Dynamics of rotating machinery:
                        analysis, identi“cation and control
                                      Athesis submitted to the University of Pisa
                                        for the degree of Doctor of Philosophy
                                                         By
                                              EMILIANO RUSTIGHI
                                                     Supervisors
                                   Prof. C. Carmignani           Prof.ssa. P. Forte
                             Corso di dottorato di ricerca in Ingegneria Meccanica, II◦ Ciclo
                            Department of Mechanical, Nuclear and Production Engineering
                                               University of Pisa, Italy
                                                   February 2004
            Title: Dynamics of rotating machinery: analysis, identi“cation and controlŽ
            Abstract: The performance requirements that modern rotating machines
          must satisfy have introduced a trend toward higher speeds and more stringent
          vibration levels. The basic tools to ful“l the reduction of vibrations are the analy-
          sis and the identi“cation of rotor systems to design proper rotating elements, and
          the use of control devices.
            Supports, which are important rotor elements, are characterized with diffi-
          culty. The modulating functions identi“cation method was applied to identify the
          parameters of hydrodynamic bearings. They were identi“ed, both numerically and
          experimentally, with encouraging results.
            Moreover, the design of a magneto-rheological squeeze “lm damper is presented
          anddiscussed. A numerical simulation and an experimental campaign were carried
          out. Since the damping characteristics can be varied continuously by controlling
          the magnetic “eld, it is possible to set the optimum conditions for each operating
          condition. An automatic semi-active control algorithm was devised by means of
          fuzzy logic and genetic algorithm.
            Finally, the vibrations of ”exible rotating disks in the presence of dry friction
          were studied. This is a crucial problem, common to many industrial “elds. The
          results of an experimental investigation, carried out on a commercial paper cut-
          ting machine and on a test rig, are presented and discussed. The investigation
          has shown the in”uence of some operating and design parameters on the system
          dynamic behaviour.
            Titolo: Dinamica degli organi rotanti: analisi, identi“cazione e controlloŽ
            Sommario: Gli organi rotanti di macchinari moderni sono soggetti a velocit`a
          sempre piu` elevate e limiti vibratori sempre piu` ristretti. Gli strumenti per ridurre
          tali vibrazioni sono lanalisi e lidenti“cazione dei sistemi per un opportuno dimen-
          sionamento delle parti rotanti, e lutilizzo di appropriati smorzatori.
            Elementi importanti nella dinamica dei rotori ma di difficile caratterizzazione
          sono i supporti. Il metodo identi“cativo delle funzioni modulanti `e stato applicato
          allidenti“cazione dei coefficienti dinamici di cuscinetti idrodinamici. Sono stati
          ottenuti risultati incoraggianti sia dalle analisi numeriche che sperimentali.
            Inoltre `e presentato il progetto di uno smorzatore magnetoreologico a squeeze-
          “lmŽ. Sonostaticondottisiaunaanalisinumericacheunacampagnasperimentale.
          Poich`e il coefficiente smorzante del cuscinetto pu`o essere variato con continuit`a`e
          stato possibile impostare le condizioni di funzionamento ottimo per ogni condizione
          operativa. Un controllore automatico `e stato progettato con luso di logica Fuzzy
          e algoritmi genetici.
            In“ne sono state studiate le vibrazioni di dischi sottili rotanti in presenza di
          attrito secco, problema molto complesso e molto sentito in vari ambiti industriali.
          Sonoquindipresentatiediscussiirisultati di unindagine sperimentale condotta sia
          su un macchinario commerciale di una cartiera che su una attrezzatura sperimen-
            `
          tale. E stata mostrata lin”ueza di alcuni parametri sullinsorgere delle vibrazioni.
         Acknowledgements
         I would like to express my gratitude to my supervisors, Prof. C. Carmignani
         and Prof.ssa P. Forte. I gratefully acknowledge their technical and strategic
         expertise, as well as their immense patience.
           Special thanks are extended to my colleagues and friends for the useful
         discussions, ideas and help. In particular I would like to thank Riccardo
         Ciolini for his encouraging support and friendship.
           Furthermore, I am indebted to the students Cristiano Arfanotti, Alessan-
         dro Bechi, Gabriele Bicci, Andrea Borzoni, Marco Patern`o and Marcello
         Venturi for their valuable contribution to my work.
           Finally, I would like to thank my family and my girlfriend Ilaria for their
         love, patience and support. Without their help this thesis would not have
         been completed.
                    Contents
                    1 Introduction                                                           1
                    2 Identi“cation of rotor supports                                        6
                        2.1 Introduction............................ 6
                        2.2  Parametric identi“cation techniques ............... 9
                             2.2.1  The modulating function identi“cation algorithm . . .     9
                             2.2.2  The recursive identi“cation algorithm .......... 12
                        2.3  Simulated identi“cation of mechanical systems ......... 13
                             2.3.1 Oneandtwodegreeoffreedomsystems......... 13
                             2.3.2 Therotor-bearingsystem................. 23
                        2.4  Experimental tests on a single degree of freedom system  . . . 27
                             2.4.1 Designofthetestrig................... 27
                             2.4.2 Experimentalresults................... 28
                        2.5  Experimental tests on a hydrodynamic bearing ......... 34
                             2.5.1 Designofthetestrig................... 34
                             2.5.2 Experimentalresults................... 35
                        2.6  Conclusions ............................ 38
                    3 Semi-active control of a rotating shaft: the magnetorheolog-
                        ical squeeze-“lm damper                                             39
                        3.1 Introduction............................ 39
                        3.2  Passive, active and semi-active control of rotors ........ 40
                        3.3  Squeeze “lm bearings ....................... 43
                        3.4  The magnetorheological ”uids .................. 44
                        3.5  Adjustable squeeze “lm dampers    ................ 50
                        3.6  Modelling of a squeeze “lm damper with magnetorheological
                             ”uid ................................ 55
                        3.7  Modelling of the rotor-damper system .............. 59
                        3.8  Design of the MR squeeze-“lm damper ............. 68
                             3.8.1 Descriptionofthedevice................. 68
                             3.8.2  Design of the magnetic circuit .............. 69
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