Bifurcation of limit cycles in fluid film bearings

Rotors supported by journal bearings may become unstable due to self-excited vibrations when a critical rotor speed is exceeded. Linearised analysis is usually used to determine the stability boundaries. Non-linear bifurcation theory or numerical integration is required to predict stable or unstable periodic oscillations close to the critical speed. In this paper, a dynamic model of a short journal bearing is used to analyse the bifurcation of the steady state equilibrium point of the journal centre. Numerical continuation is applied to determine stable or unstable limit cycles bifurcating from the equilibrium point at the critical speed. Under certain working conditions, limit cycles themselves are shown to disappear beyond a certain rotor speed and to exhibit a fold bifurcation giving birth to unstable limit cycles surrounding the stable supercritical limit cycles. Numerical integration of the system of equations is used to support the results obtained by numerical continuation. Numerical simulation permitted a partial validation of the analytical investigation.     

Effect of natural and magnetic convections on the structure of electrodeposited zinc-nickel alloy

The effects of a magnetic field applied in a direction parallel or perpendicular to the cathode substrate plane, during electrodeposition process of Zn-Ni alloy have been investigated by means of chronoamperometric measurements, X-ray diffraction and EDX analysis. The modification of crystal orientation of the alloy by the superimposition of a high magnetic field is discussed for alloys with a content of nickel range 6-13 at%. Whatever the phase composition obtained without magnetic field, either γ-Ni₅Zn₂₁ or a mixture of the γ and zinc phases, which depends on the concentration of Ni²⁺ in the electrolyte bath, the preferential orientation (1 0 1) of the zinc phase is always favoured with perpendicular and parallel magnetic field. There is no saturation of this effect with amplitude of B up to 8 T. A study of different geometric configurations of the cathode, which induce more or less natural convection, consolidates these results. The structural modifications of Zn-Ni alloy electrodeposits are thus probably due to a magnetohydrodynamic effect. An additional phenomenon is observed in presence of a perpendicular applied magnetic field since the (3 3 0) preferential orientation of the γ-Ni₅Zn₂₁ disappears with high values of B.