Crack Detection and Dynamic Analysis of a Cracked Rotor with Soft Bearings Using Different Methods of Solution

The ratio of bearing stiffness to the shaft stiffness has a significant impact on the lower frequencies, mode shapes and, consequently, the whirl orbits. Most works studying crack detection methods in rotating systems use bearings relatively stiff, where the shaft bending is very pronounced. This paper analyzes how the nonlinear effect of the crack in the whirl orbits and the diagnostic forces technique for detecting cracks behave for soft bearings. The results show that the extra loops, very well known in the literature, are not present for the soft bearings. On the other hand, diagnostic peaks were successful in both cases. The efficiency of these methods depends on the mathematical model of the cracked rotor. This work considers the breathing mechanism in formulating the time-varying finite element stiffness matrix of the cracked element, requiring the solution of a set of equations at each time-step. With this concern, two approaches for the solution of the dynamic response are compared: direct time integration method using Newmark’s method and solution of discrete-time state equations. The Newmark’s method requires small time-step for the accuracy of the response, however, the processing time is much smaller when compared to solution of discrete-time state equations.