On the application of directional time-frequency distributions to the identification of simultaneous forward and backward whirling in flexible rotors

Abstract

One of the greatest advantages of using complex coordinates on the study of rotating machinery is the gain on the physical insight into the forward and backward precessional modes. Together with the complex modal analysis formulation, other interesting tools were developed to characterize the shape and directivity of the whirl modes. These tools are helpful in understanding the bizarre phenomenon of mixed operational modes in rotors where some stations describe their precessional movement in the forward direction while others move in the backward direction. This paper enhances the discussion on the existence of these modes in flexible rotors when the rotating system is subjected to multiple unbalance forces applied on some stations of the rotor. It is worth noting that the concepts of the complex modal analysis are valid only for rotors operating at constant rotational speed. Consequently, if it is necessary to investigate the whirling motion of each station of the rotor when it is operating under non-stationary conditions, other procedures must be used. In this work, it is used the directional Wigner distribution, which is able to split the total response of any station of the rotor into its forward and backward components. The considered rotor is supported on anisotropic bearings and operates at varying rotational speed. The experimental results are presented, showing the usefulness of time-frequency distributions as an alternative tool to identify mixed modes.

Keywords:

• flexible rotors
• backward whirl
• mixed modes
• time-frequency

Additional information

Notes on contributors

M Dias

Milton Dias received the BS, MS and PhD degrees in mechanical engineering from the Faculty of Mechanical Engineering of the State University of Campinas, Campinas, Brazil in 1984, 1987 and 1994, respectively. From 1999 to 2000, he was a visiting research assistant at the Structural Dynamics Research Laboratory of the University of Cincinnati, Cincinnati, USA. His research and teaching interests include dynamics and control of mechanical systems, modal analysis of structures, mechanical vibrations and signal processing. He is currently an associated professor at the Faculty of Mechanical Engineering of the State University of Campinas, Campinas, Brazil, where he is the coordinator of the course of Automation and Control Engineering.

U A Miranda

Sérgio Idehara received the graduate and MS degrees in mechanical engineering from the University of Campinas in 2001 and 2003, respectively. He is currently studying at the same university for the PhD degree. His research interests include signal processing, parameter identification of rotative systems under non-stationary condition and modal analysis.

A L A Mesquita

Ubatan Miranda recieved the BS degree in mechanical engineering in 1999 from the Federal University of Bahia, Salvador, Brazil, and the MS degree in solid mechanics from the State University of Campinas, Campinas, Brazil, in 2002. He is currently a PhD student in solid mechanics at the Department of Mechanical Design of the Faculty of Mechanical Engineering, State University of Campinas, Campinas, Brazil. His research interests include the dynamic behavior of mechanical systems, in particular rotating systems, using signal processing and time-frquency analysis techniques. His current activity is focused on the time-frequency vibrational features of cracked rotors.

S J Idehara

Alexandre Mesquita recieved the BS degree in mechanical engineering in 1992 from the Federal University of Pará, Belém, Brazil; the MS degree in solid mechanics in 1996 from the University of Brasília (UnB), Brasília, Brazil, and the PhD degree in mechanical engineering from the State University of Campinas, Campinas, Brazil, in 2004. He is currently a professor at the Department of Mechanical Engineering of the Federal University of Pará. His research interests include vibration, modal anaysis, and dynamic of rotating systems.