The present paper provides the spectral solution of the Reynolds’film lubrication equation for finite length journal bearing which is an exact solution for infinite series expansion. Due to the intrinsic symmetries of the bearing geometry and flow field, the relevant 2nd order 2D quasi-linear PDE in the rectangular domain with periodic and homogenous BCs has been solved through suitable sinusoidal eigenfunctions which proved to be complete orthonormal systems over the integration domain. The spectral solution has been used to computed the performance of bearings with aspect ratio in the proximity of one that represents a condition far from the typical approximations of “long” and “short” bearing. The comparison between the “exact” solution and the approximated ones confirms that the approximated solutions do not provide neither an effective estimation of the performance nor a conservative one. Finally, a more refined field of applicability of the “long” and “short” bearing approximations has been identified through the comparison of their results with the “exact” performance provided by the spectral solution.
Spectral Solution of Reynolds’ Film Lubrication Equation for Finite Length Journal Bearing
Pasini A.;Apollonio A.;d’Agostino L.
In corso di stampa
Abstract
The present paper provides the spectral solution of the Reynolds’film lubrication equation for finite length journal bearing which is an exact solution for infinite series expansion. Due to the intrinsic symmetries of the bearing geometry and flow field, the relevant 2nd order 2D quasi-linear PDE in the rectangular domain with periodic and homogenous BCs has been solved through suitable sinusoidal eigenfunctions which proved to be complete orthonormal systems over the integration domain. The spectral solution has been used to computed the performance of bearings with aspect ratio in the proximity of one that represents a condition far from the typical approximations of “long” and “short” bearing. The comparison between the “exact” solution and the approximated ones confirms that the approximated solutions do not provide neither an effective estimation of the performance nor a conservative one. Finally, a more refined field of applicability of the “long” and “short” bearing approximations has been identified through the comparison of their results with the “exact” performance provided by the spectral solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
