A theoretical analysis is presented to study the effect of support sti
ffness and damping on the transient response of flexibly supported rot
or-bearing systems, considering surface roughness. The transient respo
nse of rotor is plotted in the form of trajectories. The average Reyno
lds equation, which uses the Patir and Cheng flow simulation model of
rough surfaces, is solved by the finite difference method with a succe
ssive over-relaxation scheme (Gauss-Seidel), while the equations of mo
tion of both the rotor and bearing are solved by the fourth-order Rung
e-Kutta method. It has been found that the surface roughness considera
bly affects the stability of a rotor-bearing system and the stability
may be improved greatly by a proper design of bearing supports.