Successive over relaxation technique for steady state and dynamic characteristics of a cylindrical bore bearing - Yaacob, Zaihar (2005)
The knowledge of static and dynamic characteristics of journal bearings is crucial for the accurate detennination of the critical speed of a shaft and also for studying the stability of the rotating shaft against self-excited vibrations. These characteristics are detennined from the solutions of Reynolds equation numerically using finite difference methods with successive over relaxation technique (SOR). In order to implement SOR effectively, the optimum value for over relaxation factor Q had to be found first. In this thesis, the exact value of Q was calculated by using a fornmla proposed by G.D. Smith. Khonsari and Booser (K&B) found the value of Q, by trial and error which is not exact and time consuming. While Orcutt and Arwas (O&A) used Gauss-Seidel technique which has a much slower convergence rate compared to SOR, also they used two convergence limits which had to be satisfied before tenninations of the iteration procedure. This thesis is intended to improve both works by calculating the exact value for Q and employed the SOR technique using only one convergence limit. The dynamic coefficients were then used as an input data for studying the stability characteristics of the rotor-bearing system and the threshold of instability were also plot. The computer program was written using FORTRAN 95 programming language and run in the Microsoft Developer Studio environment. Method in this thesis shows that the time taken for a complete solution for the steady state and dynamic characteristics of a cylindrical bore bearing were greatly shortened in tenns of number of iterations (about 90%) and the automatic calculation of Q. The accuracy of the results were good with less than 10% in difference when compared to results from both K&B and O&A. It is then concluded that the finite difference method and successive over relaxation technique used in this thesis can predict accurately and effectively the static and dynamic characteristics of a cylindrical bore bearing.