An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

Lahmar, Mustapha; Haddad, A.; Nicolas, D.

doi:10.1016/s0997-7538(00)00139-x

Cited by 30 publications

(22 citation statements)

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“…m c x x t ‡DtˆPx, t ‡Dt …21 † Eliminating the acceleration terms by using expressions of the form given by equations (18) and (19) and by multiplying the previous equations by Dt 2 b, Dt 2 …1 ¡ 2b † and Dt 2 b respectively, adding and rearranging then gives…”

Section: Discussionmentioning

confidence: 99%

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

Ashmore

Williams

McWilliam

2003

Proceedings of the Institution of Mechanical Engineers, Part G:

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Although many attempts have been made to model rolling-element bearings with innerpiloted cages, they all simplify the hydrodynamic cage-support mechanism. This can mean that some cage behaviour is inadequately explained, such as cage lap. This paper presents the development of a new three-dimensional analysis of the hydrodynamic support for an inner-piloted cage for a rollingelement bearing incorporating starved-®lm conditions. The solution of the generalized Reynolds equation along with a continuity equation leads to analytical expressions for the hydrodynamic forces. The equations of motion for the cage are then integrated numerically using the Newmark beta method to predict the cage response. The availability of analytical hydrodynamic force expressions means that the numerical integration process is computationally ef®cient. The in¯uence of key parameters such as the level of lubrication and the angular velocity of the inner race are investigated.

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Section: Discussionmentioning

confidence: 99%

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

Ashmore

Williams

McWilliam

2003

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…In order to reduce the calculation time, we have used an approach based on the theory of optimized short bearing in which the curve of pressure according to the axial direction of bearing is supposed to be of parabolic form; this assumption is valid for an aligned bearing [11]. Consider…”

Section: Methodsmentioning

confidence: 99%

Nonlinear Dynamical Analysis for a Plain Bearing

Belhamra

Meramria

Kahine

et al. 2014

Advances in Mechanical Engineering

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This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing) lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film). The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance) and asynchrony (whipping) amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances).

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“…3. Compute the dynamic coefficients from equation (31). There is no dependence between dynamic coefficients and frequency ratio because the deformations due to the dynamic pressures at the fluid-film -bearing-liner interface are neglected.…”

Section: Methods Of Solution Under Dynamic Conditionsmentioning

confidence: 99%

Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids

Lahmar

2005

Proceedings of the Institution of Mechanical Engineers, Part J:

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Elastohydrodynamic (EHD) analysis of a journal bearing with a realistic model for the bearing made of two distinct layers is extended to include couple-stress effects in lubricants blended with polymer additives. Based on the Stokes microcontinuum theory, a transient pressure differential equation (modified Reynolds' equation) is derived from the fluid motion equations and solved numerically. The elegant and powerful semi-analytical approach based on the complex variable theory developed in an earlier work is extended to solve linear elastostatics problems for a double-layered journal bearing. The EHD solution in isothermal conditions is obtained numerically by means of an iterative procedure. By the finite perturbation technique, the eight fluid-film stiffness and damping coefficients are determined. At the threshold of instability, the dynamic coefficients are used as input data for studying the linear stability of the rotor-bearing system. According to the results obtained, the influence of couple-stress parameter on the static and dynamic performance characteristics of the compliant journal-bearing system is physically apparent and not negligible. Compared with the Newtonian lubricants case, lubricants with couple-stresses provide an increase in the load-carrying capacity and stability, a reduction in the attitude angle and the friction factor. It is also found that the fluid -solid interaction effect on the performance characteristics is more important, especially for high values of couple-stress parameter and relative rigidity of liner-bush assembly.

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An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

Cited by 30 publications

References 0 publications

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

Nonlinear Dynamical Analysis for a Plain Bearing

Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids

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