Non-linear transient analysis of a rigid rotor supported by non-circular bearings

The calculation of the complete transient path of the rotor is the best analytical method of evaluating the characteristics of a rotor-bearing system. This type of calculation requires the solution of Reynolds' equation for the hydrodynamic forces at each time step. Since a large number of time steps are involved (about 1,000) the computer run times are prohibitive in cost. Thus an accurate approximate solution to Reynolds’ equation that has a rapid execution rate would be invaluable for the determination of transient rotor orbits.
Reynolds’ equation is solved by an implicit numerical method for the case of a rotor supported by non-circular hydrodynamic bearings using compressible or incompressible lubricants. This exact method of determining hydrodynamic forces is used to verify the accuracy of an approximate method that is developed in the thesis. The approximate method consists of solving the infinite bearing problem and then correcting this solution for end leakage to obtain an approximation to the finite bearing.