modelling of thermo-elastohydrodynamic lubrication between two contacting bodies containing hydrodynamic, thermodynamic, and strength problems is a highly non-linear system which becomes even more so if the temperature and pressure dependence of the material properties are considered. To solve this system, scientists started to use the finite element formulation in the 1960s and it was found to be a promising and reliable method. Earlier, the lubrication analysts used only the h-version finite element method (h-FEM) till 1991, when the first usage of the p-version finite element method (p-FEM) was published in the literature. In order to reduce the problem, in case of point or line contact, the contact bodies can be handled as semi-infinite ones. Following this simplification that had been successfully applied for the gap size determination, a substructure model was defined using analytical solution of the moving heat source. Instead of an iterative way between the solid and fluid problem, in this paper we present an efficient solution when thermal model for lubricant and surfaces were coupled and solved by a direct numerical method in one step.

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“…Taking (7) into consideration term div(u) in Equation (37) of thermal conductivity may be written in the following form:…”

Section: Consideration Of Cavitationmentioning

confidence: 99%

“…In case of these solving systems, a very high number of points of grid is needed. The finite element formulation is researched by Reddi [6] (1969), Reddi and Chu [7] (1970), Rohde [8] (1974), Rohde and Oh [9] (1975), Garcia-Suarez et al [10] (1984), and Freund and Tieu (1993) [11].…”

Section: Introductionmentioning

confidence: 99%

Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

Szávai

2020

Processes

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“…Appropriate weight functions associated with the finite element approach are suggested to avoid the oscillations exhibited in FDM. Reddi and Chu [105] initiated the FEM-based analysis of compressible fluids within a grooved gas bearing applied for video and audio tapes in 1970. In an analysis of HGJBs with a small number of grooves, Bonneau and Absi [82] adopted self-adaptive upwind schemes, which used Petrov-Galerkin weighted functions varying with surface velocity, mesh quality, viscosity, pressure, and thickness.…”

Section: Direct Discretization Of the Reynolds Equation For Grooved Bmentioning

confidence: 99%

A Review of Grooved Dynamic Gas Bearings

Guenat

Schiffmann

2019

Applied Mechanics Reviews

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This paper offers an extensive review of publications dealing with the modeling, the design, and the experimental investigation of grooved dynamic gas-lubricated bearings. Recent years have witnessed a rise in small-scale and high-speed turbomachinery applications. Besides the well-known gas foil bearings, grooved bearings offer attractive advantages, which unveil their potential in particular at small scale due to the structural simplicity as well as satisfying predictability. This paper starts with a general background of the application of gas-lubricated bearings and introduces and compares the different gas bearing topologies. Further, the state-of-the-art modeling of grooved gas-lubricated bearings is introduced, systematically assessing the advantages and inconveniences of two major approaches, i.e., the narrow groove theory (NGT) and direct discretization method. Since the NGT method is an elegant and efficient approach to model the complex effects of periodic grooves, a critical section is dedicated to the NGT. In a second phase, different models to include additional physical phenomena such as real gas lubrication, rarefaction, or turbulence effects are reviewed. The paper concludes with a critical assessment of the state-of-the-art and indicates potential fields of research that would allow to shed more light into the understanding of these bearings, as well as with some thoughts on the integrated design methodologies of gas bearing supported rotors.

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“…To overcome the limitation of the NGT, the finite element method (FEM) and finite difference method (FDM) were adopted to predict the performances of HGJBs and SGTBs. Reddi and Chu 5 adopted the Galerkin weighted residual method to derive the finite element formula and studied the static performance of the SGTB at low bearing numbers. Bonneau and Absi 6 employed the FEM to analyze the HGJB and compared their results with those using the NGT as well as via a finite difference model.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of spiral grooved opposed-hemisphere gas bearings: A parametric study

Yang

Ge²,

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part J:

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Although the spiral grooved opposed-hemisphere gas bearings have been widely applied in supporting the spin axis of inertial grade gyroscopes, the accurate prediction of the performance characteristics of the bearings is still very difficult because of their structural complexity. In this paper, the static characteristics of the bearings considering the coupling effects between the journal and two hemisphere bearings are obtained theoretically. The Reynolds equations modeling the journal and hemisphere bearings are solved simultaneously by the finite element method satisfying the continuous boundary conditions between these three bearings. The fluctuations of the bearing load and reaction torque caused by rotating grooves are shown and can be neglected at large number of grooves. The results show that neglecting the coupling effects between the journal and two hemisphere bearings will result in large discrepancies at high rotational speeds and large eccentricity ratios. And the hydrodynamic effect can be divided into two regions for spiral grooved gas bearings: the groove effect domain region and the converged wedge effect domain region. A parametric study provides efficient guidance for the optimal design of the opposed-hemisphere gas bearing.

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Finite Element Solution of the Steady-State Compressible Lubrication Problem

Abstract: Direct and incremental variational formulations for the steady-state compressible Reynolds’ equation are given. Finite element equations for these are derived and sample solutions are presented.

Cited by 63 publications

References 0 publications

Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

Temperature Variation at Solid-Fluid Interface of Thin Film Lubricated Contact Problems

A Review of Grooved Dynamic Gas Bearings

Numerical analysis of spiral grooved opposed-hemisphere gas bearings: A parametric study

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