Abstract: A simulation scheme of rotational motions for predictions of bump-type gas foil bearings operating at steady-state is proposed. The scheme is based on multi-physics coupling computer aided engineering packages modularized with computational fluid dynamic model and structure elasticity model to numerically solve the dynamic equation of motions of a hydrodynamic loaded shaft supported by an elastic bump foil. The bump foil is assumed to be modelled as infinite number of Hookean springs mounted on stiff wall. Hence, the top foil stiffness is constant on the periphery of the bearing housing. The hydrodynamic pressure generated by the air film lubrication transfers to the top foil and induces elastic deformation needed to be solved by a finite element method program, whereas the pressure profile applied on the top foil must be solved by a finite element method program based on Reynolds Equation in lubrication theory. As a result, the equation of motions for the bearing shaft are iteratively solved via coupling of the two finite element method programs simultaneously. In conclusion, the two-dimensional center trajectory of the shaft plus the deformation map on top foil at constant rotational speed are calculated for comparisons with the experimental results.
Abstract: Compliant foil gas lubricated bearings are used for the
support of light loads in the order of few kilograms at high speeds, in
the order of 50,000 RPM. The stiffness of the foil bearings depends
both on the stiffness of the compliant foil and on the lubricating
gas film. The stiffness of the bearings plays a crucial role in the
stable operation of the supported rotor over a range of speeds. This
paper describes a numerical approach to estimate the stiffness of the
bearings using pseudo spectral scheme. Methodology to obtain the
stiffness of the foil bearing as a function of weight of the shaft is
given and the results are presented.
Abstract: A theoretical investigation on the effects of both
steady-state and dynamic deformations of the foils on the dynamic
performance characteristics of a self-acting air foil journal bearing
operating under small harmonic vibrations is proposed. To take into
account the dynamic deformations of foils, the perturbation method is
used for determining the gas-film stiffness and damping coefficients
for given values of excitation frequency, compressibility number, and
compliance factor of the bump foil. The nonlinear stationary
Reynolds’ equation is solved by means of the Galerkins’ finite
element formulation while the finite differences method are used to
solve the first order complex dynamic equations resulting from the
perturbation of the nonlinear transient compressible Reynolds’
equation. The stiffness of a bump is uniformly distributed throughout
the bearing surface (generation I bearing). It was found that the
dynamic properties of the compliant finite length journal bearing are
significantly affected by the compliance of foils especially whenthe
dynamic deformation of foils is considered in addition to the static
one by applying the principle of superposition.