Theoretical and experimental identification of the simultaneous occurrence of unbalance and shaft bow in a Laval rotor

• A method of fault identification based on correlation matrices is proposed.
• Two simultaneous and synchronous to the machine´s operating speed faults are studied: unbalance and shaft bow.
• Model order reduction was used to identify the faults using the measurements at specific degrees of freedom of the rotor.
• The proposed methodology identified the fault parameters with success and without major deviations.

This paper discusses the theoretical and experimental identification of two of the most common faults that occur in rotating machines: unbalance and residual shaft bow. The identification procedure is based on the mathematical modeling system. The dynamic system was modeled using finite elements and the faults were identified using an approach based on correlation analysis that involves the rotor responses in the time domain. The identification equation derives from the Lyapunov matrix equation of the reduced system model, which contains only the measured degrees of freedom, and the fault parameters are identified by least-square fitting. The Differential Evolution (DE) optimization technique was used to identify the bearing physical properties as well as the coupling and rotor damping. The faults were identified theoretically, considering seven different cases of unbalance and bow locations, after which the rotor was subjected to four different unbalance situations in order to identify both the unbalance and the unknown shaft bow, based on experimental measurements. The proposed procedure proved consistent in identifying two faults that occur simultaneously and similar symptoms.