An Evaluation of Finite Difference and Finite Element Methods for the Solution of the Reynolds Equation

Gero, L. R.; Ettles, C. M. McC.

doi:10.1080/05698198608981674

Cited by 30 publications

(8 citation statements)

References 8 publications

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“…Much research considers only the linear first order approximations while others consider higher order approximation (Lund 1965, Lund and Thomsen 1978, Qiu and Tieu 1996, Miura et al 2017. There are different methods to obtain the bearing coefficients,such as, experimental (Tiwari et al 2004, Mao et al 2016analytical (Chasalevris andSfyris, Wang andKhonsari 2006, Miraskari et al 2018a), finite difference method(FDM) (Gero and McC. Ettles 1986, Qiu and Tieu 1995, Goodwin et al 1997, finite element method (FEM) (Wada et al 1971, Mourelatos 1985, Arregui and Vázquez 2001, Nair and Nair 2004, Awasthi et al 2006, Hili et al 2010 , mesh less method with radial basis (MMRB) (Nicoletti 2013) and computational fluid dynamics (CFD) (Gao et al 2014, Zhang et al 2015.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

El-Sayed

Sayed

2021

Preprint

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Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.

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Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

El-Sayed

Sayed

2021

Preprint

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“…In 1985, Gero and Ettles [6] evaluated the relative precision of the FDM and FEM approaches when applied to a steady, isoviscous, incompressible lubrication problem. In their study, it was assumed that the solution of a complicated coupled problem could be derived by solving a sequential series of simple, uncoupled, steady problems.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of high speed spindle air bearings by a hybrid numerical method

Wang

Yau

2010

Applied Mathematics and Computation

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“…10 conducted stability analysis of a rigid rotor supporting hydrodynamic journal bearings with rough surfaces using a stochastic FEM. Gero and Ettles 11 conducted a comparison between FDM and FEM for a two-dimensional steady-state, isoviscous, and incompressible lubrication problem, from which the results showed that the former one has both a smaller relative error and a higher efficiency. Tala-Ighil and Fillon 12 studied the thermal effect with a numerical approach of FDM.…”

Section: Introductionmentioning

confidence: 99%

The flow-difference feedback iteration method for aerostatic thrust bearings and its convergence characteristics

Zhou

Zhang

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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The flow-difference feedback iteration method for aerostatic thrust bearings is proposed to the flow balance-based iteration, and two modification methods are further provided to improve the adaptability. The bearing capability calculated by the proposed method is validated by the experimental data. Moreover, the influence of convergence rate factors, iterative initial values, and mesh grids on the iteration ratio is investigated. Compared with the conventional iteration methods, the proposed method with appropriate convergence rate factors provides a higher convergence efficiency. In addition, good convergence behavior under different iterative initial values and the mesh grid size is shown, and the convergence rate is insensitive to the finite difference method parameters. A series of calculations are conducted to investigate the generality of the proposed methods.

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An Evaluation of Finite Difference and Finite Element Methods for the Solution of the Reynolds Equation

Cited by 30 publications

References 8 publications

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

Theoretical analysis of high speed spindle air bearings by a hybrid numerical method

The flow-difference feedback iteration method for aerostatic thrust bearings and its convergence characteristics

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