Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids

Lahmar, Mustapha; Bou‐Saïd, Benyebka

doi:10.3390/lubricants3020281

Cited by 8 publications

(1 citation statement)

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“…Owing to its relative mathematical simplicity, the couple‐stress fluid model has been widely applied to analyse various hydrodynamic as well as thermo‐hydrodynamic lubrication problems . The theoretical results obtained showed that the presence of the couple stress provides an enhancement of the steady‐state and dynamic characteristics of liquid‐lubricated journal bearings when compared with the Newtonian lubricant case.…”

Section: Introductionmentioning

confidence: 99%

Analysis of couple‐stress effects in gas foil bearings using the V. K. Stokes micro‐continuum theory

Laouadi

Lahmar

Bou‐Saïd

et al. 2018

Lubrication Science

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This paper presents an original theoretical investigation of the steady‐state and dynamic characteristics of foil journal bearings lubricated with contaminated air taking into account couple stresses because of the presence of pollutant substances. The substance can be solid particles (eg dust, ash, pollen, and smoke). In aerodynamic lubrication theory, a fluid with couple stresses so‐called couple stress or polar fluid may be considered as one characterised by the 2 physical constants μ and η, which are the absolute viscosity assumed to be independent of the particle volume fraction and the new material constant responsible for couple stress or polar property. The effects of couple stresses on the oil‐lubricated sliding bearings are usually studied by defining the parameter 0.25eml=η/μ12 or its normalised form truel~=l/C . The couple‐stress parameter l, which has the dimension of length, can be thought of as a fluid property depending on the size of the particle contained in the base fluid (solvent). To determine the aerodynamic pressure and the power loss, the governing modified Reynolds' equation and the viscous dissipation term appearing on the right‐hand side of the modified energy equation are derived by using the Vijay Kumar Stokes micro‐continuum theory. The system of partial differential equations resulting from analytical perturbation of the transient modified Reynolds' equation is solved for the steady‐state and dynamic pressures by means of the finite difference method considering both the static and dynamic deformations of the bump foil. Using the complex variable technique, the analytical perturbation process leads to 2 first‐order uncoupled partial differential equations instead of 4 coupled equations as it is usually found in the technical literature. On the other hand, the 2 Cartesian coordinates of the equilibrium position for a given applied static load are iteratively determined by solving the nonlinear equilibrium equations of the journal bearing system with the improved Newton‐Raphson method. According to the obtained results, the effects of couple stresses on the steady‐state and dynamic behaviour of foil self‐acting gas bearings are significant and cannot be overlooked. The results also show that the dynamic deformation of the bump foil should be included in calculating the dynamic performance characteristics of foil journal bearings.

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Section: Introductionmentioning

confidence: 99%